12-equal Vs. Just tuning

Hi all,

Well it's been some time. If you can all remember, I first wrote to the group with the slightly controversial claim that the 12 tone equal temperament was not a compromise - and that only these 12 notes (with exact logarithmic spacing) were all that was needed for the best music.

I've since tried to 'get used to' certain perfect ratios, and particularly the Just tuned pitches. Using the computer, I also performed various experiments, but in the end, I still believe my original claim to be true.

In fact I almost got round to posting a poll with a few samples comparing 12-tET against Just. A few things stopped me though. I wanted to be sure of the best possible pitch/tune tests from which one could form a conclusion. This raises a few questions...

One test involved a simple rising scale. However, I was told that doing such a thing using the 'Just' pitches in such a fashion was 'melodically awkward' - so mean-tone would be better for this test. The thing is though, I really wanted the test to compare only the 'Just' and 12-tET temperaments - as mean-tone is (certainly) a compromise in one way or another.
Basically, my question is this:

What is the /furthest/ one can go before a 'tune' using the 'Just' pitches no longer becomes absolutely perfect?... For example, can one create a fairly complex chord with rippling notes, or is one confined to switching between octaves, perfect fifths, fourths and thirds? Remember, it can contain no pitch flaws (no matter how slight) whatsoever.

As a part of my own research, I compared the major chord from both temperaments:
Just: 1.0, 1.25 & 1.5 (0 Cents, 386.31 cents, & 701.95 cents respectively)
12-tET: 1.0, 1.25992 & 1.4983 (0 Cents, 400 cents, & 700 cents respectively)

At first, I used sine waves to experiment, and not surprisingly, they were very close, but in my opinion, the 12-tET major chord were sweeter and better sounding.
I then tried the same test using a pure ramp wave. This is a 'harsher' sound than the sine wave, and is reportedly more appropriate for these kind of experiments.

Interestingly, due to reasons of maths, I found the Just major chord to sound awful compared to 12-tET, but not because it was (too) off pitch - but because the sound timbre was very 'flat'. The reason it sounds flat compared to 12-tET is due to the pitches being perfect ratios of each other.
However, when using the apparently 'imperfect' 12-tET pitches, despite the (supposedly bad) 'beats' that it was producing, it of course sounded much better - thanks to the 'evolving' timbre. This of course isn't any real evidence against the 'Just' pitches - in fact - when I was testing using sine waves instead of ramp waves, both the Just pitches /and/ 12-tET sounded 'flat'.

Anyway, I still wanted to test using the ramp wave, so now I had to find another test - which was this:

If the Just ratios/pitches really are sweeter sounding than 12-tET, then the 'other side' of Just (even further away from 12-tET) should sound as 'bad' as 12-tET itself (according to the people who prefer Just). Observe:

12-tET: 1.0, 1.25992 & 1.4983 - (0 Cents, 400 cents, & 700 cents respectively)
Just: 1.0, 1.25 & 1.5 - (0 Cents, 386.31 cents, & 701.95 cents respectively)
'Other side of Just': 1.0, 1.24015 & 1.5017 - (0 cents, 372.617 cents, & 703.916 cents respectively)

1.24015 is gotten by 1.25/(1.25992/1.25)
1.5017 is gotten by 1.5/(1.4983/1.5)

Cleverly, this new 'Other side of Just' chord avoids the 'flat' sound of the Just version, as now the timbre 'evolves' just like the 12-tET chord. But how does it sound in terms of pitch?

Well, I'm not sure about some of you, but I found this to sound dreadful, and obviously even worse than the Just chord. However, I could be wrong.
To those who think that the sweetest sounding major chord is comprised of the pitches 1, 1.25 and 1.5 (Just), then this new chord should sound only as 'bad' as 12-tET sounded in the first place. Does it?
If anyone's interested, I'll post these different chords (in ramp, and sine wave format) up to the files section.

On top of all this, I still think dynamically altered (during the tune) Pythagoras pitches /also/ have a chance of being the best/sweetest pitches. I'll stop here though, as this is complex enough...

Cheers, Daniel

http://www.skytopia.com

--- In tuning@y..., "Daniel White" <soundburst@l...> wrote:

> Interestingly, due to reasons of maths, I found the Just major chord to sound awful compared to 12-tET, but not because it was (too) off pitch - but because the sound timbre was very 'flat'. The reason it sounds flat compared to 12-tET is due to the pitches being perfect ratios of each other.
> However, when using the apparently 'imperfect' 12-tET pitches, despite the (supposedly bad) 'beats' that it was producing, it of course sounded much better - thanks to the 'evolving' timbre. This of course isn't any real evidence against the 'Just' pitches - in fact - when I was testing using sine waves instead of ramp waves, both the Just pitches /and/ 12-tET sounded 'flat'.

If this is what you want, I suggest you forget about JI and compare 12-et to 31-et using actual musical examples.

In a message dated 9/25/02 11:21:18 PM Central Daylight Time,
soundburst@lycos.com writes:

> I first wrote to the group with the slightly controversial claim that the 12
> tone equal temperament was not a compromise - and that only these 12 notes
> (with exact logarithmic spacing) were all that was needed for the best
> music.

Daniel,

Mutation stops on pipe organs are tuned to just intonation. When the rest of
the organ is tuned to ET, the 1 3/5' stops are way out of tune with the major
thirds! Thus for most key signatures Meantone (0 - 2 #/b) or Werckmeister
(0-3 #/4 b) is a better tuning.

> What is the /furthest/ one can go before a 'tune' using the 'Just' pitches
> no longer becomes absolutely perfect?... For example, can one create a
> fairly complex chord with rippling notes, or is one confined to switching
> between octaves, perfect fifths, fourths and thirds? Remember, it can
> contain no pitch flaws (no matter how slight) whatsoever.

Any theoretical just interval can be tuned +/- 2 cents the theoretical value
and still sound normal to the ear. And +/- 3 cents still sounds in tune, but
has a celeste (vibrato) quality. Any greater out-of-tuneness destroys the
natural Difference and Sumational Combinational tomes. These are obviously
destroyed, or at the wrong pitch, via ET tuning!

Sincerely,
Moderator, <A HREF="/JustIntonationOrganSchool/">Just Intonation Organ eSchool</A>

--- In tuning@y..., "Daniel White" <soundburst@l...> wrote:

/tuning/topicId_39089.html#39089

> Hi all,
>
> Well it's been some time. If you can all remember, I first wrote to
the group with the slightly controversial claim that the 12 tone
equal temperament was not a compromise - and that only these 12 notes
(with exact logarithmic spacing) were all that was needed for the
best music.
>

***Well, the only thing a bit problematic about your thesis results
from the question "Why 12??"

Why not pick 13 or some other number? Historically, if I understand
the "story" correctly, the emulation of your dreaded just pitches was
one reason for the choice of that particular number of steps per
octave. If you've ever seen Paul Erlich's chart comparing the ET's
with just intervals, you will see that 12-equal ranks *very* high in
just ratio emulation in the relatively lower number ETs.

We have first Pythagorean, with entirely just 3:2 ratios, and then
Meantone which "corrects" the thirds and makes them *just!* (There it
is again!) and then, later, the equivalent of 11-comma meantone or 12
equal to "smooth it all out" so we can transpose with greater
facility to different keys.

So there *is* a definite history to this and it involves *very much*
a *compromise* from low ratio intervals in its evolution.

I admit, 12-equal is a great scale (as is 19, 31 and even the new
tuning list invented "Blackjack") but it's claim to "bestness"
or "perfectness" has to end pretty much with that.

Had history gone differently, and maybe somebody like Vicentino
caught on, as I understand it, we might be using 31-tET or 19-tET
today instead!!!

J. Pehrson

hi Joe,

> From: "Joseph Pehrson" <jpehrson@rcn.com>
> To: <tuning@yahoogroups.com>
> Sent: Thursday, September 26, 2002 6:05 PM
> Subject: [tuning] Re: 12-equal Vs. Just tuning
>
>
> --- In tuning@y..., "Daniel White" <soundburst@l...> wrote:
>
> /tuning/topicId_39089.html#39089
>
> > Hi all,
> >
> > Well it's been some time. If you can all remember, I first wrote to
> the group with the slightly controversial claim that the 12 tone
> equal temperament was not a compromise - and that only these 12 notes
> (with exact logarithmic spacing) were all that was needed for the
> best music.
> >
>
> ***Well, the only thing a bit problematic about your thesis results
> from the question "Why 12??"
>
> Why not pick 13 or some other number? Historically, if I understand
> the "story" correctly, the emulation of your dreaded just pitches was
> one reason for the choice of that particular number of steps per
> octave. If you've ever seen Paul Erlich's chart comparing the ET's
> with just intervals, you will see that 12-equal ranks *very* high in
> just ratio emulation in the relatively lower number ETs.
>
> We have first Pythagorean, with entirely just 3:2 ratios, and then
> Meantone which "corrects" the thirds and makes them *just!* (There it
> is again!) and then, later, the equivalent of 11-comma meantone or 12
> equal to "smooth it all out" so we can transpose with greater
> facility to different keys.
>
> <snip>

be careful ... you mean 1/11-comma meantone == 12-equal,
*not* 11-comma.

-monz
"all roads lead to n^0"

--- In tuning@y..., "monz" <monz@a...> wrote:

/tuning/topicId_39089.html#39098

>>
>
> be careful ... you mean 1/11-comma meantone == 12-equal,
> *not* 11-comma.
>

***Whoops. Thanks Monz. Yes, 11 commas would make quite an
interval! :-)

JP

Hi all,

I might as well answer all your posts in this one (no point in posting multiple messages).

