Rational vs Irrational Scales: a response to Rick

> --I keep on going on about it to you because you keep on missing the
> point. And I have --listened to the site and already said that it
> sounds out of tune.

We've been battling on the topic of if irrational numbers CAN be a good option for generating consonant scales OR if irrational numbers will always be the best options.

>>>>>>>>>>>>>
And I've come to the conclusion that we're both right; they both can AND can't. :-D

In short...they can be based on irrational generators but, afterward, it always seems to help to round the irrational results to the nearest rational ones. :-)
<<<<<<<<<<<<<<<

The result below is a melodic example of a scale made of rational numbers built to closely approximate the original irrational-number-generated PHI scale I made:

http://www.geocities.com/djtrancendance/micro/rationallytemperedPHItuning.wav

Does this STILL sound "out of tune" to you? :-)

BTW, the ratios the above scale uses are:
10/9
19/16
4/3
16/11
25/16
13/8

(all ratios either based on the x/9 or x/16 harmonic series OR 'tempered' sound quite close to them (IE 16/11 instead of 13/9).

The idea is to use rational numbers to improve my tuning while still keeping intervals that are very close (in cents) to the irrational/PHI-based version of the scale. Indeed, at least to my ears, the PHI version sounds better with PURE sine wave as instruments but, for realistic instruments with linear overtones, the rational number "tempered version" sounds a good deal better to me.

-Michael

--- In tuning@yahoogroups.com, "djtrancendance" <djtrancendance@...> wrote:
>
> > --I keep on going on about it to you because you keep on missing the
> > point. And I have --listened to the site and already said that it
> > sounds out of tune.
>
> We've been battling on the topic of if irrational numbers CAN be a good option for generating consonant scales OR if irrational numbers will always be the best options.
>
> >>>>>>>>>>>>>
> And I've come to the conclusion that we're both right; they both can AND can't. :-D
>
> In short...they can be based on irrational generators but, afterward, it always seems to help to round the irrational results to the nearest rational ones. :-)
> <<<<<<<<<<<<<<<
>
> The result below is a melodic example of a scale made of rational numbers built to closely approximate the original irrational-number-generated PHI scale I made:
>
> http://www.geocities.com/djtrancendance/micro/rationallytemperedPHItuning.wav
>
> Does this STILL sound "out of tune" to you? :-)
>
> BTW, the ratios the above scale uses are:
> 10/9
> 19/16
> 4/3
> 16/11
> 25/16
> 13/8
>
> (all ratios either based on the x/9 or x/16 harmonic series OR 'tempered' sound quite close to them (IE 16/11 instead of 13/9).
>
> The idea is to use rational numbers to improve my tuning while still keeping intervals that are very close (in cents) to the irrational/PHI-based version of the scale. Indeed, at least to my ears, the PHI version sounds better with PURE sine wave as instruments but, for realistic instruments with linear overtones, the rational number "tempered version" sounds a good deal better to me.
>
> -Michael
>
Thanks Michael,

What I'm specifically talking about is not rational verses irrationals per se. Rather, what I'm taking to task is the general scientific assumption that the only way the harmonic series applies to music is by creating boundary conditions eg the string length b/w nut and bridge giving frequencies 1, 2, 3, etc... so that harmonies are created by adding upper harmonics to the fundamental. What this model does not take into account is the fact that the same conditions of rational-periodicity apply b/w two or more boundary conditions themselves AND ALSO when no boundary exists at all. All that is required for a tonic/fundamental to be produced is that the two frequencies bear a rational relation, the resultant wave giving a number of cycles corresponding to the GCD.
eg: we all 'know' that given the two freq's 6 and 9, the resultant frequency will be 3. Their appearance together puts them in the role of 2nd and 3rd harmonics to tonic 3. Observe also that taking the harmonic series of 6 and 9 will give each harmonic as a GCD; 12 and 18 have GCD 6, 18 and 27 have GCD 9, and so on. Thus, two violins when played simultaneously can produce a third harmonic series comprised of GCD's. Obviously it does not matter whether the frequencies are generated by a computer or a kazoo.

In my considered opinion, failure to recognise this subtle distinction has led scientists to underestimate the role that musical harmony actually plays in their underlying philosophy. It has also left the impression that mathematics is somehow more fundamental and important than musical harmony, that we impose maths onto music rather than vice-versa (PHI being one example. Why is the Fibbinachi series more 'natural' than the harmonic series?). In view of the fact that both light and matter are also waves and that all waves display the same behaviour, I would suggest that it is rather the other way around.

So if this is correct, the million dollar question for the tuning group is and has always been: where does this leave irrationals (especially considering the commonality of 12 edo)? One possible explanation is that the irrationals themselves are an idealisation, that in reality the notes with which we are familiar are rational harmonics in the higher registers (i.e. perhaps we can only discern to a few decimal places?). Since the tonic needs to be 8ve to the tonic frequency, I propose that we should look for a tuning system based on minor third 609/512 and major third 645/512. These not only have the correct tonic of 512 as 2 power of 9, but also correctly approximate their irrational counterparts to 4 decimal places. OR as I have been trying to find out with Carl/Erlich's Entropy model, is there a certain 'give' around the number of cycles for each interval, or such a thing as 'almost periodic'? These seem to me to be the most pressing problems for a group committed to tuning (which can/should also mean tuning our ideas with practice).

I hope this makes things a little clearer.

-Rick

---so that harmonies are created by adding upper harmonics to the fundamental.
    Right meaning...adding notes that intersect the harmonic series of the root note (if I have it right).  Then again (if I have it right), that's what Sethares does, only for things like 10TET he 'de-stretches' the overtones/timbre to match the new 'shrunk' (vs. 12TET) tuning.

--All that is required for a tonic/fundamental to be produced is that the
two frequencies bear --a rational relation, the resultant wave giving a
number of cycles corresponding to the GCD.
---eg: we all 'know' that given the two freq's 6 and 9, the resultant frequency will be 3.
---Their appearance together puts them in the role of 2nd and 3rd harmonics to tonic 3.
   Right meaning...given two harmonics/overtones you can automatically derive where the root/bottom tone of the series is (it is the GCD). 
   BTW, I have to clarify myself: when I say "sounds harmonic", I mean that it sounds revolved rather than matches the mathematical construct explained above (which, of course, also sounds resolved). I realize the way I stated it before could come across as confusing. :-)

---It has also left the impression that mathematics is somehow more
fundamental and ---important than musical harmony, that we impose maths
onto music rather than vice-versa
-- (PHI being one example. Why is the
Fibbinachi series more 'natural' than the harmonic --series?).

      Simple answer: it's not.  If we played the harmonics of the harmonics series 1 to 15 at the same, for example (anything without the excessive beating of harmonics 19+), it would likely sound more natural than PHI mean-tone.
  One slight problem: we'd only have about one area (near harmonics 7-14 or 8-16) that would actually fit at least 7 notes per 2/1 octave.  And then we have the problem of that harmonics 1 to 19 only covers some 2.5 octaves or so and the notes at the bottom (harmonics 1 to 4 or so) are ridiculously spread out...far too much so to work as bass notes.  And with JI, as you know from music theory, the majority of combinations of notes make sour chords (which is why music theory is so complex...and important with diatonic scales),
   These realistic restrictions of using the harmonic series as a scale
make me reconsider PHI.  With scales derived from a PHI tuning I can get pretty close to a "scale that is a chord" (IE very hard to find sour combinations of notes) without the above mentioned limitations of using the harmonic series as a scale.

--One possible explanation is that the irrationals themselves are an
idealisation, that in ---reality the notes with which we are familiar are
rational harmonics in the higher registers
 
   Could be.  Or they could simply be very near rational values...enough so that the ear barely notices (IE in my rational version of the irrational PHI scale).  Lastly, I strongly suspect it all comes down to "the ear likes predictable beating...either with a constant beating rate between notes (harmonic series), or a situation where beating rates are multiples of each other (PHI).

-Michael  

Hi Michael;

I am glad to read that you (and others) are exploring this paradox, for I also feel that the JI assumption that musical "harmonics" are only exactly at integer frequency ratios, and that "good" tunings should be constructed only from integer ratios is wrong.

(and in my view both naive and simplistic).

I agree with you that the beating seems to be as a result of "deviations" from integer frequency ratios, and that the "musical ear" hears beating in harmony as being acceptable.

Where our views diverge is on finding a mathematical model which gives us the appropriate interval sizes and consequential optimal beat rates.

I make no claims of having been the first to discover how well using the radian angle (assuming an octave is one complete revolution) as the Large interval (the difference between the fourth and fifth) works.

John Harrison clearly wrote this in the late 1700's, and the more I experiment and work with his specifications the more convinced I become that he had found a viable solution which "sounds" right and works musically.

I realise that I have written this comment in a wordy and pompous form, for there are many "nit-pickers" amongst the tunaniks (no names;-), who are quick to point out any discrepancies.

This fact doesn't encourage "a fluid" writing style, although I do appreciate the precision that it demands.

I have yet to improve on Harrison's formula.

I wish you good fortune in finding a better solution and model for mapping musical harmony, scales, and tunings.

On 23 Mar 2009, at 02:40, djtrancendance@... wrote:

> ---so that harmonies are created by adding upper harmonics to the > fundamental.
> Right meaning...adding notes that intersect the harmonic series > of the root note (if I have it right). Then again (if I have it > right), that's what Sethares does, only for things like 10TET he 'de-> stretches' the overtones/timbre to match the new 'shrunk' (vs. > 12TET) tuning.
>
> --All that is required for a tonic/fundamental to be produced is > that the two frequencies bear --a rational relation, the resultant > wave giving a number of cycles corresponding to the GCD.
> ---eg: we all 'know' that given the two freq's 6 and 9, the > resultant frequency will be 3.
> ---Their appearance together puts them in the role of 2nd and 3rd > harmonics to tonic 3.
> Right meaning...given two harmonics/overtones you can > automatically derive where the root/bottom tone of the series is (it > is the GCD).
> BTW, I have to clarify myself: when I say "sounds harmonic", I > mean that it sounds revolved rather than matches the mathematical > construct explained above (which, of course, also sounds resolved). > I realize the way I stated it before could come across as > confusing. :-)
>
> ---It has also left the impression that mathematics is somehow more > fundamental and ---important than musical harmony, that we impose > maths onto music rather than vice-versa
> -- (PHI being one example. Why is the Fibbinachi series more > 'natural' than the harmonic --series?).
>
> Simple answer: it's not. If we played the harmonics of the > harmonics series 1 to 15 at the same, for example (anything without > the excessive beating of harmonics 19+), it would likely sound more > natural than PHI mean-tone.
> One slight problem: we'd only have about one area (near harmonics > 7-14 or 8-16) that would actually fit at least 7 notes per 2/1 > octave. And then we have the problem of that harmonics 1 to 19 only > covers some 2.5 octaves or so and the notes at the bottom (harmonics > 1 to 4 or so) are ridiculously spread out...far too much so to work > as bass notes. And with JI, as you know from music theory, the > majority of combinations of notes make sour chords (which is why > music theory is so complex...and important with diatonic scales),
> These realistic restrictions of using the harmonic series as a > scale make me reconsider PHI. With scales derived from a PHI tuning > I can get pretty close to a "scale that is a chord" (IE very hard to > find sour combinations of notes) without the above mentioned > limitations of using the harmonic series as a scale.
>
> --One possible explanation is that the irrationals themselves are an > idealisation, that in ---reality the notes with which we are > familiar are rational harmonics in the higher registers
>
> Could be. Or they could simply be very near rational > values...enough so that the ear barely notices (IE in my rational > version of the irrational PHI scale). Lastly, I strongly suspect it > all comes down to "the ear likes predictable beating...either with a > constant beating rate between notes (harmonic series), or a > situation where beating rates are multiples of each other (PHI).
>
> -Michael
>
>
Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

Hello Charles,

if you think that the best sounding musical intervals might not be at exact integer frequency ratios then why is the octave an exception as it is at 2:1 in LucyTuning?

Kalle Aho

--- In tuning@...m, Charles Lucy <lucy@...> wrote:
>
> Hi Michael;
>
> I am glad to read that you (and others) are exploring this paradox,
> for I also feel that the JI assumption that musical "harmonics" are
> only exactly at integer frequency ratios, and that "good" tunings
> should be constructed only from integer ratios is wrong.
>
> (and in my view both naive and simplistic).
>
> I agree with you that the beating seems to be as a result of
> "deviations" from integer frequency ratios, and that the "musical ear"
> hears beating in harmony as being acceptable.
>
> Where our views diverge is on finding a mathematical model which gives
> us the appropriate interval sizes and consequential optimal beat rates.
>
> I make no claims of having been the first to discover how well using
> the radian angle (assuming an octave is one complete revolution) as
> the Large interval (the difference between the fourth and fifth) works.
>
> John Harrison clearly wrote this in the late 1700's, and the more I
> experiment and work with his specifications the more convinced I
> become that he had found a viable solution which "sounds" right and
> works musically.
>
> I realise that I have written this comment in a wordy and pompous
> form, for there are many "nit-pickers" amongst the tunaniks (no
> names;-), who are quick to point out any discrepancies.
>
> This fact doesn't encourage "a fluid" writing style, although I do
> appreciate the precision that it demands.
>
> I have yet to improve on Harrison's formula.
>
> I wish you good fortune in finding a better solution and model for
> mapping musical harmony, scales, and tunings.

Who knows?

I speculate that it is because:

? when a string is "split into two equal parts, each part becomes the "mirror" of the other.
?by definition the octave is a doubling of frequency.
?The doubling of exact frequency is in the original Harrison equation.

I observe that:

?Lightly touching a string at the octave position produces the same pitch when playing between the bridge and the finger, and between the nut and the finger on my guitars, kora, mandolin, basses and other stringed instruments, and that note has an octave ratio of two to the open string.

? You can hear it.

On 23 Mar 2009, at 21:29, Kalle Aho wrote:

> Hello Charles,
>
> if you think that the best sounding musical intervals might not be > at exact integer frequency ratios then why is the octave an > exception as it is at 2:1 in LucyTuning?
>
> Kalle Aho
>
> --- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
> >
> > Hi Michael;
> >
> > I am glad to read that you (and others) are exploring this paradox,
> > for I also feel that the JI assumption that musical "harmonics" are
> > only exactly at integer frequency ratios, and that "good" tunings
> > should be constructed only from integer ratios is wrong.
> >
> > (and in my view both naive and simplistic).
> >
> > I agree with you that the beating seems to be as a result of
> > "deviations" from integer frequency ratios, and that the "musical > ear"
> > hears beating in harmony as being acceptable.
> >
> > Where our views diverge is on finding a mathematical model which > gives
> > us the appropriate interval sizes and consequential optimal beat > rates.
> >
> > I make no claims of having been the first to discover how well using
> > the radian angle (assuming an octave is one complete revolution) as
> > the Large interval (the difference between the fourth and fifth) > works.
> >
> > John Harrison clearly wrote this in the late 1700's, and the more I
> > experiment and work with his specifications the more convinced I
> > become that he had found a viable solution which "sounds" right and
> > works musically.
> >
> > I realise that I have written this comment in a wordy and pompous
> > form, for there are many "nit-pickers" amongst the tunaniks (no
> > names;-), who are quick to point out any discrepancies.
> >
> > This fact doesn't encourage "a fluid" writing style, although I do
> > appreciate the precision that it demands.
> >
> > I have yet to improve on Harrison's formula.
> >
> > I wish you good fortune in finding a better solution and model for
> > mapping musical harmony, scales, and tunings.
>
>
Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>
>
> Who knows?
>
> I speculate that it is because:
>
> ? when a string is "split into two equal parts, each part becomes the
> "mirror" of the other.
> ?by definition the octave is a doubling of frequency.
> ?The doubling of exact frequency is in the original Harrison equation.
>
> I observe that:
>
> ?Lightly touching a string at the octave position produces the same
> pitch when playing between the bridge and the finger, and between the
> nut and the finger on my guitars, kora, mandolin, basses and other
> stringed instruments, and that note has an octave ratio of two to the
> open string.
>
> ? You can hear it.
>
>
>
> On 23 Mar 2009, at 21:29, Kalle Aho wrote:
>
> > Hello Charles,
> >
> > if you think that the best sounding musical intervals might not be
> > at exact integer frequency ratios then why is the octave an
> > exception as it is at 2:1 in LucyTuning?
> >
> > Kalle Aho
> >
> > --- In tuning@yahoogroups.com, Charles Lucy <lucy@> wrote:
> > >
> > > Hi Michael;
> > >
> > > I am glad to read that you (and others) are exploring this paradox,
> > > for I also feel that the JI assumption that musical "harmonics" are
> > > only exactly at integer frequency ratios, and that "good" tunings
> > > should be constructed only from integer ratios is wrong.
> > >
> > > (and in my view both naive and simplistic).
> > >
> > > I agree with you that the beating seems to be as a result of
> > > "deviations" from integer frequency ratios, and that the "musical
> > ear"
> > > hears beating in harmony as being acceptable.
> > >
> > > Where our views diverge is on finding a mathematical model which
> > gives
> > > us the appropriate interval sizes and consequential optimal beat
> > rates.
> > >
> > > I make no claims of having been the first to discover how well using
> > > the radian angle (assuming an octave is one complete revolution) as
> > > the Large interval (the difference between the fourth and fifth)
> > works.
> > >
> > > John Harrison clearly wrote this in the late 1700's, and the more I
> > > experiment and work with his specifications the more convinced I
> > > become that he had found a viable solution which "sounds" right and
> > > works musically.
> > >
> > > I realise that I have written this comment in a wordy and pompous
> > > form, for there are many "nit-pickers" amongst the tunaniks (no
> > > names;-), who are quick to point out any discrepancies.
> > >
> > > This fact doesn't encourage "a fluid" writing style, although I do
> > > appreciate the precision that it demands.
> > >
> > > I have yet to improve on Harrison's formula.
> > >
> > > I wish you good fortune in finding a better solution and model for
> > > mapping musical harmony, scales, and tunings.
> >
> >
>
> Charles Lucy
> lucy@...
>
> - Promoting global harmony through LucyTuning -
>
> for information on LucyTuning go to:
> http://www.lucytune.com
>
> For LucyTuned Lullabies go to:
> http://www.lullabies.co.uk
>
Hi Charles,

Haven't heard from you in a while. Keeping well I hope. You mentioned that "Lightly touching a string at the octave position produces the same pitch when playing between the bridge and the finger, and between the nut and the finger on my guitars, kora, etc". But then how does one explain the other harmonics? Lightly touching the string at lengths 1/3, 2/3, and 1/5 etc. produce the fifth and major third intervals.

Incidentally, from what I have heard on your site I do think that Harrison's tuning system sounds in tune. Since PI is also an irrational (like 12 edo) then this further suggests to me that there is more going on than meets the...ear. What are the exact ratios for major/minor thirds and perfect fifths in Lucy tuning? (I tried to calculate the larger/smaller intervals in your system but didn't quite understand).

Thanks

-Rick

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>
>
> Who knows?

Well, you should. If LucyTuned intervals are the best sounding
intervals then you should be able to find them by ear just by
listening for the best sounding ones. Can you do that? Personally,
I don't hear anything special happening around for example LucyTuned
fifth when slowly varying the fifth size. It just sounds pretty much
the same as other nearby fifths. But a fifth of 3:2 always sounds
special (not necessarily the best though) to me when played with
harmonic timbres.

> I speculate that it is because:
>
> ? when a string is "split into two equal parts, each part becomes the
> "mirror" of the other.

This doesn't explain anything. You are effectively just using
different words to say the same thing twice.

> ?by definition the octave is a doubling of frequency.

No substantial fact can follow from mere definition. (Besides, if
this definition was exactly correct, then a stretched octave would
be an impossible entity. But there are stretched octaves in pianos
for example.)

> ?The doubling of exact frequency is in the original Harrison equation.

That is just an argument from authority.

> I observe that:
>
> ?Lightly touching a string at the octave position produces the same
> pitch when playing between the bridge and the finger, and between the
> nut and the finger on my guitars, kora, mandolin, basses and other
> stringed instruments, and that note has an octave ratio of two to the
> open string.

This just follows from the tautological truth that when you halve a
string along its length you get two string-parts of equal length.
Again doesn't explain anything.

Kalle Aho

> On 23 Mar 2009, at 21:29, Kalle Aho wrote:
>
> > Hello Charles,
> >
> > if you think that the best sounding musical intervals might not be
> > at exact integer frequency ratios then why is the octave an
> > exception as it is at 2:1 in LucyTuning?
> >
> > Kalle Aho

--Since PI is also an irrational (like 12 edo) then this further suggests
to me that there is ---more going on than meets the...ear. What are the
exact ratios for major/minor thirds and ---perfect fifths in Lucy tuning?
   I know I'm being very critical here...but I think a large reason Lucy Tuning sounds "in tune" to so many people is that it's very (within about 8 cents for virtually all notes) close to 12TET.  It retains, in general, a very familiar feel while etching out some of the impurities (IE the sour minor 3rd in 12TET)
----------------------------------
   On the other hand, so far as "systems that approximate 12TET or 5-limit JI", Lucy-Tuning is among the best (at least to my ear)...just about the only one I've heard on-par with it is Wilson's MOS scales.  And both of these, I believe, sound better than non-adaptive JI...because in regular JI some interval become severely skewed/tense for the sake of making other intervals
pure (which explains the necessity of having some many different JI scales and not just one). :-P
 
   Lucy-Tuning also seems to indirectly prove that irrationals, again, can be used to generate scales that have a very "rational number" feeling of resolve to them while getting past some of the "one pure interval must come at the expense of another" type problems so common with using rational numbers as/in generators.

-Michael

--- On Tue, 3/24/09, rick_ballan <rick_ballan@...> wrote:

From: rick_ballan <rick_ballan@...>
Subject: [tuning] Re: Rational vs Irrational Scales: a response to Rick
To: tuning@yahoogroups.com
Date: Tuesday, March 24, 2009, 8:11 AM

--- In tuning@yahoogroups. com, Charles Lucy <lucy@...> wrote:

>

>

> Who knows?

>

> I speculate that it is because:

>

> ? when a string is "split into two equal parts, each part becomes the

> "mirror" of the other.

> ?by definition the octave is a doubling of frequency.

> ?The doubling of exact frequency is in the original Harrison equation.

>

> I observe that:

>

> ?Lightly touching a string at the octave position produces the same

> pitch when playing between the bridge and the finger, and between the

> nut and the finger on my guitars, kora, mandolin, basses and other

> stringed instruments, and that note has an octave ratio of two to the

> open string.

>

> ? You can hear it.

>

>

>

> On 23 Mar 2009, at 21:29, Kalle Aho wrote:

>

> > Hello Charles,

> >

> > if you think that the best sounding musical intervals might not be

> > at exact integer frequency ratios then why is the octave an

> > exception as it is at 2:1 in LucyTuning?

> >

> > Kalle Aho

> >

> > --- In tuning@yahoogroups. com, Charles Lucy <lucy@> wrote:

> > >

> > > Hi Michael;

> > >

> > > I am glad to read that you (and others) are exploring this paradox,

> > > for I also feel that the JI assumption that musical "harmonics" are

> > > only exactly at integer frequency ratios, and that "good" tunings

> > > should be constructed only from integer ratios is wrong.

> > >

> > > (and in my view both naive and simplistic).

> > >

> > > I agree with you that the beating seems to be as a result of

> > > "deviations" from integer frequency ratios, and that the "musical

> > ear"

> > > hears beating in harmony as being acceptable.

> > >

> > > Where our views diverge is on finding a mathematical model which

> > gives

> > > us the appropriate interval sizes and consequential optimal beat

> > rates.

> > >

> > > I make no claims of having been the first to discover how well using

> > > the radian angle (assuming an octave is one complete revolution) as

> > > the Large interval (the difference between the fourth and fifth)

> > works.

> > >

> > > John Harrison clearly wrote this in the late 1700's, and the more I

> > > experiment and work with his specifications the more convinced I

> > > become that he had found a viable solution which "sounds" right and

> > > works musically.

> > >

> > > I realise that I have written this comment in a wordy and pompous

> > > form, for there are many "nit-pickers" amongst the tunaniks (no

> > > names;-), who are quick to point out any discrepancies.

> > >

> > > This fact doesn't encourage "a fluid" writing style, although I do

> > > appreciate the precision that it demands.

> > >

> > > I have yet to improve on Harrison's formula.

> > >

> > > I wish you good fortune in finding a better solution and model for

> > > mapping musical harmony, scales, and tunings.

> >

> >

>

> Charles Lucy

> lucy@...

>

> - Promoting global harmony through LucyTuning -

>

> for information on LucyTuning go to:

> http://www.lucytune .com

>

> For LucyTuned Lullabies go to:

> http://www.lullabie s.co.uk

>

Hi Charles,

Haven't heard from you in a while. Keeping well I hope. You mentioned that "Lightly touching a string at the octave position produces the same pitch when playing between the bridge and the finger, and between the nut and the finger on my guitars, kora, etc". But then how does one explain the other harmonics? Lightly touching the string at lengths 1/3, 2/3, and 1/5 etc. produce the fifth and major third intervals.

Incidentally, from what I have heard on your site I do think that Harrison's tuning system sounds in tune. Since PI is also an irrational (like 12 edo) then this further suggests to me that there is more going on than meets the...ear. What are the exact ratios for major/minor thirds and perfect fifths in Lucy tuning? (I tried to calculate the larger/smaller intervals in your system but didn't quite understand).

Thanks

-Rick

Hi Rick;

The cent and Hertz values for the first 40-odd notes/intervals can be found on this page:

http://www.lucytune.com/new_to_lt/pitch_02.html

I don't know how one explains the other "harmonics", except that they are steps of fourths and fifths derived from pi.

Whether you hear it as "in tune" or not seems to be a matter of musical taste.

It works perfectly to my ears.

More research seems to be required to discover what is really happening, and why Harrison's model works so well ;-)

On 24 Mar 2009, at 15:11, rick_ballan wrote:
> >Hi Charles,
>

>
> >Haven't heard from you in a while. Keeping well I hope. You > mentioned that "Lightly touching a string at the octave position > produces the same pitch when playing between the bridge and the > finger, and between the nut and the finger on my guitars, kora, > etc". But then how does one explain the other harmonics? Lightly > touching the string at lengths 1/3, 2/3, and 1/5 etc. produce the > fifth and major third intervals.
>
> Incidentally, from what I have heard on your site I do think that > Harrison's tuning system sounds in tune. Since PI is also an > irrational (like 12 edo) then this further suggests to me that there > is more going on than meets the...ear. What are the exact ratios for > major/minor thirds and perfect fifths in Lucy tuning? (I tried to > calculate the larger/smaller intervals in your system but didn't > quite understand).
>
> Thanks
>
> -Rick
>
> _
>

Charles Lucy
lucy@...- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

Charles Lucy <lucy@...> wrote:
> Who knows?
> I speculate that it is because:
> ? when a string is "split into two equal parts, each part becomes the
> "mirror" of the other.
> ?by definition the octave is a doubling of frequency.
> I observe that:
> ?Lightly touching a string at the octave position produces the same
> pitch when playing between the bridge and the finger, and between the
> nut and the finger on my guitars, kora, mandolin, basses and other
> stringed instruments, and that note has an octave ratio of two to the
> open string.
> On 23 Mar 2009, at 21:29, Kalle Aho wrote:
> > Hello Charles,
> > if you think that the best sounding musical intervals might not be
> > at exact integer frequency ratios then why is the octave an
> > exception as it is at 2:1 in LucyTuning?
> > Kalle Aho
> Rick wrote:
> Hi Charles,
> You mentioned that "Lightly touching a string at the octave position
produces the same pitch when playing between the bridge and the finger, and
between the nut and the finger on my guitars, kora, etc". But then how does
one explain the other harmonics? Lightly touching the string at lengths 1/3,
2/3, and 1/5 etc. produce the fifth and major third intervals.

I am astonished. From past posts it is apparent that we are fortunate to
have in this list quite a few distinguished members who are eminently
knowledgeable about advanced musical acoustics (no, I am NOT including
myself among them).

Yet others, amazingly, are writing extensively on temperament proposals
while they also seem to be unaware of basic acoustical facts (e.g.
relationships between string partials, the harmonic series and related
small-integer ratio intervals) that have been known and mentioned as matter
of fact in the relevant literature ever since Sauveur (1702) put the things
together, not to speak of the mathematical explanations of Fourier a century
later.

I have a suggestion for self-improvement.
Why don't we use a more sensible sequence? such as:
1) study and understand the existing literature on historical knowledge and
recent findings,
2) ask and discuss doubts among friends
3) only then ask/discuss with specialists
3) only then write new proposals.

Kind regards,

Claudio

--- On Tue, 3/24/09, Claudio Di Veroli <dvc@...> wrote:

From: Claudio Di Veroli <dvc@...>
Subject: RE: [tuning] Re: Rational vs Irrational Scales: a response to Rick
To: tuning@yahoogroups.com
Date: Tuesday, March 24, 2009, 9:11 AM

--Yet others, amazingly, are writing extensively on temperament proposals
--while they also seem to be unaware of basic acoustical facts
--(e.g. relationships between string partials, the harmonic series and related
--small-integer ratio intervals) 
     Wait, so you are saying because someone doesn't follow these conventions, they must automatically be stereotyped as not knowing them?!
     I, for one, know a great deal about the harmonic series and how JI is derived from it.  I also know that to make several JI chords that perfectly follow the series you need to use adaptive JI and constantly swap notes for maximum purity...and, even then, you have limits (try playing a chord with more than 4 notes per octave in adaptive JI that sounds consonant...it doesn't really work, does it)?
 
   Far as how acoustic ratios have to do with instrument tuning/design...I, like many others, know very little about that area.  But how is this relevant if I'm not trying to design an instrument?  Seems just like a reason to "start an argument with a carpenter about welding technique"...it just don't see how it can help much.
 
 
--I have a suggestion for self-improvement.
--Why don't we use a more sensible sequence?  such as:
--1) study and understand the existing literature on historical knowledge and --recent findings,
  I do, but the only thing I found even remotely resembling what I've been doing is the PHI meantone scale.  And, even then, the ways I've seen it used in history are to mimic diatonic modes by using it like a MOS scale.  Far as psychoacoustics, I've read extensively and Sethares, some on Wilson, a ton on Plomp and Llevet (sp.), some on Lucy-Tuning, oodles of info on JI, and a fair amount on scales under 19-TET, 31-TET...designed to approximate JI intervals.  And I am 100% NOT trying to mimic diatonic scales.
 
--2) ask and discuss doubts among friends
   I don't know about the rest of you...but I already do this a lot.
 
--3) only then ask/discuss with specialists
  Point me to a specialist in non-diatonic scales under PHI mean-tone-style tunings and I'll be happy to.  I've seen about 12 articles about PHI scale, and none of the math behind them nor the results is anything like my own...plus 95% of the time the goal is the opposite (I'm aiming for consonance and not emulating diatonic intervals, most theories I've read aim for dissonance and following diatonic intervals).
 
--4) only then write new proposals.
  I think the general push of this note seems to be "keep things the way they are unless you have at least 100 fans of your theory".  It's the same logic the major labels use to decide with bands they will and won't sign.
  And, pardon my pessimism, I think that attitude blatantly stiffles innovation.  I don't care that much about how many books I've read, for example, that support my theory are around if the theory produces something that sounds good to my ears and at least a handful of other people's who have never liked (or heard) microtonal before.
 
   Charles can state his own side on the issue but I, for one, plead NOT guilty... :-)
 
-Michael
 
Charles Lucy <lucy@...> wrote:
> Who knows?
> I speculate that it is because:
> ? when a string is "split into two equal parts, each part becomes the
> "mirror" of the other.
> ?by definition the octave is a doubling of frequency.
> I observe that:
> ?Lightly touching a string at the octave position produces the same
> pitch when playing between the bridge and the finger, and between the
> nut and the finger on my guitars, kora, mandolin, basses and other
> stringed instruments, and that note has an octave ratio of two to the
> open string.
> On 23 Mar 2009, at 21:29, Kalle Aho wrote:
> > Hello Charles,
> > if you think that the best sounding musical intervals might not be
> > at exact integer frequency ratios then why is the octave an
> > exception as it is at 2:1 in LucyTuning?
> > Kalle Aho
> Rick wrote:
 > Hi Charles,
 >  You mentioned that "Lightly touching a string at the octave position produces the same pitch when playing between the bridge and the finger, and between the nut and the finger on my guitars, kora, etc". But then how does one explain the other harmonics? Lightly touching the string at lengths 1/3, 2/3, and 1/5 etc. produce the fifth and major third intervals. 
 
I am astonished. From past posts it is apparent that we are fortunate to have in this list quite a few distinguished members who are eminently knowledgeable about advanced musical acoustics (no, I am NOT including myself among them).
 
Yet others, amazingly, are writing extensively on temperament proposals while they also seem to be unaware of basic acoustical facts (e.g. relationships between string partials, the harmonic series and related small-integer ratio intervals) that have been known and mentioned as matter of fact  in the relevant literature ever since Sauveur (1702) put the things together, not to speak of the mathematical explanations of Fourier a century later.
 
I have a suggestion for self-improvement.
Why don't we use a more sensible sequence?  such as:
1) study and understand the existing literature on historical knowledge and recent findings,
2) ask and discuss doubts among friends
3) only then ask/discuss with specialists
3) only then write new proposals.
 
Kind regards,
 
Claudio
 

---But a fifth of 3:2 always sounds
---special (not necessarily the best though) to me when played with
---harmonic timbres.
   Indeed, any ratio from the harmonic series is going to sound special, but not necessarily the best.  I recall one theory of consonance says the equivalent of "how good something sounds is how much information it contains / how much effort it takes to process".
 
  For example, take the harmonic series x/16 (something I ran into during my old JI scale experiments).  Sounds pretty good, right?  But now try something more complex: taking the x/9, x/16, and x/13 harmonic series and mixing notes from each (so none of the two notes get too close and cause critical band roughness). 
   Doesn't the result of the second example sound better, much more full and yet still nearly as easy to process?
 
    But...you may wonder how the heck I got the certain harmonic series mentioned above.  The answer is they all approach notes in the the PHI meantone tuning: they are harmonic series approaching a very symmetrical pattern of irrational numbers.  I'm SURE there are several other symmetrical patterns in irrational number generated tunings others can discover and then summarize bakc into rational or near-rational form (ALA LucyTuning).
 
  In my case (and I'm sure many others), irrational numbers can be used to explain and find beautiful patterns in rational numbers that would not be obvious otherwise. 
 
  Believe it or not...I am convinced, in the end of the day, irrational number generated scales SHOULD be able to be simplified into a few HARMONIC SERIES (about 2 to 3) in the end of the day to become easier for the mind to process...yet still should be close enough to their irrational versions that you can tell where the irrational number pattern comes from and give your mind 2 paths through which to understand the music.
 
-Michael

--- On Tue, 3/24/09, Kalle Aho <kalleaho@...> wrote:

From: Kalle Aho <kalleaho@...>
Subject: [tuning] Re: Rational vs Irrational Scales: a response to Rick
To: tuning@yahoogroups.com
Date: Tuesday, March 24, 2009, 9:14 AM

--- In tuning@yahoogroups. com, Charles Lucy <lucy@...> wrote:
>
>
> Who knows?

Well, you should. If LucyTuned intervals are the best sounding
intervals then you should be able to find them by ear just by
listening for the best sounding ones. Can you do that? Personally,
I don't hear anything special happening around for example LucyTuned
fifth when slowly varying the fifth size. It just sounds pretty much
the same as other nearby fifths. But a fifth of 3:2 always sounds
special (not necessarily the best though) to me when played with
harmonic timbres.

> I speculate that it is because:
>
> ? when a string is "split into two equal parts, each part becomes the
> "mirror" of the other.

This doesn't explain anything. You are effectively just using
different words to say the same thing twice.

> ?by definition the octave is a doubling of frequency.

No substantial fact can follow from mere definition. (Besides, if
this definition was exactly correct, then a stretched octave would
be an impossible entity. But there are stretched octaves in pianos
for example.)

> ?The doubling of exact frequency is in the original Harrison equation.

That is just an argument from authority.

> I observe that:
>
> ?Lightly touching a string at the octave position produces the same
> pitch when playing between the bridge and the finger, and between the
> nut and the finger on my guitars, kora, mandolin, basses and other
> stringed instruments, and that note has an octave ratio of two to the
> open string.

This just follows from the tautological truth that when you halve a
string along its length you get two string-parts of equal length.
Again doesn't explain anything.

Kalle Aho

> On 23 Mar 2009, at 21:29, Kalle Aho wrote:
>
> > Hello Charles,
> >
> > if you think that the best sounding musical intervals might not be
> > at exact integer frequency ratios then why is the octave an
> > exception as it is at 2:1 in LucyTuning?
> >
> > Kalle Aho

Michael Sheiman wrote:

> I, for one, know a great deal about the harmonic series and how JI is
> derived from it. I also know that to make several JI chords that perfectly
> follow the series you need to use adaptive JI and constantly swap notes for
> maximum purity...and, even then, you have limits (try playing a chord with
> more than 4 notes per octave in adaptive JI that sounds consonant...it
> doesn't really work, does it)?

You don't need adaptive JI. You can play G, C, Em, and D in fixed JI. You can use a CPS.

4:5:6:7:9 works. Really, it does.

> Far as how acoustic ratios have to do with instrument tuning/design...I,
> like many others, know very little about that area. But how is this
> relevant if I'm not trying to design an instrument? Seems just like a
> reason to "start an argument with a carpenter about welding technique"...it
> just don't see how it can help much.

This came out of an argument Charles is having where he keeps evading the issue. It's relevant if you're trying to tune an instrument. Which is sort of the point of this list.

> --I have a suggestion for self-improvement.
> --Why don't we use a more sensible sequence? such as:
> --1) study and understand the existing literature on historical knowledge
> and --recent findings,
> I do, but the only thing I found even remotely resembling what I've been
> doing is the PHI meantone scale. And, even then, the ways I've seen it used
> in history are to mimic diatonic modes by using it like a MOS scale. Far as
> psychoacoustics, I've read extensively and Sethares, some on Wilson, a ton
> on Plomp and Llevet (sp.), some on Lucy-Tuning, oodles of info on JI, and a
> fair amount on scales under 19-TET, 31-TET...designed to approximate JI
> intervals. And I am 100% NOT trying to mimic diatonic scales.

What about O'Connell's paper then? I thought it was alarmingly similar to what you're doing but you haven't acknowledged it.

What do you mean by "mimic diatonic modes"?

> Point me to a specialist in non-diatonic scales under PHI mean-tone-style
> tunings and I'll be happy to. I've seen about 12 articles about PHI scale,
> and none of the math behind them nor the results is anything like my
> own...plus 95% of the time the goal is the opposite (I'm aiming for
> consonance and not emulating diatonic intervals, most theories I've read aim
> for dissonance and following diatonic intervals).

How did O'Connell aim for dissonance and following diatonic intervals?

Graham

>
>What are the exact ratios for major/minor thirds and perfect fifths in Lucy tuning? (I tried to calculate the larger/smaller intervals in your system but didn't quite understand).
>

Maybe these could help (a few basic ones)...

major third: 2^(1:pi)
minor third: 2^[1:2 - 3:(4pi)]
perfect fifth: 2^[1:2 + 1:(4pi)]
"larger interval": 2^[1:(2pi)]
"smaller interval": 2^[1:2 - 5:(4pi)]

djtrancendance@... wrote:

> I know I'm being very critical here...but I think a large reason Lucy Tuning > sounds "in tune" to so many people is that it's very (within about 8 cents for > virtually all notes) close to 12TET. It retains, in general, a very familiar > feel while etching out some of the impurities (IE the sour minor 3rd in 12TET)

That's not right. The fifth of LucyTuning is 4.5 cents from 12TET. The minor third is already 13.5 cents away. The 12 note circle of fifths fails to close with an interval of about a quartertone. You can't get further from 12TET without getting closer to another interval.

If you want to be close to 12TET, LucyTuning is a strange meantone to pick. 1/6 comma meantone has a fifth about 1.6 cents off. That really will give you thirds within 8 cents of 12TET, but tuned better.

> On the other hand, so far as "systems that approximate 12TET or 5-limit JI", > Lucy-Tuning is among the best (at least to my ear)...just about the only one > I've heard on-par with it is Wilson's MOS scales. And both of these, I believe, > sound better than non-adaptive JI...because in regular JI some interval become > severely skewed/tense for the sake of making other intervals pure (which > explains the necessity of having some many different JI scales and not just > one). :-P

What do you mean by "Wilson's MOS scales"? LucyTuning is full of MOS scales. I'm sure you've been told this before.

> Lucy-Tuning also seems to indirectly prove that irrationals, again, can be > used to generate scales that have a very "rational number" feeling of resolve to > them while getting past some of the "one pure interval must come at the expense > of another" type problems so common with using rational numbers as/in generators.

Why does anybody need to prove the validity of irrational generators?

Graham

Kalle,
I agree that when a harmony is played on its own, the rational frequency ratio is preferrable to an irrational frequency ratio. I myself prefer just intonation over temperaments to compose in. However, this may not mean that irrational ratios have no value at all in music. Context is everything here: some pieces may sound better in just intonation, whereas others (that do not rely on stable consonant sonorities) may sound better in LucyTuning or 23-edo or 88-cet or some other irrational tuning.

I noticed in composition and improvisation that the tuning system (and the scales used) imparts its mood on the music being played. One of the advantages of LucyTuning seems to be (this is what I understood from the website) that it can be used to approximate a wide range of tunings (from other cultures or otherwise). For example, I found that every fourth generator from LucyTuning makes an excellent 22-tET, whereas more conventionally minded musicians might prefer to use LucyTuning as a meantone. I do not see this versatility in other meantones such as 1/4 comma (where the major third is a bad magic generator) or just intonation (where neither the perfect fifth nor major third is a good generator for a linear temperament.)

Probably this versatility is what Charles means by "best sounding intervals": I interpret this to mean that LucyTuning can provide a spectrum of sounds that can fit anyone's definition of "best sounding" using a reasonable number of generators.

As far as the justness of the 2:1 is concerned, I think that it is because the 2:1 is a universal phenomenon in the music of cultures who use instruments with harmonic or near-harmonic timbres. (The same can be said for 3:2 or 4:3, but probably not for 5:4, 6:5, 7:6 and more complex intervals.) Distorting the 2:1 would make music theory in LucyTuning unnecessarily complicated, and it would directly contradict the purpose of LucyTuning, which seems to be to represent all musical cultures with a unified theory.

(However, LucyTuning (or any other tuning for that matter) can be stretched to accomodate inharmonic timbres. Even the "pure" LucyTuning has intervals resembling stretched octaves, such as the 19-generator interval.)

Praveen Venkataramana (justin_tone52)

--- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@...> wrote:
>
> --- In tuning@yahoogroups.com, Charles Lucy <lucy@> wrote:
> >
> >
> > Who knows?
>
> Well, you should. If LucyTuned intervals are the best sounding
> intervals then you should be able to find them by ear just by
> listening for the best sounding ones. Can you do that? Personally,
> I don't hear anything special happening around for example LucyTuned
> fifth when slowly varying the fifth size. It just sounds pretty much
> the same as other nearby fifths. But a fifth of 3:2 always sounds
> special (not necessarily the best though) to me when played with
> harmonic timbres.
>
> > I speculate that it is because:
> >
> > ? when a string is "split into two equal parts, each part becomes the
> > "mirror" of the other.
>
> This doesn't explain anything. You are effectively just using
> different words to say the same thing twice.
>
> > ?by definition the octave is a doubling of frequency.
>
> No substantial fact can follow from mere definition. (Besides, if
> this definition was exactly correct, then a stretched octave would
> be an impossible entity. But there are stretched octaves in pianos
> for example.)
>
> > ?The doubling of exact frequency is in the original Harrison equation.
>
> That is just an argument from authority.
>
> > I observe that:
> >
> > ?Lightly touching a string at the octave position produces the same
> > pitch when playing between the bridge and the finger, and between the
> > nut and the finger on my guitars, kora, mandolin, basses and other
> > stringed instruments, and that note has an octave ratio of two to the
> > open string.
>
> This just follows from the tautological truth that when you halve a
> string along its length you get two string-parts of equal length.
> Again doesn't explain anything.
>
> Kalle Aho
>
> > On 23 Mar 2009, at 21:29, Kalle Aho wrote:
> >
> > > Hello Charles,
> > >
> > > if you think that the best sounding musical intervals might not be
> > > at exact integer frequency ratios then why is the octave an
> > > exception as it is at 2:1 in LucyTuning?
> > >
> > > Kalle Aho
>

justin_tone52 wrote:

> I noticed in composition and improvisation that the tuning system
> (and the scales used) imparts its mood on the music being played.
> One of the advantages of LucyTuning seems to be (this is what I
> understood from the website) that it can be used to approximate a
> wide range of tunings (from other cultures or otherwise). For example,
> I found that every fourth generator from LucyTuning makes an excellent
> 22-tET, whereas more conventionally minded musicians might prefer to
> use LucyTuning as a meantone. I do not see this versatility in other
> meantones such as 1/4 comma (where the major third is a bad magic
> generator) or just intonation (where neither the perfect fifth nor
> major third is a good generator for a linear temperament.) There's nothing special about LucyTuning here. You get the usual meantone MOS scales and a good approximation to 88-tET (from which you can take a 22 note subset). The third isn't a good magic generator either. Enough fifths will approximate any interval to an arbitrary precision -- the same as quarter comma meantone, or pythagorean intonation, or various other JI subsets.

(The pythagorean perfect fifth is a good generator for a schismatic temperament. That has relevance to old Chinese, Indian, Arab/Persian, and European music. There's no "smoking gun" to prove it was in theoretical and practical use as a linear temperament in any of these cases, though.)

If you wanted to approximate arbitrary scales, the best meantone tuning would be Kornerup's based on phi. It gives a chain of MOS scales that follow the Fibonacci-like sequence 5, 7, 12, 19, 31, 50, 81, ... which all have the ratio of large to small intervals as phi, which means they all get equally close to being equal tempered.

In practice, we don't do this. What would be the point? If you know what you want, you can tune it up. There's no advantage in specifying a load of notes you'll never play from an irrelevant tuning system. Where there's a need for a universal pitch notation, use cents. You can approximate any interval with them really easily.

Graham

---4:5:6:7:9 works. Really, it does.
   I realize that, but that doesn't solve my problem.  The octave range is 2/1.  9/4 is more than 2/1.  Hence 4:5:6:7 is the 4(not 5)-note subset of that chord which fits the octave.

--It's relevant if you're trying to
--tune an instrument.
It wasn't obvious to me the first message concerned instrument tuning at all beyond that, for example, by coincidence dividing the string into 1/3 produced a "3rd" tone.
---Which is sort of the point of this list.
  Well it sure as hell doesn't say that in the list description.  I don't think instrument tuning is a bad thing at all...I just don't believe on monopolizing the subject of tuning to one very specific topic.

---What about O'Connell's paper then? I thought it was alarmingly similar to what you're ---doing but you haven't acknowledged it.

    Well, apparently he uses half steps and 3rd steps to make his scales.  Though I agree, from what I can tell, the tuning he bases his scales on IE the "circle of PHI" or "PHI mean-tone" (phi^x/2(the standard octave)^y) is the same.   But that's really just throwing a different generator into the mean-tone equation: I don't exactly think O'Connell or I did something original just by doing that alone.
   Also, to note, he tempers the generator so the 25th tone of the tuning to match the first (just as 12TET flattens the generating 5th (X) to make it fit the octave on x^12) while I don't.
*********************************************************************
---What do you mean by "mimic diatonic modes"?
   I mean those built try to best approximate intervals like 2nds, 3rds, 5ths...and, on a lower level, to match basic half steps.  For example 10TET is obviously not a diatonic scale since no two notes in it can, say, very well emulate a perfect 2nd.

--How did O'Connell aim for dissonance and following diatonic
--intervals?
  He doesn't.  I didn't say all PHI scales follow those conventions, just most.
****************************************************
  BTW, to be 100% sure what O'Connell's theories do I'd need a SCALA file example of a scale generated using his method.  Given that it should be blatantly obvious to my ear...if he and I are on the same page or not.  I'm quite willing to do the research given the material.

-Michael

--- On Tue, 3/24/09, Graham Breed <gbreed@...> wrote:

From: Graham Breed <gbreed@...>
Subject: Re: [tuning] Re: Rational vs Irrational Scales: a response to Rick
To: tuning@yahoogroups.com
Date: Tuesday, March 24, 2009, 4:19 PM

Michael Sheiman wrote:

> I, for one, know a great deal about the harmonic series and how JI is

> derived from it. I also know that to make several JI chords that perfectly

> follow the series you need to use adaptive JI and constantly swap notes for

> maximum purity...and, even then, you have limits (try playing a chord with

> more than 4 notes per octave in adaptive JI that sounds consonant... it

> doesn't really work, does it)?

You don't need adaptive JI. You can play G, C, Em, and D in

fixed JI. You can use a CPS.

4:5:6:7:9 works. Really, it does.

> Far as how acoustic ratios have to do with instrument tuning/design. ..I,

> like many others, know very little about that area. But how is this

> relevant if I'm not trying to design an instrument? Seems just like a

> reason to "start an argument with a carpenter about welding technique".. .it

> just don't see how it can help much.

This came out of an argument Charles is having where he

keeps evading the issue. It's relevant if you're trying to

tune an instrument. Which is sort of the point of this list.

> --I have a suggestion for self-improvement.

> --Why don't we use a more sensible sequence? such as:

> --1) study and understand the existing literature on historical knowledge

> and --recent findings,

> I do, but the only thing I found even remotely resembling what I've been

> doing is the PHI meantone scale. And, even then, the ways I've seen it used

> in history are to mimic diatonic modes by using it like a MOS scale. Far as

> psychoacoustics, I've read extensively and Sethares, some on Wilson, a ton

> on Plomp and Llevet (sp.), some on Lucy-Tuning, oodles of info on JI, and a

> fair amount on scales under 19-TET, 31-TET...designed to approximate JI

> intervals. And I am 100% NOT trying to mimic diatonic scales.

What about O'Connell's paper then? I thought it was

alarmingly similar to what you're doing but you haven't

acknowledged it.

What do you mean by "mimic diatonic modes"?

> Point me to a specialist in non-diatonic scales under PHI mean-tone-style

> tunings and I'll be happy to. I've seen about 12 articles about PHI scale,

> and none of the math behind them nor the results is anything like my

> own...plus 95% of the time the goal is the opposite (I'm aiming for

> consonance and not emulating diatonic intervals, most theories I've read aim

> for dissonance and following diatonic intervals).

How did O'Connell aim for dissonance and following diatonic

intervals?

Graham

The point that you have missed here Graham is that beyond the numerology, what we are mapping is musical and harmonic patterns.

Knowing that an integer frequency ratio will produce a particular interval is much less helpful to a composer or musician than knowing the musical harmonic relationship is.

So you have selected a wonderful exotic whole number ratio; now what the composer/musician needs to know is how does this exotic interval fit into my scale,
and how does it relate harmonically (in the musical harmony sense, rather than in JI numerology) to other other "notes" which I am using.

OK so it is closer to a triple flattened third than to any interval on the sharp side of the harmony "spectrum", so if I wish to introduce this interval in a "smooth/consonant" manner, I should move to it via fourths; if I wish to make it sound "jarring" or as out of scale, it can serve this purpose in a composition which is predominantly on the "sharp" side of the harmony "spectrum".

To make microtuning work you need to think and act like a musician rather than like a comptometer.

Blood for the sharks - come and get it boys;-)

On 25 Mar 2009, at 04:15, Graham Breed wrote:

> justin_tone52 wrote:
>
> > I noticed in composition and improvisation that the tuning system
> > (and the scales used) imparts its mood on the music being played.
> > One of the advantages of LucyTuning seems to be (this is what I
> > understood from the website) that it can be used to approximate a
> > wide range of tunings (from other cultures or otherwise). For > example,
> > I found that every fourth generator from LucyTuning makes an > excellent
> > 22-tET, whereas more conventionally minded musicians might prefer to
> > use LucyTuning as a meantone. I do not see this versatility in other
> > meantones such as 1/4 comma (where the major third is a bad magic
> > generator) or just intonation (where neither the perfect fifth nor
> > major third is a good generator for a linear temperament.)
>
> There's nothing special about LucyTuning here. You get the
> usual meantone MOS scales and a good approximation to 88-tET
> (from which you can take a 22 note subset). The third isn't
> a good magic generator either. Enough fifths will
> approximate any interval to an arbitrary precision -- the
> same as quarter comma meantone, or pythagorean intonation,
> or various other JI subsets.
>
> (The pythagorean perfect fifth is a good generator for a
> schismatic temperament. That has relevance to old Chinese,
> Indian, Arab/Persian, and European music. There's no
> "smoking gun" to prove it was in theoretical and practical
> use as a linear temperament in any of these cases, though.)
>
> If you wanted to approximate arbitrary scales, the best
> meantone tuning would be Kornerup's based on phi. It gives
> a chain of MOS scales that follow the Fibonacci-like
> sequence 5, 7, 12, 19, 31, 50, 81, ... which all have the
> ratio of large to small intervals as phi, which means they
> all get equally close to being equal tempered.
>
> In practice, we don't do this. What would be the point? If
> you know what you want, you can tune it up. There's no
> advantage in specifying a load of notes you'll never play
> from an irrelevant tuning system. Where there's a need for
> a universal pitch notation, use cents. You can approximate
> any interval with them really easily.
>
> Graham
>
>
Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

Hello Praveen,

> Kalle,
> I agree that when a harmony is played on its own, the rational
frequency ratio is preferrable to an irrational frequency ratio.

As I wrote:

"But a fifth of 3:2 always sounds special (not necessarily the best
though) to me when played with harmonic timbres."

I didn't say it is preferable (though it might be). All I meant was
that small number frequency ratios simply stand out when compared to
nearby intervals while nothing special occurs soundwise at the
LucyTuned intervals.

> I myself prefer just intonation over temperaments to compose in.
> However, this may not mean that irrational ratios have no value at
> all in music.

I didn't say anything to the contrary.

> Context is everything here: some pieces may sound better in just
> intonation, whereas others (that do not rely on stable consonant
> sonorities) may sound better in LucyTuning or 23-edo or 88-cet or
> some other irrational tuning.

I agree.

> I noticed in composition and improvisation that the tuning system
> (and the scales used) imparts its mood on the music being played.
> One of the advantages of LucyTuning seems to be (this is what I
> understood from the website) that it can be used to approximate a
> wide range of tunings (from other cultures or otherwise). For
> example, I found that every fourth generator from LucyTuning makes
> an excellent 22-tET, whereas more conventionally minded musicians
> might prefer to use LucyTuning as a meantone. I do not see this
> versatility in other meantones such as 1/4 comma (where the major
> third is a bad magic generator) or just intonation (where neither
> the perfect fifth nor major third is a good generator for a linear
> temperament.)

But why approximate if you can have the real thing?

> Probably this versatility is what Charles means by "best sounding
> intervals": I interpret this to mean that LucyTuning can provide a
> spectrum of sounds that can fit anyone's definition of "best
> sounding" using a reasonable number of generators.

Even assuming that there is a reason (I can't think of any) to
produce that spectrum of sounds with a single generator there is no
evidence that LucyTuning is the best possible way to do that.

> As far as the justness of the 2:1 is concerned, I think that it is
> because the 2:1 is a universal phenomenon in the music of cultures
> who use instruments with harmonic or near-harmonic timbres. (The
> same can be said for 3:2 or 4:3, but probably not for 5:4, 6:5, 7:6
> and more complex intervals.)

That misses my point: if Charles thinks that the best fifth is not
found at 3:2 then why does he assume that the best octave is at 2:1?
He has called people naive and simplistic for thinking that the
greatest harmony occurs at small number ratios but he displays the
very same naivete in relation to the octave.

> Distorting the 2:1 would make music theory in LucyTuning
> unnecessarily complicated, and it would directly contradict the
> purpose of LucyTuning, which seems to be to represent all musical
> cultures with a unified theory.

I for one get no musical or theoretical insight from knowing where
in a chain of LucyTuned fifths some interval (or its approximation) occurs.

Kalle Aho

We again get back to sonic aesthetics, although there may be an
underlying physical or biological reason which we have yet to find.

My quest in microtuning was to find a tuning system which would:

play traditional Western harmony
modulate and transpose
control consonance and dissonance
emulate all tunings and scales
use conventional notation
allow infinite notes per octave
be easy to implement and learn
“sound right and be singable”
On 25 Mar 2009, at 11:52, Kalle Aho wrote:

> Hello Praveen,
>
> > Kalle,
> > I agree that when a harmony is played on its own, the rational
> frequency ratio is preferrable to an irrational frequency ratio.
>
> As I wrote:
>
> "But a fifth of 3:2 always sounds special (not necessarily the best
> though) to me when played with harmonic timbres."
>
> I didn't say it is preferable (though it might be). All I meant was
> that small number frequency ratios simply stand out when compared to
> nearby intervals while nothing special occurs soundwise at the
> LucyTuned intervals.
>
> > I myself prefer just intonation over temperaments to compose in.
> > However, this may not mean that irrational ratios have no value at
> > all in music.
>
> I didn't say anything to the contrary.
>
> > Context is everything here: some pieces may sound better in just
> > intonation, whereas others (that do not rely on stable consonant
> > sonorities) may sound better in LucyTuning or 23-edo or 88-cet or
> > some other irrational tuning.
>
> I agree.
>
> > I noticed in composition and improvisation that the tuning system
> > (and the scales used) imparts its mood on the music being played.
> > One of the advantages of LucyTuning seems to be (this is what I
> > understood from the website) that it can be used to approximate a
> > wide range of tunings (from other cultures or otherwise). For
> > example, I found that every fourth generator from LucyTuning makes
> > an excellent 22-tET, whereas more conventionally minded musicians
> > might prefer to use LucyTuning as a meantone. I do not see this
> > versatility in other meantones such as 1/4 comma (where the major
> > third is a bad magic generator) or just intonation (where neither
> > the perfect fifth nor major third is a good generator for a linear
> > temperament.)
>
> But why approximate if you can have the real thing?
>
> > Probably this versatility is what Charles means by "best sounding
> > intervals": I interpret this to mean that LucyTuning can provide a
> > spectrum of sounds that can fit anyone's definition of "best
> > sounding" using a reasonable number of generators.
>
> Even assuming that there is a reason (I can't think of any) to
> produce that spectrum of sounds with a single generator there is no
> evidence that LucyTuning is the best possible way to do that.
>
> > As far as the justness of the 2:1 is concerned, I think that it is
> > because the 2:1 is a universal phenomenon in the music of cultures
> > who use instruments with harmonic or near-harmonic timbres. (The
> > same can be said for 3:2 or 4:3, but probably not for 5:4, 6:5, 7:6
> > and more complex intervals.)
>
> That misses my point: if Charles thinks that the best fifth is not
> found at 3:2 then why does he assume that the best octave is at 2:1?
> He has called people naive and simplistic for thinking that the
> greatest harmony occurs at small number ratios but he displays the
> very same naivete in relation to the octave.
>
> > Distorting the 2:1 would make music theory in LucyTuning
> > unnecessarily complicated, and it would directly contradict the
> > purpose of LucyTuning, which seems to be to represent all musical
> > cultures with a unified theory.
>
> I for one get no musical or theoretical insight from knowing where
> in a chain of LucyTuned fifths some interval (or its approximation)
> occurs.
>
> Kalle Aho
>
>

Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

--- In tuning@yahoogroups.com, djtrancendance@... wrote/asked:
>
> --Since PI is also an irrational (like 12 edo)
> then this further suggests
> to me that there is ---more going on than meets the...ear.
> What are the
> exact ratios for major/minor thirds and
> ---perfect fifths in Lucy tuning?

Hi Charles, Michael & all others,

usually for musically purposes it is sufficient to approximate
PI by its 11-limit convergent 22/7.

http://en.wikipedia.org/wiki/Proof_that_22/7_exceeds_%CF%80
remarks on Archimedes:
"His proof proceeds by showing that 22⁄7 is greater than the ratio of the perimeter of a circumscribed regular polygon with 96 sides to the diameter of the circle. A more accurate approximation of π is 355/113."

No human beeing can discern the ratios 22/7 versus 355/113
bearely by plain ears, not to mention Feynman's approximation
at the 762th decimal after the dot:

http://en.wikipedia.org/wiki/Feynman_point

Conclusion:
Hence there is no need to exceed 11-limit by 113-limit,
for gaining an properly approximation of Lucy-Tuning
by rationals within the discrimination of resolution-capacity
in human ears.

bye
A.S.

> Hi Charles, Michael & all others,
>
> usually for musically purposes it is sufficient to approximate
> PI by its 11-limit convergent 22/7.
>

Very true. I tend to think of 88-edo as being a form of Lucy Tuning, just with pi approximated to 22:7.

This may be true if you are only considering one pitch at a time, and
not moving many steps from your tonic; yet what deviations do you get
from your calculations for beat frequency differences at say 16 steps
of fourths or fifths from the tonic?

On 25 Mar 2009, at 12:35, Andreas Sparschuh wrote:

>
>
> --- In tuning@yahoogroups.com, djtrancendance@... wrote/asked:
> >
> > --Since PI is also an irrational (like 12 edo)
> > then this further suggests
> > to me that there is ---more going on than meets the...ear.
> > What are the
> > exact ratios for major/minor thirds and
> > ---perfect fifths in Lucy tuning?
>
> Hi Charles, Michael & all others,
>
> usually for musically purposes it is sufficient to approximate
> PI by its 11-limit convergent 22/7.
>
> http://en.wikipedia.org/wiki/Proof_that_22/7_exceeds_%CF%80
> remarks on Archimedes:
> "His proof proceeds by showing that 22⁄7 is greater than the ratio
> of the perimeter of a circumscribed regular polygon with 96 sides to
> the diameter of the circle. A more accurate approximation of π is
> 355/113."
>
> No human beeing can discern the ratios 22/7 versus 355/113
> bearely by plain ears, not to mention Feynman's approximation
> at the 762th decimal after the dot:
>
> http://en.wikipedia.org/wiki/Feynman_point
>
> Conclusion:
> Hence there is no need to exceed 11-limit by 113-limit,
> for gaining an properly approximation of Lucy-Tuning
> by rationals within the discrimination of resolution-capacity
> in human ears.
>
> bye
> A.S.
>
>

Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

Michael Sheiman wrote:
> ---4:5:6:7:9 works. Really, it does.
> I realize that, but that doesn't solve my problem. The octave range is 2/1. > 9/4 is more than 2/1. Hence 4:5:6:7 is the 4(not 5)-note subset of that chord > which fits the octave.

What you asked for was more than 4 notes per octave. So I gave you a chord with 4.27 notes per octave. If you have some other problem you'd better state it. I don't see why there should be anything specially bad about JI and I thought your 9 note solution used JI anyway.

> --It's relevant if you're trying to
> --tune an instrument.
> It wasn't obvious to me the first message concerned instrument tuning at all > beyond that, for example, by coincidence dividing the string into 1/3 produced a > "3rd" tone.

If you care about what another message concerned you'd better reply to that message so that we know the context. The reply I gave was to a direct question about the usefulness of ratios. You didn't say anything about dividing a string. Ratios are used when you tune an instrument to match partials or harmonics.

> ---Which is sort of the point of this list.
> Well it sure as hell doesn't say that in the list description. I don't think > instrument tuning is a bad thing at all...I just don't believe on monopolizing > the subject of tuning to one very specific topic.

You must be on the wrong list. This one's description starts "This mailing list is intended for exchanging ideas relevant to alternate musical tunings..."

> ---What about O'Connell's paper then? I thought it was alarmingly similar to > what you're ---doing but you haven't acknowledged it.
> > Well, apparently he uses half steps and 3rd steps to make his scales. > Though I agree, from what I can tell, the tuning he bases his scales on IE the > "circle of PHI" or "PHI mean-tone" (phi^x/2(the standard octave)^y) is the > same. But that's really just throwing a different generator into the mean-tone > equation: I don't exactly think O'Connell or I did something original just by > doing that alone.

It's a linear tuning. It has no more to do with meantone than any other linear tuning. The period's phi and the generator's 2. Yes, it's the same as how yours started, far from not even remotely resembling it.

> Also, to note, he tempers the generator so the 25th tone of the tuning to > match the first (just as 12TET flattens the generating 5th (X) to make it fit > the octave on x^12) while I don't.

He suggested an equal temperament in 1965. He then suggested different temperaments in the afterword. Don't confuse matters by describing it all in the present tense.

> ---What do you mean by "mimic diatonic modes"?
> I mean those built try to best approximate intervals like 2nds, 3rds, > 5ths...and, on a lower level, to match basic half steps. For example 10TET is > obviously not a diatonic scale since no two notes in it can, say, very well > emulate a perfect 2nd.

So you're not trying to do that, like the rest of us.

> BTW, to be 100% sure what O'Connell's theories do I'd need a SCALA file > example of a scale generated using his method. Given that it should be > blatantly obvious to my ear...if he and I are on the same page or not. I'm > quite willing to do the research given the material.

Isn't his 9 note scale essentially the same as your 9 note scale? Anyway, try searching oconnell*scl from the Scala archive. To hear what he intended you need the phi timbre as well and that's more difficult.

Graham

--- In tuning@yahoogroups.com, "Claudio Di Veroli" <dvc@...> wrote:
>
> Charles Lucy <lucy@> wrote:
> > Who knows?
> > I speculate that it is because:
> > ? when a string is "split into two equal parts, each part becomes the
> > "mirror" of the other.
> > ?by definition the octave is a doubling of frequency.
> > I observe that:
> > ?Lightly touching a string at the octave position produces the same
> > pitch when playing between the bridge and the finger, and between the
> > nut and the finger on my guitars, kora, mandolin, basses and other
> > stringed instruments, and that note has an octave ratio of two to the
> > open string.
> > On 23 Mar 2009, at 21:29, Kalle Aho wrote:
> > > Hello Charles,
> > > if you think that the best sounding musical intervals might not be
> > > at exact integer frequency ratios then why is the octave an
> > > exception as it is at 2:1 in LucyTuning?
> > > Kalle Aho
> > Rick wrote:
> > Hi Charles,
> > You mentioned that "Lightly touching a string at the octave position
> produces the same pitch when playing between the bridge and the finger, and
> between the nut and the finger on my guitars, kora, etc". But then how does
> one explain the other harmonics? Lightly touching the string at lengths 1/3,
> 2/3, and 1/5 etc. produce the fifth and major third intervals.
>
> I am astonished. From past posts it is apparent that we are fortunate to
> have in this list quite a few distinguished members who are eminently
> knowledgeable about advanced musical acoustics (no, I am NOT including
> myself among them).
>
> Yet others, amazingly, are writing extensively on temperament proposals
> while they also seem to be unaware of basic acoustical facts (e.g.
> relationships between string partials, the harmonic series and related
> small-integer ratio intervals) that have been known and mentioned as matter
> of fact in the relevant literature ever since Sauveur (1702) put the things
> together, not to speak of the mathematical explanations of Fourier a century
> later.
>
> I have a suggestion for self-improvement.
> Why don't we use a more sensible sequence? such as:
> 1) study and understand the existing literature on historical knowledge and
> recent findings,
> 2) ask and discuss doubts among friends
> 3) only then ask/discuss with specialists
> 3) only then write new proposals.
>
> Kind regards,
>
> Claudio
>
Thanks Claudio,

I will just add that the idea of everything being a "matter of personal taste", while it postures under the banner of "artistic freedom", is probably merely a 20th century invention by advertising executives in order to create the illusion of "more variety" and sell more products. But since it undermines artistic standards by promoting a form of laziness, and choice grows with knowledge, then it actually undermines artistic freedom. Scratch beneath the surface of the statement "I know what I like" and we get "I don't like what I don't know".

-Rick

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:
>
> justin_tone52 wrote:
>
> > I noticed in composition and improvisation that the tuning system
> > (and the scales used) imparts its mood on the music being played.
> > One of the advantages of LucyTuning seems to be (this is what I
> > understood from the website) that it can be used to approximate a
> > wide range of tunings (from other cultures or otherwise). For example,
> > I found that every fourth generator from LucyTuning makes an excellent
> > 22-tET, whereas more conventionally minded musicians might prefer to
> > use LucyTuning as a meantone. I do not see this versatility in other
> > meantones such as 1/4 comma (where the major third is a bad magic
> > generator) or just intonation (where neither the perfect fifth nor
> > major third is a good generator for a linear temperament.)
>
> There's nothing special about LucyTuning here. You get the
> usual meantone MOS scales and a good approximation to 88-tET
> (from which you can take a 22 note subset). The third isn't
> a good magic generator either. Enough fifths will
> approximate any interval to an arbitrary precision -- the
> same as quarter comma meantone, or pythagorean intonation,
> or various other JI subsets.

I agree. I myself am not a practitioner of LucyTuning (I prefer extended 7-limit just intonation, hence my pseudonym "Justin Tone":-) It just happens to be that LucyTuning has a flat enough meantone generator that four of them makes a magic generator almost identical to 22-tET. This 22-tET connection is just a numerological coincidence, based on the fact that pi is very close to 22/7. This happens to be especially interesting as traditional musicians believe that 4 perfect fifths make a major third plus two octaves.

Other than meantone and magic, however, I see no other temperaments whose structures can be reasonably approximated with LucyTuning. The minor third, for instance, is too flat to be of any use for Kleismic temperament, and the minor second is too sharp for Miracle. There seems to be nothing even remotely resembling a subminor third for Orwell.

Of course, one can concoct a kleismic temperament out of LucyTuning with every 85th generator, and a miracle with every 906th generator. However, this (i.e. trying to change a tuning in the middle of a piece from meantone to kleismic by taking every 85th generator etc.) is extremely unlikely to appear in practical music. The ear simply cannot make the connection between a minor third and a chain of 85 fifths.

So, all in all, I feel that the use of 72-tET, just intonation and other tunings (even 11 and 13-tET) in xenharmonic music is much more enlightening and provides better tonal resources than LucyTuning. These other tunings I mentioned seem to give a better "bang for the buck" in terms of new intervals (why would you want to use a chain of 85 fifths for a single minor third with 72 notes can make a complete kleismic scale in itself?) as well as unexplored possibilities that, by nature, are not consistent with a Western meantone-biased tuning like LucyTuning.

Praveen Venkataramana

P.S. Pi-based scales can be intellectually stimulating, and I think that they do not always have to be based on meantone. I can easily conjure up new Lucy-like scales with other temperaments, such as a "LucySchismic" scale with generator [8 * 2^(1/pi)]^(1/8) to fit Indian srutis, and a "LucyMiracle" scale with generator [2^(1 - 1/pi)]^(1/7). There are many options for experimentation here.

. So I

gave you a chord with 4.27 notes per octave. If you have

some other problem you'd better state it.

    I assumed it was pretty obvious I meant more than 4 >whole< numbers (since I don't hear people talk about x.xx note chords very often).  Sorry if I was unclear.

--Ratios are used when you tune an
--instrument to match partials or harmonics.
I've said in many many messages...that my intent is to produce consonance and not to align partials specifically (although that's often a side-effect).  Like Charles, I believe beating is a natural phenomena in music but, on the other hand, I agree that excessive beating is usually a bad things (IE in the harmonic series even, harmonics 24 and 25 sound too tense to be consonant despite being "periodic").

--You must be on the wrong list. This one's description
--starts "This mailing list is intended for exchanging ideas
--relevant to alternate musical tunings..."
   I know...and the idea you seem to be championing as the only valid topic "tuning musical instruments and the acoustic (of only non-electronic instruments) mathematics directly relevant to it" is NOT the only idea that falls under the umbrella.  Actually about 90% of what I hear on this list is about things like tonality diamonds, consonance curves/harmonic entropy, whether new tunings repeat historical mathematical constructs...none of those are necessarily related to "how to design an acoustic instrument".  Not that the discussion is a bad one or I think mine are better (I don't thing they are better, just attacking different goals), but I certainly do NOT deserve to have my toes stepped on because I choose to talk about aspects of alternative scales other than that.

> Also, to note, he tempers the generator so the 25th tone of the tuning to

> match the first (just as 12TET flattens the generating 5th (X) to make it fit

> the octave on x^12) while I don't.

--He suggested an equal temperament in 1965. He then
--suggested different temperaments in the afterword. Don't
--confuse matters by describing it all in the present tense.
    Huh?  I realize mine nor his are NOT equal temperaments.  Who ever said the circle of PHI formed an equal temperament?  Or even bring up the idea that my scales were equal vs. unequal?  I certainly didn't...

>For example 10TET is

> obviously not a diatonic scale since no two notes in it can, say, very well

> emulate a perfect 2nd.

---So you're not trying to do that, like the rest of us.
   EXACTLY!  That's also why, I'm guessing, I don't seem to qualify to you as making "alternative tunings"...it appears you (like many) have a preconceived notion that scales MUST meet the definition of harmonic series periodicity (the same periodicity formed by acoustic overtones) to be relevant.  If that were true we might as well just toss interesting things like Sethares' theories out the window as well as he doesn't always follow those theories either.  I just don't see a point to limiting ourselves that way in an exclusive sense...
...>>Not<<< that I mind people work on that kind of thing (I don't), but I do mind it when they take a major issue (as if it were the solution to everything) and take honor in stepping on the toes of anyone working with anything beside the pure harmonic series (or something that VERY closely approximates is ALA 12TET).

--Isn't his 9 note scale essentially the same as your 9 note
--scale?
   Absolutely not (at least from the PDF)...his is spread over many 2/1 octaves while mine fits in a 1.618033 octave.  I'll look up his other scales anyhow and let you know what I find...I certainly don't mean to ignore his work.

---Anyway, try searching oconnell*scl from the Scala
---archive. To hear what he intended you need the phi timbre
---as well and that's more difficult.
   I think that's the one thing we may have in common is that timbre.  I DID see a lot in his scales that seem to come from the same PHI^x construct, if not also the PHI^x/2^y construct I use in my own tuning.  So, I'm pretty sure our tunings are alike, if not the same.

     BTW, as we've discussed, I am taking a good few of your suggestions seriously and have been working with the idea of making a tempered scale that complies relatively well with BOTH JI and PHI and could be used easily on acoustic instruments.  So stay tuned for that... :-)

-Michael

--- On Wed, 3/25/09, Graham Breed <gbreed@gmail.com> wrote:

From: Graham Breed <gbreed@...>
Subject: Re: [tuning] Re: Rational vs Irrational Scales: a response to Rick
To: tuning@yahoogroups.com
Date: Wednesday, March 25, 2009, 7:41 PM

Michael Sheiman wrote:

> ---4:5:6:7:9 works. Really, it does.

> I realize that, but that doesn't solve my problem. The octave range is 2/1.

> 9/4 is more than 2/1. Hence 4:5:6:7 is the 4(not 5)-note subset of that chord

> which fits the octave.

What you asked for was more than 4 notes per octave. So I

gave you a chord with 4.27 notes per octave. If you have

some other problem you'd better state it. I don't see why

there should be anything specially bad about JI and I

thought your 9 note solution used JI anyway.

> --It's relevant if you're trying to

> --tune an instrument.

> It wasn't obvious to me the first message concerned instrument tuning at all

> beyond that, for example, by coincidence dividing the string into 1/3 produced a

> "3rd" tone.

If you care about what another message concerned you'd

better reply to that message so that we know the context.

The reply I gave was to a direct question about the

usefulness of ratios. You didn't say anything about

dividing a string. Ratios are used when you tune an

instrument to match partials or harmonics.

> ---Which is sort of the point of this list.

> Well it sure as hell doesn't say that in the list description. I don't think

> instrument tuning is a bad thing at all...I just don't believe on monopolizing

> the subject of tuning to one very specific topic.

You must be on the wrong list. This one's description

starts "This mailing list is intended for exchanging ideas

relevant to alternate musical tunings..."

> ---What about O'Connell's paper then? I thought it was alarmingly similar to

> what you're ---doing but you haven't acknowledged it.