--------

Hi Gene,

>>any real evidence against the 'Just' pitches - in
>>fact - when I was testing using sine waves instead
>>of ramp waves, both the Just pitches /and/ 12-tET
>>sounded 'flat'.

>If this is what you want, I suggest you forget about
>JI and compare 12-et to 31-et using actual musical
>examples.

I'll explain what I think about 19/31 ET scales later...

-------

Hi Wally paulrus,

> your reactions seem to be largely a product of
> white/european music-cultural norms. if you had
> grown up in certain parts of thailand or the
> gambia, you would probably prefer the "other
> side of just" examples to either the just or
> the 12-equal examples, since these would come
> closer to the musical intervals of your "native tongue".

There's always a chance that a whole culture could (ultimately) be mistaken - whether western or eastern, ancient or modern.
A good reason why slightly different scales exist is because the brain has a certain amount of 'tolerance' - and can get used to pitches if they sound slightly off (similar to the way when you're born - how the eye adapts an upside-down image over time and reverses it to the right way up!). However, this doesn't mean that there isn't a perfect scale from which to /deviate from/.

>take a good solid week to become acclimated to
>the music of a culture with a significantly
>different tuning system -- modern arabic music
>would be a good example -- and don't listen to
>any western music at all during that week. now
>try your experiment again. i guarantee your
>reactions will be radically different!

Well, I wouldn't mind trying the test - hmm... maybe there's a specific favourite piece of music you'd like to point me to one so I can try. The thing is, I believe that such arabic music would sound better to everyone (eventually) if it was fully converted to 12-tET.

As for the 26-equal music you mentioned, once again, I would argue that it would sound better in 12-tET. However, I can't be too sure, so maybe you could point me to a url (or email me if you like), as I would have to listen to each piece in its own right to really comment further.
Bear in mind that whatever the style of music is, due to the current quality of music out there, I only generally like (and possibly /should/ only like) the top 0.001 - 0.2 percent of each (the ones with best melody, orchestration, chords etc. etc.).... Ummm... imho ;-}

>justness may strike you as "sweet" or it may strike you as "dull and lifeless"

Well, off pitch is more like it ;) Lifeless/Flatness etc. is conditional not on the pitch - but the timbre and wave evolution of the sound I would've thought...

--------

Hi Johnny,

>Daniel--might your experiment be akin to a
>person hating the taste of coconut.

Good point :) Hmmm... well I'm not too sure about food, but I truly believe that all music has a certain universal degree of value to it - and that even if no-one knows for sure what this value is, that doesn't mean it doesn't exist. In other words, some tunes really are better/worse than other tunes (in different ways, and for different reasons - taking into account melody, intricacy, harmony, chords, orchestration, and even the 'lowest' level - the wave itself (instrument timbre etc.). Perhaps there's even a formula to create good music, but no doubt it'd be impossibly complex and certainly outside our reach for the time being :)
Anyway, my point is that this 'Universal Aesthetic' approach can be applied to scales too.

About the issue you mentioned of how (most) people prefer the Just intonation intervals, well... I'm still not 100% convinced. As I said earlier, they could have got (wrongly) used to them. I admit /I/ could be the one who's wrong, but at the moment, there still seems too many discrepancies for me to think that 12-ET is a compromise and/or not the perfect/only tuning needed for all the best music.

And yes - Coconuts are (should be) universally tasty (logarithmic score: 65.8/120 ;-)

>Go for Oum Kalthoum and try to pick out the
>quartertones.
>They are so organically integral to the music
>that all notes are fully legitimate as scale
>(or maqam) tones.

Hmmm.. once again sounds interesting, but at most, I should think that these quartertones would sound best off 'in between' beats. More likely though that it's approaching a pseudo-atonal style with glimpses of actual 12-tET melody/harmony creeping in. (disclaimer - as usual I can't be 100% sure :)
Umm... I'll give the 'Oum Kalthoum' music a look sometime soon maybe.

---------

Hi prophecyspirit,

>Mutation stops on pipe organs are tuned to just intonation.
>When the rest of the organ is tuned to ET, the 1 3/5'
>stops are way out of tune with the major thirds!

Interesting. If my theory is right then, it's a pity that the Mutation stops can't also be tuned to 12-eT...

>Any theoretical just interval can be tuned +/- 2
>cents the theoretical value and still sound normal
>to the ear. And +/- 3 cents still sounds in tune,
>but has a celeste (vibrato) quality. Any greater

Interesting. Do those values apply for the vibrato effect too?

>out-of-tuneness destroys the natural Difference
>and Sumational Combinational tomes. These are
>obviously destroyed, or at the wrong pitch, via
>ET tuning!

I would argue the exact same thing - but against
Just tuning instead :)

---------

Hi Joseph,

>***Well, the only thing a bit problematic
>about your thesis results from the question
>"Why 12??"

That's the ultimate question for which I only wish I knew the answer :)
I'm not too keen on the theory which says how it's the opposite of a prime number (many factors) - since there are other numbers good at this too.

>with just intervals, you will see that 12-equal ranks
>*very* high in just ratio emulation in the relatively
>lower number ETs.

Umm... maybe there's a possibility that possible attempts (such as this one) at 'ranking' scales is a no-go - since extremely high numbers (which might score favourably according to the ranking system) contain many dud notes - which aren't (impto*) particularly useful in the best music.
In fact, there are quite a few ranking schemes. Which one of them is right - if any?
The fact that some of the better ET's (such as 19, 31 etc.) sound better - could just mean that they give any possible tune created from these scales a better chance for 12-tET melody/harmony to creep through (and the more it does - the merrier impto).

*(impto = "in my (possibly true) opinion" - or what I'm arguing for.)

Phew, that's about all I have to say for now... :)

Cheers,
Daniel

http://www.skytopia.com
http://www.skytopia.com/project/rating.html

Hi Daniel and everybody concerned!

So, your claim seems to be that 12-equal which historically saw the
light of day as a compromise might actually be the perfect tuning for
all music in the whole universe. I assume 12-equal was chosen because
it is the smallest equal division of the octave which contains the
traditional diatonic system. And I strongly believe it was not chosen
for the quality of it's sounds. That means we have stumbled upon this
Ideal System accidentally. Pretty cosmic, ha?

While I can bend my brains to accept this as at least logically
possible state of affairs, we all understand that possibility doesn't
entail actuality.

I don't hear anything special in 12-equal intervals, but I think I
should, if indeed 12-equal is the Perfect Tuning. I can hear justness
if the ratios are sufficiently simple and timbre is pretty static,
but I don't prefer justness. In fact I don't think there is an Ideal
System. Why do you think there must be such a thing?

It's your claim, you've got the burden of proof too.

Kalle Aho

--- In tuning@y..., "Daniel White" <soundburst@l...> wrote:

/tuning/topicId_39089.html#39124

>
> >take a good solid week to become acclimated to
> >the music of a culture with a significantly
> >different tuning system -- modern arabic music
> >would be a good example -- and don't listen to
> >any western music at all during that week. now
> >try your experiment again. i guarantee your
> >reactions will be radically different!
>
> Well, I wouldn't mind trying the test - hmm... maybe there's a
specific favourite piece of music you'd like to point me to one so I
can try. The thing is, I believe that such arabic music would sound
better to everyone (eventually) if it was fully converted to 12-tET.
>

***Hello Daniel!

I'm not really much of an authority on this subject, but my
impression is that such a "conversion" would substantially take much
of the character out of this music... (Jewish cantillation, and such
like, too...)

I'm sure your comment will elicit more responses on this list...

best,

Joseph

> From: "Daniel White" <soundburst@lycos.com>
> To: <tuning@yahoogroups.com>
> Sent: Wednesday, September 25, 2002 9:20 PM
> Subject: [tuning] 12-equal Vs. Just tuning
>
>
> Hi all,
>
> Well it's been some time. If you can all remember,
> I first wrote to the group with the slightly controversial
> claim that the 12 tone equal temperament was not a
> compromise - and that only these 12 notes (with exact
> logarithmic spacing) were all that was needed for the
> best music.

sounds to me like an echo of Schoenberg -- that's almost
literally what he said about it in 1911. and that's the
pronouncement which i feel sealed the fate of tuning for
most of the 1900s. (Schoenberg's _Harmonielehre_ was
enormously important, historically.)

speaking historically, 12edo was indeed proposed and
accepted as a compromise between other available and
preferred tunings, and even Schoenberg said so, calling
it "an indefinitely extended truce" between the just
ratios and the practicalities of instrument construction,
notation, etc.

as can be seen in my Tuning Dictionary definition
</tuning/files/dict/12-eq.htm>
12edo developed out of the much older Pythagorean
(3-limit) tuning, by a simple tempering: viewed as a
chain of "5ths", the Pythagorean comma arises in comparison
of the 13th pitch with the 1st, the 13th being about
23.5 cents higher than the 1st. if the comma is
distributed among 12 pitches, the system becomes
the closed 12-tone equal-temperament.

the fact that 12edo also functions as a meantone
(~1/11-comma meantone), *and* a schismic temperament
(similar to Groven's tuning but more limited), *and*
a diesic temperament, *and* a tuning which fits into
a whole host of other types of temperament families,
*and* the fact that the pitch set is so small, helps
to explain its widespread appeal.