>

> Well, apparently he uses half steps and 3rd steps to make his scales.

> Though I agree, from what I can tell, the tuning he bases his scales on IE the

> "circle of PHI" or "PHI mean-tone" (phi^x/2(the standard octave)^y) is the

> same. But that's really just throwing a different generator into the mean-tone

> equation: I don't exactly think O'Connell or I did something original just by

> doing that alone.

It's a linear tuning. It has no more to do with meantone

than any other linear tuning. The period's phi and the

generator's 2. Yes, it's the same as how yours started, far

from not even remotely resembling it.

> Also, to note, he tempers the generator so the 25th tone of the tuning to

> match the first (just as 12TET flattens the generating 5th (X) to make it fit

> the octave on x^12) while I don't.

He suggested an equal temperament in 1965. He then

suggested different temperaments in the afterword. Don't

confuse matters by describing it all in the present tense.

> ---What do you mean by "mimic diatonic modes"?

> I mean those built try to best approximate intervals like 2nds, 3rds,

> 5ths...and, on a lower level, to match basic half steps. For example 10TET is

> obviously not a diatonic scale since no two notes in it can, say, very well

> emulate a perfect 2nd.

So you're not trying to do that, like the rest of us.

> BTW, to be 100% sure what O'Connell's theories do I'd need a SCALA file

> example of a scale generated using his method. Given that it should be

> blatantly obvious to my ear...if he and I are on the same page or not. I'm

> quite willing to do the research given the material.

Isn't his 9 note scale essentially the same as your 9 note

scale? Anyway, try searching oconnell*scl from the Scala

archive. To hear what he intended you need the phi timbre

as well and that's more difficult.

Graham

--Scratch beneath the surface of the statement "I know what I like" and we get "I don't like ---what I don't know".

    I will at least go so far as to say I DON'T believe the 2/1 octave is the be and all of scale construction.  I've seen some great work with the tri-tave and slightly stretched octaves that, to my ear, can prove equally expressive.  And, recently, I've noticed 1.618 (PHI) also makes a great octave and your mind "jumps" a lot when you veer too far above or below it (IE it has a significantly higher level of concordance/consonance with the root than just about any frequency near it).

  I, for one, agree that somewhat blindly accepting the octave should not be a necessity in tuning and I hope others take the leap and at least experiment with using other "octaves" (not 100% sure of the technical term for it) than 2/1.

-Michael

--- On Wed, 3/25/09, rick_ballan <rick_ballan@...> wrote:

From: rick_ballan <rick_ballan@...m.au>
Subject: [tuning] Re: Rational vs Irrational Scales: a response to Rick
To: tuning@yahoogroups.com
Date: Wednesday, March 25, 2009, 8:11 PM

--- In tuning@yahoogroups. com, "Claudio Di Veroli" <dvc@...> wrote:

>

> Charles Lucy <lucy@> wrote:

> > Who knows?

> > I speculate that it is because:

> > ? when a string is "split into two equal parts, each part becomes the

> > "mirror" of the other.

> > ?by definition the octave is a doubling of frequency.

> > I observe that:

> > ?Lightly touching a string at the octave position produces the same

> > pitch when playing between the bridge and the finger, and between the

> > nut and the finger on my guitars, kora, mandolin, basses and other

> > stringed instruments, and that note has an octave ratio of two to the

> > open string.

> > On 23 Mar 2009, at 21:29, Kalle Aho wrote:

> > > Hello Charles,

> > > if you think that the best sounding musical intervals might not be

> > > at exact integer frequency ratios then why is the octave an

> > > exception as it is at 2:1 in LucyTuning?

> > > Kalle Aho

> > Rick wrote:

> > Hi Charles,

> > You mentioned that "Lightly touching a string at the octave position

> produces the same pitch when playing between the bridge and the finger, and

> between the nut and the finger on my guitars, kora, etc". But then how does

> one explain the other harmonics? Lightly touching the string at lengths 1/3,

> 2/3, and 1/5 etc. produce the fifth and major third intervals.

>

> I am astonished. From past posts it is apparent that we are fortunate to

> have in this list quite a few distinguished members who are eminently

> knowledgeable about advanced musical acoustics (no, I am NOT including

> myself among them).

>

> Yet others, amazingly, are writing extensively on temperament proposals

> while they also seem to be unaware of basic acoustical facts (e.g.

> relationships between string partials, the harmonic series and related

> small-integer ratio intervals) that have been known and mentioned as matter

> of fact in the relevant literature ever since Sauveur (1702) put the things

> together, not to speak of the mathematical explanations of Fourier a century

> later.

>

> I have a suggestion for self-improvement.

> Why don't we use a more sensible sequence? such as:

> 1) study and understand the existing literature on historical knowledge and

> recent findings,

> 2) ask and discuss doubts among friends

> 3) only then ask/discuss with specialists

> 3) only then write new proposals.

>

> Kind regards,

>

> Claudio

>

Thanks Claudio,

I will just add that the idea of everything being a "matter of personal taste", while it postures under the banner of "artistic freedom", is probably merely a 20th century invention by advertising executives in order to create the illusion of "more variety" and sell more products. But since it undermines artistic standards by promoting a form of laziness, and choice grows with knowledge, then it actually undermines artistic freedom. Scratch beneath the surface of the statement "I know what I like" and we get "I don't like what I don't know".

-Rick

Much as I appreciate your wish to experiment with octave ratios other than 2; unfortunately they become difficult to implement with many of the popular DAW systems. e.g. Logic, CuBase, Cameleon, Melodyne etc.

Nevertheless it seems that Aaron Hunt's equipment can handle them.

On 26 Mar 2009, at 13:15, Michael Sheiman wrote:

> --Scratch beneath the surface of the statement "I know what I like" > and we get "I don't like ---what I don't know".
>
> I will at least go so far as to say I DON'T believe the 2/1 > octave is the be and all of scale construction. I've seen some > great work with the tri-tave and slightly stretched octaves that, to > my ear, can prove equally expressive. And, recently, I've noticed > 1.618 (PHI) also makes a great octave and your mind "jumps" a lot > when you veer too far above or below it (IE it has a significantly > higher level of concordance/consonance with the root than just about > any frequency near it).
>
> I, for one, agree that somewhat blindly accepting the octave > should not be a necessity in tuning and I hope others take the leap > and at least experiment with using other "octaves" (not 100% sure of > the technical term for it) than 2/1.
>
> -Michael
>
> -.
>
>
>
Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

--Much as I appreciate your wish to experiment with octave ratios other
--than 2; unfortunately they become difficult to implement with many of
--the popular DAW systems. e.g. Logic, CuBase, Cameleon, Melodyne --etc.
    Agreed...they really do make it tricky and, for the longest time, I also stuck myself with the 2/1 octave "because I had to in order to compose".  Even going further than re-tuning each of the 12 notes becomes a pain in many systems, especially hardware-based ones.  One of the workarounds I've found is to use the Z3ta (Cubase) and Albino (VST-plugin) softsynths that support Scala files.  It's a shame Cameleon doesn't support it b/c I love that soft-synth.

--- On Thu, 3/26/09, Charles Lucy <lucy@harmonics.com> wrote:

From: Charles Lucy <lucy@...>
Subject: Re: [tuning] Re: Rational vs Irrational Scales: a response to Rick
To: tuning@yahoogroups.com
Date: Thursday, March 26, 2009, 6:25 AM

Much as I appreciate your wish to experiment with octave ratios other than 2; unfortunately they become difficult to implement with many of the popular DAW systems. e.g. Logic, CuBase, Cameleon, Melodyne etc.
Nevertheless it seems that Aaron Hunt's equipment can handle them.

On 26 Mar 2009, at 13:15, Michael Sheiman wrote:
--Scratch beneath the surface of the statement "I know what I like" and we get "I don't like ---what I don't know".

    I will at least go so far as to say I DON'T believe the 2/1 octave is the be and all of scale construction.  I've seen some great work with the tri-tave and slightly stretched octaves that, to my ear, can prove equally expressive.  And, recently, I've noticed 1.618 (PHI) also makes a great octave and your mind "jumps" a lot when you veer too far above or below it (IE it has a significantly higher level of concordance/ consonance with the root than just about any frequency near it).

  I, for one, agree that somewhat blindly accepting the octave should not be a necessity in tuning and I hope others take the leap and at least experiment with using other "octaves" (not 100% sure of the technical term for it) than 2/1.

-Michael

-.

Charles Lucylucy@lucytune. com
- Promoting global harmony through LucyTuning -
for information on LucyTuning go to:http://www.lucytune .com
For LucyTuned Lullabies go to:http://www.lullabie s.co.uk

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>
> We again get back to sonic aesthetics, although there may be an
> underlying physical or biological reason which we have yet to find.

A physical or biological reason for using LucyTuning? Again, nothing
special seems to happen at LucyTuned intervals.

> My quest in microtuning was to find a tuning system which would:
>
> play traditional Western harmony
> modulate and transpose
> control consonance and dissonance
> use conventional notation

Any meantone tuning will allow these.

> emulate all tunings and scales
> allow infinite notes per octave

Assuming that the tuning repeats at the octave any irrational
generator that is not an integer root of the octave (as those
will give equal divisions of the octave) will approximate all the
intervals to arbitrary precision. As Graham already observed,
Kornerup's golden meantone would be the best choice for this as you
can generate as many notes as you want and they always distribute
evenly around the octave. But I don't see the point of approximating
exotic tunings with a meantone generator. What use it is to know how
many meantone fifths of fourths I have to put in a chain to get
close to the interval I want?

> be easy to implement and learn
> "sound right and be singable"

Because LucyTuning is a meantone these are probably true for Western
musicians.

Kalle Aho

HI Kalle;

It seems to me that the reason that you don't see the point about steps of fourths and fifths is because you and Graham have failed to appreciate that the purpose of this mapping is to produce harmonious music.

"Harmonious music" implies that this music will contain scales and chords.

You will need to map and organise these intervals to produce counterpoint and all the other "magical" components which we have inherited from recent centuries of traditional Western music theory and composition.

Knowing the relationship between intervals and how they fit into the structure of Western harmony, i.e. Major, minor, augmented, diminished and extensions of those triads, informs the composer/player of the compositional and harmonic structure.

Producing music is a "musical" pursuit. The arithmetic is of underlying significance, only so that the exact tuning can be generated, repeated and sorted for all musical sounds, and so that tunings and intervals will work together for any sound or instrument.

If you explore further starting from scales, you will discover how the structure of "Western" harmony works, and you may appreciate that Western harmony can be applied to any musical pattern, as we found when we produced LucyTuned Lullabies using Western harmonic structures.

Have a listen to what I mean, and how we have developed Western harmony to "enhance" melodies which had originally been collected from some non-Western cultures at:

http://www.lullabies.co.uk.

When I called my original business/site LucyScaleDevelopments, the principle reason was because I was developing scales as the fundamental foundation for tuning.

The fact that "LSD" also had other meanings; Pounds, shillings, and pence; a well-know psychotropic drug, Lucy in the Sky with Diamonds, or Sea with Dolphins was just icing on the cake to amuse those who appreciate word games.

My recent thinking on scales, their significance and potentials can be found here:

http://www.lucytune.com/scales/

If you experiment with various meantone values, and listen very attentively you may begin to appreciate how using a Large interval in the 190 to 191 cent regions (and an octave ratio of 2); seems to produce the most musically practical harmony

which matches the Western traditions as you yourself had noticed, and even Graham seems to agree with.

Although, I don't understand what he/you mean by "...... always distribute evenly around the octave."

Approaching it from the engineering point of view; the ultimate engineer's question is always: "Does it work?" and in this case the answer is a musical affirmative!

On 26 Mar 2009, at 14:48, Kalle Aho wrote:
>
>
> Assuming that the tuning repeats at the octave any irrational
> generator that is not an integer root of the octave (as those
> will give equal divisions of the octave) will approximate all the
> intervals to arbitrary precision. As Graham already observed,
> Kornerup's golden meantone would be the best choice for this as you
> can generate as many notes as you want and they always distribute
> evenly around the octave. But I don't see the point of approximating
> exotic tunings with a meantone generator. What use it is to know how
> many meantone fifths of fourths I have to put in a chain to get
> close to the interval I want?
>
> > be easy to implement and learn
> > "sound right and be singable"
>
> Because LucyTuning is a meantone these are probably true for Western
> musicians.
>
> Kalle Aho
>
>
Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

---"Harmonious music" implies that this music will contain scales and ---chords. 
---Knowing
the relationship between intervals and how they fit into the ---structure
of Western harmony, i.e. Major, minor, augmented, ---diminished and
extensions of those triads, informs the ---composer/player of the
compositional and harmonic structure.

   Hmm...if I understood this well...it would mean that rather than making a note very close to a given interval to make it "loyal to the original scale", the goal is to find intervals that can be used for similar purpose musically.
   So, in example, in a replacement interval in non-Western scale "feels augmented" or "feels diminished", there's no real "loss", since music is ultimately an emotional pursuit which just happens to have mathematical underlinings.  And, if I have it right, Charles, what you're trying to say is that even if Lucy-Tuning can't replicate certain intervals of certain scales (IE Miracle Temperament or certain Western intervals), it can create intervals with similar feel that can be used to create chords with similar feel and things like counterpoints with similar feel.  Meaning, it can create a sound "musically affirmative" even to many scales which intervals it can't match exactly.

--- On Thu, 3/26/09, Charles Lucy <lucy@...> wrote:

From: Charles Lucy <lucy@...>
Subject: Re: [tuning] Re: Rational vs Irrational Scales: a response to Rick
To: tuning@yahoogroups.com
Date: Thursday, March 26, 2009, 9:37 AM

HI Kalle;
It seems to me that the reason that you don't see the point about steps of fourths and fifths is because you and Graham have failed to appreciate that the purpose of this mapping is to produce harmonious music.
"Harmonious music" implies that this music will contain scales and chords. 
You will need to map and organise these intervals to produce counterpoint and all the other "magical" components which we have inherited from recent centuries of traditional Western music theory and composition.
Knowing the relationship between intervals and how they fit into the structure of Western harmony, i.e. Major, minor, augmented, diminished and extensions of those triads, informs the composer/player of the compositional and harmonic structure.
Producing music is a "musical" pursuit. The arithmetic is of underlying significance, only so that the exact tuning can be generated, repeated and sorted for all musical sounds, and so that tunings and intervals will work together for any sound or instrument.
If you explore further starting from scales, you will discover how the structure of "Western" harmony works, and you may appreciate that Western harmony can be applied to any musical pattern, as we found when we produced LucyTuned Lullabies using Western harmonic structures.
Have a listen to what I mean, and how we have developed Western harmony to "enhance" melodies which had originally been collected from some non-Western cultures at:
http://www.lullabie s.co.uk.
When I called my original business/site LucyScaleDevelopmen ts, the principle reason was because I was developing scales as the fundamental foundation for tuning.
The fact that "LSD" also had other meanings; Pounds, shillings, and pence; a well-know psychotropic drug, Lucy in the Sky with Diamonds, or Sea with Dolphins was just icing on the cake to amuse those who appreciate word games.
My recent thinking on scales, their significance and potentials can be found here:
http://www.lucytune .com/scales/
If you experiment with various meantone values, and listen very attentively you may begin to appreciate how using a Large interval in the 190 to 191 cent regions (and an octave ratio of 2);  seems to produce the most musically practical harmony 
which matches the Western traditions as you yourself had noticed, and even Graham seems to agree with.
Although, I don't understand what he/you mean by "...... always distribute evenly around the octave."
Approaching it from the engineering point of view; the ultimate engineer's question is always: "Does it work?" and in this case the answer is a musical affirmative!

On 26 Mar 2009, at 14:48, Kalle Aho wrote:

Assuming that the tuning repeats at the octave any irrational
generator that is not an integer root of the octave (as those
will give equal divisions of the octave) will approximate all the
intervals to arbitrary precision. As Graham already observed,
Kornerup's golden meantone would be the best choice for this as you
can generate as many notes as you want and they always distribute
evenly around the octave. But I don't see the point of approximating
exotic tunings with a meantone generator. What use it is to know how
many meantone fifths of fourths I have to put in a chain to get
close to the interval I want?

> be easy to implement and learn
> "sound right and be singable"

Because LucyTuning is a meantone these are probably true for Western
musicians.

Kalle Aho

Charles Lucylucy@lucytune. com
- Promoting global harmony through LucyTuning -
for information on LucyTuning go to:http://www.lucytune .com
For LucyTuned Lullabies go to:http://www.lullabie s.co.uk

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>
> HI Kalle;
>
> It seems to me that the reason that you don't see the point about
> steps of fourths and fifths is because you and Graham have failed
> to appreciate that the purpose of this mapping is to produce
> harmonious music.
>
> "Harmonious music" implies that this music will contain scales and
> chords.
>
> You will need to map and organise these intervals to produce
> counterpoint and all the other "magical" components which we have
> inherited from recent centuries of traditional Western music
> theory and composition.
>
> Knowing the relationship between intervals and how they fit into
> the structure of Western harmony, i.e. Major, minor, augmented,
> diminished and extensions of those triads, informs the
> composer/player of the compositional and harmonic structure.
>
> Producing music is a "musical" pursuit. The arithmetic is of
> underlying significance, only so that the exact tuning can be
> generated, repeated and sorted for all musical sounds, and so that
> tunings and intervals will work together for any sound or
> instrument.

Well Charles, I am a musician and know a thing or two about harmony
and counterpoint but I still fail to see the relevance of knowing how
many meantone generators away an interval is. Why is it important to
know even the defining meantone relation that major third equals four
fifths minus two octaves in order to produce harmony and counterpoint?

> If you explore further starting from scales, you will discover how
> the structure of "Western" harmony works, and you may appreciate
> that Western harmony can be applied to any musical pattern, as we
> found when we produced LucyTuned Lullabies using Western harmonic
> structures.
>
> Have a listen to what I mean, and how we have developed Western
> harmony to "enhance" melodies which had originally been collected from
> some non-Western cultures at:
>
> http://www.lullabies.co.uk.

While I don't much appreciate such cultural imperialism these sound
OK but not that impressive to me. The sounds have weak or inharmonic
partials and are heavily effected which is fine but makes it rather
hard to judge the merits of the tuning. The Mozart example in the
site actually sounded worse to me than 12-equal though.

> When I called my original business/site LucyScaleDevelopments, the
> principle reason was because I was developing scales as the
> fundamental foundation for tuning.
>
> The fact that "LSD" also had other meanings; Pounds, shillings, and
> pence; a well-know psychotropic drug, Lucy in the Sky with Diamonds,
> or Sea with Dolphins was just icing on the cake to amuse those who
> appreciate word games.
>
> My recent thinking on scales, their significance and potentials can be
> found here:
>
> http://www.lucytune.com/scales/

There you say that your 'hypothesis is that intervals that are closer
on the chain of fourths and fifths are more "consonant"'. Do you
think that the major second or minor seventh is more consonant than
the major third?

> If you experiment with various meantone values, and listen very
> attentively you may begin to appreciate how using a Large interval
> in the 190 to 191 cent regions (and an octave ratio of 2); seems
> to produce the most musically practical harmony

The interval region is precise but otherwise this is a rather vague
statement. I don't have the foggiest what "the most musically
practical harmony" might mean except that in your typically circular
reasoning it of course means LucyTuned harmony.

> which matches the Western traditions as you yourself had noticed,
> and even Graham seems to agree with.

Only because it is a meantone tuning.

> Although, I don't understand what he/you mean by "...... always
> distribute evenly around the octave."

In the Kornerup generator's moments of symmetries 5, 7, 12, 19, 31,
50, 81,... the ratio of L and s is always phi so there are no large
gaps or narrow spaces between tones. It is the best meantone
generator if you want both infinite number of tones and as close to
equal distribution of tones as possible. I believe this is a property
of all Wilson Golden Horagram generators (which are of course not
generally meantones) too. Someone correct me if I'm wrong.

Kalle Aho

> > My recent thinking on scales, their significance and potentials can be
> > found here:
> >
> > http://www.lucytune.com/scales/
>
> There you say that your 'hypothesis is that intervals that are
> closer on the chain of fourths and fifths are more "consonant"'. Do
> you think that the major second or minor seventh is more consonant
> than the major third?

Also if your hypothesis was true, an interval resulting from 92
LucyTuned fifths which is 385.353 cents should sound horribly dissonant
but in fact to many people it sounds better than the similar-sized
LucyTuned major third of 381.972 cents. This is explained by our "naive"
small number ratio theories but not by your hypothesis.

Kalle Aho

--- In tuning@yahoogroups.com, Michael Sheiman <djtrancendance@...> wrote:
>
> --Much as I appreciate your wish to experiment with octave ratios other
> --than 2; unfortunately they become difficult to implement with many of
> --the popular DAW systems. e.g. Logic, CuBase, Cameleon, Melodyne --etc.
>     Agreed...they really do make it tricky and, for the longest time, I also stuck myself with the 2/1 octave "because I had to in order to compose".  Even going further than re-tuning each of the 12 notes becomes a pain in many systems, especially hardware-based ones.  One of the workarounds I've found is to use the Z3ta (Cubase) and Albino (VST-plugin) softsynths that support Scala files.  It's a shame Cameleon doesn't support it b/c I love that soft-synth.

Chameleon, and the new Alchemy, support Scala files, via .tun files. There's a tutorial at the Scala site, it's a quick painless process.

And non-octave scales can be done on any native softsynth that supports .tun files.

For sampling this has got to be the new "standard", considering the virtual omnipresence of Kontakt these days:

http://12equalboresme.com/

and there you have microtonal support for any SynthEdit synth you can make or modify.

And so on... there are tons of tools now.

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:

> You will need to map and organise these intervals to produce
> counterpoint and all the other "magical" components which we have
> inherited from recent centuries of traditional Western music >theory
> and composition.
>

Nope you don't need to "map" intervals to do counterpoint and all the other magical etc., you can just do it exactly as you would by ear, only in slow motion, and use whatever the hell pile of "notes" winds up being necessary.

> Knowing the relationship between intervals and how they fit into >the
> structure of Western harmony, i.e. Major, minor, augmented, >diminished
> and extensions of those triads, informs the composer/player of the
> compositional and harmonic structure.
>
> If you explore further starting from scales, you will discover how >the
> structure of "Western" harmony works, and you may appreciate that
> Western harmony can be applied to any musical pattern, as we found
> when we produced LucyTuned Lullabies using Western harmonic >structures.

The structure of Western harmony is simply not necessary once you understand what actually lies underneath it, and its true motor.

Cameron,

Can you expand on this a little? My view is that its all about tension and
release - how doesn't matter anymore, functional harmony is a choice not a
necessity and certainly does not need be based on any specific interval
combination in any sense...

Quote Cameron:
"
The structure of Western harmony is simply not necessary once you understand
what actually lies underneath it, and its true motor."

.
>
>
>

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> Cameron,
>
> Can you expand on this a little? My view is that its all about tension and
> release - how doesn't matter anymore, functional harmony is a >choice not a
> necessity and certainly does not need be based on any specific >interval
> combination in any sense...
>
> Quote Cameron:
> "
> The structure of Western harmony is simply not necessary once you >understand
> what actually lies underneath it, and its true motor."

Tension and release, movement and shape, interplay of individual/group
identities... and a feeling for the overall harmonic spectrum created by the different voices together. Whether intervals are rational, irrational, or a mix of the two, they are always going to interact with each other within the spectra (unless you're working with pure sines, and even then I'm not sure if the human ear doesn't always jazz up a sine into something richer).

What colors, what shapes, what emotions? Those are the questions to ask of a tuning, not consonance vs. dissonance, or the worst of all, "one size fits all".

--- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@...> wrote:

> While I don't much appreciate such cultural imperialism these sound
> OK but not that impressive to me. The sounds have weak or inharmonic
> partials and are heavily effected which is fine but makes it rather
> hard to judge the merits of the tuning. The Mozart example in the
> site actually sounded worse to me than 12-equal though.

I hate to say this, but knowing about the "circle of fifths"
is pretty important to most musicians. That includes knowing
things like, if I harmonize with a min 7th, I can modulate
two fifths to make that 7th a root of something. This should
generalize to linear temperaments, where chains of generators
are used to construct scales.

-Carl

Hello Carl,

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:

> I hate to say this, but knowing about the "circle of fifths"
> is pretty important to most musicians.

Sure it is important in many ways and I did not say it isn't.

> That includes knowing
> things like, if I harmonize with a min 7th, I can modulate
> two fifths to make that 7th a root of something. This should
> generalize to linear temperaments, where chains of generators
> are used to construct scales.

OK, this really is an example where it is useful to know how many
generators some interval is made of. But is Charles doing something
like this with exotic intervals that are beyond say 12 generators?
I don't think so.

Kalle Aho

I have been looking at your suggestion, and find that using the Kornerup values of Large = 192.43 and small = 118.93
and the comparable LucyTune values of Large = 190.99 and small = 112.54.

As you are plot the positions between 0 and 1200 cents, the steps of fourths and fifths arrive at a position close to an existing previous position, at the twentieth step; for the pattern of nineteen repeats and is "transposed" after nineteen steps.

Unfortunately the AmigaBasic program which I wrote many years ago to show how this works for any JI, equal, or meantone tuning has died with the Amiga harddrive. (Although it might be somewhere on an old Amiga floppy).

(Maybe it's time to pay for a pro salvage job, or to rewrite it in a more recent system)

This occurs at the interval of the double sharp seventh (xVIIth) (C to Bx).

In Kornerup the interval is approx. 28.07 cents
In LucyTuning it becomes approx.14.37 cents

This is a difference of 13.7 cents, which I would consider to be significantly large to be noticeable, by even the thickest cloth-eared listeners.

It does as you suggest result in a "closer to equal" distribution of intervals at this level, and hence might be more appealing to the graphical and mathematically inclined as being a less "disorganised" or "skewed".

If you were to go further you will probably find that this "apparent mathematical advantage" is, to a large extent, irrelevant, as LucyTuned intervals approximate 88edo and later more closely to 1420.

As is shown on this page:

http://www.lucytune.com/tuning/equal_temp.html

My judgement of and my support of pi is a musical decision, and the fact that it doesn't happen to match some mathematically pre-conceived necessity to be closer to an equal distribution of intervals is musically irrelevant.

It's about ears, not eyes and comptometers.

On 26 Mar 2009, at 20:16, Kalle Aho wrote:

>
> In the Kornerup generator's moments of symmetries 5, 7, 12, 19, 31,
> 50, 81,... the ratio of L and s is always phi so there are no large
> gaps or narrow spaces between tones. It is the best meantone
> generator if you want both infinite number of tones and as close to
> equal distribution of tones as possible. I believe this is a property
> of all Wilson Golden Horagram generators (which are of course not
> generally meantones) too. Someone correct me if I'm wrong.
>
> Kalle Aho
>

Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>
> I have been looking at your suggestion, and find that using the
> Kornerup values of Large = 192.43 and small = 118.93 and the
> comparable LucyTune values of Large = 190.99 and small = 112.54.
>
> It does as you suggest result in a "closer to equal" distribution
> of intervals at this level, and hence might be more appealing to
> the graphical and mathematically inclined as being a less
> "disorganised" or "skewed".
>
> If you were to go further you will probably find that this
> "apparent mathematical advantage" is, to a large extent,
> irrelevant, as LucyTuned intervals approximate 88edo and later
> more closely to 1420.

The point is not to arrive at a close to equal division per se as
then you might just as well use an equal division. But as you said
you want *both* an infinite number of tones *and* to emulate all
existing tunings and scales then as Kornerup's golden meantone of
all meantones both distributes tones most evenly around the octave
and gives an infinite number of them it will more earlier than
LucyTuning get arbitrarily close to any exotic interval. Of course
LucyTuning might get closer earlier to some special intervals but
Kornerup's approximates a random interval earlier than any other
meantone because it most efficiently fills all the gaps in the
distribution of tones.

> As is shown on this page:
>
> http://www.lucytune.com/tuning/equal_temp.html
>
> My judgement of and my support of pi is a musical decision, and the
> fact that it doesn't happen to match some mathematically pre-
> conceived necessity to be closer to an equal distribution of
> intervals is musically irrelevant.
>
> It's about ears, not eyes and comptometers.

Even if you yourself insist on a very specific value for your
generator everytime your more precise claims are shown not to hold
water you start appealing to the vague notion of musicality.
Again, my ears tell me LucyTuned intervals are nothing special
soundwise, it is just a meantone in the narrower fifth range. Your
subjective view against mine doesn't advance the debate.

Kalle Aho

--- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@...> wrote:

> > I hate to say this, but knowing about the "circle of fifths"
> > is pretty important to most musicians.
>
> Sure it is important in many ways and I did not say it isn't.

You said, "I am a musician and know a thing or two about harmony
and counterpoint but I still fail to see the relevance of knowing
how many meantone generators away an interval is."

> > That includes knowing
> > things like, if I harmonize with a min 7th, I can modulate
> > two fifths to make that 7th a root of something. This should
> > generalize to linear temperaments, where chains of generators
> > are used to construct scales.
>
> OK, this really is an example where it is useful to know how many
> generators some interval is made of. But is Charles doing something
> like this with exotic intervals that are beyond say 12 generators?
> I don't think so.

His statement that it corresponds to consonance is obviously
wrong, but I see nothing wrong with thinking in terms of
generators in general, especially when the generator is an
approximate 3:2.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@> wrote:
>
> > > I hate to say this, but knowing about the "circle of fifths"
> > > is pretty important to most musicians.
> >
> > Sure it is important in many ways and I did not say it isn't.
>
> You said, "I am a musician and know a thing or two about harmony
> and counterpoint but I still fail to see the relevance of knowing
> how many meantone generators away an interval is."

I thought that the circle of fifths is more about fifth relationships
among pitch classes, chords and keys than about intervals. But yes,
your example shows that it has some relevance with them too.

> > > That includes knowing
> > > things like, if I harmonize with a min 7th, I can modulate
> > > two fifths to make that 7th a root of something. This should
> > > generalize to linear temperaments, where chains of generators
> > > are used to construct scales.
> >
> > OK, this really is an example where it is useful to know how many
> > generators some interval is made of. But is Charles doing
> > something like this with exotic intervals that are beyond say 12
> > generators?
> > I don't think so.
>
> His statement that it corresponds to consonance is obviously
> wrong, but I see nothing wrong with thinking in terms of
> generators in general, especially when the generator is an
> approximate 3:2.

OK, how is it useful when an exotic interval is distant in the chain of fifths?

Kalle Aho

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:

> His statement that it corresponds to consonance is obviously
> wrong, but I see nothing wrong with thinking in terms of
> generators in general, especially when the generator is an
> approximate 3:2.

It's not actually wrong, and you can't prove it wrong, for he has quite conveniently made it a tautology by simply redefining "consonance". Voila! But so much for all that stuff about the ears, of course.

> but I see nothing wrong with thinking in terms of

> generators in general, especially when the generator is an

> approximate 3:2.

--It's not actually wrong, and you can't prove it wrong, for he has quite
conveniently made it --a tautology by simply redefining "consonance" .
Voila! But so much for all that stuff about --the ears, of course.

taken from http://dictionary.reference.com/browse/consonance
con⋅so⋅nance 
 /ˈkɒnsənəns/ Show Spelled
Pronunciation [kon-suh-nuhns] Show IPA
–noun 1. accord or agreement. 2. correspondence of sounds; harmony of sounds. 3. Music. a simultaneous combination of tones conventionally accepted as being in a state of >>>repose<<<. Compare dissonance (def. 2).
4. Prosody. a. the correspondence of consonants, esp. those at the end of a word, in a passage of prose or verse. Compare alliteration (def. 1). b. the use of the repetition of consonants or consonant patterns as a rhyming device. 5. Physics. the property of two sounds the frequencies of which have a ratio equal to a small whole number.
 
    General comment: can we all agree that consonance is the sense of repose/relaxation in a sound and not necessarily the "physics" definition only sounds that "have a ratio equal to a small whole number"?   People here seem to constantly insist...that definitions 5 and 3 above are equivalent...when it seems pretty obvious they are not by definition equivalent.  Same goes for "harmony" vs. "harmonic series"...you can have harmony without it following the physics-based phenomena that is the harmonic series.
*************************************************
    Indeed, in the end of the day, I agree with Cameron that ears are the only way to know for sure if something works or if something is/is-not possible. Mathematics, IMVHO,
can only help us fine-tune the general areas our ears point to...and I strongly believe the best tuning wizards are the ones who don't rely mostly on math, but always "reverse solve/prove" what they find with math through their ears before accepting it as good.

-Michael

--- On Fri, 3/27/09, Cameron Bobro <misterbobro@...> wrote:

From: Cameron Bobro <misterbobro@...>
Subject: [tuning] Re: Rational vs Irrational Scales: a response to Rick
To: tuning@yahoogroups.com
Date: Friday, March 27, 2009, 1:48 PM

--- In tuning@yahoogroups. com, "Carl Lumma" <carl@...> wrote:

> His statement that it corresponds to consonance is obviously

> wrong, but I see nothing wrong with thinking in terms of

> generators in general, especially when the generator is an

> approximate 3:2.

It's not actually wrong, and you can't prove it wrong, for he has quite conveniently made it a tautology by simply redefining "consonance" . Voila! But so much for all that stuff about the ears, of course.

You are too eager to condemn it Carl.
You should try the consonance patterns in LucyTuning and you may begin to understand what I am hearing.

On 27 Mar 2009, at 17:31, Carl Lumma wrote:

> --- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@...> wrote:
>
> > > I hate to say this, but knowing about the "circle of fifths"
> > > is pretty important to most musicians.
> >
> > Sure it is important in many ways and I did not say it isn't.
>
> You said, "I am a musician and know a thing or two about harmony
> and counterpoint but I still fail to see the relevance of knowing
> how many meantone generators away an interval is."
>
> > > That includes knowing
> > > things like, if I harmonize with a min 7th, I can modulate
> > > two fifths to make that 7th a root of something. This should
> > > generalize to linear temperaments, where chains of generators
> > > are used to construct scales.
> >
> > OK, this really is an example where it is useful to know how many
> > generators some interval is made of. But is Charles doing something
> > like this with exotic intervals that are beyond say 12 generators?
> > I don't think so.
>
> His statement that it corresponds to consonance is obviously
> wrong, but I see nothing wrong with thinking in terms of
> generators in general, especially when the generator is an
> approximate 3:2.
>
> -Carl
>
>
Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

Obviously it doesn't agree with your definition #5 as that view of
Physics, assumes that JI integer ratios are the only possible "bee's
knees" ;-)

On 27 Mar 2009, at 21:11, djtrancendance@... wrote:

> > but I see nothing wrong with thinking in terms of
> > generators in general, especially when the generator is an
> > approximate 3:2.
>
> --It's not actually wrong, and you can't prove it wrong, for he has
> quite conveniently made it --a tautology by simply redefining
> "consonance" . Voila! But so much for all that stuff about --the
> ears, of course.
>
> taken from http://dictionary.reference.com/browse/consonance
> con⋅so⋅nance
>
>    /ˈkɒnsənəns/ Show Spelled Pronunciation [kon-suh-
> nuhns] Show IPA –noun
> 1. accord or agreement.
> 2. correspondence of sounds; harmony of sounds.
> 3. Music. a simultaneous combination of tones conventionally
> accepted as being in a state of >>>repose<<<. Compare dissonance
> (def. 2).
> 4. Prosody.
> a. the correspondence of consonants, esp. those at the end of a
> word, in a passage of prose or verse. Compare alliteration (def. 1).
> b. the use of the repetition of consonants or consonant patterns as
> a rhyming device.
> 5. Physics. the property of two sounds the frequencies of which have
> a ratio equal to a small whole number.
>
>
> General comment: can we all agree that consonance is the sense
> of repose/relaxation in a sound and not necessarily the "physics"
> definition only sounds that "have a ratio equal to a small whole
> number"? People here seem to constantly insist...that definitions
> 5 and 3 above are equivalent...when it seems pretty obvious they are
> not by definition equivalent. Same goes for "harmony" vs. "harmonic
> series"...you can have harmony without it following the physics-
> based phenomena that is the harmonic series.
> *************************************************
> Indeed, in the end of the day, I agree with Cameron that ears
> are the only way to know for sure if something works or if something
> is/is-not possible. Mathematics, IMVHO, can only help us fine-tune
> the general areas our ears point to...and I strongly believe the
> best tuning wizards are the ones who don't rely mostly on math, but
> always "reverse solve/prove" what they find with math through their
> ears before accepting it as good.
>
> -Michael
>
> --- On Fri, 3/27/09, Cameron Bobro <misterbobro@...> wrote:
>
> From: Cameron Bobro <misterbobro@...>
> Subject: [tuning] Re: Rational vs Irrational Scales: a response to
> Rick
> To: tuning@yahoogroups.com
> Date: Friday, March 27, 2009, 1:48 PM
>
> --- In tuning@yahoogroups. com, "Carl Lumma" <carl@...> wrote:
>
> > His statement that it corresponds to consonance is obviously
> > wrong, but I see nothing wrong with thinking in terms of
> > generators in general, especially when the generator is an
> > approximate 3:2.
>
> It's not actually wrong, and you can't prove it wrong, for he has
> quite conveniently made it a tautology by simply redefining
> "consonance" . Voila! But so much for all that stuff about the ears,
> of course.
>
>
>

Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

--Obviously it doesn't agree with your definition #5 as that view of
Physics, assumes that JI --integer ratios are the only possible "bee's
knees" ;-)

  Exactly.  :-)
      Sometimes I wonder if this list should be re-named "the JI and diatonic mean-tone tuning list".  It seems every other time (at least) someone mentions anything not directly related to the above two they get a steady stream of nasty insults about how they "simply didn't read the manual"...as if anyone who read it would say "aha, the answer is JI!" and give up on all other tuning endeavors.

    My personal view is that if everything revolved around whole-number ratios then why isn't all MIDI music done in adaptive JI by now?

**************************************************************
   Dare I ask the question, does anyone else beside myself find even adaptive-JI rather nervous/unrested/unstable sounding?  It's like watching a gymnast perform moves perfectly but then noticing his arm is shaking wildly under the stress and his face looks like he's about to explode (not exactly beautiful to
watch).
**************************************************************

    Though I respect those who work with that sort of thing on a historical level...so far as tuning and new scales go I see very little going on that has impressed me (either what's going on sounds almost exactly like 12TET and/or there is too much dissonance for it to be used practically by most musicians).

    Wilson's MOS scales, Sethares' timbre alignment for "impossible tunings" (ALA 10TET)...both qualify to me as being truly something new and more than a masterful statement of mastery of music (and mathematical) history.  But little else that I've heard, sadly, does...

   Even Lucy-Tuning, dare I say it, seems to sound more like a slight consonance touch-up job on 12TET than a way toward chords and ultimately songs that sound significantly different (meaning on an emotional level) than historical tunings (and
yes, I consider JI historical since 12TET is historical and 5-limit JI somewhat approximates 12TET.

  Come on guys...where's the sense of adventure here?  Something both non-diatonic and highly consonant...any ideas?

-Michael

--- On Fri, 3/27/09, Charles Lucy <lucy@...> wrote:

From: Charles Lucy <lucy@...>
Subject: Re: [tuning] Re: Rational vs Irrational Scales: a response to Rick
To: tuning@yahoogroups.com
Date: Friday, March 27, 2009, 2:51 PM

Obviously it doesn't agree with your definition #5 as that view of Physics, assumes that JI integer ratios are the only possible "bee's knees" ;-)
On 27 Mar 2009, at 21:11, djtrancendance@ yahoo.com wrote:
> but I see nothing wrong with thinking in terms of
> generators in general, especially when the generator is an
> approximate
3:2.

--It's not actually wrong, and you can't prove it wrong, for he has quite conveniently made it --a tautology by simply redefining "consonance" . Voila! But so much for all that stuff about --the ears, of course.

taken from http://dictionary. reference. com/browse/ consonance
con⋅so⋅nance   /ˈkɒnsənəns/ Show Spelled Pronunciation [kon-suh-nuhns] Show IPA –noun 1. accord or agreement. 2. correspondence of sounds; harmony of sounds. 3. Music. a simultaneous combination of tones conventionally accepted as being in a state of >>>repose<<<. Compare dissonance (def. 2). 4. Prosody. a. the correspondence of consonants, esp. those at the end of a word, in a passage of prose or verse. Compare alliteration (def. 1). b. the use of the repetition of consonants or consonant patterns as a rhyming device. 5. Physics. the property of two sounds the frequencies of which have a ratio equal to a small whole number.
 
    General comment: can we all agree that consonance is the sense of repose/relaxation in a sound and not necessarily the "physics" definition only sounds that "have a ratio equal to a small whole number"?   People here seem to constantly insist...that definitions 5 and 3 above are equivalent.. .when it seems pretty obvious they are not by definition equivalent.  Same goes for "harmony" vs. "harmonic series"...you can have harmony without it following the physics-based phenomena that is the harmonic series.
************ ********* ********* ********* ********* *
    Indeed, in the end of the day, I agree with Cameron that ears are the
only way to know for sure if something works or if something is/is-not possible. Mathematics, IMVHO, can only help us fine-tune the general areas our ears point to...and I strongly believe the best tuning wizards are the ones who don't rely mostly on math, but always "reverse solve/prove" what they find with math through their ears before accepting it as good.

-Michael

--- On Fri, 3/27/09, Cameron Bobro <misterbobro@ yahoo.com> wrote:

From: Cameron Bobro <misterbobro@ yahoo.com>
Subject: [tuning] Re: Rational vs Irrational Scales: a response to Rick
To: tuning@yahoogroups. com
Date: Friday, March 27, 2009, 1:48 PM

--- In tuning@yahoogroups. com, "Carl Lumma" <carl@...> wrote:

> His statement that it corresponds to consonance is
obviously
> wrong, but I see nothing wrong with thinking in terms of
> generators in general, especially when the generator is an
> approximate 3:2.

It's not actually wrong, and you can't prove it wrong, for he has quite conveniently made it a tautology by simply redefining "consonance" . Voila! But so much for all that stuff about the ears, of course.

Charles Lucylucy@lucytune. com
-
Promoting global harmony through LucyTuning -
for information on LucyTuning go to:http://www.lucytune .com
For LucyTuned Lullabies go to:http://www.lullabie s.co.uk

--- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@...> wrote:

> > His statement that it corresponds to consonance is obviously
> > wrong, but I see nothing wrong with thinking in terms of
> > generators in general, especially when the generator is an
> > approximate 3:2.
>
> OK, how is it useful when an exotic interval is distant in the
> chain of fifths?

It tells us we aren't likely to get that interval in that linear
temperament using scales of a normal size. Precisely that the
interval is exotic.

-Carl

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>
> You are too eager to condemn it Carl.

Thanks for the advice, but I won't be dragged into another
argument about this topic, which has been settled long ago.
Kalle is merely the latest in a long line of clear thinkers
who have pointed this out to you. I do find it ironic that
this is the thanks I get for sticking up for you in this
thread.

-Carl

HI Carl;

There is a track which is being worked on at the moment by a very multinational band (Brit. Cypriot, Iragi, Oz) (provisionally called ZipGun).

The track is called Blue Lagoon, which demonstrates very well how you can use this type of LucyTuned harmony to move smoothly between remote keys.
This involved bouncing to audio a number of times in Logic, as it uses more than a dozen notes per octave during various stages of the track.
Unfortunately I have yet to have permission for it to be posted onto the net.
When it is eventually released, I'll give you links, so that you can comment (or should that be slag it off;-)

On 27 Mar 2009, at 22:26, Carl Lumma wrote:

> --- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@...> wrote:
>
> > > His statement that it corresponds to consonance is obviously
> > > wrong, but I see nothing wrong with thinking in terms of
> > > generators in general, especially when the generator is an
> > > approximate 3:2.
> >
> > OK, how is it useful when an exotic interval is distant in the
> > chain of fifths?
>
> It tells us we aren't likely to get that interval in that linear
> temperament using scales of a normal size. Precisely that the
> interval is exotic.
>
> -Carl
>
>
Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

Thanks Carl;

On 27 Mar 2009, at 22:28, Carl Lumma wrote:

> --- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
> >
> > You are too eager to condemn it Carl.
>
> Thanks for the advice, but I won't be dragged into another
> argument about this topic, which has been settled long ago.
> Kalle is merely the latest in a long line of clear thinkers
> who have pointed this out to you. I do find it ironic that
> this is the thanks I get for sticking up for you in this
> thread.
>
> -Carl
>
>
Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@> wrote:
>
> > > His statement that it corresponds to consonance is obviously
> > > wrong, but I see nothing wrong with thinking in terms of
> > > generators in general, especially when the generator is an
> > > approximate 3:2.
> >
> > OK, how is it useful when an exotic interval is distant in the
> > chain of fifths?
>
> It tells us we aren't likely to get that interval in that linear
> temperament using scales of a normal size. Precisely that the
> interval is exotic.

Charles claimed that "Western harmony can be applied to any musical
pattern" and "we have developed Western harmony to "enhance" melodies
which had originally been collected from some non-Western cultures".
He wrote also this: "So you have selected a wonderful exotic whole
number ratio; now what the composer/musician needs to know is how
does this exotic interval fit into my scale".

I understand Charles to mean that emulating all possible tunings with
LucyTuning somehow allows applying Western harmony to them. I would
like to see and hear how this is supposed to work. Those lullaby
samples didn't convince me because the melodies didn't sound that
exotic.

Kalle Aho

Hi Kalle;

You might like to look at the scores of the lullabies, which tell you much more about the harmonic structure, which can be a little more complex that you might appreciate at first listening.

The scores are very simple, and include chord symbols; downloadable from this page:

http://www.lullabies.co.uk/downloads.html

I'll attempt to explain the concept.

You know the cent values of the "original" intervals; so you select which LucyTuned intervals approximate them.

You can do this to whatever level of precision you find acceptable.

In this way you consider all the notes which are used in the melody/composition which you are intending to make into a LucyTuned rendition.

Having a list of all the requisite "notes", you can construct a scalecoding for the piece.

This should result in your being able to select a scale from the 2300 + database, which can be found at:

http://www.lucytune.com/scales

Having selected the scale from the database, you at the same time discover which triads can be used in the selected scale. (assuming that you transposed it into C, as the triads are listed as chord names assuming C to be the tonic)

The available triads act as a starting point from which to develop "Western" harmony to "arrange/orchestrate" your piece.

You can, of course then (re)transpose the whole thing into whatever key you wish it to be played in.

If required you may add "extra" notes to your scale to enable further triads to be used, which although not in the original composition may enhance the harmony.

It is likely that these new "extra" notes will be between the "ends" of your chain of fourths and fifths, which you have defined by selecting a scale.

A couple of years ago when I started this scales database, a few tunaniks could not understand the purpose of generating lists of scales, and suggested that I was trying to reinvent what Manuel had already achieved with Scala.

Now that they can see more of the "vision" ; what I am up to may make more sense to those doubters.

On 27 Mar 2009, at 23:30, Kalle Aho wrote:

> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> >
> > --- In tuning@yahoogroups.com, "Kalle Aho" <kalleaho@> wrote:
> >
> > > > His statement that it corresponds to consonance is obviously
> > > > wrong, but I see nothing wrong with thinking in terms of
> > > > generators in general, especially when the generator is an
> > > > approximate 3:2.
> > >
> > > OK, how is it useful when an exotic interval is distant in the
> > > chain of fifths?
> >
> > It tells us we aren't likely to get that interval in that linear
> > temperament using scales of a normal size. Precisely that the
> > interval is exotic.
>
> Charles claimed that "Western harmony can be applied to any musical
> pattern" and "we have developed Western harmony to "enhance" melodies
> which had originally been collected from some non-Western cultures".
> He wrote also this: "So you have selected a wonderful exotic whole
> number ratio; now what the composer/musician needs to know is how
> does this exotic interval fit into my scale".
>
> I understand Charles to mean that emulating all possible tunings with
> LucyTuning somehow allows applying Western harmony to them. I would
> like to see and hear how this is supposed to work. Those lullaby
> samples didn't convince me because the melodies didn't sound that
> exotic.
>
> Kalle Aho
>
>
Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

djtrancendance@... wrote:

> taken from http://dictionary.reference.com/browse/consonance

<snip>

> 3. Music. a simultaneous combination of tones conventionally accepted as being > in a state of >>>repose<<<. Compare dissonance > <http://dictionary.reference.com/search?q=dissonance&db=luna> (def. 2).

<snip>

> 5. Physics. the property of two sounds the frequencies of which have a ratio > equal to a small whole number.
> > General comment: can we all agree that consonance is the sense of > repose/relaxation in a sound and not necessarily the "physics" definition only > sounds that "have a ratio equal to a small whole number"? People here seem to > constantly insist...that definitions 5 and 3 above are equivalent...when it > seems pretty obvious they are not by definition equivalent. Same goes for > "harmony" vs. "harmonic series"...you can have harmony without it following the > physics-based phenomena that is the harmonic series.

You're always talking about what "seems" to be the case. That tells us a lot about your distorted view of reality, but how about sticking to the facts? Do you have a citation for somebody insisting on this definition?

This list is about music, so naturally we'll follow the "Music" definition. I'm not even happy about the "Physics" definition in terms of physics. I notice, from that same page, that it isn't in Webster's or American Heritage. I don't have a technical dictionary to cross-reference with.

If you want to know what "we" agree on you could at least start with the Monzopedia:

http://tonalsoft.com/enc/c/consonance.aspx

> Indeed, in the end of the day, I agree with Cameron that ears are the only > way to know for sure if something works or if something is/is-not possible. > Mathematics, IMVHO, can only help us fine-tune the general areas our ears point > to...and I strongly believe the best tuning wizards are the ones who don't rely > mostly on math, but always "reverse solve/prove" what they find with math > through their ears before accepting it as good.

Of course, we'd all broadly agree with that. It's hardly controversial, is it? The best tuning wizards are the ones that exist. What a surprise!

I can still think of some reasons for not trusting your ears. Everybody hears things differently and you may be optimizing for your own, unique perception. (Scale stretches seem to be like this -- by which I mean there's evidence that different listeners have a different sense of "correct" octaves. Try Terhardt.) Your hearing might actually be faulty. Remember we all lose high frequencies as we get older. Your equipment might be faulty. This is particularly important with sine waves and beats because distortion can make you hear things that shouldn't be there. Most importantly, you're naturally going to become familiar with the tunings you work with and so you'll hear them as less strange than a naive listener will.

All these caveats matter if you want other people to listen to your music. There's always somebody who'll come along and say they don't, in which case it doesn't really matter what it sounds like. For the rest of us, it's worth paying attention to other people's reactions as well.

Graham

---"we have developed Western harmony to "enhance" melodies
---which had originally been collected from some non-Western cultures".
   This is coming across as very confusing to me.
   Isn't this, in a way, saying that Western harmony is be all and end all of cultural music (IE use the intervals in Western scales that sound most like exotic tunings and then enhance them by adding harmony)?  If so, the idea kind of scares me...it almost seems to say tuning is simply using mathematical patterns to explain and point to the superiority of Western tuning...a barrier which is exactly what I believe you said Lucy-Tuning is about breaking past.

--- On Fri, 3/27/09, Kalle Aho <kalleaho@...> wrote:

From: Kalle Aho <kalleaho@mappi.helsinki.fi>
Subject: [tuning] Re: Rational vs Irrational Scales: a response to Rick
To: tuning@yahoogroups.com
Date: Friday, March 27, 2009, 4:30 PM

--- In tuning@yahoogroups. com, "Carl Lumma" <carl@...> wrote:

>

> --- In tuning@yahoogroups. com, "Kalle Aho" <kalleaho@> wrote:

>

> > > His statement that it corresponds to consonance is obviously

> > > wrong, but I see nothing wrong with thinking in terms of

> > > generators in general, especially when the generator is an

> > > approximate 3:2.

> >

> > OK, how is it useful when an exotic interval is distant in the

> > chain of fifths?

>

> It tells us we aren't likely to get that interval in that linear

> temperament using scales of a normal size. Precisely that the

> interval is exotic.

Charles claimed that "Western harmony can be applied to any musical

pattern" and "we have developed Western harmony to "enhance" melodies

which had originally been collected from some non-Western cultures".

He wrote also this: "So you have selected a wonderful exotic whole

number ratio; now what the composer/musician needs to know is how

does this exotic interval fit into my scale".

I understand Charles to mean that emulating all possible tunings with

LucyTuning somehow allows applying Western harmony to them. I would

like to see and hear how this is supposed to work. Those lullaby

samples didn't convince me because the melodies didn't sound that

exotic.

Kalle Aho

Michael Sheiman wrote:
> ---"we have developed Western harmony to "enhance" melodies
> ---which had originally been collected from some non-Western cultures".
> This is coming across as very confusing to me.
> Isn't this, in a way, saying that Western harmony is be all and end all of > cultural music (IE use the intervals in Western scales that sound most like > exotic tunings and then enhance them by adding harmony)? If so, the idea kind > of scares me...it almost seems to say tuning is simply using mathematical > patterns to explain and point to the superiority of Western tuning...a barrier > which is exactly what I believe you said Lucy-Tuning is about breaking past.

It's saying LucyTuning is the be all and end all of music. Welcome to his world!

Graham

---You're always talking about what "seems" to be the case.
I'm talking about what I've seen as at least across the board agreement at a subjective level.  The reason I don't say objective is that I realize saying music is objective is an outright lie. 

---
This list is about music, so naturally we'll follow the
---"Music" definition.
And there's something particularly wrong with that?

--I'm not even happy about the "Physics" definition in terms of physics.
Even though, apparently, it sounds like you are leaning highly toward supporting the physics definition over the musical one, otherwise why would it bother you so much it's not "100% complete"?

--I notice, from that same page, that it isn't in Webster's or American Heritage. I
--don't have a technical dictionary to cross-reference with.
I'd be interested...go ahead and find one and we can compare.  No, seriously. :-)

----http://tonalsoft. com/enc/c/ consonance. aspx
   Ironically...your "counter-proof" definition sited above actually sounds a LOT more like the musical definition than the "physics" one. 
It seems to be, simply, a much more elaborate version of the "music" definition of consonance I mentioned before...it certainly doesn't contradict it.

>but always "reverse solve/prove" what they find with math

> through their ears before accepting it as good.

-Of course, we'd all broadly agree with that.
     Right, it's obvious.  My overall point is...there are instances where people will think certain intervals that do NOT trickle down into parts of a harmonic series sound better than ones that do by ear (which consequently violates the "physics" definition I mention that two consonant tones are multiples of a root IE a harmonic series). My point, again, is that I don't see any potential increase in productivity from hiding behind a book.

********************************************************************************
--I can still think of some reasons for not trusting your

--ears. Everybody hears things differently and you may be

--optimizing for your own, unique perception.

Ok, now it seems we're getting "to the point", cool. :-)

--optimizing for your own, unique perception.

    Agreed, to an extent.  This is why, after spending hours working on
my scales, for example, I sleep, wake up the next morning, listen to
the 12TET scale and THEN play my scale when it's NOT fresh in my
mind/"adapted to".  True, ears can lie after too long of listening to
the same weird scale and adapting...but I'm pretty damn sure they don't
lie when presented with a scale fresh.
--Most importantly, you're naturally going to become

--familiar with the tunings you work with and so you'll hear

--them as less strange than a naive listener will.
  
Which is why I do the above mentioned step and show the results to some of the more critical people I know (the types who will say "this sucks" to a good proportion, IE over half, of my tunings).  True a larger sample test would help...but I can assure you the judgements from my results are a good deal more carefully tested than simply my listening to a scale and giving it a thumbs up.

--Remember we all lose high frequencies
--as we get older.
   Right, but only down to about 15-16khz and well over the range of most decently loud peaks...unless you are playing, say, the highest C on the piano, which is not how I test my scales on anyone elses.  I have programmed DSP and dealt with mp3-type compression and masking + hearing-curves so I'm pretty familiar with all of that.

---Your equipment might be faulty.
   I seriously doubt my $300 15-inch monitors lie THAT much.

--All these caveats matter if you want other people to listen
---to your music.
    Pardon my french but no sh*t.  Seriously do you think I'd go around asking what people think on a list like this rather than just trying to say, push it to major labels if I didn't not want an honest opinion?  I can't count how many times I've posted something, had someone correct something in it, and then
turned around and used that advice for my next scale.  You may not like my scales but, if you can't even recognize my efforts to improve and get input, that's your problem, not mine.

--There's always somebody who'll come along

--and say they don't, in which case it doesn't really matter

--what it sounds like.
     Right, and when that does happen I always ask "well, what do you think sounds bad"?  Usually if I play things slowly enough they will pinpoint a note.  And I will use math to re-tune that note a bit and re-play it to them until they think it sounds better.  And sometimes ithat doesn't happen and I just have to drop the thing and move on.

***************************************************
--For the rest of us, it's worth paying
--attention to other people's reactions as well.
   Again, with your my-way-or-the-highway aggressiveness toward me here, it seems pretty obvious your point is "you are losing site of reality simply by not following JI math, which is always better than your ears because your ears can become accustomed to weird scales "normal" people will hate...and you are so stuck up you refuse to listen to them."

   Think what you may, the
fact is I come here asking for advice, but the kind of advice relative to what they think sounds good/bad rather than just what checks/fits into JI math.  That does NOT mean you get to accuse me of not listening or seeking a second opinion...the only caveat to advice listening habits is that the complaint "it's not JI" in any form to me does not count automatically as justification for saying I should change something in my scale.  It has to be something closer related to the MUSICAL definition of consonance and less toward the physics one (IE "JI") to really get my attention. 

   I think in terms of "sounds tense" or "sounds relaxed" NOT "sounds JI" or "sounds bad/uneducated"; that does NOT mean I don't seek (or incorporate) advice or second opinions.  And I know a good few people who DON'T like how even 5-limit JI sounds...like I said before, music is subjective saying "is" and not "seems a lot like" is really
a lie in most cases on musical grounds.

-Michael

Michael Sheiman wrote:

> --Ratios are used when you tune an
> --instrument to match partials or harmonics.
> I've said in many many messages...that my intent is to produce consonance and > not to align partials specifically (although that's often a side-effect). Like > Charles, I believe beating is a natural phenomena in music but, on the other > hand, I agree that excessive beating is usually a bad things (IE in the harmonic > series even, harmonics 24 and 25 sound too tense to be consonant despite being > "periodic").

I didn't realize this was about you. Your question was about what ratios are used for, outside of instrument design. They are, in fact, used in contexts that have nothing to do with beating. Harmonics, for example. You keep ignoring harmonics. They're a standard part of guqin technique and also used with the violin family. Charles used them to support using pure octaves on a guitar. It was surely worth asking him why that doesn't extend to other ratios. But the discussion had nothing to do with either of us.

Of course excessive beating is a bad thing. Otherwise it wouldn't be excessive, would it? I bet you're one of those nuts who thinks cholesterol's bad for you as well :-)

> --You must be on the wrong list. This one's description
> --starts "This mailing list is intended for exchanging ideas
> --relevant to alternate musical tunings..."
> I know...and the idea you seem to be championing as the only valid topic > "tuning musical instruments and the acoustic (of only non-electronic > instruments) mathematics directly relevant to it" is NOT the only idea that > falls under the umbrella. Actually about 90% of what I hear on this list is > about things like tonality diamonds, consonance curves/harmonic entropy, whether > new tunings repeat historical mathematical constructs...none of those are > necessarily related to "how to design an acoustic instrument". Not that the > discussion is a bad one or I think mine are better (I don't thing they are > better, just attacking different goals), but I certainly do NOT deserve to have > my toes stepped on because I choose to talk about aspects of alternative scales > other than that.

You "seem" to think I'm a hypocrite then. I didn't step on your toes. If your toes are hurting maybe you should stop walking into the furniture.

> > Also, to note, he tempers the generator so the 25th tone of the tuning to
> > match the first (just as 12TET flattens the generating 5th (X) to make it fit
> > the octave on x^12) while I don't.
> --He suggested an equal temperament in 1965. He then
> --suggested different temperaments in the afterword. Don't
> --confuse matters by describing it all in the present tense.
> Huh? I realize mine nor his are NOT equal temperaments. Who ever said the > circle of PHI formed an equal temperament? Or even bring up the idea that my > scales were equal vs. unequal? I certainly didn't...

Circles of phi don't form an equal temperament. Neither do circles of 2:1 modulo phi. But after O'Connell tempered his generator, he got an equal temperament, as you observed. That should hardly surprise us as the article was originally written for die Reihe. The step size is 33.3236 cents, as he said in the afterword. It isn't far from pure, and doesn't matter much, but the quotes there show that you did bring it up.

Note that he also proposed another equal temperament in the afterword, dividing phi into 18, or 46.2828 cent steps.

> >For example 10TET is
> > obviously not a diatonic scale since no two notes in it can, say, very well
> > emulate a perfect 2nd.
> ---So you're not trying to do that, like the rest of us.
> EXACTLY! That's also why, I'm guessing, I don't seem to qualify to you as > making "alternative tunings"...it appears you (like many) have a preconceived > notion that scales MUST meet the definition of harmonic series periodicity (the > same periodicity formed by acoustic overtones) to be relevant. If that were > true we might as well just toss interesting things like Sethares' theories out > the window as well as he doesn't always follow those theories either. I just > don't see a point to limiting ourselves that way in an exclusive sense...

I'm not interested in your delusions.

> ...>>Not<<< that I mind people work on that kind of thing (I don't), but I do > mind it when they take a major issue (as if it were the solution to everything) > and take honor in stepping on the toes of anyone working with anything beside > the pure harmonic series (or something that VERY closely approximates is ALA 12TET).

12TET isn't a very (let alone VERY) close approximation to the harmonic series. Get real.

> --Isn't his 9 note scale essentially the same as your 9 note
> --scale?
> Absolutely not (at least from the PDF)...his is spread over many 2/1 octaves > while mine fits in a 1.618033 octave. I'll look up his other scales anyhow and > let you know what I find...I certainly don't mean to ignore his work.

I don't know what information you want the English language to give you, but it's unlikely to yield to torture. 1.618033 is not an octave. O'Connell talks about a 9 note scale that fits into an equivalence interval of 1.618033.... That looks, to me, essentially the same as yours -- before you moved it to JI, and as far as I understood you. There's a minor issue of temperament. If it differs in any other way, let us know.

> ---Anyway, try searching oconnell*scl from the Scala
> ---archive. To hear what he intended you need the phi timbre
> ---as well and that's more difficult.
> I think that's the one thing we may have in common is that timbre. I DID see > a lot in his scales that seem to come from the same PHI^x construct, if not also > the PHI^x/2^y construct I use in my own tuning. So, I'm pretty sure our tunings > are alike, if not the same.

You use the same timbre? You didn't mention the timbre before.

Yes, they look the same, give or take some temperament.

> BTW, as we've discussed, I am taking a good few of your suggestions > seriously and have been working with the idea of making a tempered scale that > complies relatively well with BOTH JI and PHI and could be used easily on > acoustic instruments. So stay tuned for that... :-)

That's good, but there are lots of precedents out there for JI scales.

Graham

--It's saying LucyTuning is the be all and end all of music.
--Welcome to his world!
   To be honest, I think it's more like putting a killer wax job on an Oldsmobile (where 12TET tuning = the Oldsmobile).  It makes it look/sound a bit nicer but doesn't really change it's functionality.

  The flip side is, based on your last somewhat charged response to me, even if he was "in his world"...is your view on JI superiority really any less "uselessly proud" (I kind of doubt it)?! :-(

   Once again my point is...come on guys, can't we move past analyzing and making scales that either
A) Imitate JI and/or diatonic intervals in general (yes, this includes 12TET, meantone, or subsets of 19TET, 31TET, 53TET...meant to match diatonic intervals).
  OR
B) Don't even try for harmony or are used for purposes of "experimenting with dissonance".

Again, as counter-examples I would say Wilson (for example his 9-tone MOS scales) and Sethares.  And again, in my mind so far as I've seen, these two people constitute most (if not all) of truly modern tuning (IE that which sounds both consonant in terms of polyphonic use and quite different from anything from the past).  If you want to know why, look back at A) and B) above and notice those two people's work appears to defy both.

-Michael

--- On Fri, 3/27/09, Graham Breed <gbreed@...> wrote:

From: Graham Breed <gbreed@...>
Subject: Re: [tuning] Re: Rational vs Irrational Scales: a response to Rick
To: tuning@yahoogroups.com
Date: Friday, March 27, 2009, 8:02 PM

Michael Sheiman wrote:

> ---"we have developed Western harmony to "enhance" melodies

> ---which had originally been collected from some non-Western cultures".

> This is coming across as very confusing to me.

> Isn't this, in a way, saying that Western harmony is be all and end all of

> cultural music (IE use the intervals in Western scales that sound most like

> exotic tunings and then enhance them by adding harmony)? If so, the idea kind

> of scares me...it almost seems to say tuning is simply using mathematical

> patterns to explain and point to the superiority of Western tuning...a barrier

> which is exactly what I believe you said Lucy-Tuning is about breaking past.

It's saying LucyTuning is the be all and end all of music.

Welcome to his world!

Graham

--They're a standard part of guqin
--technique and also used with the violin family. Charles
--used them to support using pure octaves on a guitar.
    That's great and all but, as I've said many many times, I'm NOT interested in designing or analyzing the overtones of acoustic instruments (IE this point seems rather off-topic vis-a-vis my goal here). :-P

--Of course excessive beating is a bad thing. Otherwise it
--wouldn't be excessive, would it? I bet you're one of those
---nuts who thinks cholesterol' s bad for you as well :-)
Hehehe...very funny.  And yes, I hate cholesterol only in excess amounts...I realize some of it is actually vital.  Same goes with beating and music...a little is quite natural (IE smooth violin sound with some beating vs. rough organ sound with
virtually none). :-)

--You "seem" to think I'm a hypocrite then. I didn't step on
--your toes. If your toes are hurting maybe you should stop
--walking into the furniture.
    Aww...why the drama.  I ride motorcycles, I could care less about stubbing something small like my toes (LOL).  But my point isn't dramatic: I'm talking about consonance in and of itself and not related to acoustic instrument design...even though you seem to insist in dragging everything I say back to acoustic instrument design.  Yes, I know what a harmonic series overtone is...no it's not the be-all-end-all of defining consonance.  If it were, we'd all be singing Gregorian Chant or something... :-)

--Circles of phi don't form an equal temperament. Neither do
---circles of 2:1 modulo phi. But after O'Connell tempered his
---generator, he got an equal temperament, as you observed.
   
Argh...here we go again, I made a point I didn't care about whether PHI tuning is equal or not and here you go telling me all sorts of cool tricks from O'Connell's article about how to make PHI into an equal temperament.  Again, I don't care about that aspect.

--but the quotes there show that you did
--bring it up.
I said
""Huh? I realize mine nor his are NOT equal temperaments. Who ever said the
 
circle of PHI formed an equal temperament? Or even bring up the idea that my
 
scales were equal vs. unequal? I certainly didn't...""
    Yes, you're right, I missed the part about his "tempering out" his scales into equal temperament.  But, regardless...look at the above quote...my point is I don't give a care about whether his or my temperaments are equal or not and consonance, NOT equal tempering, was my point in the PHI scale. 

--12TET isn't a very (let alone VERY) close approximation to
--the harmonic series. Get real.
    Neither is JI.  It certainly doesn't put the intervals in nearly the same order of the harmonic series IE 2/1,3/2,4/3,5/4....  However, a major second in 12TET, for example, is pretty close to it's nearest neighbor in 5-limit JI...that's what I was referring to when I said "harmonic series".

--I'm not interested in your delusions.
    The only things I referred to were that people like Sethares did things far from
JI and managed to sound consonant.  And I'm not the only one who also thinks that...so, no, it's not a delusion: you can have a consonant scale that is not diatonic.

> the PHI^x/2^y construct I use in my own tuning. So, I'm pretty sure our tunings

> are alike, if not the same.

---You use the same timbre? You didn't mention the timbre before.
   I don't use that to generate the timbre...I use it to generate the tuning itself. 

---Yes, they look the same, give or take some temperament.
  The tunings do, I believe that much.  But my scales are different...his 9-tone scale is much wider (IE takes up much more vast of a frequency range for 9 notes).

> BTW, as we've discussed, I am taking a good few of your suggestions

> seriously and have been working with the idea of making a tempered scale that

> complies relatively well with BOTH JI and PHI and could be used easily on

> acoustic instruments. So stay tuned for that... :-)

--That's good, but there are lots of precedents out there for
--JI scales.
   Precedents such as? 
******************************************************************************************
   My point in such a scale is that irrational generators can form patterns that have CLOSE ties with harmonic-series-type intervals many of which are NOT near diatonic intervals...and yet still sound very consonant.  Again, here's the my PHI scale converted to very nearby JI ratios (again, just a few cents away at most from tones in the PHI tuning):
1
17/16
9/8
19/16
5/4
4/3
7/5
28/19
14/9
21/13  (1.6153846) apx 1.618033

    I dare you to find a duplicate of that scale: without PHI leading me past the basic interval areas above I likely would have never found this pattern. :-)

-Michael

--- On Fri, 3/27/09, Graham Breed <gbreed@gmail.com> wrote:

From: Graham Breed <gbreed@...>
Subject: Re: [tuning] Re: Rational vs Irrational Scales: a response to Rick
To: tuning@yahoogroups.com
Date: Friday, March 27, 2009, 8:40 PM

Michael Sheiman wrote:

> --Ratios are used when you tune an

> --instrument to match partials or harmonics.

> I've said in many many messages...that my intent is to produce consonance and

> not to align partials specifically (although that's often a side-effect) . Like

> Charles, I believe beating is a natural phenomena in music but, on the other

> hand, I agree that excessive beating is usually a bad things (IE in the harmonic

> series even, harmonics 24 and 25 sound too tense to be consonant despite being

> "periodic").

I didn't realize this was about you. Your question was

about what ratios are used for, outside of instrument

design. They are, in fact, used in contexts that have

nothing to do with beating. Harmonics, for example. You

keep ignoring harmonics. They're a standard part of guqin

technique and also used with the violin family. Charles

used them to support using pure octaves on a guitar. It was

surely worth asking him why that doesn't extend to other

ratios. But the discussion had nothing to do with either of us.

Of course excessive beating is a bad thing. Otherwise it

wouldn't be excessive, would it? I bet you're one of those

nuts who thinks cholesterol' s bad for you as well :-)

> --You must be on the wrong list. This one's description

> --starts "This mailing list is intended for exchanging ideas

> --relevant to alternate musical tunings..."

> I know...and the idea you seem to be championing as the only valid topic

> "tuning musical instruments and the acoustic (of only non-electronic

> instruments) mathematics directly relevant to it" is NOT the only idea that

> falls under the umbrella. Actually about 90% of what I hear on this list is

> about things like tonality diamonds, consonance curves/harmonic entropy, whether

> new tunings repeat historical mathematical constructs.. .none of those are

> necessarily related to "how to design an acoustic instrument". Not that the

> discussion is a bad one or I think mine are better (I don't thing they are

> better, just attacking different goals), but I certainly do NOT deserve to have

> my toes stepped on because I choose to talk about aspects of alternative scales

> other than that.

You "seem" to think I'm a hypocrite then. I didn't step on

your toes. If your toes are hurting maybe you should stop

walking into the furniture.

> > Also, to note, he tempers the generator so the 25th tone of the tuning to

> > match the first (just as 12TET flattens the generating 5th (X) to make it fit

> > the octave on x^12) while I don't.

> --He suggested an equal temperament in 1965. He then

> --suggested different temperaments in the afterword. Don't

> --confuse matters by describing it all in the present tense.

> Huh? I realize mine nor his are NOT equal temperaments. Who ever said the

> circle of PHI formed an equal temperament? Or even bring up the idea that my

> scales were equal vs. unequal? I certainly didn't...

Circles of phi don't form an equal temperament. Neither do

circles of 2:1 modulo phi. But after O'Connell tempered his

generator, he got an equal temperament, as you observed.

That should hardly surprise us as the article was originally

written for die Reihe. The step size is 33.3236 cents, as

he said in the afterword. It isn't far from pure, and

doesn't matter much, but the quotes there show that you did

bring it up.

Note that he also proposed another equal temperament in the

afterword, dividing phi into 18, or 46.2828 cent steps.

> >For example 10TET is

> > obviously not a diatonic scale since no two notes in it can, say, very well

> > emulate a perfect 2nd.

> ---So you're not trying to do that, like the rest of us.

> EXACTLY! That's also why, I'm guessing, I don't seem to qualify to you as

> making "alternative tunings"...it appears you (like many) have a preconceived

> notion that scales MUST meet the definition of harmonic series periodicity (the

> same periodicity formed by acoustic overtones) to be relevant. If that were

> true we might as well just toss interesting things like Sethares' theories out

> the window as well as he doesn't always follow those theories either. I just

> don't see a point to limiting ourselves that way in an exclusive sense...

I'm not interested in your delusions.

> ...>>Not<<< that I mind people work on that kind of thing (I don't), but I do

> mind it when they take a major issue (as if it were the solution to everything)

> and take honor in stepping on the toes of anyone working with anything beside

> the pure harmonic series (or something that VERY closely approximates is ALA 12TET).

12TET isn't a very (let alone VERY) close approximation to

the harmonic series. Get real.

> --Isn't his 9 note scale essentially the same as your 9 note

> --scale?

> Absolutely not (at least from the PDF)...his is spread over many 2/1 octaves

> while mine fits in a 1.618033 octave. I'll look up his other scales anyhow and

> let you know what I find...I certainly don't mean to ignore his work.

I don't know what information you want the English language

to give you, but it's unlikely to yield to torture.

1.618033 is not an octave. O'Connell talks about a 9 note

scale that fits into an equivalence interval of 1.618033....

That looks, to me, essentially the same as yours -- before

you moved it to JI, and as far as I understood you. There's

a minor issue of temperament. If it differs in any other

way, let us know.

> ---Anyway, try searching oconnell*scl from the Scala

> ---archive. To hear what he intended you need the phi timbre

> ---as well and that's more difficult.

> I think that's the one thing we may have in common is that timbre. I DID see

> a lot in his scales that seem to come from the same PHI^x construct, if not also

> the PHI^x/2^y construct I use in my own tuning. So, I'm pretty sure our tunings

> are alike, if not the same.

You use the same timbre? You didn't mention the timbre before.

Yes, they look the same, give or take some temperament.

> BTW, as we've discussed, I am taking a good few of your suggestions

> seriously and have been working with the idea of making a tempered scale that

> complies relatively well with BOTH JI and PHI and could be used easily on

> acoustic instruments. So stay tuned for that... :-)

That's good, but there are lots of precedents out there for

JI scales.

Graham

--- In tuning@yahoogroups.com, Graham Breed <gbreed@...> wrote:

> I can still think of some reasons for not trusting your
> ears. Everybody hears things differently and you may be
> optimizing for your own, unique perception. (Scale
> stretches seem to be like this -- by which I mean there's
> evidence that different listeners have a different sense of
> "correct" octaves. Try Terhardt.) Your hearing might
> actually be faulty. Remember we all lose high frequencies
> as we get older. Your equipment might be faulty. This is
> particularly important with sine waves and beats because
> distortion can make you hear things that shouldn't be there.

Moreover, there are the well-known cognitive biases:

http://en.wikipedia.org/wiki/List_of_cognitive_biases

-Carl

--Moreover, there are the well-known cognitive biases:
--http://en.wikipedia .org/wiki/ List_of_cognitiv e_biases

But such errors-of-bias can work both ways...
For example, a few of these include.......
********************************************************************
--Framing
— by using a too narrow approach or description of the situation or
issue. Also --framing effect — drawing different conclusions based on how
data are presented.
**This tuning group seems to a huge extent "JI framed".  In virtually all of my past scales as soon as I converted them to JI equivalents the response to them improved dramatically, even if the actual notes were changed by a few cents at most thus representing almost no audible difference psycho-acoustically.  Lucy-tuning?  Mean-tone?  5-limit JI?  It's all relatively diatonic, which ties right smack back to 12TET.**

Status quo bias — the tendency for people to like things to stay relatively the same (see also loss aversion, endowment effect, and system
justification).[7]
Mere exposure effect — the tendency for people to express undue liking for things merely --because they are familiar with them.
***Familiar with 12TET?  Many will move-to/like 5-limit JI, which is very very closely related.***

---Congruence bias — the tendency to test hypotheses exclusively through direct testing, in ---contrast to tests of possible alternative hypotheses.
    How come so many people are very willing to test JI scales, but unwilling
to spend much time testing non-JI ones?  Non-JI fits into the "possible alternative
hypothesis" section above...