12edo first became popular as a tuning for the lute
and other fretted string instruments, c. 1500. because
of the fact that in those days frets were created by
tying pieces of gut around the neck of the instrument,
the frets had to go straight across the fingerboard.
so the staggered frets needed for just-intonation were
impossible then.

as an aside, i'd also like to mention my speculations
that 12edo could be as old as civilization itself:
/tuning/files/monzo/sumerian/sumeriantuning.htm

in any case, with the widespread (and continuously
growing) interest in microtonality, as well as a
greater consciousness concerning faithfulness to the
intended tunings of pre-Romantic-era composers, it
seems rather pointless to me at this late date to
try to shoehorn all the "best" music into 12edo.

in general, Renaissance vocal music sounds best in a
form of adaptive-JI, Renaissance keyboard and Baroque
orchestral music sounds best in meantone, Classical
keyboard music sounds best in a well-temperament, and
jazz sounds best in 12edo. of course there are exceptions,
but these were the intended tunings in these repertoires,
and the music was written with the purpose of exploiting
the particular tuning's characteristics. and the better
the music (and the composer), the better the tuning's
characteristics are exploited, and thus the more important
it is to render that repertoire in the intended tuning.

as an experiment, i'd love to hear you retune some of
Harry Partch's music into 12edo and tell me how much
you think you've "improved" it. i tried it once with
_Barstow_, and trust me, it wasn't better.

-monz
"all roads lead to n^0"

In a message dated 9/29/02 8:52:58 AM Central Daylight Time,
kalleaho@mappi.helsinki.fi writes:

> I don't prefer justness.

Kalle,

I believe why some don't prefer perfect just tuning is because it's
unnatural. It doesn't occur in the natural harmonic spectrum to any extent.
As the exact harmonic intervals produced depend on many variables--how the
tones are produced, the sound-producing material, weather, temperature,
biometric pressure, sound strength, and so forth. Thus, when just tuning is
produced to its exact theoretical values, it's still not a natural sound!

To sound natural just intonation needs to be detuned slightly up to 2 cents
+/- the theoretical values. The result is just temperament, not theoretical
just intonation. The exact amount of detuning depends on how the scale and
what scale is produced.

The tones in my just-temperament organ are produced by frequency-divider tone
generators tuned to ET. Presently there are six of them. Theoretically there
should be eight. As the stops are split at Middle C to provide the greatest
stop selection.

On each keyboard half one tone generator is tuned to C. +/- 0 cents, another
to E +/- 386, and another to 7 Bb +/- 969 cents. There should be another
tuned to +/- 155 cents for 7 D, to provide a harmonic 7th for E.

The present value for C and its 5ths circle is 0 cents (making the 5ths worth
700 cents), E and its 5ths circle 384 cents and 7 Bb and its 5ths circle 968
cents.

The minor 7th for E and its 5ths circle is presently 168 cents. This produces
a large minor 7th for E and its 5ths circle worth 984 cents. This is taken
from the 30/17 harmonic ratio worth 983 cents. This compromise was made
presently because the E 386 cents harmonic minor 7th and its 5ths circle is
rarely used in any given composition. And because it would cost me several
hundred dollars to add two more tone generators.

The final result is the practical just-temperament scale and its keyboard
layout I posted here some time back. For a given key signature there are 19
notes to the octave. So split digitals were added to each keyboard to provide
the extra seven notes. These are rarely used in a given composition, but need
to be instantly available when needed.

In fact I don't think there is an Ideal > System.

I believe my just temperament scale is as ideal as one can make for a
keyboard instrument! Even the diminished harmonic-minor 7th chord is
harmonious--worth 884 cents.

Sincerely,
Pauline W. Phillips, Moderator, <A HREF="/JohannusOrgansSchool ">Johannus Organs eSchool</A>
Johannus Orgelbouw, Holland, builds pipe, pipe-digital, digital-sampled
organs.
Moderator, <A HREF="/JustIntonationOrganSchool/">Just Intonation Organ eSchool</A>

In a message dated 9/29/02 11:12:21 AM Central Daylight Time,
monz@attglobal.net writes:

> with the widespread (and continuously
> growing) interest in microtonality, as well as a
> greater consciousness concerning faithfulness to the
> intended tunings of pre-Romantic-era composers, it
> seems rather pointless to me at this late date to
> try to shoehorn all the "best" music into 12edo.
>
monz,

My practical just-temperament keyboard scale posted here before has three
pitches per diatonic and chromatic digital, and theoreticaly should have
four. So I, too, see no light in the idea of ET being the right scale!

Sincerely,
Pauline W. Phillips, Moderator, <A HREF="/JohannusOrgansSchool ">Johannus Organs eSchool</A>
Johannus Orgelbouw, Holland, builds pipe, pipe-digital, digital-sampled
organs.
Moderator, <A HREF="/JustIntonationOrganSchool/">Just Intonation Organ eSchool</A>

Hi Daniel,

IMHO claim that 12ET represents a sort of natural perfection is
disproved by a simple fact: 12ET thirds are nearly impossible to sign
in harmony! In cadential context, when there is enough time to settle
a perfect chord, even average amateur singers are strongly attracted
to JI third.

Try this very simple experiment, play any note on a piano, sustain it,
sign the third, sustain it for a few seconds, then play the third on
the piano. Result: most people are too low (by some 15 cents) wrt to
piano. That works nearly all the time for nearly anybody with minimal
musical training.

This cannot be demonstrated as simply for JI fourth and fifth which
are less than 2 cents off their 12ET counterpart.

Nevertheless, the pervasiveness of 12ET in our environment is such
that most singers uses ET in MELODIC context or as initial value (for
a few tenth of seconds or less depending of the skill of the singers)
in harmonic context, but JI thirds has very strong attraction in long
chords.

In fact, except when explicitly seeking for some some roughness, most
a capella music is performed (consciously or not) in some form of
adaptative JI.

I am no musicologist, but I noted that a composer such as Fauré,
wisdomly avoid doubling the vocal thirds in keyboard accompagnment of
multipart vocal music, in order (I think) to let the vocal harmony
settle naturally. He cleverly managed to make JI and ET work together.

yours truly

François Laferrière

--- In tuning@y..., prophecyspirit@a... wrote:

> To sound natural just intonation needs to be detuned slightly up to 2 cents
> +/- the theoretical values. The result is just temperament, not theoretical
> just intonation.

This suggests then following possibilities:

5 limit: 53 et
7 limit: 99 et
11 and 13 limits: 224 et
beyond 13: 311 et

Other possibilities are 65, 84, and 87 for the 5-limit, 130 or 140 for the 7-limit (171 being too much of a good thing) and 270 or 311 for the 11 and 13 limits. 311 is a kind of universal temperament for those who prefer an error within 2 cents, but not no error at all. Monz can mark me down as advocating it if he likes. :)

In a message dated 9/30/02 4:52:12 AM Central Daylight Time,
francois.laferriere@oxymel.com writes:

> when there is enough time to settle
> a perfect chord, even average amateur singers are strongly attracted
> to JI third.
>
This is true. it's very common among singers who re-record themselves singing
harmony to their melody. They then sing the perfect third so closely to the
theoretical value, and with the same vocal harmonic content in both parts,
that it creates the reedy sound I mentoned in a prior post!

I ocne had a digital-sampled organ demo tape. It was introduced by an opera
orchestra playing a bit from an opera piece. Right away I noticed how closely
to the harmonic-minor 7th the orchestra played. Much closer than I'd ever
heard in an orchestra before. That reminded me of the fact Monteverde began
using the minor 7th in his music before other major composers did.

The German Lutherans first used the minor 7th chord in their congregational
hymns where the people were supposed to sing in four parts. And Christian
hymns to this day freely use the minor 7th chord. And four-part harmony
sounds wonderful on the just-temperament organ I'm building! So much so I've
come to prefer four-part music better than any other kind. It's the purest
musical form there is.

Pauline

In a message dated 9/30/02 8:07:35 AM Central Daylight Time,
genewardsmith@juno.com writes:

> a kind of universal temperament for those who prefer an error within 2
> cents, but not no error at all.

No, minute just temperament isn't any error. It's what occurs in nature. I
had a book on organ stops where the author pointed out that the harmonics in
organ pipes, as well as in musical instruments, aren't 100% their theoretical
values--for more reasons than I listed in a prior post.

I once had a top-octave tone generator that used various IC chips to create a
12-note scale where every interval was justly tuned to the theoretical values
escept Bb-F. I connected this to a three-octave frequency divider. The more I
played and listened to this setup the more my ears told me it was an
unnatural, artificial sound! I

n contrast the ET 4trh and 5th detuned 2 cents sound natural. So I created a
scale that provided the JI slight detuning, using three ET tone generators
rather than one. In the process it proved to be a practical scale for any key
signature.

Even the octave in the keyboard middle sounds better detuned slightely. As,
when it's 100% true, it emphasizes itself stronger there than it should in a
chord. That's oen reason why I split the keybaord at Middle C with each half
using different tone generators. That way all octaves from Tenor C-B into the
Alto range are slightly detuned, but much less than 2 cents. When an octave
is detuned 2 cents, it creates a celeste tone.