------------------------------------------------------------------------------------------------------------------------
So I think it's fair to say COGNITIVE BIASES lend themselves as much toward problems with things "forcedly" staying the same (IE diatonic interval based scales) as they do to my supposed biases toward "being un-naturally used to my own scales." 
   Yes, I do test my scales on other people beside myself and, no, those people are not yes men, in fact I purposefully pick people who complain about my scales a lot though not always (Machiavelli would be proud...I don't purposefully select those who kiss up to me instead of forcing me to become stronger).

  So, in short...I am sure cognitive bias is a null argument here.  What still baffles me is (in native JI-style form)...why no one yet has been able to find a sour interval in the following PHI-based (but JI
compliant) scale I made (which no one seems to be responding much to, positively or negatively):

1
17/16
9/8
19/16
5/4
4/3
7/5
28/19
14/9
21/13  (1.6153846) apx 1.618033
------------------------------------------------------------
   If you REALLY want to convince me how "cognitively biased" I am...please pick apart my scale and find an interval or chord in it that you thinks sounds bad (without simply using the excuse "it doesn't sound like 5-limit JI".

--- On Fri, 3/27/09, Carl Lumma <carl@...> wrote:

From: Carl Lumma <carl@...>
Subject: [tuning] Re: Rational vs Irrational Scales: a response to Rick
To: tuning@yahoogroups.com
Date: Friday, March 27, 2009, 9:31 PM

--- In tuning@yahoogroups. com, Graham Breed <gbreed@...> wrote:

> I can still think of some reasons for not trusting your

> ears. Everybody hears things differently and you may be

> optimizing for your own, unique perception. (Scale

> stretches seem to be like this -- by which I mean there's

> evidence that different listeners have a different sense of

> "correct" octaves. Try Terhardt.) Your hearing might

> actually be faulty. Remember we all lose high frequencies

> as we get older. Your equipment might be faulty. This is

> particularly important with sine waves and beats because

> distortion can make you hear things that shouldn't be there.

Moreover, there are the well-known cognitive biases:

http://en.wikipedia .org/wiki/ List_of_cognitiv e_biases

-Carl

djtrancendance@... wrote:
> ---You're always talking about what "seems" to be the case.
> I'm talking about what I've seen as at least across the board agreement at a > subjective level. The reason I don't say objective is that I realize saying > music is objective is an outright lie. You're talking about what you think you see, not what really is. I don't know what other people's intentions are, and I don't much care, but from what you say below you clearly have mine wrong.

> --- This list is about music, so naturally we'll follow the
> ---"Music" definition.
> And there's something particularly wrong with that?

No.

> --I'm not even happy about the "Physics" definition in terms of physics.
> Even though, apparently, it sounds like you are leaning highly toward supporting > the physics definition over the musical one, otherwise why would it bother you > so much it's not "100% complete"?

When did I say "100% complete"? It's not a question of supporting one or the other. Music definitions are valid for music and physics definitions for physics. It's possible for the same words to be used differently in the different contexts. The word "harmonic" could be an example of this. But in this case I still don't think the definition of "consonance" given for physics is right for physics.

> --I notice, from that same page, that it isn't in Webster's or American Heritage. I
> --don't have a technical dictionary to cross-reference with.
> I'd be interested...go ahead and find one and we can compare. No, seriously. :-)

I can check the library this afternoon.

> ----http://tonalsoft. com/enc/c/ consonance. aspx > <http://tonalsoft.com/enc/c/consonance.aspx>
> Ironically...your "counter-proof" definition sited above actually sounds a > LOT more like the musical definition than the "physics" one. It seems to be, > simply, a much more elaborate version of the "music" definition of consonance I > mentioned before...it certainly doesn't contradict it.

Here we go! There's nothing ironic because it isn't a counter-proof. Of course it follows the "music" definition. I can read it as well as you can.

> >but always "reverse solve/prove" what they find with math
> > through their ears before accepting it as good.
> -Of course, we'd all broadly agree with that.
> Right, it's obvious. My overall point is...there are instances where > people will think certain intervals that do NOT trickle down into parts of a > harmonic series sound better than ones that do by ear (which consequently > violates the "physics" definition I mention that two consonant tones are > multiples of a root IE a harmonic series). My point, again, is that I don't see > any potential increase in productivity from hiding behind a book.

But there is a book explaining this so it isn't a stunning revelation.

> --I can still think of some reasons for not trusting your
> --ears. Everybody hears things differently and you may be
> --optimizing for your own, unique perception.
> > Ok, now it seems we're getting "to the point", cool. :-)

Could be, but I've snipped it because I didn't have any interesting comments.

> --For the rest of us, it's worth paying
> --attention to other people's reactions as well.
> Again, with your my-way-or-the-highway aggressiveness toward me here, it > seems pretty obvious your point is "you are losing site of reality simply by not > following JI math, which is always better than your ears because your ears can > become accustomed to weird scales "normal" people will hate...and you are so > stuck up you refuse to listen to them."

I only mentioned that because this subject has come up before and is controversial. If it were about you and I really thought that I could hardly complain anyway, could I? You are following JI math.

> Think what you may, the fact is I come here asking for advice, but the kind > of advice relative to what they think sounds good/bad rather than just what > checks/fits into JI math. That does NOT mean you get to accuse me of not > listening or seeking a second opinion...the only caveat to advice listening > habits is that the complaint "it's not JI" in any form to me does not count > automatically as justification for saying I should change something in my > scale. It has to be something closer related to the MUSICAL definition of > consonance and less toward the physics one (IE "JI") to really get my attention. Another fact is that there are so many reasons we could be wrong (see also Carl's link for cognitive biases) that some of us don't push our own opinions too heavily. Hence we tend to give factual answers that you choose to interpret as accusations. Where somebody does, nevertheless, give opinions you could assume they're based on listening.

JI is about music, not physics.

> I think in terms of "sounds tense" or "sounds relaxed" NOT "sounds JI" or > "sounds bad/uneducated"; that does NOT mean I don't seek (or incorporate) advice > or second opinions. And I know a good few people who DON'T like how even > 5-limit JI sounds...like I said before, music is subjective saying "is" and not > "seems a lot like" is really a lie in most cases on musical grounds.

There's a famous experiment showing that one group of listeners preferred pure intervals and the other didn't, fairly consistently. I don't have a reference to hand. But a lot depends on context. Not liking 5-limit JI is similar to not liking jazz.

Graham

   As a foreword, now I realize you are not arguing for or against the "physics" definition of consonance...

> ---You're always talking about what "seems" to be the case.

> I'm talking about what I've seen as at least across the board agreement at a

> subjective level. The reason I don't say objective is that I realize saying

> music is objective is an outright lie.
--You're talking about what you think you see, not what really
--is. I don't know what other people's intentions are, and I
--don't much care, but from what you say below you clearly
--have mine wrong.
    If you are so sure "what really is"...go ahead and justify it.  Regardless of personal intentions you have brought up all sorts of instrument acoustics theories into a discussion I started about consonance in general and not specific to acoustic instruments. 

--But there is a book explaining this so it isn't a stunning
--revelation.
So if a book explains how instrumental overtones are aligned (the harmonic series) the simple fact an explanation exists makes it "law"?

...talking about can irrational scales be an alternative to JI
--I only mentioned that because this subject has come up
--before and is controversial. If it were about you
and I
--really thought that I could hardly complain anyway, could I?

--You are following JI math.
  True enough (in my modified version of the PHI tuning). :-) 
  Again, my point is the irrational tuning and one nearest rational approximation are very very alike...thus proving that PHI is by no means "anti-consonance" even in the pure harmonic series "physics" sense. 

--Another fact is that there are so many reasons we could be
--wrong (see also Carl's link for cognitive biases) that some

--of us don't push our own opinions too heavily.
  Right, but at the same time I don't see a point in not at least trying to solve something until an obvious loophole is revealed. :-)   Call me a crazy optimist, but I'm just trying to be "wreck-lessly productive"...

--Hence we tend to give factual answers that you choose to interpret as
--accusations.
    I don't believe that JI = the only way to produce decent consonance is a factual statement.  Again...Sethares' use of 10TET with "warped" timbres is a counter example that you can actually sit down and listen to.  I've shown some of my friends it and about 70% say it sounds good 30% say it's "just out of tune not good"...but it's close enough to really make you wonder if you get my drift.

--Where somebody does, nevertheless, give
--opinions you could assume they're based on listening.
   Most of the opinions I've gotten
here are on the level of "it's not JI, learn JI...I haven't listened but I can tell by the lack of ratios you are barking up the wrong tree" rather than something I can actually use like "try 21/13 as a JI approximation of PHI" (which is a tip I took, obviously).

---JI is about music, not physics.
   Too subjective to argue either way IMVHO.  I'll stick to that JI is about music, but it IS NOT the definition of music...meaning something not made in JI can still just as competently qualify as music.

--There's a famous experiment showing that one group of
--listeners preferred pure intervals and the other didn't,
--fairly consistently. I don't have a reference to hand. But
--a lot depends on context. Not liking 5-limit JI is similar
--to not liking jazz.
  Exactly...going back to the idea that music is subjective and "very likely" is about the best level of "factuality" you can get in music, even with bluntly executed tuning math.  Again...it seems obvious there is no one tuning which has a "monopoly"...thus leaving room for the idea that tunings that don't follow that one model (IE irrationally generated tunings) may also work either as well or nearly as
well (and perhaps provide some new artistic/emotional freedom on the side). :-)

-Michael
 

--- On Sat, 3/28/09, Graham Breed <gbreed@...> wrote:

From: Graham Breed <gbreed@...>
Subject: Re: [tuning] Re: Rational vs Irrational Scales: a response to Rick
To: tuning@yahoogroups.com
Date: Saturday, March 28, 2009, 12:18 AM

djtrancendance@ yahoo.com wrote:

> ---You're always talking about what "seems" to be the case.

> I'm talking about what I've seen as at least across the board agreement at a

> subjective level. The reason I don't say objective is that I realize saying

> music is objective is an outright lie.

You're talking about what you think you see, not what really

is. I don't know what other people's intentions are, and I

don't much care, but from what you say below you clearly

have mine wrong.

> --- This list is about music, so naturally we'll follow the

> ---"Music" definition.

> And there's something particularly wrong with that?

No.

> --I'm not even happy about the "Physics" definition in terms of physics.

> Even though, apparently, it sounds like you are leaning highly toward supporting

> the physics definition over the musical one, otherwise why would it bother you

> so much it's not "100% complete"?

When did I say "100% complete"? It's not a question of

supporting one or the other. Music definitions are valid

for music and physics definitions for physics. It's

possible for the same words to be used differently in the

different contexts. The word "harmonic" could be an example

of this. But in this case I still don't think the

definition of "consonance" given for physics is right for

physics.

> ----http://tonalsoft. com/enc/c/ consonance. aspx

> <http://tonalsoft. com/enc/c/ consonance. aspx>

> Ironically.. .your "counter-proof" definition sited above actually sounds a

> LOT more like the musical definition than the "physics" one. It seems to be,

> simply, a much more elaborate version of the "music" definition of consonance I

> mentioned before...it certainly doesn't contradict it.

Here we go! There's nothing ironic because it isn't a

counter-proof. Of course it follows the "music" definition.

I can read it as well as you can.

> >but always "reverse solve/prove" what they find with math

> > through their ears before accepting it as good.

> -Of course, we'd all broadly agree with that.

> Right, it's obvious. My overall point is...there are instances where

> people will think certain intervals that do NOT trickle down into parts of a

> harmonic series sound better than ones that do by ear (which consequently

> violates the "physics" definition I mention that two consonant tones are

> multiples of a root IE a harmonic series). My point, again, is that I don't see

> any potential increase in productivity from hiding behind a book.

But there is a book explaining this so it isn't a stunning

revelation.

> --I can still think of some reasons for not trusting your

> --ears. Everybody hears things differently and you may be

> --optimizing for your own, unique perception.

>

> Ok, now it seems we're getting "to the point", cool. :-)

Could be, but I've snipped it because I didn't have any

interesting comments.

> --For the rest of us, it's worth paying

> --attention to other people's reactions as well.

> Again, with your my-way-or-the- highway aggressiveness toward me here, it

> seems pretty obvious your point is "you are losing site of reality simply by not

> following JI math, which is always better than your ears because your ears can

> become accustomed to weird scales "normal" people will hate...and you are so

> stuck up you refuse to listen to them."

I only mentioned that because this subject has come up

before and is controversial. If it were about you and I

really thought that I could hardly complain anyway, could I?

You are following JI math.

> Think what you may, the fact is I come here asking for advice, but the kind

> of advice relative to what they think sounds good/bad rather than just what

> checks/fits into JI math. That does NOT mean you get to accuse me of not

> listening or seeking a second opinion...the only caveat to advice listening

> habits is that the complaint "it's not JI" in any form to me does not count

> automatically as justification for saying I should change something in my

> scale. It has to be something closer related to the MUSICAL definition of

> consonance and less toward the physics one (IE "JI") to really get my attention.

Another fact is that there are so many reasons we could be

wrong (see also Carl's link for cognitive biases) that some

of us don't push our own opinions too heavily. Hence we

tend to give factual answers that you choose to interpret as

accusations. Where somebody does, nevertheless, give

opinions you could assume they're based on listening.

JI is about music, not physics.

> I think in terms of "sounds tense" or "sounds relaxed" NOT "sounds JI" or

> "sounds bad/uneducated" ; that does NOT mean I don't seek (or incorporate) advice

> or second opinions. And I know a good few people who DON'T like how even

> 5-limit JI sounds...like I said before, music is subjective saying "is" and not

> "seems a lot like" is really a lie in most cases on musical grounds.

There's a famous experiment showing that one group of

listeners preferred pure intervals and the other didn't,

fairly consistently. I don't have a reference to hand. But

a lot depends on context. Not liking 5-limit JI is similar

to not liking jazz.

Graham

--- In tuning@yahoogroups.com, djtrancendance@... wrote:

>My point in such a scale is that irrational generators can form
patterns that have CLOSE ties with harmonic-series-type intervals
many of which are NOT near diatonic intervals...and yet still sound
very consonant.  Again, here's the my PHI scale converted to very
nearby JI ratios (again, just a few cents away at most from tones in
the PHI tuning):
> 1
> 17/16
> 9/8
> 19/16
> 5/4
> 4/3
> 7/5
> 28/19
> 14/9
> 21/13  (1.6153846) apx 1.618033

Michael,

have you heard John Chowning's composition Stria (1977)? It also uses
a 9-tone division of Phi but he uses an equal division instead. The
sounds used are FM tones where the M:C-ratio is Phi which produces
quite smooth sounds and they make the Phi-interval sound like a
pseudo-octave.

Kalle Aho

--- In tuning@yahoogroups.com, Charles Lucy <lucy@...> wrote:
>
> Hi Kalle;
>
> You might like to look at the scores of the lullabies, which tell
> you much more about the harmonic structure, which can be a little
> more complex that you might appreciate at first listening.
>
> The scores are very simple, and include chord symbols; downloadable
> from this page:
>
> http://www.lullabies.co.uk/downloads.html

Looking at the scores only confirmed what I heard: the melodies don't
stray far from basic diatonicism. So this does nothing to convince
me of your claim that "Western harmony can be applied to any musical
pattern".

Kalle Aho

Michael Sheiman wrote:
> --It's saying LucyTuning is the be all and end all of music.
> --Welcome to his world!
> To be honest, I think it's more like putting a killer wax job on an > Oldsmobile (where 12TET tuning = the Oldsmobile). It makes it look/sound a bit > nicer but doesn't really change it's functionality.

Now I have to find out what an Oldsmobile is, to give an informed answer. Wikipedia tells me it's an old brand (or "marque") of car. I don't know what special features they have to fit your analogy ... so I'm none the wiser.

LucyTuning can, at least, be substantially different to 12TET. It depends on how you use it. With enough notes it can suit any other scale you like.

> The flip side is, based on your last somewhat charged response to me, even if > he was "in his world"...is your view on JI superiority really any less > "uselessly proud" (I kind of doubt it)?! :-(

Well, I hope not, of course.

> Once again my point is...come on guys, can't we move past analyzing and > making scales that either
> A) Imitate JI and/or diatonic intervals in general (yes, this includes 12TET, > meantone, or subsets of 19TET, 31TET, 53TET...meant to match diatonic intervals).
> OR
> B) Don't even try for harmony or are used for purposes of "experimenting with > dissonance".

Imitating JI is the obvious way of getting harmony to work. It's where you've ended up. Do you have any other ideas? Depending on how define JI, it can be very difficult to avoid, what with the density of the rationals.

> Again, as counter-examples I would say Wilson (for example his 9-tone MOS > scales) and Sethares. And again, in my mind so far as I've seen, these two > people constitute most (if not all) of truly modern tuning (IE that which sounds > both consonant in terms of polyphonic use and quite different from anything from > the past). If you want to know why, look back at A) and B) above and notice > those two people's work appears to defy both.

So what 9-tone MOS scales are you talking about? You keep mentioning them but no details. Erv Wilson has done a lot of work with just intonation. I'd put him squarely in A).

Bill Sethares has, as we know, done work with alternative timbres. That may or may not count as JI depending on your definition. It's worth pointing out that he wasn't the first to do this as he sometimes gets more credit than he deserves -- which is still considerable.

Graham

djtrancendance@... wrote:

> --12TET isn't a very (let alone VERY) close approximation to
> --the harmonic series. Get real.
> Neither is JI. It certainly doesn't put the intervals in nearly the same > order of the harmonic series IE 2/1,3/2,4/3,5/4.... However, a major second in > 12TET, for example, is pretty close to it's nearest neighbor in 5-limit > JI...that's what I was referring to when I said "harmonic series".

How are you defining "5-limit JI"? As an odd limit, the nearest neighbor is 6/5. About 115 cents away. As a prime limit, the nearest neighbor of anything is 0 cents away so that isn't very interesting.

As a sensible extension of the odd limit, you'll get a 9/8, which is pretty close. But this is extended 3-limit, which 12TET generally does better than the 5-limit. It is still very efficient at approximating the 5-limit but not so close as that in absolute terms. You're likely to use a 25:24 in extended 5-limit JI. That's about 30 cents out in 12TET, or 30% of a scale step. If that's very close there can't be anything (with enough notes, at least) that's very far away.

> --I'm not interested in your delusions.
> The only things I referred to were that people like Sethares did things far > from JI and managed to sound consonant. And I'm not the only one who also > thinks that...so, no, it's not a delusion: you can have a consonant scale that > is not diatonic.

No, that isn't all. You also said "... I don't seem to qualify to you as making 'alternative tunings'...it appears you ... have a preconceived notion that scales MUST meet the definition of harmonic series periodicity ... to be relevant." This is delusional and I have no more to say about it.

> > > the PHI^x/2^y construct I use in my own tuning. So, I'm pretty sure our tunings
> > are alike, if not the same.
> ---You use the same timbre? You didn't mention the timbre before.
> I don't use that to generate the timbre...I use it to generate the tuning > itself. You snipped the relevant part, which was "I think that's the one thing we may have in common is that timbre." What did you mean by it? What timbre are you using?

> > ---Yes, they look the same, give or take some temperament.
> The tunings do, I believe that much. But my scales are different...his 9-tone > scale is much wider (IE takes up much more vast of a frequency range for 9 notes).

His is about 3 cents wider. So it's the tunings that are slightly different.

> > BTW, as we've discussed, I am taking a good few of your suggestions
> > seriously and have been working with the idea of making a tempered scale that
> > complies relatively well with BOTH JI and PHI and could be used easily on
> > acoustic instruments. So stay tuned for that... :-)
> --That's good, but there are lots of precedents out there for
> --JI scales.
> Precedents such as? There's the one I found in Huainanzi. Or the various ones Ptolemy listed. Or Al Farabi's. Plenty of more recent examples as well.

> My point in such a scale is that irrational generators can form patterns that > have CLOSE ties with harmonic-series-type intervals many of which are NOT near > diatonic intervals...and yet still sound very consonant. Again, here's the my > PHI scale converted to very nearby JI ratios (again, just a few cents away at > most from tones in the PHI tuning):
> 1
> 17/16
> 9/8
> 19/16
> 5/4
> 4/3
> 7/5
> 28/19
> 14/9
> 21/13 (1.6153846) apx 1.618033
> > I dare you to find a duplicate of that scale: without PHI leading me past > the basic interval areas above I likely would have never found this pattern. :-)

How do you get 4/3? The simplest match I can find within 5 cents is -10 2:1 generators. And 5/4??? That could be -33 generators. What, in fact, is this "PHI tuning"?

I note that 4 of your first 5 notes are within 5 cents of 12TET. The exception is 5/4. So if 12TET is very close to 5-limit JI, this scale starts even closer. The last three are further away, of course. All steps but the last are within 16 cents of 12TET. Only one other is more than 12 cents out.

Graham

djtrancendance@... wrote:
> As a foreword, now I realize you are not arguing for or against the "physics" > definition of consonance...

I am arguing against it. I've checked two physics dictionaries (Oxford and Penguin) and neither contain it. I don't think it's a valid physics term at all.

> > ---You're always talking about what "seems" to be the case.
> > I'm talking about what I've seen as at least across the board agreement at a
> > subjective level. The reason I don't say objective is that I realize saying
> > music is objective is an outright lie.
> --You're talking about what you think you see, not what really
> --is. I don't know what other people's intentions are, and I
> --don't much care, but from what you say below you clearly
> --have mine wrong.
> If you are so sure "what really is"...go ahead and justify it. Regardless > of personal intentions you have brought up all sorts of instrument acoustics > theories into a discussion I started about consonance in general and not > specific to acoustic instruments. What you said was "People here seem to constantly insist...that definitions 5 and 3 above are equivalent." How does answering your question about ratios (in a sub-thread started by Charles and Kalle) say anything about definitions of consonance? If you're sure that the things you seem to see really happen, find some examples.

> --But there is a book explaining this so it isn't a stunning
> --revelation.
> So if a book explains how instrumental overtones are aligned (the harmonic > series) the simple fact an explanation exists makes it "law"?

No, but it means it's not something we're going to get excited about.

> ...talking about can irrational scales be an alternative to JI

This line has nothing to do with the quotes that followed it. Why did you put it there?

> --You are following JI math.
> True enough (in my modified version of the PHI tuning). :-) > Again, my point is the irrational tuning and one nearest rational > approximation are very very alike...thus proving that PHI is by no means > "anti-consonance" even in the pure harmonic series "physics" sense. Phi is as far from a rational number as you can get.

> --Another fact is that there are so many reasons we could be
> --wrong (see also Carl's link for cognitive biases) that some
> --of us don't push our own opinions too heavily.
> Right, but at the same time I don't see a point in not at least trying to > solve something until an obvious loophole is revealed. :-) Call me a crazy > optimist, but I'm just trying to be "wreck-lessly productive"...

That's not a "but" it's the reason you should keep trying.

> --Hence we tend to give factual answers that you choose to interpret as
> --accusations.
> I don't believe that JI = the only way to produce decent consonance is a > factual statement. Again...Sethares' use of 10TET with "warped" timbres is a > counter example that you can actually sit down and listen to. I've shown some > of my friends it and about 70% say it sounds good 30% say it's "just out of tune > not good"...but it's close enough to really make you wonder if you get my drift.

Do you expect us to get excited about it?

> --opinions you could assume they're based on listening.
> Most of the opinions I've gotten here are on the level of "it's not JI, learn > JI...I haven't listened but I can tell by the lack of ratios you are barking up > the wrong tree" rather than something I can actually use like "try 21/13 as a JI > approximation of PHI" (which is a tip I took, obviously).

What happened to the "seems"? These may be things that seemed to you to happen but they aren't things that really did happen.

> ---JI is about music, not physics.
> Too subjective to argue either way IMVHO. I'll stick to that JI is about > music, but it IS NOT the definition of music...meaning something not made in JI > can still just as competently qualify as music.

Well, of course JI isn't the definition of music. What kind of nonsense is that?

> --There's a famous experiment showing that one group of
> --listeners preferred pure intervals and the other didn't,
> --fairly consistently. I don't have a reference to hand. But
> --a lot depends on context. Not liking 5-limit JI is similar
> --to not liking jazz.
> Exactly...going back to the idea that music is subjective and "very likely" is > about the best level of "factuality" you can get in music, even with bluntly > executed tuning math. Again...it seems obvious there is no one tuning which has > a "monopoly"...thus leaving room for the idea that tunings that don't follow > that one model (IE irrationally generated tunings) may also work either as well > or nearly as well (and perhaps provide some new artistic/emotional freedom on > the side). :-)

My point, which may not have been clear, is that there are so many different styles that are called "jazz" that it's almost impossible for the same person to dislike them all. But still you hear people with apparently normal hearing say "I don't like jazz". There are also so many ways of making music with 5-limit JI, depending on the definition, that everybody must like at least one of them. But you insist that you know people who don't. Maybe they don't like music at all.

Graham

--have you heard John Chowning's composition Stria (1977)? It also uses
--a 9-tone division of Phi but he uses an equal division instead. The
--sounds used are FM tones where the M:C-ratio is Phi which produces
--quite smooth sounds and they make the Phi-interval sound like a
--pseudo-octave.
    Sounds quite interesting: it really does sound like John went very much along the same path as I did IE using PHI as a pseudo-octave instead of simply "going diatonic".  I definitely want to check it out.  Do you happen to have a link to a midi/mp3 file handy?

--- On Sat, 3/28/09, Kalle Aho <kalleaho@...> wrote:

From: Kalle Aho <kalleaho@...nki.fi>
Subject: [tuning] Re: Rational vs Irrational Scales: a response to Rick
To: tuning@yahoogroups.com
Date: Saturday, March 28, 2009, 3:46 AM

--- In tuning@yahoogroups. com, djtrancendance@ ... wrote:

>My point in such a scale is that irrational generators can form

patterns that have CLOSE ties with harmonic-series- type intervals

many of which are NOT near diatonic intervals... and yet still sound

very consonant.  Again, here's the my PHI scale converted to very

nearby JI ratios (again, just a few cents away at most from tones in

the PHI tuning):

> 1

> 17/16

> 9/8

> 19/16

> 5/4

> 4/3

> 7/5

> 28/19

> 14/9

> 21/13  (1.6153846) apx 1.618033

Michael,

have you heard John Chowning's composition Stria (1977)? It also uses

a 9-tone division of Phi but he uses an equal division instead. The

sounds used are FM tones where the M:C-ratio is Phi which produces

quite smooth sounds and they make the Phi-interval sound like a

pseudo-octave.

Kalle Aho

I take it this is the same Chowning that help invent or at least desribe FM synthesis? If so I had no idea he composed
Sent via BlackBerry from T-Mobile

-----Original Message-----
From: Michael Sheiman <djtrancendance@yahoo.com>

Date: Sat, 28 Mar 2009 09:14:36
To: <tuning@yahoogroups.com>
Subject: Re: [tuning] Re: Rational vs Irrational Scales: a response to Rick

--have you heard John Chowning's composition Stria (1977)? It also uses
--a 9-tone division of Phi but he uses an equal division instead. The
--sounds used are FM tones where the M:C-ratio is Phi which produces
--quite smooth sounds and they make the Phi-interval sound like a
--pseudo-octave.
    Sounds quite interesting: it really does sound like John went very much along the same path as I did IE using PHI as a pseudo-octave instead of simply "going diatonic".  I definitely want to check it out.  Do you happen to have a link to a midi/mp3 file handy?

--- On Sat, 3/28/09, Kalle Aho <kalleaho@mappi.helsinki.fi> wrote:

From: Kalle Aho <kalleaho@mappi.helsinki.fi>
Subject: [tuning] Re: Rational vs Irrational Scales: a response to Rick
To: tuning@yahoogroups.com
Date: Saturday, March 28, 2009, 3:46 AM

--- In tuning@yahoogroups. com, djtrancendance@ ... wrote:

>My point in such a scale is that irrational generators can form

patterns that have CLOSE ties with harmonic-series- type intervals

many of which are NOT near diatonic intervals... and yet still sound

very consonant.  Again, here's the my PHI scale converted to very

nearby JI ratios (again, just a few cents away at most from tones in

the PHI tuning):

> 1

> 17/16

> 9/8

> 19/16

> 5/4

> 4/3

> 7/5

> 28/19

> 14/9

> 21/13  (1.6153846) apx 1.618033

Michael,

have you heard John Chowning's composition Stria (1977)? It also uses

a 9-tone division of Phi but he uses an equal division instead. The

sounds used are FM tones where the M:C-ratio is Phi which produces

quite smooth sounds and they make the Phi-interval sound like a

pseudo-octave.

Kalle Aho

--Now I have to find out what an Oldsmobile is, to give an
--informed answer. Wikipedia tells me it's an old brand (or
--"marque") of car. I don't know what special features they
--have to fit your analogy ... so I'm none the wiser.
    Hehe...well it was partly a joke.  :-)  The idea is making scales that are almost indistinguishably close to being "perfectly diatonic" so far as the intervals they use may add extra consonance but, in the greater scheme of things, really function like part of something very very old.  I used the Oldsmobile as an example as it is a brand that went out of production (unlike most car brands, which never have) IE has a very old basis...and the example of "waxing" is a metaphor for trying to make it look new even though, functionally, for the most part
it's still just an old car. 
----------------------------------------------------------------------------------
--LucyTuning can, at least, be substantially different to
--12TET. It depends on how you use it. With enough notes it
--can suit any other scale you like.
  Interesting...I wonder why most of the examples I've found on LucyTune.com have been oriented toward diatonic modes (and am interested in where I can find Lucy-tuned non-diatonic scale.

--Imitating JI is the obvious way of getting harmony to work.
--It's where you've ended up. Do you have any other ideas?
  Considering everything I got via JI is within a few cents of what I got from the "circle of PHI" tuning...I'm pretty sure it is the other way around IE JI is estimating PHI (in the same way 12TET estimates 5-limit JI)...and not the other way around.  The fact the "pseudo-octave" of the resulting scale is PHI and not the standard
"ultimate" JI ratio 2/1 seems to point to this as well.  But, between which one you like better (the PHI or very close JI version)...it all comes down to taste.  I've had some people say the PHI version sounds better and others the JI "estimated PHI" version...it seems to present similar results to the fact some people like 12TET better than 5-limit JI and vice-versa.

--So what 9-tone MOS scales are you talking about? You keep
--mentioning them but no details. Erv Wilson has done a lot
--of work with just intonation. I'd put him squarely in A).
    The 9-tone ones based on the Golden Horagram.   Technically, yes, they do use JI-style low numbered integer ratios, but there's nothing I could find diatonic (IE imitating perfect 3rds, 2nds...) about them.   They are likely about as much JI as, say, my "JI estimated" PHI scale is..maybe a bit more since they still stick with the 2/1
octave.

> The flip side is, based on your last somewhat charged response to me, even if

> he was "in his world"...is your view on JI superiority really any less

> "uselessly proud" (I kind of doubt it)?! :-(

--Well, I hope not, of course.
   I'll say this much...I think JI will likely "intersect" a lot of tuning innovations.  It intersects with Sethares work (assuming a non-modified timbre Sethares' own dyadic consonance algorithm can derive JI) and in a way intersects with mine (my PHI scale, again, can be estimated quite well by JI).  Even if JI was somehow explainable as a basis for generating (rather than estimating) my PHI scale would it really help to form a blindly golden rule "everything therefore must be based on JI"? 
**********************************************************************************************
    As a counter example, try mathematically explaining why, for example, my PHI gets a whole bunch of small intervals between any two notes in it using only the basic harmonic series to explain why the ratios go in the order they do. 
   It's very tricky to derive a
pattern: for example, the "limit" of my scale is actually quite high (around 19 or so)...so you'd think consonance would go to hell by your average JI-theory.   But it doesn't, at least not half as much as you'd think (compare it to 11-limit JI and you'll quite likely see what I mean).  Why this odd exception?  I'm quite sure the answer can be found in the relationship between beating and the use of PHI as a generator rather than in JI...

**********************************************************************************************
--Bill Sethares has, as we know, done work with alternative
--timbres.
    Right, as in that's how he "gets around" JI...changing the timbre allows him to also change the scale to match it (IE so the overtones of each instrument match well with both each other and the scale...on the average...but in different ways than they do when using the harmonic series as the timbre).
--That may or may not count as JI depending on your

--definition.
   IMVHO, it is JI like in that the overtones and timbres are designed to match each other in a similar fashion to JI.  But, still, he manages to trick often not-so-whole and/or non-diatonic number ratios into sounding consonant.  True, he "cheats" by using timbre and uses harmonic/overtone matching just like JI does and doesn't, say, experiment much with warping periodicity or finding special combination of non-excessive beating that sound good...but, still, his work represents a different form of organization...even if to some people it comes across as a "different way to organize JI".

--It's worth pointing out that he wasn't the
--first to do this as he sometimes gets more credit than he
--deserves -- which is still considerable.
   I'd be interested to know who did this before him (minus ancient cultural scales built to match timbres of certain in-harmonic instruments...with the
scales found solely by ear IE Pelog scales).  I know his scales were based on P&L's consonance curves...but I have no clue who preceded him before that.

-Michael

--How are you defining "5-limit JI"? As an odd limit, the
--nearest neighbor is 6/5. About 115 cents away. As a prime
--limit, the nearest neighbor of anything is 0 cents away so
--that isn't very interesting.
  I'm comparing 5-limit JI (starting at C) to the major scale starting at C.  As I recall from a previous discussion the maximum difference was about 13 cents off for the 3rd.

--You snipped the relevant part, which was "I think that's the
--one thing we may have in common is that timbre." What did
--you mean by it? What timbre are you using?
   I'm using the harmonic series as the timbre (rather than phi^x)...but not trying to match the partials but rather make them "beat in a predictable and listenable fashion".

--His is about 3 cents wider. So it's the
tunings that are
--slightly different.
  Sounds like a very slight side-effect of his tempering (as you were saying he tempered his tuning before).

--How do you get 4/3? The simplest match I can find within 5
--cents is -10 2:1 generators. And 5/4??? That could be -33
--generators. What, in fact, is this "PHI tuning"?
   PHI^x/2^y  For example, so (PHI^12)/(2^8) = 1.2578 (not too far from 1.25 IE 5/4). 
   I some cases, it hits some very low limit JI intervals dead-on...in others it "wonders off onto a different course". 

--I note that 4 of your first 5 notes are within 5 cents of
--12TET.
  I noticed that as well...the beginning (IE the 2nd, 3rd, and sus4) are a lot alike and almost exactly the same.  Though, at least I noticed, many of the other notes are 8+ cents off, thus often pushing them into being interpreted as different tones so far as the brain
is concerned (huygens tritone, 17th harmonic, 19th harmonic, septimal minor 6th, and then there's that odd 28/19 ratio and 21/13 (IE those mysterious "last few ratios") you mentioned).

--The last three are further away, of course. All steps but the last are
--within 16 cents of 12TET. Only one other is more than 12
--cents out.
   Interesting...it seems you're right they are more commonalities than I realize, at least within the first "pseudo octave" of the PHI scale.

  Although, just for grins...try extending my scale into more octaves IE past 1.618 and up to 1.618 and THEN compare it to 12TET going up to about 1.618^2.  It may be that the scale simply skews itself relative to 12TET as it moves to higher harmonics...remember we are using apx. 1.618 as the octave and not 2/1...I think it's pretty safe to assume that will cause an increasingly significant difference in how the ratios play out at higher
octaves.

-Michael

--- On Sat, 3/28/09, Graham Breed <gbreed@...> wrote:

From: Graham Breed <gbreed@...>
Subject: Re: [tuning] Re: Rational vs Irrational Scales: a response to Rick
To: tuning@yahoogroups.com
Date: Saturday, March 28, 2009, 6:30 AM

djtrancendance@ yahoo.com wrote:

> --12TET isn't a very (let alone VERY) close approximation to

> --the harmonic series. Get real.

> Neither is JI. It certainly doesn't put the intervals in nearly the same

> order of the harmonic series IE 2/1,3/2,4/3, 5/4.... However, a major second in

> 12TET, for example, is pretty close to it's nearest neighbor in 5-limit

> JI...that's what I was referring to when I said "harmonic series".

How are you defining "5-limit JI"? As an odd limit, the

nearest neighbor is 6/5. About 115 cents away. As a prime

limit, the nearest neighbor of anything is 0 cents away so

that isn't very interesting.

As a sensible extension of the odd limit, you'll get a 9/8,

which is pretty close. But this is extended 3-limit, which

12TET generally does better than the 5-limit. It is still

very efficient at approximating the 5-limit but not so close

as that in absolute terms. You're likely to use a 25:24 in

extended 5-limit JI. That's about 30 cents out in 12TET, or

30% of a scale step. If that's very close there can't be

anything (with enough notes, at least) that's very far away.

> --I'm not interested in your delusions.

> The only things I referred to were that people like Sethares did things far

> from JI and managed to sound consonant. And I'm not the only one who also

> thinks that...so, no, it's not a delusion: you can have a consonant scale that

> is not diatonic.

No, that isn't all. You also said "... I don't seem to

qualify to you as making 'alternative tunings'...it appears

you ... have a preconceived notion that scales MUST meet the

definition of harmonic series periodicity ... to be

relevant." This is delusional and I have no more to say

about it.

>

> > the PHI^x/2^y construct I use in my own tuning. So, I'm pretty sure our tunings

> > are alike, if not the same.

> ---You use the same timbre? You didn't mention the timbre before.

> I don't use that to generate the timbre...I use it to generate the tuning

> itself.

You snipped the relevant part, which was "I think that's the

one thing we may have in common is that timbre." What did

you mean by it? What timbre are you using?

>

> ---Yes, they look the same, give or take some temperament.