Sincerely,
Pauline W. Phillips, Moderator, <A HREF="/JohannusOrgansSchool ">Johannus Organs eSchool</A>
Johannus Orgelbouw, Holland, builds pipe, pipe-digital, digital-sampled
organs.
Moderator, <A HREF="/JustIntonationOrganSchool/">Just Intonation Organ eSchool</A>

--- In tuning@y..., "Daniel White" <soundburst@l...> wrote:
> -------
>
> Hi Wally paulrus,
>
> >take a good solid week to become acclimated to
> >the music of a culture with a significantly
> >different tuning system -- modern arabic music
> >would be a good example -- and don't listen to
> >any western music at all during that week. now
> >try your experiment again. i guarantee your
> >reactions will be radically different!
>
> Well, I wouldn't mind trying the test - hmm... maybe there's a
specific favourite piece of music you'd like to point me to one so I
can try. The thing is, I believe that such arabic music would sound
better to everyone (eventually) if it was fully converted to 12-tET.

In response to this, let me relate something from my past experience.

When I first investigated alternative tuning systems in 1963, one of
the things I did was to retune my electronic organ to the meantone
temperament, which is practically the same thing as a subset of 31-
ET. This was in the days before digital music electronics, and
lacking an electronic tuning aid, I did the tuning by timing the
beating fifths against a metronome, after calculating the beat rates
using logarithm tables. It was very time-consuming, but the result
was quite accurate.

I kept the organ tuned this way for several weeks and was absolutely
delighted with the way older organ music (such as Bach and Handel)
sounded, as long as I didn't try to make enharmonic substitutions (in
order to avoid the "wolf" fifth). Particularly intriguing was the
fact that augmented seconds and diminished sevenths sounded different
from (i.e., more dissonant than) minor thirds and major sixths,
something that we don't have with 12-ET.

But I did miss the ability to modulate freely, and so I put the organ
back into 12-ET. I was totally unprepared for the shock that I
received when, after playing no more than two or three chords, I
found my ears literally assaulted by dissonant triads that would find
no resolution or rest until, in desperation, I omitted the third of
the chord, leaving an open fifth. In meantone I could easily flee
the wolf by playing in another key, but in 12-ET there was no
escape. Not only did the thirds and sixths have a jarring effect,
but everything sounded out of tune. It suddenly became obvious to me
why organs were not generally tuned in equal temperament in England
until after 1850; if I found the change hard to accept after only a
few weeks in meantone, how difficult it must have been for those who
had spent all their lives with it to put up with 12-ET, in which you
have three times the error in the major and minor triads.

The out-of-tune sensation of equal temperament left me after a short
while, but I have never been satisfied with its unending dissonance
since that time. I soon solved the problem by devising a well-
temperament that would give me more consonant-sounding triads in at
least a few keys, until such time as I was able to obtain an
instrument with more than twelve keys per octave. So I now have the
meantone sound in 31 different keys (plus 7 and 11 harmony).

By the way, if you intend to conduct this sort of experiment
yourself, you need to use timbres with harmonic partials -- sine
waves or bells won't do.

> >justness may strike you as "sweet" or it may strike you as "dull
and lifeless"
>
> Well, off pitch is more like it ;) Lifeless/Flatness etc. is
conditional not on the pitch - but the timbre and wave evolution of
the sound I would've thought...

The lifeless or stagnant effect that some have objected to with just
intonation is a result of the absence of disturbances caused by
beating harmonics or non-coincident combinational tones, so interval
size has a lot to do with it.

But any lack of life you might perceive in just intonation with sine
waves would have more to do with the just major third being smaller,
which makes the leading lower in pitch and less effective
melodically. If you were to try 17-ET with sine waves; I suspect you
would find that it makes 12-ET sound lifeless and bland by
comparison. (At least that has been my experience with it.) So I
would say that 12-ET is about as good melodically as it is
harmonically -- a compromise that does both about equally well (or
badly, depending on your point of view).

> ---------
>
> Hi prophecyspirit,
>
> >Mutation stops on pipe organs are tuned to just intonation.
> >When the rest of the organ is tuned to ET, the 1 3/5'
> >stops are way out of tune with the major thirds!
>
> Interesting. If my theory is right then, it's a pity that the
Mutation stops can't also be tuned to 12-eT...

Well, they could, but then they wouldn't be in a true harmonic
relationship with the pipes sounding the fundamental pitch and would
beat against the harmonics of those pipes, causing each and every
single note to be literally out of tune all by itself.

> >Any theoretical just interval can be tuned +/- 2
> >cents the theoretical value and still sound normal
> >to the ear. And +/- 3 cents still sounds in tune,
> >but has a celeste (vibrato) quality. Any greater
>
> Interesting. Do those values apply for the vibrato effect too?

The beating of the thirds in 12-ET is so fast that it's not even a
vibrato; I would describe it as more of a grating effect. But you
don't fully realize how bad it is until you've spent a little time
with something that has (harmonically) better thirds.

> >out-of-tuneness destroys the natural Difference
> >and Sumational Combinational tomes. These are
> >obviously destroyed, or at the wrong pitch, via
> >ET tuning!
>
> I would argue the exact same thing - but against
> Just tuning instead :)

You can't. In JI the combinational tones are in exact mathematical
relationship with the fundamental, but in 12-ET they're quite
discordant (by practically anyone's definition of the term). This is
in addition to the fast-beating harmonics in the thirds, so 12-ET
leaves a lot to be desired.

It looks like the only way to convince you is to have you try
something like my meantone experiment.

--George

Explain how a tuning can be both Just and Tempered?

I thought it's either Just OR Tempered.

* David Beardsley
* http://biink.com
* http://mp3.com/davidbeardsley

In a message dated 10/1/02 7:56:24 AM Central Daylight Time,
davidbeardsley@biink.com writes:

> Explain how a tuning can be both Just and Tempered?
> I thought it's either Just OR Tempered.
>
An interval is just when it's within the limits the ear accepts as just,
which for intervals other than the octave is +/- 2 cents. A few more cents
off still sound just to the ear, but with a celeste effect such as is done
via a violin vibrato when double stopped.

Technically, any interval tuned to other than it's theoretical value is by
definition tempered. But most intervals most of the time don't occur in
nature at their exact theoretical values. Thus the term "just temperament,"
which I think I coined, is the realistic term to use, and which makes the
most musical sense.

Organs have celeste and tremulant stops. These vary the pitch above and below
the normal pitch. Thus whatever tuning is used, just, meantone, Werckmeister,
or ET is off momentarily the intervals' mathematical values. So the matter
boils down to whether we want to talk math here or music. I as a trained
organist and organbuilder prefer to talk in musical terms more so than math.

And thus haven't mentioned intervals in cents to the third decimal point. And
because in just temperament such exactness is meaningless to the ear!

Sincerely,
Pauline W. Phillips, Moderator, <A HREF="/JohannusOrgansSchool ">Johannus Organs eSchool</A>
Johannus Orgelbouw, Holland, builds pipe, pipe-digital, digital-sampled
organs.
Moderator, <A HREF="/JustIntonationOrganSchool/">Just Intonation Organ eSchool</A>

> An interval is just when it's within the limits the ear accepts as just,
> which for intervals other than the octave is +/- 2 cents. A few more cents
> off still sound just to the ear, but with a celeste effect such as is done
> via a violin vibrato when double stopped.

Hello. I don't think you can make a blanket statement like the above.
Whether or not an interval sounds pure/just depends on the beholder. I
would bet that most folks wouldn't even notice a difference of 2 cents.
The fact that our ears will accept an ET major third that's 14 cents
sharp (and still kind of sounds like a JI major third) says something.
Perhaps the brain makes the correction for us. In the grand scheme of
musical performance I think being a couple of cents off is down in the
noise. Sincerely,

In a message dated 10/2/02 6:48:10 AM Central Daylight Time,
arl_123@hotmail.com writes:

> The fact that our ears will accept an ET major third that's 14 cents
> sharp (and still kind of sounds like a JI major third) says something.
>
Tuning shouldn't be based on interval sounds alone. But on how complete
chords sound, in root position and every inversion. Minor 7th, diminished
minor 7th and 9th chords sound very dissonet when tuned to ET. Whereas in
just intonation or just temperament each chord sounds harmonious, and least
in the scale I invented. As the 7th and 9th chords are harmonic 7th and 9ths,
and the dim. 7th is worth 884 cents, a just major 6th.

Sincerely,
Pauline W. Phillips, Moderator, <A HREF="/JohannusOrgansSchool ">Johannus Organs eSchool</A>
Johannus Orgelbouw, Holland, builds pipe, pipe-digital, digital-sampled
organs.
Moderator, <A HREF="/JustIntonationOrganSchool/">Just Intonation Organ eSchool</A>

Hello Pauline,

It has been interesting for me to read your posts. You have a sureness to your writing that makes it clear where you are on most musical questions.

2 points to add. The term "Just Temperament" is quite old. It was used by Murray Barbour and I've noticed it in Ethnomusicology articles. But I believe it is an oxymoron. Temperament is the movement from Just.

Regarding 2 cents as just: Much has to do with the ears attached to the mind. This would bother me, musically, even if it would not bother most others. I would rather move people's hearing toward greater perceptions, even if the may not be immediately recognizeable consciously by the listener.

For people using just intonation on winds, it is possible to be more exact. And it is a different reference, allowing movement away from the mathematical perfection to be perceived as expression.

best, Johnny Reinhard

In a message dated 10/2/02 5:07:59 PM Central Daylight Time, Afmmjr@aol.com
writes:

> Regarding 2 cents as just: Much has to do with the ears attached to the
> mind. This would bother me, musically, even if it would not bother most
> others. I would rather move people's hearing toward greater perceptions,
> even if the may not be immediately recognizeable consciously by the
> listener.
>
> Johnny Reinhard
>
Johnny,

Since you say I didn't invent the term "just temperament," it adds force to
what I've been saying on the subject. As a writer, I have invended words. In
some caes I may not have originated them, but I hadn't read them before.
Sometimes moe than one person invents the same thing. I began using "just
temperament" in the 1990s.