> The tunings do, I believe that much. But my scales are different... his 9-tone

> scale is much wider (IE takes up much more vast of a frequency range for 9 notes).

His is about 3 cents wider. So it's the tunings that are

slightly different.

> > BTW, as we've discussed, I am taking a good few of your suggestions

> > seriously and have been working with the idea of making a tempered scale that

> > complies relatively well with BOTH JI and PHI and could be used easily on

> > acoustic instruments. So stay tuned for that... :-)

> --That's good, but there are lots of precedents out there for

> --JI scales.

> Precedents such as?

There's the one I found in Huainanzi. Or the various ones

Ptolemy listed. Or Al Farabi's. Plenty of more recent

examples as well.

> My point in such a scale is that irrational generators can form patterns that

> have CLOSE ties with harmonic-series- type intervals many of which are NOT near

> diatonic intervals... and yet still sound very consonant. Again, here's the my

> PHI scale converted to very nearby JI ratios (again, just a few cents away at

> most from tones in the PHI tuning):

> 1

> 17/16

> 9/8

> 19/16

> 5/4

> 4/3

> 7/5

> 28/19

> 14/9

> 21/13 (1.6153846) apx 1.618033

>

> I dare you to find a duplicate of that scale: without PHI leading me past

> the basic interval areas above I likely would have never found this pattern. :-)

How do you get 4/3? The simplest match I can find within 5

cents is -10 2:1 generators. And 5/4??? That could be -33

generators. What, in fact, is this "PHI tuning"?

I note that 4 of your first 5 notes are within 5 cents of

12TET. The exception is 5/4. So if 12TET is very close to

5-limit JI, this scale starts even closer. The last three

are further away, of course. All steps but the last are

within 16 cents of 12TET. Only one other is more than 12

cents out.

Graham

--How does answering your question about ratios (in a
--sub-thread started by Charles and Kalle) say anything about
--definitions of consonance?
  It says that there is more than one way to achieve it IE it's not limited to using both
A) the harmonic series as the timbre
B) JI as the matching scale
  Again, Sethares breaks this as does things like using warped/non-harmonic-series timbres and, say, 10TET(non-JI) as the scale and yet achieves a good deal of the sense of "relaxation" as stated in the definition of consonance.

> ...talking about can irrational scales be an alternative to JI

--This line has nothing to do with the quotes that followed
--it. Why did you put it there?
   It has everything to with this argument. :-D  My point is (mentioned here for about the 20th time) that consonance can exist beyond the restrictions of both A) and B) mentioned above.

>I've shown some

> of my friends it and about 70% say it sounds good 30% say it's "just out of tune

> not good"...but it's close enough to really make you wonder if you get my drift.

---Do you expect us to get excited about it?
   Not really..."take it seriously enough to take some time to help me develop it and not just debate it" is more in-line with my goal here.  :-)

   Which is mostly why I get frustrated when someone tries to simply dismiss my scales as something tied to history and says "just study the history" and drops it OR just says "it's too weird/unlike history to work". 

--My point, which may not have been clear, is that there are
--so many different styles that are called "jazz" that it's
--almost impossible for the same person to dislike them all.
--But still you hear people with apparently normal hearing say
--"I don't like jazz". There are also so many ways of making
--music with 5-limit JI, depending on the definition, that
--everybody must like at least one of them. But you insist
--that you know people who don't. Maybe they don't like music
--at
all.
  They DO like music immensely. But if I just, say, play the 5-limit JI scale note by note vs. my own vs. 12TET I often don't get across the board reactions saying "out of the 3 this one is easily the best".  Meanwhile scales in systems like 19TET, to their ears, or even Wilson's MOS scales (the ones over 6-notes) continuously sounded worse according to their ears (BTW, I didn't tell them which scale I was playing...it was a blind test).

   It's not that they dislike music...and I have many friends who love music made in scale systems they hate, for example (IE my own song Melancholy in Yellow (19TET 8 tone scales) which got a 2.5 star rating even though Carl here and few of my friends in Texas thought it was very very good and asked me to leave it on repeat in my car (I didn't tell them I made it))...but that there are both certain scale systems that do vs. don't work for them and, at the same time, nothing shows a
huge preference for either JI or 12TET across the board IE it definitely seems worth exploring other options.

-Michael

--- On Sat, 3/28/09, Graham Breed <gbreed@...> wrote:

From: Graham Breed <gbreed@...>
Subject: Re: [tuning] Re: Rational vs Irrational Scales: a response to Rick
To: tuning@yahoogroups.com
Date: Saturday, March 28, 2009, 7:00 AM

djtrancendance@ yahoo.com wrote:

> As a foreword, now I realize you are not arguing for or against the "physics"

> definition of consonance.. .

I am arguing against it. I've checked two physics

dictionaries (Oxford and Penguin) and neither contain it. I

don't think it's a valid physics term at all.

> > ---You're always talking about what "seems" to be the case.

> > I'm talking about what I've seen as at least across the board agreement at a

> > subjective level. The reason I don't say objective is that I realize saying

> > music is objective is an outright lie.

> --You're talking about what you think you see, not what really

> --is. I don't know what other people's intentions are, and I

> --don't much care, but from what you say below you clearly

> --have mine wrong.

> If you are so sure "what really is"...go ahead and justify it. Regardless

> of personal intentions you have brought up all sorts of instrument acoustics

> theories into a discussion I started about consonance in general and not

> specific to acoustic instruments.

What you said was "People here seem to constantly

insist...that definitions 5 and 3 above are equivalent."

How does answering your question about ratios (in a

sub-thread started by Charles and Kalle) say anything about

definitions of consonance? If you're sure that the things

you seem to see really happen, find some examples.

> --But there is a book explaining this so it isn't a stunning

> --revelation.

> So if a book explains how instrumental overtones are aligned (the harmonic

> series) the simple fact an explanation exists makes it "law"?

No, but it means it's not something we're going to get

excited about.

> ...talking about can irrational scales be an alternative to JI

This line has nothing to do with the quotes that followed

it. Why did you put it there?

> --You are following JI math.

> True enough (in my modified version of the PHI tuning). :-)

> Again, my point is the irrational tuning and one nearest rational

> approximation are very very alike...thus proving that PHI is by no means

> "anti-consonance" even in the pure harmonic series "physics" sense.

Phi is as far from a rational number as you can get.

> --Another fact is that there are so many reasons we could be

> --wrong (see also Carl's link for cognitive biases) that some

> --of us don't push our own opinions too heavily.

> Right, but at the same time I don't see a point in not at least trying to

> solve something until an obvious loophole is revealed. :-) Call me a crazy

> optimist, but I'm just trying to be "wreck-lessly productive". ..

That's not a "but" it's the reason you should keep trying.

> --Hence we tend to give factual answers that you choose to interpret as

> --accusations.

> I don't believe that JI = the only way to produce decent consonance is a

> factual statement. Again...Sethares' use of 10TET with "warped" timbres is a

> counter example that you can actually sit down and listen to. I've shown some

> of my friends it and about 70% say it sounds good 30% say it's "just out of tune

> not good"...but it's close enough to really make you wonder if you get my drift.

Do you expect us to get excited about it?

> --opinions you could assume they're based on listening.

> Most of the opinions I've gotten here are on the level of "it's not JI, learn

> JI...I haven't listened but I can tell by the lack of ratios you are barking up

> the wrong tree" rather than something I can actually use like "try 21/13 as a JI

> approximation of PHI" (which is a tip I took, obviously).

What happened to the "seems"? These may be things that

seemed to you to happen but they aren't things that really

did happen.

> ---JI is about music, not physics.

> Too subjective to argue either way IMVHO. I'll stick to that JI is about

> music, but it IS NOT the definition of music...meaning something not made in JI

> can still just as competently qualify as music.

Well, of course JI isn't the definition of music. What kind

of nonsense is that?

> --There's a famous experiment showing that one group of

> --listeners preferred pure intervals and the other didn't,

> --fairly consistently. I don't have a reference to hand. But

> --a lot depends on context. Not liking 5-limit JI is similar

> --to not liking jazz.

> Exactly...going back to the idea that music is subjective and "very likely" is

> about the best level of "factuality" you can get in music, even with bluntly

> executed tuning math. Again...it seems obvious there is no one tuning which has

> a "monopoly".. .thus leaving room for the idea that tunings that don't follow

> that one model (IE irrationally generated tunings) may also work either as well

> or nearly as well (and perhaps provide some new artistic/emotional freedom on

> the side). :-)

My point, which may not have been clear, is that there are

so many different styles that are called "jazz" that it's

almost impossible for the same person to dislike them all.

But still you hear people with apparently normal hearing say

"I don't like jazz". There are also so many ways of making

music with 5-limit JI, depending on the definition, that

everybody must like at least one of them. But you insist

that you know people who don't. Maybe they don't like music

at all.

Graham

djtrancendance@... wrote:
> --How are you defining "5-limit JI"? As an odd limit, the
> --nearest neighbor is 6/5. About 115 cents away. As a prime
> --limit, the nearest neighbor of anything is 0 cents away so
> --that isn't very interesting.
> I'm comparing 5-limit JI (starting at C) to the major scale starting at C. As > I recall from a previous discussion the maximum difference was about 13 cents > off for the 3rd.

Comparing the roots? Then the maximum difference is over 15 cents for the sixth, assuming it approximates 5/3. We've moved from 12TET being a very close approximation to the harmonic series to the diatonic scale in 12TET being a vague approximation to 5-limit JI. I don't remember what that was intended to prove.

> --You snipped the relevant part, which was "I think that's the
> --one thing we may have in common is that timbre." What did
> --you mean by it? What timbre are you using?
> I'm using the harmonic series as the timbre (rather than phi^x)...but not > trying to match the partials but rather make them "beat in a predictable and > listenable fashion".

If you care about beats with harmonic timbres, try looking at the Mt Meru tunings. They follow from the horagrams you say you like. If you aren't using inharmonic timbres, stop talking about Sethares.

> --His is about 3 cents wider. So it's the tunings that are
> --slightly different.
> Sounds like a very slight side-effect of his tempering (as you were saying he > tempered his tuning before).

No, it's because he uses phi but you use a rational approximation.

> --How do you get 4/3? The simplest match I can find within 5
> --cents is -10 2:1 generators. And 5/4??? That could be -33
> --generators. What, in fact, is this "PHI tuning"?
> PHI^x/2^y For example, so (PHI^12)/(2^8) = 1.2578 (not too far from 1.25 IE > 5/4). > I some cases, it hits some very low limit JI intervals dead-on...in others it > "wonders off onto a different course". 1.2578 is over 10 cents from 1.25. That's not "a few cents away at most" as you claimed. Now, how about that 7/5?

Of course, if "the phi scale" is the infinite set generated by octaves modulo phi you can get any JI interval dead-on.

> --I note that 4 of your first 5 notes are within 5 cents of
> --12TET.
> I noticed that as well...the beginning (IE the 2nd, 3rd, and sus4) are a lot > alike and almost exactly the same. Though, at least I noticed, many of the > other notes are 8+ cents off, thus often pushing them into being interpreted as > different tones so far as the brain is concerned (huygens tritone, 17th > harmonic, 19th harmonic, septimal minor 6th, and then there's that odd 28/19 > ratio and 21/13 (IE those mysterious "last few ratios") you mentioned).
> > --The last three are further away, of course. All steps but the last are
> --within 16 cents of 12TET. Only one other is more than 12
> --cents out.
> Interesting...it seems you're right they are more commonalities than I > realize, at least within the first "pseudo octave" of the PHI scale.

If you're comparing to 12-equal, and checking with people who are used to 12-equal, it's hardly surprising you end up with the best fit to 12-equal that's possible within your constraints.

> Although, just for grins...try extending my scale into more octaves IE past > 1.618 and up to 1.618 and THEN compare it to 12TET going up to about 1.618^2. > It may be that the scale simply skews itself relative to 12TET as it moves to > higher harmonics...remember we are using apx. 1.618 as the octave and not > 2/1...I think it's pretty safe to assume that will cause an increasingly > significant difference in how the ratios play out at higher octaves.

The steps sizes will be the same whatever register you look at. Melodies will sound like 12TET, with a few steps wrong. Only two steps are outside the tolerance range for the rationals matching phi ratios, or the 12TET diatonic being "very close" to 5-limit JI. This is as close as you can get to 12TET and keep the equivalence interval near to phi.

Graham

djtrancendance@... wrote:
> Hehe...well it was partly a joke. :-) The idea is making scales that are > almost indistinguishably close to being "perfectly diatonic" so far as the > intervals they use may add extra consonance but, in the greater scheme of > things, really function like part of something very very old. I used the > Oldsmobile as an example as it is a brand that went out of production (unlike > most car brands, which never have) IE has a very old basis...and the example of > "waxing" is a metaphor for trying to make it look new even though, functionally, > for the most part it's still just an old car. Like most car analogies it falls apart very quickly. Cars are supposed to move and keep the rain off, but all scales do is list pitches. Two scales with different pitches are completely different but two cars that look different may be, in a sense, the same. LucyTuning is much older than any Oldsmobile.

> --LucyTuning can, at least, be substantially different to
> --12TET. It depends on how you use it. With enough notes it
> --can suit any other scale you like.
> Interesting...I wonder why most of the examples I've found on LucyTune.com > have been oriented toward diatonic modes (and am interested in where I can find > Lucy-tuned non-diatonic scale.

Why not tune it up yourself if you're so interested?

> --Imitating JI is the obvious way of getting harmony to work.
> --It's where you've ended up. Do you have any other ideas?
> Considering everything I got via JI is within a few cents of what I got from > the "circle of PHI" tuning...I'm pretty sure it is the other way around IE JI is > estimating PHI (in the same way 12TET estimates 5-limit JI)...and not the other > way around. The fact the "pseudo-octave" of the resulting scale is PHI and not > the standard "ultimate" JI ratio 2/1 seems to point to this as well. But, > between which one you like better (the PHI or very close JI version)...it all > comes down to taste. I've had some people say the PHI version sounds better and > others the JI "estimated PHI" version...it seems to present similar results to > the fact some people like 12TET better than 5-limit JI and vice-versa.

How do you tell which way round the approximation is?

> --So what 9-tone MOS scales are you talking about? You keep
> --mentioning them but no details. Erv Wilson has done a lot
> --of work with just intonation. I'd put him squarely in A).
> The 9-tone ones based on the Golden Horagram. Technically, yes, they do > use JI-style low numbered integer ratios, but there's nothing I could find > diatonic (IE imitating perfect 3rds, 2nds...) about them. They are likely > about as much JI as, say, my "JI estimated" PHI scale is..maybe a bit more since > they still stick with the 2/1 octave.

Golden Horagrams, right. Now which ones? They use integer ratios? Then they're not MOS scales. But they must be JI, depending on your definition.

> I'll say this much...I think JI will likely "intersect" a lot of tuning > innovations. It intersects with Sethares work (assuming a non-modified timbre > Sethares' own dyadic consonance algorithm can derive JI) and in a way intersects > with mine (my PHI scale, again, can be estimated quite well by JI). Even if JI > was somehow explainable as a basis for generating (rather than estimating) my > PHI scale would it really help to form a blindly golden rule "everything > therefore must be based on JI"? Of course not.

> As a counter example, try mathematically explaining why, for example, my PHI > gets a whole bunch of small intervals between any two notes in it using only the > basic harmonic series to explain why the ratios go in the order they do. > It's very tricky to derive a pattern: for example, the "limit" of my scale is > actually quite high (around 19 or so)...so you'd think consonance would go to > hell by your average JI-theory. But it doesn't, at least not half as much as > you'd think (compare it to 11-limit JI and you'll quite likely see what I > mean). Why this odd exception? I'm quite sure the answer can be found in the > relationship between beating and the use of PHI as a generator rather than in JI...

Try writing out the scale tree (Farey or Stern-Brocot tree) to cover the intervals within your limit. Then write out all the pitches from your phi scale that are simple enough to consider. Try to find a correlation between the two. Then try again for any randomly chosen generator.

> --That may or may not count as JI depending on your
> --definition.
> IMVHO, it is JI like in that the overtones and timbres are designed to match > each other in a similar fashion to JI. But, still, he manages to trick often > not-so-whole and/or non-diatonic number ratios into sounding consonant. True, > he "cheats" by using timbre and uses harmonic/overtone matching just like JI > does and doesn't, say, experiment much with warping periodicity or finding > special combination of non-excessive beating that sound good...but, still, his > work represents a different form of organization...even if to some people it > comes across as a "different way to organize JI".

What is your definition?

> --It's worth pointing out that he wasn't the
> --first to do this as he sometimes gets more credit than he
> --deserves -- which is still considerable.
> I'd be interested to know who did this before him (minus ancient cultural > scales built to match timbres of certain in-harmonic instruments...with the > scales found solely by ear IE Pelog scales). I know his scales were based on > P&L's consonance curves...but I have no clue who preceded him before that.

Amazingly, you still don't have a clue about O'Connell or Chowning then. You could also try reading the book Bill Sethares wrote about tunings, timbres, spectrums, and scales, whatever that was called. In particular, section 6.4 "Past Explorations".

Graham

--Two scales with different pitches are
--completely different but two cars that look different may
--be, in a sense, the same.
    That wasn't my point, my point was that changing a tiny piece of something (IE the look of a car or intervals between notes by very few cents in a scale) is not going to change the function.  Waxing an Oldsmobile is not going to make it perform or be as reliable as a new Honda, for example...even if it improves its re-sale value a bit. :-)   And, yes, I am stubborn and think cars are worth more than getting from point a to b.  And old car can do that...with thousands of dollars worth in repairs, loads of family/job time spent getting it fixed, great loss in resale value...to an extent it can turn in to more lost value than it's worth. 
 
Not to say slightly modifying old scales has the same problem...but to say I think it would be really nice if someone stood up and said "let's start from scratch and build something new and, only as we enter the latter stages of developing it, worry about linking it to some of the older features we like (IE rounding my scale to closest rational equivalents). :-)

---Why not tune it up yourself if you're so interested?
   I haven't found any scala files based on LucyTuning that are not unabashedly diatonic.  Do you do have any?...I'll gladly try them.

--Golden Horagrams, right. Now which ones? They use integer
--ratios? Then they're not MOS scales. But they must be JI,
--depending on your definition.
  As I recall MOS means they use two distinct size interval gaps.  I wish the page hadn't been taken down but I recall the ones I mentioned (particularly the 6-tone ones) had been mentioned by Carl
Lumma as MOS.  Furthermore, Marcus Satellite (one of my favorite micro-tonal artists) confirmed to me the Wilson scales he used were MOS.  Carl...can you back me up on this?
   But, yes, you're right...in the sense that they use whole number ratios they are JI.  But the way they are generated, as I understand, is far from the way JI is generated.  Kind of like the way my scale approaches on many JI ratios (despite only using PHI^(1 to 15) and not the infinite set of PHI^(0-infinity)), but is not JI generated.

***********************************************************************************************
> It's very tricky to derive a pattern: for example, the "limit" of my scale is

> actually quite high (around 19 or so)...so you'd think consonance would go to

> hell by your average JI-theory. But it doesn't, at least not half as much as

> you'd think (compare it to 11-limit JI and you'll quite likely see what I

> mean). Why this odd exception? I'm quite sure the answer can be found in the

> relationship between beating and the use of PHI as a generator rather than in JI...

--Try writing out the scale tree (Farey or Stern-Brocot tree)
--to cover the intervals within your limit. Then write out
--all the pitches from your phi scale that are simple enough
--to consider. Try to find a correlation between the two.
--Then try again for any randomly chosen generator.

Will do...

>>>What is your definition?
    I don't have an exact definition, but, rather, a continuum between JI and "any ratio reduceable to a fraction".  Since JI is related to the harmonic series I consider how JI a scale is to how much it resembles the series. 

   The "most" JI scale would probably be something very very otonal, like this
4/4 5/4 6/4 7/4 8/4
--
  Meanwhile, something o-tonal and a bit u-tonal would be "second most JI" (4/3 and 7/5 being the u-tonal interval)
4/4 5/4 (4/3) (7/5) 6/4 7/4 8/4
--
  Then you get scales with
elements that are neither o-tonal nor u-tonal like
    28/19,14/9,21/3
OR 4/3,7/5         (note: these are both from my "rationally approximated PHI scale)
  Note...such low-limitation scales can cover virtually any possible interval within abotu 10 cents...so they are pretty good at matching irrationally generated scales unlike strictly o-tonal or u-tonal ones
--.

  Lastly, you get scales with most or all elements that are exclusively neither o-tonal nor u-tonal (and may or may not be very high limit) like
19/16 (1.1875)
33/23 (1.43478)
29/19 (1.5263...)
34/15 (1.7894....)
 which can be very "low numbered fraction-based"...but not at all high on JI-ness in my book.
**************************************************************
--Amazingly, you still don't have a clue about O'Connell or
--Chowning then.
Hadn't heard of either of them
until you brought them up, honestly.

--You could also try reading the book Bill
--Sethares wrote about tunings, timbres, spectrums, and

--scales, whatever that was called. In particular, section
--6.4 "Past Explorations" .
   I've read tons of Sethares' online articles, but not the book: but I believe you that O'Connell may have preceded his work and P&L's (even though I haven't been able to find articles on O'Connels work anywhere so far vs., say, someone like Partch or Wendy Carlos who has articles everywhere).  I'll see if I can find Sethares' full book...

-Michael

--- On Sat, 3/28/09, Graham Breed <gbreed@...m> wrote:

From: Graham Breed <gbreed@...>
Subject: Re: [tuning] Re: Rational vs Irrational Scales: a response to Rick
To: tuning@...m
Date: Saturday, March 28, 2009, 10:25 PM

djtrancendance@ yahoo.com wrote:

> Hehe...well it was partly a joke. :-) The idea is making scales that are

> almost indistinguishably close to being "perfectly diatonic" so far as the

> intervals they use may add extra consonance but, in the greater scheme of

> things, really function like part of something very very old. I used the

> Oldsmobile as an example as it is a brand that went out of production (unlike

> most car brands, which never have) IE has a very old basis...and the example of

> "waxing" is a metaphor for trying to make it look new even though, functionally,

> for the most part it's still just an old car.

Like most car analogies it falls apart very quickly. Cars

are supposed to move and keep the rain off, but all scales

do is list pitches. Two scales with different pitches are

completely different but two cars that look different may

be, in a sense, the same. LucyTuning is much older than any

Oldsmobile.

> --LucyTuning can, at least, be substantially different to

> --12TET. It depends on how you use it. With enough notes it

> --can suit any other scale you like.

> Interesting. ..I wonder why most of the examples I've found on LucyTune.com

> have been oriented toward diatonic modes (and am interested in where I can find

> Lucy-tuned non-diatonic scale.

Why not tune it up yourself if you're so interested?

> --Imitating JI is the obvious way of getting harmony to work.

> --It's where you've ended up. Do you have any other ideas?

> Considering everything I got via JI is within a few cents of what I got from

> the "circle of PHI" tuning...I'm pretty sure it is the other way around IE JI is

> estimating PHI (in the same way 12TET estimates 5-limit JI)...and not the other

> way around. The fact the "pseudo-octave" of the resulting scale is PHI and not

> the standard "ultimate" JI ratio 2/1 seems to point to this as well. But,

> between which one you like better (the PHI or very close JI version)...it all

> comes down to taste. I've had some people say the PHI version sounds better and

> others the JI "estimated PHI" version...it seems to present similar results to

> the fact some people like 12TET better than 5-limit JI and vice-versa.

How do you tell which way round the approximation is?

> --So what 9-tone MOS scales are you talking about? You keep

> --mentioning them but no details. Erv Wilson has done a lot

> --of work with just intonation. I'd put him squarely in A).

> The 9-tone ones based on the Golden Horagram. Technically, yes, they do

> use JI-style low numbered integer ratios, but there's nothing I could find

> diatonic (IE imitating perfect 3rds, 2nds...) about them. They are likely

> about as much JI as, say, my "JI estimated" PHI scale is..maybe a bit more since

> they still stick with the 2/1 octave.

Golden Horagrams, right. Now which ones? They use integer

ratios? Then they're not MOS scales. But they must be JI,

depending on your definition.

> I'll say this much...I think JI will likely "intersect" a lot of tuning

> innovations. It intersects with Sethares work (assuming a non-modified timbre

> Sethares' own dyadic consonance algorithm can derive JI) and in a way intersects

> with mine (my PHI scale, again, can be estimated quite well by JI). Even if JI

> was somehow explainable as a basis for generating (rather than estimating) my

> PHI scale would it really help to form a blindly golden rule "everything

> therefore must be based on JI"?

Of course not.

> As a counter example, try mathematically explaining why, for example, my PHI

> gets a whole bunch of small intervals between any two notes in it using only the

> basic harmonic series to explain why the ratios go in the order they do.

> It's very tricky to derive a pattern: for example, the "limit" of my scale is

> actually quite high (around 19 or so)...so you'd think consonance would go to

> hell by your average JI-theory. But it doesn't, at least not half as much as

> you'd think (compare it to 11-limit JI and you'll quite likely see what I

> mean). Why this odd exception? I'm quite sure the answer can be found in the

> relationship between beating and the use of PHI as a generator rather than in JI...

Try writing out the scale tree (Farey or Stern-Brocot tree)

to cover the intervals within your limit. Then write out

all the pitches from your phi scale that are simple enough

to consider. Try to find a correlation between the two.

Then try again for any randomly chosen generator.

> --That may or may not count as JI depending on your

> --definition.

> IMVHO, it is JI like in that the overtones and timbres are designed to match

> each other in a similar fashion to JI. But, still, he manages to trick often

> not-so-whole and/or non-diatonic number ratios into sounding consonant. True,

> he "cheats" by using timbre and uses harmonic/overtone matching just like JI

> does and doesn't, say, experiment much with warping periodicity or finding

> special combination of non-excessive beating that sound good...but, still, his

> work represents a different form of organization. ..even if to some people it

> comes across as a "different way to organize JI".

What is your definition?

> --It's worth pointing out that he wasn't the

> --first to do this as he sometimes gets more credit than he

> --deserves -- which is still considerable.

> I'd be interested to know who did this before him (minus ancient cultural

> scales built to match timbres of certain in-harmonic instruments. ..with the

> scales found solely by ear IE Pelog scales). I know his scales were based on

> P&L's consonance curves...but I have no clue who preceded him before that.

Amazingly, you still don't have a clue about O'Connell or

Chowning then. You could also try reading the book Bill

Sethares wrote about tunings, timbres, spectrums, and

scales, whatever that was called. In particular, section

6.4 "Past Explorations" .

Graham

Hi Michael

You can find about fifty different LucyTuned Scale files by downloading the Logic files (which are .scl format) from this url:

http://www.lucytune.com/midi_and_keyboard/pitch_bend.html

The tunings on the Scala site, as you suggest, are very limited and I cannot guarantee their accuracy.

You can generate some pretty dissonant intervals using the higher numbered Logic files (if that is your bag;-)

Enjoy!

On 29 Mar 2009, at 16:05, djtrancendance@... wrote:

>
> I haven't found any scala files based on LucyTuning that are not > unabashedly diatonic. Do you do have any?...I'll gladly try them.
>
> --.
>
>
>
Charles Lucy
lucy@...

- Promoting global harmony through LucyTuning -

for information on LucyTuning go to:
http://www.lucytune.com

For LucyTuned Lullabies go to:
http://www.lullabies.co.uk

--If you aren't using inharmonic timbres, stop
--talking about Sethares.
    Right...agreed I am not using his "warped" timbres and wasn't trying to make a point about that Sethares would contribute to my particular theory (I agree his work doesn't)...but rather the idea that the ear can perceive something other than JI as consonant (something his quest has in common with mine).

--No, it's because he uses phi but you use a rational
--approximation.
    Oh, ok...I thought you were comparing my original PHI scale to his and not my modified "rational" version.  Again, though, the rational version was created to closely estimate the irrational version...and not the other way around (it is, essentially, still an irrationally generated scale).

--Of course, if "the phi
scale" is the infinite set generated
--by octaves modulo phi you can get any JI interval dead-on.
    Right, but I'm not using that huge of a set here...I am only going up to PHI^15/2^x...and not something extreme like PHI^128/2^x.  Again I'm trying to get rational numbers to match the PHI tuning, and not the other way around.  Though admitedly, you're right, some of the PHI approximations are off as much as, say, 12TET is from JI.

--If you're comparing to 12-equal, and checking with people
--who are used to 12-equal, it's hardly surprising you end up
--with the best fit to 12-equal that's possible within your
--constraints.
    Firstly, a lot people people ranked my scale as better than 5-limit diatonic JI, which is a lot closer to 12TET than my scale cent-wise in most cases.

   Secondly, I'd hardly say my scale is 12TET, sure some of the notes are dead-on.
Look at
the differences (in cents):
My scale   
0
104.95    
203.91
297.51
386.31
498.04
582.51
671.31
764.91
830.25

12TET 
100 (off 4-5 cents)
200 (off 4 cents)
300 (off 2.5 cents)
400 (off 400-386 = !14! cents)
500 (off 2 cents)
600 (off !18! cents)
700 (off !19! cents)
800 (off !35! cents to 764 and !30! cents to 830)

   Saying something consistently off 12TET by an 8th tone or so, at least in my opinion, is a bit of a stretch.  And, you have to remember, if a quarter tone away from the nearest 12TET note (IE 750 cents, 50 cents away from 700 and 800 cents) is the maximum distance...a good 3-4 notes in my scale are approaching half way to that maximum.

--Only two steps are outside the tolerance range for the
--rationals matching phi ratios, or the 12TET diatonic being
--"very close" to 5-limit JI.
  
Looking at the above comparison, it looks more like 3 to 4 notes are significantly off from 12TET.  The only one I see as debatable is the 386 cent note, which is "only" off by 14 cents in 12TET (and I'm not exactly sure how far away from JI-diatonic).

    And you have to remember, that's 3 to 4 notes out of the ONLY 9 notes in my scale, not 12 (so it's a good 1/3rd or more of notes in my scale that are off from 12TET).  One interesting test would be to see if the notes that are off in my scale beat "pleasantly" against their nearest 12TET equivalents...

   Also, true, a lot of parts look profoundly like 5-limit JI...but there are some difference fractions in my scale like 4/3 followed by 7/5 and 14/9 followed by 21/13...which create some weird "switching" interval areas between the harmonic-series type patterns in it which look nothing like either the harmonic series or 12TET.

  I think it's
fair to say those odd areas are where I hope people will investigate "what's going on here?" psycho-acoustically...and also figure out why 1.618033 is able to work as an octave in this case (for grins, I tried stretching/forcing 12TET so it matches the 1.618 octave...and it sounds like crap). :-D.

-Michael

--- On Sat, 3/28/09, Graham Breed <gbreed@...> wrote:

From: Graham Breed <gbreed@...>
Subject: Re: [tuning] Re: Rational vs Irrational Scales: a response to Rick
To: tuning@yahoogroups.com
Date: Saturday, March 28, 2009, 9:29 PM

djtrancendance@ yahoo.com wrote:

> --How are you defining "5-limit JI"? As an odd limit, the

> --nearest neighbor is 6/5. About 115 cents away. As a prime

> --limit, the nearest neighbor of anything is 0 cents away so

> --that isn't very interesting.

> I'm comparing 5-limit JI (starting at C) to the major scale starting at C. As

> I recall from a previous discussion the maximum difference was about 13 cents

> off for the 3rd.

Comparing the roots? Then the maximum difference is over 15

cents for the sixth, assuming it approximates 5/3. We've

moved from 12TET being a very close approximation to the

harmonic series to the diatonic scale in 12TET being a vague

approximation to 5-limit JI. I don't remember what that was

intended to prove.

> --You snipped the relevant part, which was "I think that's the

> --one thing we may have in common is that timbre." What did

> --you mean by it? What timbre are you using?

> I'm using the harmonic series as the timbre (rather than phi^x)...but not

> trying to match the partials but rather make them "beat in a predictable and

> listenable fashion".

If you care about beats with harmonic timbres, try looking

at the Mt Meru tunings. They follow from the horagrams you

say you like. If you aren't using inharmonic timbres, stop

talking about Sethares.

> --His is about 3 cents wider. So it's the tunings that are

> --slightly different.

> Sounds like a very slight side-effect of his tempering (as you were saying he

> tempered his tuning before).

No, it's because he uses phi but you use a rational

approximation.

> --How do you get 4/3? The simplest match I can find within 5

> --cents is -10 2:1 generators. And 5/4??? That could be -33

> --generators. What, in fact, is this "PHI tuning"?

> PHI^x/2^y For example, so (PHI^12)/(2^ 8) = 1.2578 (not too far from 1.25 IE

> 5/4).

> I some cases, it hits some very low limit JI intervals dead-on...in others it

> "wonders off onto a different course".

1.2578 is over 10 cents from 1.25. That's not "a few cents

away at most" as you claimed. Now, how about that 7/5?

Of course, if "the phi scale" is the infinite set generated

by octaves modulo phi you can get any JI interval dead-on.

> --I note that 4 of your first 5 notes are within 5 cents of

> --12TET.

> I noticed that as well...the beginning (IE the 2nd, 3rd, and sus4) are a lot

> alike and almost exactly the same. Though, at least I noticed, many of the

> other notes are 8+ cents off, thus often pushing them into being interpreted as

> different tones so far as the brain is concerned (huygens tritone, 17th

> harmonic, 19th harmonic, septimal minor 6th, and then there's that odd 28/19

> ratio and 21/13 (IE those mysterious "last few ratios") you mentioned).

>

> --The last three are further away, of course. All steps but the last are

> --within 16 cents of 12TET. Only one other is more than 12

> --cents out.

> Interesting. ..it seems you're right they are more commonalities than I

> realize, at least within the first "pseudo octave" of the PHI scale.

If you're comparing to 12-equal, and checking with people

who are used to 12-equal, it's hardly surprising you end up

with the best fit to 12-equal that's possible within your

constraints.

> Although, just for grins...try extending my scale into more octaves IE past

> 1.618 and up to 1.618 and THEN compare it to 12TET going up to about 1.618^2.

> It may be that the scale simply skews itself relative to 12TET as it moves to

> higher harmonics... remember we are using apx. 1.618 as the octave and not

> 2/1...I think it's pretty safe to assume that will cause an increasingly

> significant difference in how the ratios play out at higher octaves.

The steps sizes will be the same whatever register you look

at. Melodies will sound like 12TET, with a few steps wrong.

Only two steps are outside the tolerance range for the

rationals matching phi ratios, or the 12TET diatonic being

"very close" to 5-limit JI. This is as close as you can get

to 12TET and keep the equivalence interval near to phi.

Graham

--- In tuning@yahoogroups.com, Michael Sheiman <djtrancendance@...> wrote
>
>   I, for one, agree that somewhat blindly accepting the octave should not be a necessity in tuning and I hope others take the leap and at least experiment with using other "octaves" (not 100% sure of the technical term for it) than 2/1.

There is a whole community quite dedicated to that:

http://nonoctave.com/

And of course there are two intervals which are intervals of equivalence/repetition since time out of mind, 4/3 and 3/2. Read John Chalmer's "Divisions of the Tetrachord" and try to find some authentic Georgian vocal music, which uses 3/2 as the "octave". I got a tape of this about 20 years ago, great stuff.

--There is a whole community quite dedicated to that:
--http://nonoctave. com/
Thanks Cameron, I had no clue that existed/exists...definitely worth a look. :-)

--of course there are two intervals which are intervals of equivalence/ repetition since time --out of mind, 4/3 and 3/2.
    Good point.  You know, even out of JI or mean-tone fanatics...you'd think a lot of such people would at least question the possibility using 3/2 as the octave...after all, diatonic theory revolves around the circle of fifths, does it not? 

--- On Mon, 3/30/09, Cameron Bobro <misterbobro@...> wrote:

From: Cameron Bobro <misterbobro@...>
Subject: [tuning] Re: Rational vs Irrational Scales: a response to Rick
To: tuning@yahoogroups.com
Date: Monday, March 30, 2009, 5:33 AM

--- In tuning@yahoogroups. com, Michael Sheiman <djtrancendance@ ...> wrote

>

>   I, for one, agree that somewhat blindly accepting the octave should not be a necessity in tuning and I hope others take the leap and at least experiment with using other "octaves" (not 100% sure of the technical term for it) than 2/1.

There is a whole community quite dedicated to that:

http://nonoctave. com/

And of course there are two intervals which are intervals of equivalence/ repetition since time out of mind, 4/3 and 3/2. Read John Chalmer's "Divisions of the Tetrachord" and try to find some authentic Georgian vocal music, which uses 3/2 as the "octave". I got a tape of this about 20 years ago, great stuff.

The answer is yes.... this is the same John Chowning

and here is a link to 30 seconds of Stria

http://www.last.fm/music/John+Chowning/_/Stria

in a way it reminds me of my piece

http://www.traxinspace.com/song/39946

spectrograph cornfields recursively which was arrived at by taking a
"normal" piece and heavily and repeatedly applying FFT noise reduction.

for what it is worth.