The musical reason for just temperament is to keep the notes making intervals
from being in phase. Such does not occur in nature to any extent in the
harmonic spectrum beyond the 1st octave in acoustic musical instruments nor
organ pipes.

When the major just 3rd has its notes in phase and the minor 3rd added to
make a just triad, the result is a reedy quality not wanted in most
music.I've noticed this in my own experiments as well as via singers who
record themselves twice so as to sing ithe melody and a major 3rd below.

Sincerely,
Pauline W. Phillips, Moderator, <A HREF="/JohannusOrgansSchool ">Johannus Organs eSchool</A>
Johannus Orgelbouw, Holland, builds pipe, pipe-digital, digital-sampled
organs.
Moderator, <A HREF="/JustIntonationOrganSchool/">Just Intonation Organ eSchool</A>

----- Original Message -----
From: <Afmmjr@aol.com>

> The term "Just Temperament" is quite old. It was used by
>Murray Barbour and I've noticed it in Ethnomusicology
>articles. But I believe it is an oxymoron. Temperament is
>the movement from Just.

That I can agree with!

dB

* David Beardsley
* http://biink.com
* http://mp3.com/davidbeardsley

--- In tuning@y..., David Beardsley <davidbeardsley@b...> wrote:
> ----- Original Message -----
> From: <Afmmjr@a...>
>
> > The term "Just Temperament" is quite old. It was used by
> >Murray Barbour and I've noticed it in Ethnomusicology
> >articles. But I believe it is an oxymoron. Temperament is
> >the movement from Just.
>
> That I can agree with!

more specifically, temperament is an adjustment from just where
specific "commas" are made to vanish; that is, certain pitches at
some distance from one another in the lattice, which are different in
just intonation, are made to coincide in a tempered tuning. this is
the whole point of temperament.

if someone were to (very reasonably) desire a simple modification
from just intonation so that harmonies aren't phase-locked, with the
static pattern of destructively and constructively interfering
partials that this implies (and which some people find unpleasant), i
would describe this simply as "deliberate mistuning". "temperament",
however, is more specific; etymologically it refers to "taming the
wolves", or intervals that are a comma removed from pure consonance,
that arise in just intonation. if no wolves are being tamed, we
have "deliberate mistuning", but no "temperament".

Maybe it is in one's personal temperament to describe "deliberate mistuning" as distinctive from "temperament." All temperament is a deliberate mistuning.

best, Johnny Reinhard

In a message dated 10/4/02 11:35:51 AM Central Daylight Time,
wallyesterpaulrus@yahoo.com writes:

> more specific; etymologically it refers to "taming the
> wolves", or intervals that are a comma removed from pure consonance,
> that arise in just intonation. if no wolves are being tamed, we
> have "deliberate mistuning", but no "temperament".
>
In the just-temperament scale I posted here there's a wolf--between C# and
G#. However the slight detuning doesn't remove it, and isn't intended to. As
the C key signature doesn't use the interval. But another wolf is
removed--between D# and Bb.
The detuning turns D# into both D# and Eb. Thus both the B major and septimal
c minor triads can be used . G# is turned into both G# and Ab, so both the E
major and septimal f minor chords can be used.

Sincerely,
Pauline W. Phillips, Moderator, <A HREF="/JohannusOrgansSchool ">Johannus Organs eSchool</A>
Johannus Orgelbouw, Holland, builds pipe, pipe-digital, digital-sampled
organs.
Moderator, <A HREF="/JustIntonationOrganSchool/">Just Intonation Organ eSchool</A>

--- In tuning@y..., Afmmjr@a... wrote:
> Maybe it is in one's personal temperament to describe "deliberate
mistuning" as distinctive from "temperament." All temperament is a
deliberate mistuning.
>
> best, Johnny Reinhard

True, but all deliberate mistuning is not temperament.

Kalle

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>

/tuning/topicId_39089.html#39238

wrote:
> --- In tuning@y..., David Beardsley <davidbeardsley@b...> wrote:
> > ----- Original Message -----
> > From: <Afmmjr@a...>
> >
> > > The term "Just Temperament" is quite old. It was used by
> > >Murray Barbour and I've noticed it in Ethnomusicology
> > >articles. But I believe it is an oxymoron. Temperament is
> > >the movement from Just.
> >
> > That I can agree with!
>
> more specifically, temperament is an adjustment from just where
> specific "commas" are made to vanish; that is, certain pitches at
> some distance from one another in the lattice, which are different
in
> just intonation, are made to coincide in a tempered tuning. this is
> the whole point of temperament.
>
> if someone were to (very reasonably) desire a simple modification
> from just intonation so that harmonies aren't phase-locked, with
the
> static pattern of destructively and constructively interfering
> partials that this implies (and which some people find unpleasant),
i
> would describe this simply as "deliberate
mistuning". "temperament",
> however, is more specific; etymologically it refers to "taming the
> wolves", or intervals that are a comma removed from pure
consonance,
> that arise in just intonation. if no wolves are being tamed, we
> have "deliberate mistuning", but no "temperament".

***Wasn't there, Paul, a procedure called "microtemperament" advanced
by Dave Keenan, where the objective was to go *in the direction* of
just intonation... or am I confused about this??

Thanks!

Joseph

--- In tuning@y..., "Kalle Aho" <kalleaho@m...> wrote:
> --- In tuning@y..., Afmmjr@a... wrote:
> > Maybe it is in one's personal temperament to describe "deliberate
> mistuning" as distinctive from "temperament." All temperament is a
> deliberate mistuning.
> >
> > best, Johnny Reinhard
>
> True, but all deliberate mistuning is not temperament.
>
> Kalle

you got the right idea kalle. yes, johnny is correct. your statement,
though, would be more correctly phrased "not all deliberate mistuning
is temperament".

in other words, the set of temperaments is a subset of the set of
deliberate mistunings.

--- In tuning@y..., prophecyspirit@a... wrote:
> In a message dated 10/4/02 11:35:51 AM Central Daylight Time,
> wallyesterpaulrus@y... writes:
>
>
> > more specific; etymologically it refers to "taming the
> > wolves", or intervals that are a comma removed from pure
consonance,
> > that arise in just intonation. if no wolves are being tamed, we
> > have "deliberate mistuning", but no "temperament".
> >
> In the just-temperament scale I posted here there's a wolf--between
C# and
> G#. However the slight detuning doesn't remove it, and isn't
intended to. As
> the C key signature doesn't use the interval. But another wolf is
> removed--between D# and Bb.

ah -- thanks for pointing this out! i had missed this feature --
sorry!

> The detuning turns D# into both D# and Eb.

i know you don't like math, but it will help some of us if you use
ratios. in other words, think in just intonation for a moment. do you
mean you're using one note for both 75/64 and for 7/6? then you're
tempering out 225:224, or at least ignoring it.

> Thus both the B major and septimal
> c minor triads can be used . G# is turned into both G# and Ab, so
both the E
> major and septimal f minor chords can be used.

i'd like to understand this better. is this another instance of
225:224 being tempered out?

are there any other "commas" besides 225:224 being tempered out?

if not, your system may bear some relationship with the planar
temperament defined by 225:224. on this list several scales from this
system have come up, such as the 12-note lumma/fokker system and the
19-note vitale/keenan system . . .

if you are tempering out some other "comma" as well, then you may be
essentially using some subset of a linear temperament, which has a
single generating interval. if we can determine this other "comma",
we can find the generator . . .

in any case, there has been a large body of discussion
on "microtemperament", which typically involves tempering out small
intervals such as 225:224, 2400:2401, etc., both on this list and on
the tuning-math list, and hence involves only tiny deviations from
just intonation. may i humbly suggest that such terminology
("microtemperament") may be more acceptable to some of the advocates
of strict, pure just intonation, who would prefer to reserve use of
the term "just" for situations which are inherently _untempered_?

In a message dated 10/7/02 3:34:24 PM Central Daylight Time,
wallyesterpaulrus@yahoo.com writes:

> it will help some of us if you use
> ratios. in other words, think in just intonation for a moment.

Every note in my just scale is a harmonic partial ratio, except the possible
use of 30/17 for the E and B harmonic minor 7ths. Thus some of the numbers
aer quite high. And I don't remember them all either. The tempered values are
even harder to keep track of.

For example, D# is 75/64. But Eb as 267 (269) cents as the harmonic minor 7th
for F is very much higher. However, it can be seen as 7/6 as an interval
ratioo. Ab in relation to F is also 7/6. G# is 25/20. C# is 135/128. F# is
45/32. Bb is 7/4 (7/6 to G).

Pauline

--- In tuning@y..., prophecyspirit@a... wrote:
> In a message dated 10/7/02 3:34:24 PM Central Daylight Time,
> wallyesterpaulrus@y... writes:
>
>
> > it will help some of us if you use
> > ratios. in other words, think in just intonation for a moment.
>
> Every note in my just scale is a harmonic partial ratio, except the
possible
> use of 30/17 for the E and B harmonic minor 7ths. Thus some of the
numbers
> aer quite high. And I don't remember them all either. The tempered
values are
> even harder to keep track of.

hi pauline, some of us will be quite grateful for any clues you may
provide us with. keep the info coming.

> For example, D# is 75/64. But Eb as 267 (269) cents as the harmonic
minor 7th
> for F is very much higher. However, it can be seen as 7/6 as an
interval
> ratioo. Ab in relation to F is also 7/6. G# is 25/20. C# is
135/128. F# is
> 45/32. Bb is 7/4 (7/6 to G).

hi pauline, you appear to be simply talking about some pure just
intonation scale here. what some of us are trying to figure out is
exactly where the temperament comes into your system. at least two of
us independently came up with the hunch that you're tempering out the
septimal kleisma, or 225:224. also, in another post you mentioned the
schisma, 32805:32768, or the difference between eight perfect fifths
up and a major third down (octave reduced, of course). are you
tempering this out too?

[perhaps, then, the linear temperament defined by 225:224 and
32805:32768 would be a good fit -- can anyone remind me what system
that is, by working out the appropriate wedgies or whatever?]

In a message dated 10/7/02 5:27:34 PM Central Daylight Time,
wallyesterpaulrus@yahoo.com writes:

> what some of us are trying to figure out is
> exactly where the temperament comes into your system.

I'm not a mathite. I caculated cents to the 3rd decimal point for just
pitches, and computed harmonic-partial ratios for specific notes. I tempered
386.314 to +/- 384. Orginally it was 385. But decided on3e84 to allow using a
tempered 30/17 ratio for the 384 harmonic minor 7th. I tune by ear.

I don't know what the ratio is for 385. 384 in Helmholz' book is 8192/6561.
It doesn't reakly matter. It takes three decibels +/- to notice any
difference in loudness. Likewise it takes 3 cents +/- to notice any
difference in pitch unless one listens very carefully for it, or has a
comparison to go by.

Pauline

--- In tuning@y..., prophecyspirit@a... wrote:
> In a message dated 10/7/02 5:27:34 PM Central Daylight Time,
> wallyesterpaulrus@y... writes:
>
>
> > what some of us are trying to figure out is
> > exactly where the temperament comes into your system.
>
> I'm not a mathite. I caculated cents to the 3rd decimal point for
just
> pitches, and computed harmonic-partial ratios for specific notes. I
tempered
> 386.314 to +/- 384. Orginally it was 385. But decided on3e84 to
allow using a
> tempered 30/17 ratio for the 384 harmonic minor 7th. I tune by ear.
>
> I don't know what the ratio is for 385.

whether it's 385 or 384, or the exact ratios for these intervals, is
completely unrelated to what i was asking.

> 384 in Helmholz' book is 8192/6561.

that's the ratio you get if you tune 8 perfect fifths down in just
intonation.

> It doesn't reakly matter. It takes three decibels +/- to notice any
> difference in loudness. Likewise it takes 3 cents +/- to notice any
> difference in pitch unless one listens very carefully for it, or
has a
> comparison to go by.

hi pauline,

i'm afraid you're missing the point of my question.

obviously your 384-cent interval is *functioning* as a 5:4 ratio, and
in that context alone (ignoring other functions) it doesn't matter if
it's 385, 388, or whatever.

what i'm trying to get at is the set of *compromises* that are
inherent to your system.

if you understand meantone temperament, you can see that it functions
by tempering out the 81:80. for example, in just intonation, the
major sixth above an arbitrary pitch is sometimes 5/3, but it's
sometimes 27/16, but in meantone they're the same pitch. so the ratio
of the interval between these two pitches, (27/16)/(5/3) = 81/80, is
the interval that's tempered out in meantone, and in a sense it's the
*defining comma* of meantone.

the helmholtz and groven systems that have been discussed recently
operate differently, and have intervals much closer to just
intonation. helmholtz and groven tempered each perfect fifth narrow
by about 1/4 of 1 cent, so that the interval formed by tuning 8
fifths down would be a just 5:4 "major third". they used 24 and 36
notes, respectively, in order to be able to obtain mostly just
(within 1/4 of 1 cent) harmony in all 12 keys of written classical
music. we call these systems examples of "schismic temperament",
because the schisma is the difference between eight perfect fifths
down and one major third up in just intonation.

schismic is just one example of the many microtemperaments, including
some that involve ratios of 7 and even higher primes, that have been
discussed on this list and on the tuning-math list. it appears your
system may be another such example. what i'm trying to determine is,
which one?

-paul

In a message dated 10/7/02 6:58:41 PM Central Daylight Time,
wallyesterpaulrus@yahoo.com writes:

> it appears your
> system may be another such example. what i'm trying to determine is,
> which one?
>
> -paul
>
I don't have enough info to say exactly what my system would be described as.
All I can do is give the figures. Theoretically D# is 274 cents from B 1088.
7Eb is 269 from F 500. G# is 772 from E 386. 7Ab is 768 (from Bb 999--57th
harmonic).

These b/# differences are merged by using the ET 5th worth 700 cents and
making the major 3rds 384 cents. Then D#/Eb are 268 cents. If the major 3rds
are made 385 cents, D#/Eb would be 270. Either way the results for both uses
sound just to the ear and are very harmonious.

I think it's pretty slick to be able to have a single note work as both a #
and a b harmonic 7th! This also allows playing in septimal minor. Which,
according to the harmonic numbers, is preferable to tertian minor--6-7-9 v.
10-12-15. Thus my C major scale also plays in 7c minor. It in conjunction
with another scale will also play in tertian e minor, all depending on what
notes are called for in a given composition.

The relative minor a for C is actually the tertian minor for the F scale.

Pauline

--- In tuning@y..., prophecyspirit@a... wrote:
> In a message dated 10/7/02 6:58:41 PM Central Daylight Time,
> wallyesterpaulrus@y... writes:
>
>
> > it appears your
> > system may be another such example. what i'm trying to determine
is,
> > which one?
> >
> > -paul
> >
> I don't have enough info to say exactly what my system would be
described as.
> All I can do is give the figures. Theoretically D# is 274 cents
from B 1088.
> 7Eb is 269 from F 500. G# is 772 from E 386. 7Ab is 768 (from Bb
999--57th
> harmonic).
>
> These b/# differences are merged by using the ET 5th worth 700
cents and
> making the major 3rds 384 cents. Then D#/Eb are 268 cents. If the
major 3rds
> are made 385 cents, D#/Eb would be 270. Either way the results for
both uses
> sound just to the ear and are very harmonious.
>
> I think it's pretty slick to be able to have a single note work as
both a #
> and a b harmonic 7th! This also allows playing in septimal minor.
Which,
> according to the harmonic numbers, is preferable to tertian minor--
6-7-9 v.
> 10-12-15. Thus my C major scale also plays in 7c minor. It in
conjunction
> with another scale will also play in tertian e minor, all depending
on what
> notes are called for in a given composition.
>
> The relative minor a for C is actually the tertian minor for the F
scale.
>
> Pauline

the best i can tell is that you're still talking about 75/64 and 7/6
coming out to the same pitch in your system, which means 225:224 is
indeed being tempered out. assuming that's all that's being tempered
out, at least in the 7-limit, what you have is a planar temperament
(that is, a temperament constructed from two independent generators,
not including the octave).

last year on the tuning-math list, gene ward smith derived the
optimal generators for this temperament, given a just octave of 1200
cents. they are:

699.812912 cents and
384.171625 cents

hence your observation that

"These b/# differences are merged by using the ET 5th worth 700 cents
and making the major 3rds 384 cents."

seems exactly right -- in fact you couldn't possibly have done better
in whole number cents, as both of your values here are less than 0.2
cents from optimal!

dave keenan suggested the name "byzantine" for this temperament some
time ago, since rami vitale's 19-note scale seemed so strongly to
imply this system, though that didn't seem appropriate to me. perhaps
we should name it "phillips" in your honor instead (is that your last
name?)

so, for the sake of fostering better communication on this list in
the future, it might be helpful if you were to describe this system
as "the 225:224 microtemperament" or something, rather than
continuing to use the word "just", which means something very special
to some highly committed musicians.

assuming the above is correct, the next topics might be: how do you
propose to handle I-vi-ii-V-I and I-IV-ii-V-I progressions when scale
degree 2 is prominent in the melody; and how do you propose to handle
five-part chords like C-E-G-A-D?

In a message dated 10/7/02 9:08:21 PM Central Daylight Time,
wallyesterpaulrus@yahoo.com writes:

> perhaps
> we should name it "phillips" in your honor instead (is that your last
> name?)

Yes. In my formal discussion as posted in my forum (see sig file), I've
called my scale the Phillips just-temperament scale. If you want to call it
the Phillips 225:224 microtemperament scale, OK.

> for the sake of fostering better communication on this list in
> the future, it might be helpful if you were to describe this system
> as "the 225:224 microtemperament" or something, rather than
> continuing to use the word "just", which means something very special
> to some highly committed musicians.

When an acoustic string instrument is justly tuned as accurately as possible,
it's detuned the first time it's played, or even if it isn't used after
tuning. So I have no problem calling a deliberate slight detuing as just
temperament. As such occurs in nature. And wind instruments have to be warmed
up to be in tune. It's only electronic instruments that can produce
theoretical just intonation, and keep it.

> assuming the above is correct, the next topics might be: how do you
> propose to handle I-vi-ii-V-I and I-IV-ii-V-I progressions when scale
> degree 2 is prominent in the melody; and how do you propose to handle
> five-part chords like C-E-G-A-D?
>
My scale has the above chords and the above notes. So I see no problem. The F
scale might be needed as well as the C, depending on what kind of chord is
called.for. The ii chord is normally a septimal chord. The vi can be also, or
A-C-E 400. The latter note being a split digital in C or F.