On Sat, Mar 28, 2009 at 12:30 PM, <chrisvaisvil@...> wrote:

> I take it this is the same Chowning that help invent or at least desribe FM
> synthesis? If so I had no idea he composed
>
> Sent via BlackBerry from T-Mobile
>
> ------------------------------
> *From*: Michael Sheiman
> *Date*: Sat, 28 Mar 2009 09:14:36 -0700 (PDT)
> *To*: <tuning@yahoogroups.com>
> *Subject*: Re: [tuning] Re: Rational vs Irrational Scales: a response to
> Rick
>
> --have you heard John Chowning's composition Stria (1977)? It also uses
> --a 9-tone division of Phi but he uses an equal division instead. The
> --sounds used are FM tones where the M:C-ratio is Phi which produces
> --quite smooth sounds and they make the Phi-interval sound like a
> --pseudo-octave.
> Sounds quite interesting: it really does sound like John went very much
> along the same path as I did IE using PHI as a pseudo-octave instead of
> simply "going diatonic". I definitely want to check it out. Do you happen
> to have a link to a midi/mp3 file handy?
>
> --- On *Sat, 3/28/09, Kalle Aho <kalleaho@...>* wrote:
>
>
> From: Kalle Aho <kalleaho@...>
> Subject: [tuning] Re: Rational vs Irrational Scales: a response to Rick
> To: tuning@yahoogroups.com
> Date: Saturday, March 28, 2009, 3:46 AM
>
> --- In tuning@yahoogroups. com<http://mc/compose?to=tuning%40yahoogroups.com>,
> djtrancendance@ ... wrote:
>
> >My point in such a scale is that irrational generators can form
> patterns that have CLOSE ties with harmonic-series- type intervals
> many of which are NOT near diatonic intervals... and yet still sound
> very consonant. Again, here's the my PHI scale converted to very
> nearby JI ratios (again, just a few cents away at most from tones in
> the PHI tuning):
> > 1
> > 17/16
> > 9/8
> > 19/16
> > 5/4
> > 4/3
> > 7/5
> > 28/19
> > 14/9
> > 21/13 (1.6153846) apx 1.618033
>
> Michael,
>
> have you heard John Chowning's composition Stria (1977)? It also uses
> a 9-tone division of Phi but he uses an equal division instead. The
> sounds used are FM tones where the M:C-ratio is Phi which produces
> quite smooth sounds and they make the Phi-interval sound like a
> pseudo-octave.
>
> Kalle Aho
>
>
>

djtrancendance@... wrote:

> --Golden Horagrams, right. Now which ones? They use integer
> --ratios? Then they're not MOS scales. But they must be JI,
> --depending on your definition.
> As I recall MOS means they use two distinct size interval gaps. I wish the > page hadn't been taken down but I recall the ones I mentioned (particularly the > 6-tone ones) had been mentioned by Carl Lumma as MOS. Furthermore, Marcus > Satellite (one of my favorite micro-tonal artists) confirmed to me the Wilson > scales he used were MOS. Carl...can you back me up on this?

Golden horagrams give you an MOS and a Mt Meru scale that tends towards it. I believe Marcus Satellite used MOS scales but what does that have to do with the scales you're talking about? Anyway, try reading The Scales of Mt. Meru here:

http://www.anaphoria.com/wilson.html

> But, yes, you're right...in the sense that they use whole number ratios they > are JI. But the way they are generated, as I understand, is far from the way JI > is generated. Kind of like the way my scale approaches on many JI ratios > (despite only using PHI^(1 to 15) and not the infinite set of PHI^(0-infinity)), > but is not JI generated.

If they're JI, they must be generated the way JI is generated.

> --You could also try reading the book Bill
> --Sethares wrote about tunings, timbres, spectrums, and
> --scales, whatever that was called. In particular, section
> --6.4 "Past Explorations" .
> I've read tons of Sethares' online articles, but not the book: but I believe > you that O'Connell may have preceded his work and P&L's (even though I haven't > been able to find articles on O'Connels work anywhere so far vs., say, someone > like Partch or Wendy Carlos who has articles everywhere). I'll see if I can > find Sethares' full book...

The book's on SpringerLink. You may have access to it. If you want to do anything original with consonance it's pretty much required reading.

Yes, there isn't much written about O'Connell, but what does that prove? This isn't a popularity contest. You have the original article.

Graham

--If they're JI, they must be generated the way JI is generated.

   Put it this way...they have a pattern within JI and could have been generated that way.

   But if you look at the pattern in JI it looks rather scattered and random.  Put the same pattern compared to the golden ratio tuning and it looks much more obvious.

--Yes, there isn't much written about O'Connell, but what does
--that prove?
    Nothing, I'm just having a tough time reading this and trying to construe it in a way that matches my system.

--This isn't a popularity contest. You have the
--original article.
    I know...I'm just having a tough time reading the original article, that's why I was looking for more info: I don't really care how popular his material is.   Heck, Sethares isn't "that" popular either and I look over his stuff (at least what's published on the web already via his site) a lot.

   To me what O'Connell does simply does not look much like what I'm doing, minus his taking PHI^x to make his tuning like I am.  Taking the pattern 3,3,2,   3,3,3,2,  3,3 (his 9-tone scale) within the PHI^x/y^2 tuning I use to make my scales gives
1.05902,1.14124 (OFF),1.20859 (OFF),     
1.30902(OFF), 1.41064,1.55473, 1.61803
1.74365 (OFF), 1.92142
  So, by my calculations, out of 9 notes of the scale 4 of his are different, plus his octave in his a lot close to 2/1 than 1.61803 judging by the best I can make of his document.

--The book's on SpringerLink. You may have access to it. If
---you want to do anything original with consonance it's pretty
---much required reading.
I'll definitely look that up, thank you for the tip.

-Michael

--- On Mon, 3/30/09, Graham Breed <gbreed@...> wrote:

From: Graham Breed <gbreed@gmail.com>
Subject: Re: [tuning] Re: Rational vs Irrational Scales: a response to Rick
To: tuning@yahoogroups.com
Date: Monday, March 30, 2009, 3:53 PM

djtrancendance@ yahoo.com wrote:

> --Golden Horagrams, right. Now which ones? They use integer

> --ratios? Then they're not MOS scales. But they must be JI,

> --depending on your definition.

> As I recall MOS means they use two distinct size interval gaps. I wish the

> page hadn't been taken down but I recall the ones I mentioned (particularly the

> 6-tone ones) had been mentioned by Carl Lumma as MOS. Furthermore, Marcus

> Satellite (one of my favorite micro-tonal artists) confirmed to me the Wilson

> scales he used were MOS. Carl...can you back me up on this?

Golden horagrams give you an MOS and a Mt Meru scale that

tends towards it. I believe Marcus Satellite used MOS

scales but what does that have to do with the scales you're

talking about? Anyway, try reading The Scales of Mt. Meru here:

http://www.anaphori a.com/wilson. html

> But, yes, you're right...in the sense that they use whole number ratios they

> are JI. But the way they are generated, as I understand, is far from the way JI

> is generated. Kind of like the way my scale approaches on many JI ratios

> (despite only using PHI^(1 to 15) and not the infinite set of PHI^(0-infinity) ),

> but is not JI generated.

If they're JI, they must be generated the way JI is generated.

> --You could also try reading the book Bill

> --Sethares wrote about tunings, timbres, spectrums, and

> --scales, whatever that was called. In particular, section

> --6.4 "Past Explorations" .

> I've read tons of Sethares' online articles, but not the book: but I believe

> you that O'Connell may have preceded his work and P&L's (even though I haven't

> been able to find articles on O'Connels work anywhere so far vs., say, someone

> like Partch or Wendy Carlos who has articles everywhere). I'll see if I can

> find Sethares' full book...

The book's on SpringerLink. You may have access to it. If

you want to do anything original with consonance it's pretty

much required reading.

Yes, there isn't much written about O'Connell, but what does

that prove? This isn't a popularity contest. You have the

original article.

Graham

Michael Sheiman wrote:

> To me what O'Connell does simply does not look much like what I'm doing, > minus his taking PHI^x to make his tuning like I am. Taking the pattern > 3,3,2, 3,3,3,2, 3,3 (his 9-tone scale) within the PHI^x/y^2 tuning I use to > make my scales gives
> 1.05902,1.14124 (OFF),1.20859 (OFF), > 1.30902(OFF), 1.41064,1.55473, 1.61803
> 1.74365 (OFF), 1.92142

Where are these numbers coming from? Some of them are ratios from the phi scale with descending octaves (positive x for you) when O'Connell said he used mostly ascending octaves. Some of them I don't know. And some are larger than phi, so they should have been reduced.

I'm checking with the Scala files, and neither of the 9 note scales named after him are a consecutive set of octaves. So here's what I make the chain of pure octaves as frequency ratios:

1.3090 1.0000 1.2361 1.5279 1.1672 1.4427 1.1021 1.3623 1.0407

In scale order:

1.0000 1.0407 1.1021 1.1672 1.2361 1.3090 1.3623 1.4427 1.5279

In terms of the 25 note equal tempered scale, ordered by generators:

13.989 0.000 11.011 22.021 8.032 19.042 5.053 16.063 2.074

Sorted and rounded off:

0 2 5 8 11 14 16 19 22

That matches the scale on page 8 of Xenharmonikon or page 6 of the PDF.

> So, by my calculations, out of 9 notes of the scale 4 of his are different, > plus his octave in his a lot close to 2/1 than 1.61803 judging by the best I can > make of his document.

Of course his octave is close to 2/1. That's what an octave is. Nothing you can say will change it. His equivalence interval (or relation) is, however, 1.61803. The same as yours.

Graham

--- In tuning@yahoogroups.com, Michael Sheiman <djtrancendance@...> wrote:

>     Good point.  You know, even out of JI or mean-tone >fanatics...you'd think a lot of such people would at least question >the possibility using 3/2 as the octave...after all, diatonic theory >revolves around the circle of fifths, does it not? 

You really should print this out (it's a small book, in PDF format) and read it:

http://eamusic.dartmouth.edu/~larry/published_articles/divisions_of_the_tetrachord/index.html

>I'm checking with the Scala files, and neither of the 9 note

>scales named after him are a consecutive set of octaves. So

>here's what I make the chain of pure octaves as frequency

>ratios:

>1.0000 X1.0407X X1.1021X 1.1672 1.2361 X1.3090X 1.3623 X1.4427X X1.5279X

    I believe you; of course, the SCALA files are closer than taking the first 25 consecutive PHI octaves (as I did), ordering them, and using his scale steps. 

    Still (in the above scale you gave as his), look at all the X's (meaning notes 15+ cents off my scale values) I found just at a glance...
  About half of them are not on my scale.  As I've been saying, the tuning he's basing this all on seems the same, but scales we use within the tuning are a LOT different.  Still, this is good info and I'll gladly plug this in and test it for consonance for comparison (FINALLY, an actual scale I can get my hands on and not just complex documentation). :-)

>>His equivalence
>>interval (or relation) is, however, 1.61803. The same as yours.
Of course, but that basically says he's using the same tuning...rather than the same scale.     As I've said many times before I wholeheartedly agree he's using the same tuning...in fact all the numbers in his scale come up in the tuning I used to create my scale.

-Michael

--- On Mon, 3/30/09, Graham Breed <gbreed@...> wrote:

From: Graham Breed <gbreed@...>
Subject: Re: [tuning] Re: Rational vs Irrational Scales: a response to Rick
To: tuning@yahoogroups.com
Date: Monday, March 30, 2009, 11:15 PM

Michael Sheiman wrote:

> To me what O'Connell does simply does not look much like what I'm doing,

> minus his taking PHI^x to make his tuning like I am. Taking the pattern

> 3,3,2, 3,3,3,2, 3,3 (his 9-tone scale) within the PHI^x/y^2 tuning I use to

> make my scales gives

> 1.05902,1.14124 (OFF),1.20859 (OFF),

> 1.30902(OFF) , 1.41064,1.55473, 1.61803

> 1.74365 (OFF), 1.92142

Where are these numbers coming from? Some of them are

ratios from the phi scale with descending octaves (positive

x for you) when O'Connell said he used mostly ascending

octaves. Some of them I don't know. And some are larger

than phi, so they should have been reduced.

I'm checking with the Scala files, and neither of the 9 note

scales named after him are a consecutive set of octaves. So

here's what I make the chain of pure octaves as frequency

ratios:

1.3090 1.0000 1.2361 1.5279 1.1672 1.4427 1.1021 1.3623 1.0407

In scale order:

1.0000 1.0407 1.1021 1.1672 1.2361 1.3090 1.3623 1.4427 1.5279

In terms of the 25 note equal tempered scale, ordered by

generators:

13.989 0.000 11.011 22.021 8.032 19.042 5.053 16.063 2.074

Sorted and rounded off:

0 2 5 8 11 14 16 19 22

That matches the scale on page 8 of Xenharmonikon or page 6

of the PDF.

> So, by my calculations, out of 9 notes of the scale 4 of his are different,

> plus his octave in his a lot close to 2/1 than 1.61803 judging by the best I can

> make of his document.

Of course his octave is close to 2/1. That's what an octave

is. Nothing you can say will change it. His equivalence

interval (or relation) is, however, 1.61803. The same as yours.

Graham

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...> wrote:
>
> --- In tuning@yahoogroups.com, Michael Sheiman <djtrancendance@> wrote:
>
> > Good point. You know, even out of JI or mean-tone >fanatics...you'd think a lot of such people would at least question >the possibility using 3/2 as the octave...after all, diatonic theory >revolves around the circle of fifths, does it not?
>
> You really should print this out (it's a small book, in PDF format) and read it:
>
> http://eamusic.dartmouth.edu/~larry/published_articles/divisions_of_the_tetrachord/index.html
>

What is all this about calling the fifth or phi the octave "from another point of view"? The octave is the eighth note of the major scale (as in oct = 8). Why not call an elephant a banana? Even my nine year old niece, being naturally musically talented, will automatically sing melodies an octave above what she hears on the radio, and she has no "hidden agenda". For those who need a scientific explanation, the octave comes from the fact that when you take the absolute value of a wave function, such as is required to calculate air pressure on the ear drum, the frequency doubles. Sure, certain talented composers such as Bartok or Sethares have explored Phi etc...and written some interesting pieces. But they are already equipped with a deeply instilled musicality which rubs off even despite the maths (Berg being another wonderful example of "defying" serialism with his lyrical sensibility). But you must learn to crawl before you can walk. It would be at least something if certain people on this list were good at maths. But it seems that they are using it to cover for being tone-deaf. Having said that, it seems to me that many branches of so-called alternate musical harmony such as the nonoctave group have all the appearance of being well thought out. But they are applying mathematics as if it were a closed circuit independent from either musical harmony or wave theory. You don't learn French by studying English and then trying to find interesting translations. You learn it by living it.

-Rick

PS: Despite all of the responses with my name attached to it, not one of you has actually understood the gravity of my original question, let alone answered it.

--What is all this about calling the fifth or phi the octave "from another point of view"?
Because it functions in the same way...>>regardless<< of the name.

--Even my nine year old niece, being naturally musically talented, will
automatically sing --melodies an octave above what she hears on the
radio, and she has no "hidden agenda".
   That's AKA just plain old "adapting to Western culture/music".  I'm sure if she were raised listening to tritave-based scales she's sing a tri-tave over what she hears.

---But it seems that they are using it to cover for being tone-deaf.
   This is pretty odd as a criticism considering every time I make a new scale I post a sound sample.
   BTW, if you want to base everything on the standard 2/1 octave, how your daughter imitates pop music...and then define anything too far from that as "tone deaf"...why not just drop off this list entirely and study 12TET music for the rest of your life?  See the problem here?

--You don't learn French by studying English and then trying to find interesting translations.

    Exactly...apparently you keep on trying to find convenient ways to "force" my scales into some JI, mean-tone,
octave...construct you favor and then complain how it doesn't work in such constructs (and that's rather like translating English to French with Babelfish and then using your lines on a French woman). 

   I'd highly suggest you either accept that people here are sometimes going to build things that are, from scratch, quite different from what you have "learned to love".  I, for one, do follow psychoacoustic theory, the fact the ear hears exponentially, the fact two tones too close together melds into one "chorus-sounding" tone.  Unless you can take one of my scales and say something specific like "aha! this note when played in this chord in your scale sounds quite off"...I don't know what productivity I'm going to be able to make of your rants here,

BTW, the latest version of my scale is

18/17
 9/8
 19/16
 5/4
 4/3
 7/5
 28/19
 14/9
 21/13

...feel free to tear it apart and find errors in it (with your ears, of course)...but please don't bug me about how my scale, referring to your "French" example "it simply wrong because it sounds too much like a foreign language where I can't find a good mathematical translator to what my daughter sings".  Think with your ears... :-)

-Michael

--- On Tue, 3/31/09, rick_ballan <rick_ballan@...> wrote:

From: rick_ballan <rick_ballan@...>
Subject: [tuning] Re: Rational vs Irrational Scales: a response to Rick
To: tuning@yahoogroups.com
Date: Tuesday, March 31, 2009, 9:08 AM

--- In tuning@yahoogroups. com, "Cameron Bobro" <misterbobro@ ...> wrote:

>

> --- In tuning@yahoogroups. com, Michael Sheiman <djtrancendance@ > wrote:

>

> > Good point. You know, even out of JI or mean-tone >fanatics... you'd think a lot of such people would at least question >the possibility using 3/2 as the octave...after all, diatonic theory >revolves around the circle of fifths, does it not?

>

> You really should print this out (it's a small book, in PDF format) and read it:

>

> http://eamusic. dartmouth. edu/~larry/ published_ articles/ divisions_ of_the_tetrachor d/index.html

>

What is all this about calling the fifth or phi the octave "from another point of view"? The octave is the eighth note of the major scale (as in oct = 8). Why not call an elephant a banana? Even my nine year old niece, being naturally musically talented, will automatically sing melodies an octave above what she hears on the radio, and she has no "hidden agenda". For those who need a scientific explanation, the octave comes from the fact that when you take the absolute value of a wave function, such as is required to calculate air pressure on the ear drum, the frequency doubles. Sure, certain talented composers such as Bartok or Sethares have explored Phi etc...and written some interesting pieces. But they are already equipped with a deeply instilled musicality which rubs off even despite the maths (Berg being another wonderful example of "defying" serialism with his lyrical sensibility) . But you must learn to crawl before you can walk. It would be at
least something if certain people on this list were good at maths. But it seems that they are using it to cover for being tone-deaf. Having said that, it seems to me that many branches of so-called alternate musical harmony such as the nonoctave group have all the appearance of being well thought out. But they are applying mathematics as if it were a closed circuit independent from either musical harmony or wave theory. You don't learn French by studying English and then trying to find interesting translations. You learn it by living it.

-Rick

PS: Despite all of the responses with my name attached to it, not one of you has actually understood the gravity of my original question, let alone answered it.

--- In tuning@yahoogroups.com, djtrancendance@... wrote:
>
> --What is all this about calling the fifth or phi the octave "from another point of view"?
> Because it functions in the same way...>>regardless<< of the name.
>
> --Even my nine year old niece, being naturally musically talented, will
> automatically sing --melodies an octave above what she hears on the
> radio, and she has no "hidden agenda".
> That's AKA just plain old "adapting to Western culture/music". I'm sure if she were raised listening to tritave-based scales she's sing a tri-tave over what she hears.
>
> ---But it seems that they are using it to cover for being tone-deaf.
> This is pretty odd as a criticism considering every time I make a new scale I post a sound sample.
> BTW, if you want to base everything on the standard 2/1 octave, how your daughter imitates pop music...and then define anything too far from that as "tone deaf"...why not just drop off this list entirely and study 12TET music for the rest of your life? See the problem here?
>
> --You don't learn French by studying English and then trying to find interesting translations.
>
> Exactly...apparently you keep on trying to find convenient ways to "force" my scales into some JI, mean-tone,
> octave...construct you favor and then complain how it doesn't work in such constructs (and that's rather like translating English to French with Babelfish and then using your lines on a French woman).
>
> I'd highly suggest you either accept that people here are sometimes going to build things that are, from scratch, quite different from what you have "learned to love". I, for one, do follow psychoacoustic theory, the fact the ear hears exponentially, the fact two tones too close together melds into one "chorus-sounding" tone. Unless you can take one of my scales and say something specific like "aha! this note when played in this chord in your scale sounds quite off"...I don't know what productivity I'm going to be able to make of your rants here,
>
> BTW, the latest version of my scale is
>
> 18/17
> 9/8
> 19/16
> 5/4
> 4/3
> 7/5
> 28/19
> 14/9
> 21/13
>
> ...feel free to tear it apart and find errors in it (with your ears, of course)...but please don't bug me about how my scale, referring to your "French" example "it simply wrong because it sounds too much like a foreign language where I can't find a good mathematical translator to what my daughter sings". Think with your ears... :-)
>
> -Michael
>
>
> --- On Tue, 3/31/09, rick_ballan <rick_ballan@...> wrote:
>
> From: rick_ballan <rick_ballan@...>
> Subject: [tuning] Re: Rational vs Irrational Scales: a response to Rick
> To: tuning@yahoogroups.com
> Date: Tuesday, March 31, 2009, 9:08 AM
>
> "What is all this about calling the fifth or phi the octave "from another point of view"?
> Because it functions in the same way...>>regardless<< of the name."

No it doesn't function the same. It functions differently which is why it has a different name.
>
>"That's AKA just plain old "adapting to Western culture/music". I'm sure if she were raised listening to tritave-based scales she's sing a tri-tave over what she hears".

No, she wouldn't because singing fifths above is a much more complex process than singing octaves. Even professional singers have to work at that. In fact the use of mathematics in music itself comes from the west. So why are you using "western ratios"? No, appealing to "western bias" is a lazy and predictable way of getting out of study and practice. For a correct account of the evolution of Western Music and the harmonic series I suggest reading "The Craft of Musical Composition book 1 by Paul Hindemith".
>
>"BTW, if you want to base everything on the standard 2/1 octave, how your daughter imitates pop music...and then define anything too far from that as "tone deaf"...why not just drop off this list entirely and study 12TET music for the rest of your life? See the problem here?"

Well first she is my niece. Second, I said nothing about pop music which is your assumption. Third, 2/1 is standard for a reason, a musical reason. And fourthly, you can't seem to be able to make the distinction between "alternate tuning" and "alternate mistuning". And yet you respond to everything like the worlds greatest expert. See the problem here?
>
>"BTW, the latest version of my scale is
>
> 18/17
> 9/8
> 19/16
> 5/4
> 4/3
> 7/5
> 28/19
> 14/9
> 21/13"

This isn't your scale. It is a JI with a few other intervals thrown in for good measure. The problem is is that 18/17, 28/19, 14/9 and 21/13 don't have 2^N in either the numerator or the denominator, or multiples of them for key changes, yet more proof that you're groping in the dark.
>
>Finally, Cameron, you said "Good point. You know, even out of JI or mean-tone >fanatics... you'd think a lot of such people would at least question >the possibility using 3/2 as the octave...after all, diatonic theory >revolves around the circle of fifths, does it not?". Why use the term "fanatics" which is also a loaded term designed to undermine actual musical harmony? And creating mod 7 has already been explored many times in serial music, which is tantamount to treating the fifth like the octave. As Shoernberg said, "To those of you who "won't go too far" but cannot explain why you go "so far"." Why not call the semitone the octave, or the flat fifth, or the square root of phi divided by the log of 433, and so on to infinity? After all, not to do so would be just another form of "western bias".

-Rick
>
>
>
>
>
>

--- In tuning@yahoogroups.com, djtrancendance@... wrote:
>
> --What is all this about calling the fifth or phi the octave "from another point of view"?
> Because it functions in the same way...>>regardless<< of the name.
>
> --Even my nine year old niece, being naturally musically talented, will
> automatically sing --melodies an octave above what she hears on the
> radio, and she has no "hidden agenda".
> That's AKA just plain old "adapting to Western culture/music". I'm sure if she were raised listening to tritave-based scales she's sing a tri-tave over what she hears.
>
> ---But it seems that they are using it to cover for being tone-deaf.
> This is pretty odd as a criticism considering every time I make a new scale I post a sound sample.
> BTW, if you want to base everything on the standard 2/1 octave, how your daughter imitates pop music...and then define anything too far from that as "tone deaf"...why not just drop off this list entirely and study 12TET music for the rest of your life? See the problem here?
>
> --You don't learn French by studying English and then trying to find interesting translations.
>
> Exactly...apparently you keep on trying to find convenient ways to "force" my scales into some JI, mean-tone,
> octave...construct you favor and then complain how it doesn't work in such constructs (and that's rather like translating English to French with Babelfish and then using your lines on a French woman).
>
> I'd highly suggest you either accept that people here are sometimes going to build things that are, from scratch, quite different from what you have "learned to love". I, for one, do follow psychoacoustic theory, the fact the ear hears exponentially, the fact two tones too close together melds into one "chorus-sounding" tone. Unless you can take one of my scales and say something specific like "aha! this note when played in this chord in your scale sounds quite off"...I don't know what productivity I'm going to be able to make of your rants here,
>
> BTW, the latest version of my scale is
>
> 18/17
> 9/8
> 19/16
> 5/4
> 4/3
> 7/5
> 28/19
> 14/9
> 21/13
>
> ...feel free to tear it apart and find errors in it (with your ears, of course)...but please don't bug me about how my scale, referring to your "French" example "it simply wrong because it sounds too much like a foreign language where I can't find a good mathematical translator to what my daughter sings". Think with your ears... :-)
>
> -Michael
>
>
> --- On Tue, 3/31/09, rick_ballan <rick_ballan@...> wrote:
>
> From: rick_ballan <rick_ballan@...>
> Subject: [tuning] Re: Rational vs Irrational Scales: a response to Rick
> To: tuning@yahoogroups.com
> Date: Tuesday, March 31, 2009, 9:08 AM
>
>
>
>
>
>
>
>
>
>
>
>
> --- In tuning@yahoogroups. com, "Cameron Bobro" <misterbobro@ ...> wrote:
>
> >
>
> > --- In tuning@yahoogroups. com, Michael Sheiman <djtrancendance@ > wrote:
>
> >
>
> > > Good point. You know, even out of JI or mean-tone >fanatics... you'd think a lot of such people would at least question >the possibility using 3/2 as the octave...after all, diatonic theory >revolves around the circle of fifths, does it not?
>
> >
>

>
In fact, to those who would like to call the fifth the octave, let me get this straight. So starting from C we would call a G by the new name C since they are now equivalent. Then, since D is the fifth of G, this would be called C too. In fact if we keep on going, successive fifths would include all notes since we arrive back at C after 7 8ve's. Therefore all notes would be called C. Harmonizing in 'octaves' would simply mean playing all notes of a melody in all keys at once, at least in the 12 tet. That would sound nice. OR, if we choose instead to call the fifth 3/2, since this never returns back to the same note, then we would spiral off into an infinity of keys, now all called "C notes", all playing simultaneously. That would sound even nicer. Yeah "good point".

-Rick

> >Finally, Cameron, you said "Good point. You know, even out of JI >or mean-tone >fanatics... you'd think a lot of such people would at >least question >the possibility using 3/2 as the octave...after all, >diatonic theory >revolves around the circle of fifths, does it >not?".

I did not say this, Michael did. My response to this was to point Michael to John Chalmer's Divisions of the Tetrachord. It's clear to me that you don't bother to read my posts, otherwise you'd immediately know that I wouldn't make a statement like: "after all, diatonic theory revolves around the circle of fifths, does it not?".

Yikes!

>(Rick)Why use the term "fanatics" which is also a loaded term >designed to undermine actual musical harmony?

Your response is also very loaded. Notice that I imply no agreement or disagreement with your equation of JI with "actual musical harmony".

>And creating mod 7 has already been explored many times in serial >music, which is tantamount to treating the fifth like the octave. As >Shoernberg said, "To those of you who "won't go too far" but cannot >explain why you go "so far"." Why not call the semitone the octave, <or the flat fifth, or the square root of phi divided by the log of >433, and so on to infinity? After all, not to do so would be just >another form of "western bias".

Michael is simply using the word "octave" incorrectly. What he means is "interval of equivalence/repetition".

>(and that's rather like translating English >to French with >Babelfish and then using your lines on a French >woman).

Oddly enough, this is a very effective way to get laid. Or so I have heard... :-D

> No, she wouldn't because singing fifths above is a much more >complex process than singing octaves.

Not necessarily- it's a natural transposition for some "naive" singers and in certain folk musics. In moving I have "mislayed" many pounds of books, but somewhere I have an ethnomusicological study illustrating sudden transpostions of pure fifths when a monophonic line goes out of range for a particular voice, in Balkan music. IMO, it's one of the pretty damn obvious ursprings of harmonizing itself.

>Even professional singers have to work at that.

Doesn't seem to have slowed down the age of parallel organum much though.

>In fact the use of mathematics in music itself comes from the west.

Wrong, so wrong it's scary.

>So why are you using "western ratios"? No, appealing to "western >bias" is a lazy and predictable way of getting out of study and >practice.

I agree with this...

For a correct account of the evolution of Western Music >and the harmonic series I suggest reading "The Craft of Musical >Composition book 1 by Paul Hindemith".

...but, oh, good G-d.

> This isn't your scale. It is a JI with a few other intervals thrown >in for good measure. The problem is is that 18/17, 28/19, 14/9 and >21/13 don't have 2^N in either the numerator or the denominator, or >multiples of them for key changes, yet more proof that you're >groping in the dark.

I don't get this- 6/5 isn't a JI interval?

--- In tuning@yahoogroups.com, "rick_ballan" <rick_ballan@...> wrote:

> In fact, to those who would like to call the fifth the octave, let >me get this straight. So starting from C we would call a G by the >new name C since they are now equivalent. Then, since D is the fifth >of G, this would be called C too. In fact if we keep on going, >successive fifths would include all notes since we arrive back at C >after 7 8ve's. Therefore all notes would be called C. Harmonizing in >'octaves' would simply mean playing all notes of a melody in all >keys at once, at least in the 12 tet. That would sound nice. OR, if >we choose instead to call the fifth 3/2, since this never returns >back to the same note, then we would spiral off into an infinity of >keys, now all called "C notes", all playing simultaneously. That >would sound even nicer. Yeah "good point".
>
> -Rick

I call my notes things like "Frank", "Mathilda" and "golden-orange".

By the way you are overlooking a very big and fundamental historical and practical concept: in real life, we usually have gamut and ambitus, and division of labor, not an infinite piano keyboard. Tetrachordal and pentachordal music for example is historically quite bound to specific ranges.

Anyway, noone is calling a fifth an octave except Michael, as I pointed out before, and I'm sure he'll settle on "interval of equivalence" or "period" or whatever once he realizes how confusing it is to say "octave" in this case.

And- you said something earlier about "noone answering your question"? What question was that, I seemed to have missed it?

Definitely yes, and not only in Balcan music, it can be found in Hungarian csardas, in many Slovakian, Moravian and Bohemian songs, and it continues to the Eastern Slaves as well. Not only pure fifth, also the other intervals (sometimes even change from major to minor or opposite), but always sudden jump - which reflects itself in interesting harmonization sometimes. I don't think the reason is that melody goes out of range of voice, why. A sequence which jumps has often small range, not bigger then fifth-sixth. One of the very characteristic principles in this regional folklore, I didn't found many examples of this in Scandinavian, Romanic or Germanic folklore, to talk just about European ethnic music.

Daniel Forro

On 1 Apr 2009, at 4:16 PM, Cameron Bobro wrote:
> Not necessarily- it's a natural transposition for some "naive" > singers and in certain folk musics. In moving I have "mislayed" > many pounds of books, but somewhere I have an ethnomusicological > study illustrating sudden transpostions of pure fifths when a > monophonic line goes out of range for a particular voice, in Balkan > music. IMO, it's one of the pretty damn obvious ursprings of > harmonizing itself.
>

--- In tuning@yahoogroups.com, Daniel Forro <dan.for@...> wrote:
>
> Definitely yes, and not only in Balcan music, it can be found in
> Hungarian csardas, in many Slovakian, Moravian and Bohemian songs,
> and it continues to the Eastern Slaves as well. Not only pure fifth,
> also the other intervals (sometimes even change from major to minor
> or opposite), but always sudden jump - which reflects itself in
> interesting harmonization sometimes. I don't think the reason is that
> melody goes out of range of voice, why. A sequence which jumps has
> often small range, not bigger then fifth-sixth. One of the very
> characteristic principles in this regional folklore, I didn't found
> many examples of this in Scandinavian, Romanic or Germanic folklore,
> to talk just about European ethnic music.
>
> Daniel Forro

I think that shifting because of vocal range is a natural source of this, way back when in the days of yore. Not the only source certainly, and not a direct cause anymore in folk music that has this built into the tradition, ie., you'll jump even where the vocal ambitus doesn't require it, but nevertheless a plausible origin in the physical world.

It also seems to me that the ultimate origin of harmony began exactly as Rick described his niece singing in octaves with him- my son did this at six months so I'm pretty dubious about it being a matter of "conditioning".

By the way, you should be careful about writing "Slav" as Slav, not "Slave", especially because there's a bogus racist etymology in the West that claims the words are related, just like there's a bogus Eastern etymology claiming Slav comes from Slava :-D (the most sensible IMO being from slov-, compared with the Germanic peoples of nem-, ie., people of the word, language, and people not.)

Oh yes, my English typing is worse and worse... one more "e" in such word, what a shame being myself of Slavonic origin :-) (Yes, usual etymology goes to Indoeuropean klou-, Latin cluere - to wash, from the name of rivers like Slava, Sluja, Slave, Slavica, and from slovo, slout, slyset - word, to be known, to hear. Similar in Albanian "shqiptar" - who speaks clearly. "Nemec" = German in Slavonic languages means dumb, unable to speak, German calls themselves differently of course. But you know well all this. Interesting is also glas, hlas, golos = voice, Slovenian glasba = music. Does it mean they mainly sing?)

How do you mean "origin of harmony"? I wouldn't call octave interval "harmony" in that sense we use it now.

Daniel Forro

On 1 Apr 2009, at 5:34 PM, Cameron Bobro wrote:

> --- In tuning@yahoogroups.com, Daniel Forro <dan.for@...> wrote:
> >
> > Definitely yes, and not only in Balcan music, it can be found in
> > Hungarian csardas, in many Slovakian, Moravian and Bohemian songs,
> > and it continues to the Eastern Slaves as well. Not only pure fifth,
> > also the other intervals (sometimes even change from major to minor
> > or opposite), but always sudden jump - which reflects itself in
> > interesting harmonization sometimes. I don't think the reason is > that
> > melody goes out of range of voice, why. A sequence which jumps has
> > often small range, not bigger then fifth-sixth. One of the very
> > characteristic principles in this regional folklore, I didn't found
> > many examples of this in Scandinavian, Romanic or Germanic folklore,
> > to talk just about European ethnic music.
> >
> > Daniel Forro
>
> I think that shifting because of vocal range is a natural source of > this, way back when in the days of yore. Not the only source > certainly, and not a direct cause anymore in folk music that has > this built into the tradition, ie., you'll jump even where the > vocal ambitus doesn't require it, but nevertheless a plausible > origin in the physical world.
>
> It also seems to me that the ultimate origin of harmony began > exactly as Rick described his niece singing in octaves with him- my > son did this at six months so I'm pretty dubious about it being a > matter of "conditioning".
>
> By the way, you should be careful about writing "Slav" as Slav, not > "Slave", especially because there's a bogus racist etymology in the > West that claims the words are related, just like there's a bogus > Eastern etymology claiming Slav comes from Slava :-D (the most > sensible IMO being from slov-, compared with the Germanic peoples > of nem-, ie., people of the word, language, and people not.)
>

--- In tuning@yahoogroups.com, Daniel Forró <dan.for@...> wrote:
>
> Oh yes, my English typing is worse and worse... one more "e" in such
> word, what a shame being myself of Slavonic origin :-) (Yes, usual
> etymology goes to Indoeuropean klou-, Latin cluere - to wash, from
> the name of rivers like Slava, Sluja, Slave, Slavica, and from >slovo,
> slout, slyset - word, to be known, to hear. Similar in Albanian
> "shqiptar" - who speaks clearly. "Nemec" = German in Slavonic
> languages means dumb, unable to speak, German calls themselves
> differently of course. But you know well all this.

My dad goes for the (very highly dubious) slava (glory) hehe. But anyway the root of Slav is quite clearly "word", the same concept exists in old English as well, theod, a single word meaning both people and language. Unfortunately "theod" seems to be popular today among groups of people that make you say "hm..."; Anglo-Saxon neo-paganism and stuff that gives off a faint whiff of Nazi crap, to my nose.

>Interesting is
> also glas, hlas, golos = voice, Slovenian glasba = music. Does it
> mean they mainly sing?)

Q: what do you call three Slovenes?
A: a choir!

Isn't music "hudba" in Czech? In Slovene godba means band music, like the factory bands of horns and reeds, but I think it used to mean music in general because it is still used that way, like the Druga Godba festival for "other music".

>
> How do you mean "origin of harmony"? I wouldn't call octave >interval
> "harmony" in that sense we use it now.

The idea of together, same-but-different, and so on, rather than monophonic. Had to start somewhere! Octaves and fifths are the obvious ones for different voice ranges singing what was originally "one" melody.

--- In tuning@yahoogroups.com, "rick_ballan" <rick_ballan@...> wrote:

> PS: Despite all of the responses with my name attached to it, not one of you has actually understood the gravity of my original question, let alone answered it.
>

What question was this?

Could you also try harder to arrange your answers so that I can figure out who said what and so on- I know it's a real pain in the butt in Yahoo, compared to using a proper forum software, and I've also misattributed quotes more than once, I'm sure.

On 1 Apr 2009, at 7:39 PM, Cameron Bobro wrote:
> My dad goes for the (very highly dubious) slava (glory) hehe. But > anyway the root of Slav is quite clearly "word", the same concept > exists in old English as well, theod, a single word meaning both > people and language. Unfortunately "theod" seems to be popular > today among groups of people that make you say "hm..."; Anglo-Saxon > neo-paganism and stuff that gives off a faint whiff of Nazi crap, > to my nose.
>
>
Am I right it's same root as Deutsch, Dutch, Tedesco, Teuton? It reminds also Latin totus, French tout... Then I understand finally why French use Allemand = all men = people.
> Q: what do you call three Slovenes?
> A: a choir!
>
:-)

> Isn't music "hudba" in Czech? In Slovene godba means band music, > like the factory bands of horns and reeds, but I think it used to > mean music in general because it is still used that way, like the > Druga Godba festival for "other music".
>
>
That's interesting, I thought they have only one term for music. Yes, "hudba" is music, originally in the Middle Age this word was used only for bowed strings instruments' music (so "hudec" was such performer, and famous living Czech violinist has a name Hudecek [-czech], which is diminutivum from hudec - nomen omen). Wind and brass music was "pistba" [s=sh], performer is "pistec".

We use also "muzika" in colloquial Czech, but as a word of German origin it's considered only as a part of folk or rather inferior language.

> > How do you mean "origin of harmony"? I wouldn't call octave > >interval
> > "harmony" in that sense we use it now.
>
> The idea of together, same-but-different, and so on, rather than > monophonic. Had to start somewhere! Octaves and fifths are the > obvious ones for different voice ranges singing what was originally > "one" melody.
>
Yes, such organum can be found in some African responsorial singing if I'm not wrong...

Daniel Forro

--- In tuning@yahoogroups.com, Daniel Forro <dan.for@...> wrote:
>
> Definitely yes, and not only in Balcan music, it can be found in
> Hungarian csardas, in many Slovakian, Moravian and Bohemian songs,
> and it continues to the Eastern Slaves as well. Not only pure fifth,
> also the other intervals (sometimes even change from major to minor
> or opposite), but always sudden jump - which reflects itself in
> interesting harmonization sometimes. I don't think the reason is that
> melody goes out of range of voice, why. A sequence which jumps has
> often small range, not bigger then fifth-sixth. One of the very
> characteristic principles in this regional folklore, I didn't found
> many examples of this in Scandinavian, Romanic or Germanic folklore,
> to talk just about European ethnic music.
>
> Daniel Forro
>
> On 1 Apr 2009, at 4:16 PM, Cameron Bobro wrote:
> > Not necessarily- it's a natural transposition for some "naive"
> > singers and in certain folk musics. In moving I have "mislayed"
> > many pounds of books, but somewhere I have an ethnomusicological
> > study illustrating sudden transpostions of pure fifths when a
> > monophonic line goes out of range for a particular voice, in Balkan
> > music. IMO, it's one of the pretty damn obvious ursprings of
> > harmonizing itself.
> >
>I'm not saying that harmonizing in fifths isn't natural or traditional, just that its not the octave. Sudden transpositions up a fifth is really not the same as treating it as an octave equivalent as my last post makes clear. And Cameron, I thought it was out of character for you so I apologise for the misunderstanding. Rick.

--Third, 2/1 is standard for a reason, a musical reason.
--No, she wouldn't because singing fifths above is a much more complex --process than singing octaves. Even professional singers have to work --at that.
    My point is that the octave is equivalent to the area where intervals in the scale begin to repeat again.  This is, of course, true in scales with more than 7 notes where the 8th note is NOT the repeating period.
    If you want to get technical and "make like a grammar school instructor", fine, I can say "PHI is the PERIOD of my scale"...but I figured it would be easier for most people to understand as being called the "pseudo-octave".
    Yes, 1.5 AKA the 5th is harder for people to sing.  But who said we were talking about making a scale that's trivial to sing in the first place? 
Heck, there are so many scales already that use tri-taves which, of course, have NOTHING to do with being the third note of the major scale.

   You have this one example with your niece about singing you seem stuck on and, it seems, all of a sudden anything I come up with that's not ideal for making things easier for someone in her position automatically becomes wrong. 
   If singers hate non-2/1-octave scale, cool, and great for them; that was not my point anyhow and I've have never (and probably will never want to) sing in my life. :-D  My point: I'm working on scales made to enhance compositional possibilities on electronic instruments and, perhaps with some clever design tricks, acoustic ones as well...and I'm developing my scales by composing with them myself rather than, say, testing them on singers. :-)

-Michael

--- On Tue, 3/31/09, rick_ballan <rick_ballan@yahoo.com.au> wrote:

From: rick_ballan <rick_ballan@...>
Subject: [tuning] Re: Rational vs Irrational Scales: a response to Rick
To: tuning@yahoogroups.com
Date: Tuesday, March 31, 2009, 9:14 PM

--- In tuning@yahoogroups. com, djtrancendance@ ... wrote:

>

> --What is all this about calling the fifth or phi the octave "from another point of view"?

> Because it functions in the same way...>>regardless< < of the name.

>

> --Even my nine year old niece, being naturally musically talented, will

> automatically sing --melodies an octave above what she hears on the

> radio, and she has no "hidden agenda".

> That's AKA just plain old "adapting to Western culture/music" . I'm sure if she were raised listening to tritave-based scales she's sing a tri-tave over what she hears.

>

> ---But it seems that they are using it to cover for being tone-deaf.

> This is pretty odd as a criticism considering every time I make a new scale I post a sound sample.

> BTW, if you want to base everything on the standard 2/1 octave, how your daughter imitates pop music...and then define anything too far from that as "tone deaf"...why not just drop off this list entirely and study 12TET music for the rest of your life? See the problem here?

>

> --You don't learn French by studying English and then trying to find interesting translations.

>

> Exactly...apparentl y you keep on trying to find convenient ways to "force" my scales into some JI, mean-tone,

> octave...construct you favor and then complain how it doesn't work in such constructs (and that's rather like translating English to French with Babelfish and then using your lines on a French woman).

>

> I'd highly suggest you either accept that people here are sometimes going to build things that are, from scratch, quite different from what you have "learned to love". I, for one, do follow psychoacoustic theory, the fact the ear hears exponentially, the fact two tones too close together melds into one "chorus-sounding" tone. Unless you can take one of my scales and say something specific like "aha! this note when played in this chord in your scale sounds quite off"...I don't know what productivity I'm going to be able to make of your rants here,

>

> BTW, the latest version of my scale is

>

> 18/17

> 9/8

> 19/16

> 5/4

> 4/3

> 7/5

> 28/19

> 14/9

> 21/13

>

> ...feel free to tear it apart and find errors in it (with your ears, of course)...but please don't bug me about how my scale, referring to your "French" example "it simply wrong because it sounds too much like a foreign language where I can't find a good mathematical translator to what my daughter sings". Think with your ears... :-)

>

> -Michael

>

>

> --- On Tue, 3/31/09, rick_ballan <rick_ballan@ ...> wrote:

>

> From: rick_ballan <rick_ballan@ ...>

> Subject: [tuning] Re: Rational vs Irrational Scales: a response to Rick

> To: tuning@yahoogroups. com

> Date: Tuesday, March 31, 2009, 9:08 AM

>

> "What is all this about calling the fifth or phi the octave "from another point of view"?

> Because it functions in the same way...>>regardless< < of the name."

No it doesn't function the same. It functions differently which is why it has a different name.

>

>"That's AKA just plain old "adapting to Western culture/music" . I'm sure if she were raised listening to tritave-based scales she's sing a tri-tave over what she hears".

No, she wouldn't because singing fifths above is a much more complex process than singing octaves. Even professional singers have to work at that. In fact the use of mathematics in music itself comes from the west. So why are you using "western ratios"? No, appealing to "western bias" is a lazy and predictable way of getting out of study and practice. For a correct account of the evolution of Western Music and the harmonic series I suggest reading "The Craft of Musical Composition book 1 by Paul Hindemith".

>

>"BTW, if you want to base everything on the standard 2/1 octave, how your daughter imitates pop music...and then define anything too far from that as "tone deaf"...why not just drop off this list entirely and study 12TET music for the rest of your life? See the problem here?"

Well first she is my niece. Second, I said nothing about pop music which is your assumption. Third, 2/1 is standard for a reason, a musical reason. And fourthly, you can't seem to be able to make the distinction between "alternate tuning" and "alternate mistuning". And yet you respond to everything like the worlds greatest expert. See the problem here?

>

>"BTW, the latest version of my scale is

>

> 18/17

> 9/8

> 19/16

> 5/4

> 4/3

> 7/5

> 28/19

> 14/9

> 21/13"

This isn't your scale. It is a JI with a few other intervals thrown in for good measure. The problem is is that 18/17, 28/19, 14/9 and 21/13 don't have 2^N in either the numerator or the denominator, or multiples of them for key changes, yet more proof that you're groping in the dark.

>

>Finally, Cameron, you said "Good point. You know, even out of JI or mean-tone >fanatics... you'd think a lot of such people would at least question >the possibility using 3/2 as the octave...after all, diatonic theory >revolves around the circle of fifths, does it not?". Why use the term "fanatics" which is also a loaded term designed to undermine actual musical harmony? And creating mod 7 has already been explored many times in serial music, which is tantamount to treating the fifth like the octave. As Shoernberg said, "To those of you who "won't go too far" but cannot explain why you go "so far"." Why not call the semitone the octave, or the flat fifth, or the square root of phi divided by the log of 433, and so on to infinity? After all, not to do so would be just another form of "western bias".

-Rick

>

>

>

>

>

>

--In fact, to those who would like to call the fifth the octave, let me
get ---this straight. So starting from C we would call a G by the new name
C ---since they are now equivalent. Then, since D is the fifth of G, this
---would be called C too.
    You're right, it would make 12TET/"5-limit" type 7-note scale theories a scrambled mess...but I'm discussing scales other than 12TET rather than "forcing non-12TET theories onto 12TET".  If you want to push absolutely everything under the sun into strict 12TET terms, though, why bother with this list?  

    Do you think tri-tave scales would work with the concept of an octave, for example?  Of course not...you need to stretch your mappings to fit the tri-tave.  There's no problem with periods other than the octave...unless you mix different terms from different theories (IE using a circle of 5ths in 10TET, a 5th for a 9-tone scale, or a 2/1 octave for all scales including tri-tave based ones)...which is exactly what you are doing here.
  
-Michael

--- On Tue, 3/31/09, rick_ballan <rick_ballan@...> wrote:

From: rick_ballan <rick_ballan@...>
Subject: [tuning] Re: Rational vs Irrational Scales: a response to Rick
To: tuning@yahoogroups.com
Date: Tuesday, March 31, 2009, 10:07 PM

--- In tuning@yahoogroups. com, djtrancendance@ ... wrote:

>

> --What is all this about calling the fifth or phi the octave "from another point of view"?

> Because it functions in the same way...>>regardless< < of the name.

>

> --Even my nine year old niece, being naturally musically talented, will

> automatically sing --melodies an octave above what she hears on the

> radio, and she has no "hidden agenda".

> That's AKA just plain old "adapting to Western culture/music" . I'm sure if she were raised listening to tritave-based scales she's sing a tri-tave over what she hears.

>

> ---But it seems that they are using it to cover for being tone-deaf.

> This is pretty odd as a criticism considering every time I make a new scale I post a sound sample.

> BTW, if you want to base everything on the standard 2/1 octave, how your daughter imitates pop music...and then define anything too far from that as "tone deaf"...why not just drop off this list entirely and study 12TET music for the rest of your life? See the problem here?

>

> --You don't learn French by studying English and then trying to find interesting translations.

>

> Exactly...apparentl y you keep on trying to find convenient ways to "force" my scales into some JI, mean-tone,

> octave...construct you favor and then complain how it doesn't work in such constructs (and that's rather like translating English to French with Babelfish and then using your lines on a French woman).

>

> I'd highly suggest you either accept that people here are sometimes going to build things that are, from scratch, quite different from what you have "learned to love". I, for one, do follow psychoacoustic theory, the fact the ear hears exponentially, the fact two tones too close together melds into one "chorus-sounding" tone. Unless you can take one of my scales and say something specific like "aha! this note when played in this chord in your scale sounds quite off"...I don't know what productivity I'm going to be able to make of your rants here,

>

> BTW, the latest version of my scale is

>

> 18/17

> 9/8

> 19/16

> 5/4

> 4/3

> 7/5

> 28/19

> 14/9

> 21/13

>

> ...feel free to tear it apart and find errors in it (with your ears, of course)...but please don't bug me about how my scale, referring to your "French" example "it simply wrong because it sounds too much like a foreign language where I can't find a good mathematical translator to what my daughter sings". Think with your ears... :-)

>

> -Michael

>

>

> --- On Tue, 3/31/09, rick_ballan <rick_ballan@ ...> wrote:

>

> From: rick_ballan <rick_ballan@ ...>

> Subject: [tuning] Re: Rational vs Irrational Scales: a response to Rick

> To: tuning@yahoogroups. com

> Date: Tuesday, March 31, 2009, 9:08 AM

>

>

>

>

>

>

>

>

>

>

>

>

> --- In tuning@yahoogroups. com, "Cameron Bobro" <misterbobro@ ...> wrote:

>

> >

>

> > --- In tuning@yahoogroups. com, Michael Sheiman <djtrancendance@ > wrote:

>

> >

>

> > > Good point. You know, even out of JI or mean-tone >fanatics... you'd think a lot of such people would at least question >the possibility using 3/2 as the octave...after all, diatonic theory >revolves around the circle of fifths, does it not?

>

> >

>

>

In fact, to those who would like to call the fifth the octave, let me get this straight. So starting from C we would call a G by the new name C since they are now equivalent. Then, since D is the fifth of G, this would be called C too. In fact if we keep on going, successive fifths would include all notes since we arrive back at C after 7 8ve's. Therefore all notes would be called C. Harmonizing in 'octaves' would simply mean playing all notes of a melody in all keys at once, at least in the 12 tet. That would sound nice. OR, if we choose instead to call the fifth 3/2, since this never returns back to the same note, then we would spiral off into an infinity of keys, now all called "C notes", all playing simultaneously. That would sound even nicer. Yeah "good point".

-Rick

--Michael is simply using the word "octave" incorrectly. What he means --is "interval of equivalence/ repetition" .
    Right, but wouldn't it be really redundant to keep saying "interval of equivalence/ repetition" again and again?  The octave is an "interval of equivalence/ repetition"...so I figured most people would be able to bridge the gap.  If I looked up the terminology correctly, I'll use the term PERIOD from here on in...then would we be on the same page?

> This isn't your scale. It is a JI with a few other intervals
thrown
>in for good measure.
   If that's the case, please show me the nearest scale that has been created that proves it "almost completely copied"...

>The problem is is that 18/17, 28/19,
14/9 and 21/13 don't have 2^N in >either the numerator or the
denominator, or multiples of them for key >changes,
    Darn...that's about half the scale that deviates from your idea of pure-JI then...pretty far fetched to say it's not original...regardless of if you hate it. :-)
    Which is...simply evidence that it's based on PHI and NOT the idea of making a low-limit JI scale!  21/13, for example, is an estimated value for PHI.  It is SIMPLY the PHI scale estimated to nearby rational numbered values...if the rational-numberness makes it look like JI to you then any JI-ness is a side-effect, and NOT the basis of the scale!
    You seem to be accusing me of making an JI scale and a scale that breaks the low-limit rules for JI at the same time.  I really don't care on that ground...here's my real question: what's your point so far as consonance (as in actually listening to the scale, rather than comparing it to JI)?

--- On Wed, 4/1/09, Cameron Bobro <misterbobro@...> wrote:

From: Cameron Bobro <misterbobro@...>
Subject: [tuning] Re: Rational vs Irrational Scales: a response to Rick
To: tuning@yahoogroups.com
Date: Wednesday, April 1, 2009, 12:16 AM

> >Finally, Cameron, you said "Good point. You know, even out of JI >or mean-tone >fanatics... you'd think a lot of such people would at >least question >the possibility using 3/2 as the octave...after all, >diatonic theory >revolves around the circle of fifths, does it >not?".

I did not say this, Michael did. My response to this was to point Michael to John Chalmer's Divisions of the Tetrachord. It's clear to me that you don't bother to read my posts, otherwise you'd immediately know that I wouldn't make a statement like: "after all, diatonic theory revolves around the circle of fifths, does it not?".

Yikes!

>(Rick)Why use the term "fanatics" which is also a loaded term >designed to undermine actual musical harmony?

Your response is also very loaded. Notice that I imply no agreement or disagreement with your equation of JI with "actual musical harmony".

>And creating mod 7 has already been explored many times in serial >music, which is tantamount to treating the fifth like the octave. As >Shoernberg said, "To those of you who "won't go too far" but cannot >explain why you go "so far"." Why not call the semitone the octave, <or the flat fifth, or the square root of phi divided by the log of >433, and so on to infinity? After all, not to do so would be just >another form of "western bias".

Michael is simply using the word "octave" incorrectly. What he means is "interval of equivalence/ repetition" .

>(and that's rather like translating English >to French with >Babelfish and then using your lines on a French >woman).

Oddly enough, this is a very effective way to get laid. Or so I have heard... :-D

> No, she wouldn't because singing fifths above is a much more >complex process than singing octaves.

Not necessarily- it's a natural transposition for some "naive" singers and in certain folk musics. In moving I have "mislayed" many pounds of books, but somewhere I have an ethnomusicological study illustrating sudden transpostions of pure fifths when a monophonic line goes out of range for a particular voice, in Balkan music. IMO, it's one of the pretty damn obvious ursprings of harmonizing itself.

>Even professional singers have to work at that.

Doesn't seem to have slowed down the age of parallel organum much though.

>In fact the use of mathematics in music itself comes from the west.

Wrong, so wrong it's scary.

>So why are you using "western ratios"? No, appealing to "western >bias" is a lazy and predictable way of getting out of study and >practice.

I agree with this...

For a correct account of the evolution of Western Music >and the harmonic series I suggest reading "The Craft of Musical >Composition book 1 by Paul Hindemith".

...but, oh, good G-d.

> This isn't your scale. It is a JI with a few other intervals thrown >in for good measure. The problem is is that 18/17, 28/19, 14/9 and >21/13 don't have 2^N in either the numerator or the denominator, or >multiples of them for key changes, yet more proof that you're >groping in the dark.

I don't get this- 6/5 isn't a JI interval?

--Anyway, noone is calling a fifth an octave except Michael, as I pointed --out
    I NEVER called the fifth an octave. 
    I said the fifth is often a basis through which scales are created (IE mean-tone) and could also become an used as a period/repeating-interval for NEW scales. 
    I am NOT (and never was) saying the 5th should be the octave in traditional Western scales...no way in hell...anyone trying to force my statement into that context is taking it all wrong.  Heck, O'Connell used PHI as the period/repeating-interval"pseudo-octave" and it also forms the circle/spiral in his scale...I'm just saying that, for some scales, the idea of using the repeating interval as the same interval that forms the "circle/spiral-of-xths" is NOT that alien of a concept to try. :-)

--- On Wed, 4/1/09, Cameron Bobro <misterbobro@...> wrote:

From: Cameron Bobro <misterbobro@...>
Subject: [tuning] Re: Rational vs Irrational Scales: a response to Rick
To: tuning@yahoogroups.com
Date: Wednesday, April 1, 2009, 12:26 AM

--- In tuning@yahoogroups. com, "rick_ballan" <rick_ballan@ ...> wrote:

> In fact, to those who would like to call the fifth the octave, let >me get this straight. So starting from C we would call a G by the >new name C since they are now equivalent. Then, since D is the fifth >of G, this would be called C too. In fact if we keep on going, >successive fifths would include all notes since we arrive back at C >after 7 8ve's. Therefore all notes would be called C. Harmonizing in >'octaves' would simply mean playing all notes of a melody in all >keys at once, at least in the 12 tet. That would sound nice. OR, if >we choose instead to call the fifth 3/2, since this never returns >back to the same note, then we would spiral off into an infinity of >keys, now all called "C notes", all playing simultaneously. That >would sound even nicer. Yeah "good point".

>

> -Rick

I call my notes things like "Frank", "Mathilda" and "golden-orange" .

By the way you are overlooking a very big and fundamental historical and practical concept: in real life, we usually have gamut and ambitus, and division of labor, not an infinite piano keyboard. Tetrachordal and pentachordal music for example is historically quite bound to specific ranges.

Anyway, noone is calling a fifth an octave except Michael, as I pointed out before, and I'm sure he'll settle on "interval of equivalence" or "period" or whatever once he realizes how confusing it is to say "octave" in this case.

And- you said something earlier about "noone answering your question"? What question was that, I seemed to have missed it?

--- In tuning@yahoogroups.com, "Cameron Bobro" <misterbobro@...> wrote:
>
> --- In tuning@yahoogroups.com, "rick_ballan" <rick_ballan@> wrote:
>
> > PS: Despite all of the responses with my name attached to it, not one of you has actually understood the gravity of my original question, let alone answered it.
> >
>
> What question was this?
>
> Could you also try harder to arrange your answers so that I can figure out who said what and so on- I know it's a real pain in the butt in Yahoo, compared to using a proper forum software, and I've also misattributed quotes more than once, I'm sure.
>
Yes it does get very confusing sometimes. I'd fix it if I knew how. The question, or rather problem, that began just before this thread started was, if a) tonality requires ratios a/b where a and b are whole, and b) no number a/b exists for irrationals (eg Pythagorean proof of sqroot 2), then c) where does this leave 12 tet and other equal distributions which are based on all irrationals and yet sound tonal?

To rephrase the question, could it be that the 12 tet intervals are not irrational at all but are in reality harmonics in the upper registers. For example, min 3rd 2^1/4 is close to 609/512, maj 3rd 2^1/3 close to 645/512, and fifth 2^7/12 approximates 767/512. (Note that 512 is the 9th octave to the tonic 1,2,4,8 etc...and that the numerators are odd). My suspicion is that because 'true' irrationals have an infinite number of digits and we can only discern to a few decimal places, then perhaps THEY are the idealism, not the harmonics as we always suspected? So on a practical level, my specific question was: can you hear any difference b/w these intervals just given and their tempered counterparts? Are they below the schizma threshold? Thanks,

-Rick

--My suspicion is that because 'true' irrationals have an infinite number
of digits and we can --only discern to a few decimal places, then perhaps
THEY are the idealism, not the --harmonics as we always suspected? So on
a practical level, my specific question was: --can you hear any
difference b/w these intervals just given and their tempered
--counterparts?

    I, for one, think you can hear a difference between irrationals and low-numbered fractions, but not a huge one.
   Take all the whole numbered ratios up to a denominator value of about 23 (almost about where the harmonic series begins beating too much to sound consonant: between the 23rd and 24th overtone)...and you can summarize most irrational values within about 10-15 cents...about as well as 12TET approximates diatonic 5-limit JI.
********************************************
   What does this mean?  I think it's a really lousy (though often followed) idea to think in terms of black and white and say either "JI is the best" or "irrational ratios are the best". 

   Rather, I think the best lies in compromising between the two...as in, for example, taking irrational number generated scales with very proportional difference tones and rounding them to very
nearby low-numbered fractions.

****************************************************
   Want something that has both dead-perfect equal difference tones (like noble-number generated scales) AND perfect fractions?  Then you're stuck with the harmonic series!!...where any two overtones next to each other are the same difference tone away from each other.  But, guess what...your ear will summarize the result down to a single tone...leaving little possibility contrast or tonal color changes.  Plus you can only get two to three octaves of range before you run into excessive beating problems around the 24th overtone.
   
   Want something that has good/proportional difference tones, tons of different tonal colors, and can be tied pretty closely, although not perfectly, to a harmonic-series-like feel of resolve?  Try rounding irrational-number generated scales (especially those generated by
noble numbers) to low-numbered fractions, trying to create scales where each note is a small-numbered fraction interval relative to both the last note in the scale and the root. 
    I've had much better luck than, say, my old favorite: x/16 harmonic series-based JI scales, so far as getting listeners to think such scales sound good...and they are much easier to compose with.

  So at least my answer to this question is...rational isn't an approximate of ideal rational scales or vice-versa...they both have properties evident in the harmonic series that can be synergized, mixed, matched, and used together to create something approaching the consonance of the harmonic series but with the kind of new and vast tonal color irrational scales can offer (rather than the "single tonality" feel of the harmonic series).

-Michael

--- On Wed, 4/1/09, rick_ballan <rick_ballan@yahoo.com.au>
wrote:

From: rick_ballan <rick_ballan@...>
Subject: [tuning] Re: Rational vs Irrational Scales: a response to Rick
To: tuning@yahoogroups.com
Date: Wednesday, April 1, 2009, 6:38 PM

--- In tuning@yahoogroups. com, "Cameron Bobro" <misterbobro@ ...> wrote:

>

> --- In tuning@yahoogroups. com, "rick_ballan" <rick_ballan@ > wrote:

>

> > PS: Despite all of the responses with my name attached to it, not one of you has actually understood the gravity of my original question, let alone answered it.

> >

>

> What question was this?

>

> Could you also try harder to arrange your answers so that I can figure out who said what and so on- I know it's a real pain in the butt in Yahoo, compared to using a proper forum software, and I've also misattributed quotes more than once, I'm sure.

>

Yes it does get very confusing sometimes. I'd fix it if I knew how. The question, or rather problem, that began just before this thread started was, if a) tonality requires ratios a/b where a and b are whole, and b) no number a/b exists for irrationals (eg Pythagorean proof of sqroot 2), then c) where does this leave 12 tet and other equal distributions which are based on all irrationals and yet sound tonal?

To rephrase the question, could it be that the 12 tet intervals are not irrational at all but are in reality harmonics in the upper registers. For example, min 3rd 2^1/4 is close to 609/512, maj 3rd 2^1/3 close to 645/512, and fifth 2^7/12 approximates 767/512. (Note that 512 is the 9th octave to the tonic 1,2,4,8 etc...and that the numerators are odd). My suspicion is that because 'true' irrationals have an infinite number of digits and we can only discern to a few decimal places, then perhaps THEY are the idealism, not the harmonics as we always suspected? So on a practical level, my specific question was: can you hear any difference b/w these intervals just given and their tempered counterparts? Are they below the schizma threshold? Thanks,

-Rick

--- In tuning@yahoogroups.com, djtrancendance@... wrote:
>
>     I, for one, think you can hear a difference between irrationals
> and low-numbered fractions, but not a huge one.

Not having followed the whole discussion - but to this sentence, as stated above, there is definitely only one answer: no, you cannot.

Reason: for any low-numbered (or high numbered or whatever) fraction, you can find irrationals arbitrarily close to it, so close that no human will ever hear the difference - so close that no instrument ever can produce the pitch with such accuracy.

But maybe you meant something different, not ANY irrational but one of a limited colelction, such as an equal temperament or so? That would be different.
--
Hans Straub

--- In tuning@yahoogroups.com, "hstraub64" <straub@...> wrote:
>
> --- In tuning@yahoogroups.com, djtrancendance@ wrote:
> >
> > I, for one, think you can hear a difference between irrationals
> > and low-numbered fractions, but not a huge one.
>
> Not having followed the whole discussion - but to this sentence, as stated above, there is definitely only one answer: no, you cannot.
>
> Reason: for any low-numbered (or high numbered or whatever) fraction, you can find irrationals arbitrarily close to it, so close that no human will ever hear the difference - so close that no instrument ever can produce the pitch with such accuracy.
>
> But maybe you meant something different, not ANY irrational but one of a limited colelction, such as an equal temperament or so? That would be different.
> --
> Hans Straub
>
Thanks Hans,

I'm not certain if you're answering me (Rick) or Michael, but if it was me, then yes, I was talking about something related but slightly different. Rather than asking which irrationals approx. small numbered fractions, which is the usual approach, I was asking the question the other way around i.e. whether or not the 12 tet intervals themselves, due to limits in hearing, are actually upper harmonics in the higher octaves.

For example, the tempered 3rd is 2^1/3 = 1.25992105...The "..." here means that, theoretically speaking, there are an infinite amount of digits after the decimal point, which as you said "no human will ever hear the difference". Therefore, if there is a finite number of digits after the decimal, then the 12 tet intervals might not be irrational at all. Ratios in the form "odd/8ve" that are successively closer to this tempered 3rd are 5/4 = 1.25, 81/64 = 1.265625, 161/128 = 1.2578125, 323/256 = 1.26171875, and 645/512 = 1.25976562. As we see, this last is exact to 3 decimal places. I'm guessing that we can't hear the difference but would like someone to test it for me anyway, just for the record.

Thanks again

Rick

-But maybe you meant something different, not ANY irrational but one of
-a limited collection, such as an equal temperament or so? That would -be
different.
  Yes, actually...I meant the degree of error as a result of rounding between irrational numbers in defined patterns (IE 24-or-less equal-temperament and noble-numbered scale)...rather than the infinite set of all irrational numbers. :-)

--Reason: for any low-numbered (or high numbered or whatever) --fraction,
you can find irrationals arbitrarily close to it, so close that no
--human will ever hear the difference - so close that no instrument ever
--can produce the pitch with such accuracy.
    In the above situation I mentioned...sometimes you can hear a difference (though, again, not a huge one).

    What I meant is...let's say you take an irrational generator the PHI, the Silver Ratio, PI or whatever and make a scale using something very purely based on that interval IE PI^x.

   My point is that, even with just low-numbered ratios (meaning up to about x/20)...you can still summarize most of such scales with rational values within a 10 cent or so margin...but not all.  It works well, obviously with the use of most tones in 12TET IE 2^(x/12)...where, say, the irrational value 1.05946 (the first semi tone) is indistinguishably close from the rational value 18/17 (1.0588).  However, there are some rough areas such as those ratios around 1.26....2^4/12 (1.2599) is around 13 cents from 5/4 IE 1.25...plus anything too close IE 1.035
simply can not be summarized without using ratios like 30/29 (beginning to move toward high and not low numbered ratios).
***************************************
    Side question: a lot of my scales have the same problem 12TET does...they have values near 1.26 which can't be easily summarized into rational ratios (there's always a noticeable difference to the ear between,say 1.258 and 1.25).  Do you know any tricks to get by this limitation?

-Michael

--- On Thu, 4/2/09, hstraub64 <straub@...> wrote:

From: hstraub64 <straub@...>
Subject: [tuning] Re: Rational vs Irrational Scales: a response to Rick
To: tuning@yahoogroups.com
Date: Thursday, April 2, 2009, 6:21 AM

--- In tuning@yahoogroups. com, djtrancendance@ ... wrote:

>

>     I, for one, think you can hear a difference between irrationals

> and low-numbered fractions, but not a huge one.

Not having followed the whole discussion - but to this sentence, as stated above, there is definitely only one answer: no, you cannot.

Reason: for any low-numbered (or high numbered or whatever) fraction, you can find irrationals arbitrarily close to it, so close that no human will ever hear the difference - so close that no instrument ever can produce the pitch with such accuracy.

But maybe you meant something different, not ANY irrational but one of a limited colelction, such as an equal temperament or so? That would be different.

--

Hans Straub

--645/512 = 1.25976562. As we see, this last is exact to 3 decimal
--places. I'm guessing that we can't hear the difference but would like
--someone to test it for me anyway, just for the record.
Wow, talk about having a very very high overtone where it matches!! :-D

   The problem I see is that instruments focus most of their volume on the first 3-5 overtones...and therefore having, say, a very faint overtone #30 perfectly in tune does not help much...if it exists at all (IE anything over about 600 times the 30th overtone escapes the range of human hearing around 17000 altogether).

   And, for the record, I've tried the test and...1.25992 sounds significantly different than 1.25...but not so far the the mind can't correct it pretty well among the other overtones of, say, a chord.  My own PHI scale has this same problem 12TET does that way: it's VERY hard to link a rational fraction to the area around 1.26: my own scale has about 1.2580 in it and you (Rick) kept asking me why I'm rounding the nearest rational number by more than 10 cents. 
Well, that's why! :-)

-Michael
--- On Thu, 4/2/09, rick_ballan <rick_ballan@...> wrote:

From: rick_ballan <rick_ballan@...>
Subject: [tuning] Re: Rational vs Irrational Scales: a response to Rick
To: tuning@yahoogroups.com
Date: Thursday, April 2, 2009, 7:30 AM

--- In tuning@yahoogroups. com, "hstraub64" <straub@...> wrote:

>

> --- In tuning@yahoogroups. com, djtrancendance@ wrote:

> >

> > I, for one, think you can hear a difference between irrationals

> > and low-numbered fractions, but not a huge one.

>

> Not having followed the whole discussion - but to this sentence, as stated above, there is definitely only one answer: no, you cannot.

>

> Reason: for any low-numbered (or high numbered or whatever) fraction, you can find irrationals arbitrarily close to it, so close that no human will ever hear the difference - so close that no instrument ever can produce the pitch with such accuracy.

>

> But maybe you meant something different, not ANY irrational but one of a limited colelction, such as an equal temperament or so? That would be different.

> --

> Hans Straub

>

Thanks Hans,

I'm not certain if you're answering me (Rick) or Michael, but if it was me, then yes, I was talking about something related but slightly different. Rather than asking which irrationals approx. small numbered fractions, which is the usual approach, I was asking the question the other way around i.e. whether or not the 12 tet intervals themselves, due to limits in hearing, are actually upper harmonics in the higher octaves.

For example, the tempered 3rd is 2^1/3 = 1.25992105.. .The "..." here means that, theoretically speaking, there are an infinite amount of digits after the decimal point, which as you said "no human will ever hear the difference". Therefore, if there is a finite number of digits after the decimal, then the 12 tet intervals might not be irrational at all. Ratios in the form "odd/8ve" that are successively closer to this tempered 3rd are 5/4 = 1.25, 81/64 = 1.265625, 161/128 = 1.2578125, 323/256 = 1.26171875, and 645/512 = 1.25976562. As we see, this last is exact to 3 decimal places. I'm guessing that we can't hear the difference but would like someone to test it for me anyway, just for the record.

Thanks again

Rick

Hello Rick,

--- In tuning@yahoogroups.com, "rick_ballan" <rick_ballan@...> wrote:

> The question, or rather problem, that began just before this thread
started was, if a) tonality requires ratios a/b where a and b are
whole, and b) no number a/b exists for irrationals (eg Pythagorean
proof of sqroot 2), then c) where does this leave 12 tet and other
equal distributions which are based on all irrationals and yet sound
tonal?

I don't think your a) is correct. In musical listening we hear
intervals categorically which is sufficient for tonality i.e. the
frequency ratios don't need to be exact for this to happen, for
example vibrations in the frequency ratios of 1:2^(7/12) and 3:2 both
produce an experience of a perfect fifth interval. They are also not
heard as 3:2s because we don't strictly speaking hear numbers or
frequency ratios, we hear intervals which are pitch relations. Pitch
is not the same thing as frequency even though it correlates strongly
with frequency. Why not? Many people with absolute pitch have noticed
a shift in their internal pitch standard with age and normal healthy
subjects can hear different pitches when a sine wave of same
frequency is presented separately to both ears (binaural diplacusis).
Pitch also depends on loudness in ways that vary greatly between
subjects.

> To rephrase the question, could it be that the 12 tet intervals are
not irrational at all but are in reality harmonics in the upper
registers.

No because strictly speaking intervals qua heard pitch relations are
not the sort of thing that can be said to be irrational (or
rational). Harmonics are also not intervals or even frequency ratios,
they are frequencies. It is true that we often talk in a way that
equates intervals and frequency ratios and this might explain why you
would think up such a question.

> For example, min 3rd 2^1/4 is close to 609/512, maj 3rd 2^1/3 close
to 645/512, and fifth 2^7/12 approximates 767/512. (Note that 512 is
the 9th octave to the tonic 1,2,4,8 etc...and that the numerators are
odd). My suspicion is that because 'true' irrationals have an
infinite number of digits and we can only discern to a few decimal
places,

Now hold on a second...

What do you mean we can only discern to a few decimal places? Again,
we don't hear numbers and even if we did why would that have anything
to do with decimal base for expressing numbers which is an arbitrary
choice?

> then perhaps THEY are the idealism, not the harmonics as we
always suspected? So on a practical level, my specific question was:
can you hear any difference b/w these intervals just given and their
tempered counterparts?

Even if we didn't detect any difference that wouldn't prove that we
hear the numbers you presented because we don't hear numbers. I don't
even believe there is any way to rephrase your question so that it
takes these considerations into account. Thus, your problem is not
solved, it is shown to be nonsensical.

> Are they below the schizma threshold?

What is that?

Kalle Aho

--- In tuning@yahoogroups.com, "rick_ballan" <rick_ballan@...> wrote:
>
> Thanks Hans,
>
> I'm not certain if you're answering me (Rick) or Michael,

I looked at the posting I answered to and have to say I myself cabbot tell for sure...

> but if it was me, then yes, I was talking about something related
> but slightly different.

Alright then - sorry for breaking in in any case.

>
> For example, the tempered 3rd is 2^1/3 = 1.25992105...The "..."
> here means that, theoretically speaking, there are an infinite
> amount of digits after the decimal point, which as you said "no
> human will ever hear the difference". Therefore, if there is a
> finite number of digits after the decimal, then the 12 tet
> intervals might not be irrational at all.

Sure. There is even no "might" - decimals with a finite number of digits are never irrational.

> Ratios in the form "odd/8ve" that are successively closer to this
> tempered 3rd are 5/4 = 1.25, 81/64 = 1.265625, 161/128 = 1.2578125,
> 323/256 = 1.26171875, and 645/512 = 1.25976562. As we see, this
> last is exact to 3 decimal places. I'm guessing that we can't hear
> the difference but would like someone to test it for me anyway,
> just for the record.
>

Well, the values of the above rations in cents are: 386.31, 407.82, 397.1, 402.47, 399.79. Without having it tested myself, I am quite sure that there is no audible pitch difference between 399.79 cents and 400 cents. I am not sure whether there might be an effect on the timbre, though (beating waves or so).
--
Hans Straub

--- In tuning@yahoogroups.com, "hstraub64" <straub@...> wrote:
>
> --- In tuning@yahoogroups.com, "rick_ballan" <rick_ballan@> wrote:
> >
> > Thanks Hans,
> >
> > I'm not certain if you're answering me (Rick) or Michael,
>
> I looked at the posting I answered to and have to say I myself cabbot tell for sure...
>
> > but if it was me, then yes, I was talking about something related
> > but slightly different.
>
> Alright then - sorry for breaking in in any case.
>
> >
> > For example, the tempered 3rd is 2^1/3 = 1.25992105...The "..."
> > here means that, theoretically speaking, there are an infinite
> > amount of digits after the decimal point, which as you said "no
> > human will ever hear the difference". Therefore, if there is a
> > finite number of digits after the decimal, then the 12 tet
> > intervals might not be irrational at all.
>
> Sure. There is even no "might" - decimals with a finite number of digits are never irrational.
>
> > Ratios in the form "odd/8ve" that are successively closer to this
> > tempered 3rd are 5/4 = 1.25, 81/64 = 1.265625, 161/128 = 1.2578125,
> > 323/256 = 1.26171875, and 645/512 = 1.25976562. As we see, this
> > last is exact to 3 decimal places. I'm guessing that we can't hear
> > the difference but would like someone to test it for me anyway,
> > just for the record.
> >
>
> Well, the values of the above rations in cents are: 386.31, 407.82, 397.1, 402.47, 399.79. Without having it tested myself, I am quite sure that there is no audible pitch difference between 399.79 cents and 400 cents. I am not sure whether there might be an effect on the timbre, though (beating waves or so).
> --
> Hans Straub
>
Ah of course you're right. How could there be a difference in less than one cent, stupid me. And who knows what other mitigating factors such as beats might be in play.

-Rick