The 520-cent interval between E and A in the C scale is used. It sounds fine
when resolved to G. Some chords in theri inversions might need to use a
different note from the root position, depending on whether its smooth. On
the other hand, some note combinations will cover slight undulation.

Sincerely,
Pauline W. Phillips, Moderator, <A HREF="/JohannusOrgansSchool ">Johannus Organs eSchool</A>
Johannus Orgelbouw, Holland, builds pipe, pipe-digital, digital-sampled
organs.
Moderator, <A HREF="/JustIntonationOrganSchool/">Just Intonation Organ eSchool</A>

Hi all,
Once again, your favourite subject ;) - and another 'multi-post' coming up.=
......

------------

Hi Kalle Aho,

>So, your claim seems to be that 12-equal which historically saw the
>light of day as a compromise might actually be the perfect tuning for
>all music in the whole universe.

I couldn't have put it any better myself :D

>I don't hear anything special in 12-equal intervals, but I think I
>should, if indeed 12-equal is the Perfect Tuning. I can hear justness

Hmm.. the intervals on their 'own' (either as a chord or sequence) sound 'o=
k', which is what would be expected really... It's when the notes are put in=
to (good) intricate harmonious/melodic music, when they really become specia=
l :)

>if the ratios are sufficiently simple and timbre is pretty static,
>but I don't prefer justness. In fact I don't think there is an Ideal
>System. Why do you think there must be such a thing?

I guess maybe for the same reason I also believe that every piece of music =
can be 'rated'...
Also, I suppose most in this group would think that Just (or near Just) pit=
ches are best for harmony in 12 note music (correct me if I'm wrong). I'm no=
t sure if I agree with that (as you all well know ;), but the point is that =
there must be (mathematical) reasons why certain pitches/intervals are bette=
r than others.

>It's your claim, you've got the burden of proof too.

Hehe - proof is such a difficult (but perhaps not impossible) thing in the =
world of music =)

-------

Hi Prophecyspirit,

>The problem with ET tuning is that no matter how the
>intervals are tuned, the harmonic spectrums created
>by the notes involved, when produced by wind or
>string instrumens or sung, are nontheless naturally
>tuned to just intonation!

If by 'harmonic spectrums', you're referring to the harmonic overtones, the=
n I think I see your point. Perhaps the reason why certain instruments (such=
as pianos and organs) might sound better with tunings slightly different to=
exact 12-ET - is that maybe one should also consider the overtones.
It wouldn't surprise me if these instruments cause the subtle overtones to =
clash with the fundamental tones of 12-eT. If this really is the case, then =
the problem isn't specifically with 12-eT, but rather with the overtones tha=
t a particular instrument produces - meaning that 12-eT possibly isn't a com=
promise after all.
A 'perfect instrument' could avoid these (what I think are) problems, if cr=
eated mathematically from the ground up (synthesizer style). Any 'overtones'=
created could also be tuned to 12-eT.

This is really getting complicated now that overtone harmonics come into th=
e equation :)

---------

Hi François Laferrière,

>IMHO claim that 12ET represents a sort of natural perfection is
>disproved by a simple fact: 12ET thirds are nearly impossible to sign
>in harmony! In cadential context, when there is enough time to settle
>a perfect chord, even average amateur singers are strongly attracted
>to JI third.
>
>Try this very simple experiment, play any note on a piano, sustain it,
>sign the third, sustain it for a few seconds, then play the third on
>the piano. Result: most people are too low (by some 15 cents) wrt to
>piano. That works nearly all the time for nearly anybody with minimal
>musical training.

Yes, but amateur singers are more likely to get it wrong ;-)

To be honest, you make a strong case, and as I have said previously, I'm st=
ill not 100% sure.
Now these are only theories, so don't jump on them, but:

A: Maybe the singers used in any experiment were 'wavering', and they presu=
med that they were hitting 1.25 instead of 1.259 (perhaps by taking the 'tro=
ugh' of the pitch instead of the middle or peak). These two pitches are very=
close, so it can be very hard to tell.

B: Also, it could've been that maybe the singer was (mistakingly) /aiming/ =
for chords which didn't beat rather than for what actually sounded best.

C: Thirdly, as I've said in reply to Prophecyspirit, they might be hitting =
this beatless pitch to be in harmony with the (imo) faulty harmonic overtone=
s that certain instruments produce - rather than in harmony with the fundame=
ntal pitch. This could certainly be plausible.

D: Due to the acoustic properties of both the human voice and instrument in=
question, maybe there's a quasi-mathematical 'sound effect' (like some kind=
of subtle 'wowowow') that enhances the interval if sung in Just (1.25). Thi=
s though is more of an side-effect, and I guess this 'sound effect' could be=
mathematically synthesized and added to the 1.259 interval too if necessary=
- then you would have the best of both worlds.

E: Finally, perhaps the singers involved didn't quite hit the exact pitch t=
hat they should have done anyway - especially if they were 'trained' to hit =
1.25 - or even 'not trained enough' to hit 1.259

It could be one of these...or any mix of these.

-----------

Hi George,

>I was totally unprepared for the shock that I
>received when, after playing no more than two or three chords, I
>found my ears literally assaulted by dissonant triads that would find
>no resolution or rest until, in desperation, I omitted the third of
>the chord, leaving an open fifth. In meantone I could easily flee
>the wolf by playing in another key, but in 12-ET there was no
>escape. Not only did the thirds and sixths have a jarring effect,
>but everything sounded out of tune. It suddenly became obvious to me
>why organs were not generally tuned in equal temperament in England
>until after 1850;

But maybe this could be explained by the 'tolerance margin' that one can bu=
ild up over time. To myself, Just intervals grate - not 12-eT. Also, the oth=
er possiblity could be thanks to point C in my previous reply.
Interesting story btw.

>But any lack of life you might perceive in just intonation with sine
>waves would have more to do with the just major third being smaller,
>which makes the leading lower in pitch and less effective
>melodically. If you were to try 17-ET with sine waves; I suspect you
>would find that it makes 12-ET sound lifeless and bland by
>comparison. (At least that has been my experience with it.) So I

Well, I don't really mind the flatness too much (which can be countered by =
having a decent vibrato anyway, complex timbre, or going slightly above 'Jus=
t' as a few have suggested in this thread). It's the pitch itself I have pro=
blems with :)

>would say that 12-ET is about as good melodically as it is
>harmonically -- a compromise that does both about equally well (or
>badly, depending on your point of view).

Maybe I'm mistaken, but I think I recall someone in this group saying how f=
or /melodic/ purposes, 12-eT is perfect, whilst harmonically it isn't perfec=
t (well, he got one of those right ;)...

>> I would argue the exact same thing - but against
>> Just tuning instead :)

>You can't. In JI the combinational tones are in exact mathematical
>relationship with the fundamental, but in 12-ET they're quite
>discordant (by practically anyone's definition of the term). This is
>in addition to the fast-beating harmonics in the thirds, so 12- ET
>leaves a lot to be desired.

Once again, I can understand that logically speaking - 'rational' numbers s=
eem as though they are the best option, but there's always a chance they mig=
ht not be.
Remember that even PI is an irrational number, but is a very important numb=
er in mathematics. The 'imperfect' beating of course is a by-product from th=
e irrational numbers, but perhaps ultimately not one which is of any signifi=
cance. Maybe the ear really wants to hear 'irrational' logarithmic intervals=
...

>It looks like the only way to convince you is to have you try
>something like my meantone experiment.

Hmm.. maybe you could put up something on the web?
In the mean time, do you know of a comparison anywhere on the web which dem=
onstrates a good (say... classical) tune with examples of 12-eT vs Just tuni=
ng? I should imagine the web is filled with such comparisons - all waiting t=
o prove me wrong! ;D

Thanks,
Daniel (soundburst@lycos.com)

http://www.skytopia.com
http://www.skytopia.com/soundburst/soundburst.html

In-Reply-To: <anteg5+k3bi@eGroups.com>
wallyesterpaulrus wrote:

> last year on the tuning-math list, gene ward smith derived the
> optimal generators for this temperament, given a just octave of 1200
> cents. they are:
>
> 699.812912 cents and
> 384.171625 cents

I don't know how these where chosen. I flatten both 3:1 and 5:1 by a
quarter of 225:224, which gives

700.03 cents and
384.39 cents

They don't fit Pauline's tuning of 105:64 as 855 cents. I get it as 853
cents, and I don't think Gene's optimum can be much different. Some
figures that do work are keeping 3:1 as 1/4 of 225:224 flat, and making
5:4 only 1/6 of 225:224 flat. The figures are

700.03 cents and
385.03 cents

This fits the major third originally being 385 cents, but altered for
convenience. 7:4 is then 1/6 of 225:224 sharp, at 970.11 cents. For
105:64, 105 factors as 3*5*7. The 5 and 7 cancel, so the ratio is flat by
1/4 of 225:224 (the same as 3:1). That makes it 855.17 cents.

With this tuning, 7:6 is 1/3 of 225:224 sharp, making it 269.44 cents.
Pauline gives it as 268 cents, and JI is 266.87 cents. So the planar
temperament overshoots.

However I look at it, Pauline's tuning is a compromise between a 225:224
planar temperament and strict JI. You may be able to tweak a specific
planar temperament to get within 1 cent, but I'm not sure. I don't think
that's how she worked it out, anyway, but she may have been applying
similar criteria.

Graham

In-Reply-To: <ant1ke+3bj6@eGroups.com>
wallyesterpaulrus wrote:

> [perhaps, then, the linear temperament defined by 225:224 and
> 32805:32768 would be a good fit -- can anyone remind me what system
> that is, by working out the appropriate wedgies or whatever?]

Is that some kind of rhetorical question, or have you really forgotten?
See <http://x31eq.com/schismic.htm>. It doesn't match
Pauline's numbers, because 3:2 and 5:4 are pulling in different
directions.

Graham

Has anyone figured out Pauline's full scale yet so I
can add it to the archive?

Manuel

In a message dated 10/8/02 4:08:21 AM Central Daylight Time,
soundburst@lycos.com writes:

> This is really getting complicated now that overtone harmonics come into th=
> e equation :)
>
Since musical instruments and their natural harmonic partials came millennia
before the ET scale was invneted, it stands to reason a proper scale should
be based on the harmonic spectrum, rather tthan make a scale first and then
force instruments to conform to it.

Pauline

In a message dated 10/7/2002 9:55:34 PM Eastern Standard Time, prophecyspirit writes:

> And wind instruments have to be warmed up to be in tune. It's only electronic instruments that can produce theoretical
> just intonation, and keep it.

I must disagree with this statement. Wind instruments that are warmed up are as flexible to pitch as the mind-ear is sensitive. If I must match a pitch someone is playing (without vibrato) then I will match it. In fact, there is jitter in the voice, but not wind instruments.

Also, even if the open string changes, willy-nilly, the astute player still references to what is in the mind-ear of the sensitive player.

The bassoon does not tune up at all. It is only through the mind-ear that it matches pitch. And one can--and does--play a straight tone that does not move even the most sensitive tuning machine.

best, Johnny Reinhard

--- In tuning@y..., "Daniel White" <soundburst@l...> wrote:
> Hi all,
> Once again, your favourite subject ;) - and another 'multi-post'
coming up.=
> ......
>
> ------------
>
> Hi George,
>
> >I was totally unprepared for the shock that I
> >received when, after playing no more than two or three chords, I
> >found my ears literally assaulted by dissonant triads that would
find
> >no resolution or rest until, in desperation, I omitted the third of
> >the chord, leaving an open fifth. In meantone I could easily flee
> >the wolf by playing in another key, but in 12-ET there was no
> >escape. Not only did the thirds and sixths have a jarring effect,
> >but everything sounded out of tune. It suddenly became obvious to
me
> >why organs were not generally tuned in equal temperament in England
> >until after 1850;
>
> But maybe this could be explained by the 'tolerance margin' that
one can bu=
> ild up over time. To myself, Just intervals grate - not 12-eT.
Also, the oth=
> er possiblity could be thanks to point C in my previous reply.
> Interesting story btw.

Since we were trying to convince you that 12-ET is not "best", it is
only necessary to establish that there is something "better"; whether
this might be JI or another temperament is secondary. Since you have
an objection to JI, I was trying to direct your attention to meantone
temperament or 31-ET (its virtual equivalent), which I don't think
anyone has ever described as harsh or grating (as long as you avoid
the wolf).

The point that I was attempting to make is that, while I was very
shocked when I again used 12-ET after several weeks of playing
exclusively in meantone, I had a very delightful experience when I
first played in meantone temperament after years of playing
exclusively in 12-ET. Surely this must say that something other than
a "tolerance margin" would be the primary consideration here.

> Maybe I'm mistaken, but I think I recall someone in this group
saying how f=
> or /melodic/ purposes, 12-eT is perfect, whilst harmonically it
isn't perfec=
> t (well, he got one of those right ;)...

There is considerable evidence to suggest that raising the leading
tone tends to improve the effect of its resolution to the tonic, both
melodically *and* harmonically(!). (I wrote an article which was
accepted for publication in the next issue of Xenharmonikon in which
I elaborate on the effectiveness of a harmonically dissonant leading
tone.)

> >It looks like the only way to convince you is to have you try
> >something like my meantone experiment.
>
> Hmm.. maybe you could put up something on the web?
> In the mean time, do you know of a comparison anywhere on the web
which dem=
> onstrates a good (say... classical) tune with examples of 12-eT vs
Just tuni=
> ng? I should imagine the web is filled with such comparisons - all
waiting t=
> o prove me wrong! ;D

I was thinking of an experiment in which you were to *listen* to what
you were *playing* so that you could try out as many different things
as possible in the new tuning. (The problem with today's digital
electronic instruments is that you have to have one that allows you
to retune the notes individually.) But if you're only going to
listen to something and not do the actual playing, then try to listen
to a number of things in the same tuning (I suggested meantone
temperament) for a number of times over a period of a couple of weeks
before you go back and listen to the *same thing(s)* (in the same
timbres) in 12-ET.

I would have to leave it to someone else to suggest the best place on
the web where you could find something for this purpose.

--George

hi pauline -|>

just a brief note to readers -- i'm not caught up yet, so if this
contradicts, parodies, or otherwise insults anything already posted,
please accept my apologies and pleas of ignorance . . .

<|-

--- In tuning@y..., prophecyspirit@a... wrote:

> > for the sake of fostering better communication on this list in
> > the future, it might be helpful if you were to describe this
system
> > as "the 225:224 microtemperament" or something, rather than
> > continuing to use the word "just", which means something very
special
> > to some highly committed musicians.
>
> When an acoustic string instrument is justly tuned as accurately as
possible,
> it's detuned the first time it's played, or even if it isn't used
after
> tuning. So I have no problem calling a deliberate slight detuing as
just
> temperament. As such occurs in nature. And wind instruments have to
be warmed
> up to be in tune. It's only electronic instruments that can produce
> theoretical just intonation, and keep it.

well, the highly committed musicians i was speaking of would probably
begin to speak in terms of an "ideal" at this point in the
conversation. let me therefore leave it to them. the promotion of
microtemperaments has not met with the warmest of responses around
here in the past.

> > assuming the above is correct, the next topics might be: how do
you
> > propose to handle I-vi-ii-V-I and I-IV-ii-V-I progressions when
scale
> > degree 2 is prominent in the melody; and how do you propose to
handle
> > five-part chords like C-E-G-A-D?
> >
> My scale has the above chords and the above notes. So I see no
problem. The F
> scale might be needed as well as the C, depending on what kind of
chord is
> called.for. The ii chord is normally a septimal chord.

i'm not sure this effect is quite what some people would accept for,
say, renaissance or baroque music. which pitches exactly would you
use?

> The vi can be also, or
> A-C-E 400. The latter note being a split digital in C or F.

so something like 16:19:24, or is the "just" premise abandoned here?

> The 520-cent interval between E and A in the C scale is used.

seems like the latter . . .

could i entreat of you to spell out the full progression, say in
cents or something?

> It sounds fine
> when resolved to G. Some chords in theri inversions might need to
use a
> different note from the root position, depending on whether its
smooth.

i thought you were going to play existing, tonal, music, as written
(?)

> On
> the other hand, some note combinations will cover slight undulation.

in the melody? still, didn't you say you worked out some full
transcriptions of substantial pieces of western repertoire?

--- In tuning@y..., "Daniel White" <soundburst@l...> wrote:

> In the mean time, do you know of a comparison anywhere on the web
which dem=
> onstrates a good (say... classical) tune with examples of 12-eT vs
Just tuni=
> ng? I should imagine the web is filled with such comparisons - all
waiting t=
> o prove me wrong! ;D

hi daniel,

it's obvious that you'll always prefer the 12-equal versions, because
your brain has been "tuned", you might say, to the 12-equal pitches.

but here goes anyway. this is adaptive tuning, not just, but it tries
to make the chords as just as possible within themselves. spend a lot
of time with these before commenting:

http://bellsouthpwp.net/j/d/jdelaub/jstudio.htm

and yes, wonderful things, such as the hammond organ, have been
acheived by simply retuning the overtones to 12-equal. even 11-equal
and 13-equal, which are extremely far from just intonation, have been
made to sound "smooth", by Bill Sethares and Jacky Ligon, among
others -- by tuning the overtones, as well as fundamentals, to the
equal tuning in question.

the ear's combinational tones (sum and difference tones) don't come
into play in a major way until the music gets very loud. however,
some people have developed a fine sensitivity to them even at quiet
volumes. there's a certain peaceful, perhaps meditational ethos to be
derived from this motionless-sounding arrangement of subjective
partials (including combinational tones), any beating to be found
within it all perfectly synchronized to multiples of a single rhythm
(whose frequency is equal to that of 1 relative to the integers
describing the chord, e.g., for 4:5:6 the frequency is 1, for
10:12:15 it is 1, etc.). any tempered arrangement will disturb this
arrangement when the combinational tones are taken into account, no
matter how the overtones are adjusted. perhaps even more important is
what you might call

harmonic entropy
or
the propensity of the central pitch processor of the brain to
recognize just and near-just harmonic series (e.g., most western
acoustic instruments and the human voice) as unified sensations,
namely single pitches, while severely altered harmonic series are
heard as more complex sensations.

while biological evidence seems to be pointing toward a periodicity
mechanism for this phenomenon (which would make just-tuned
harmonies "special" in the sense of being "simplest sensation"), the
tide swings back and forth on this every quarter-century or so . . .
so --

if you were to claim that the hammond organ and similarly-arranged
timbres were the end-all and be-all on your posited platonic rating
system for music,

then i would have no 100% solid, concrete evidence to present to you
to convince you otherwise.

on the other hand, as a musical being i *know* that all sorts of
weird-ass scales can come to sound "perfect", in the right musical
contexts, and from that point of view the idea of one "perfect"
musical scale is both absurd and very sad from the point of view of
diminishing musical richness.

--- In tuning@y..., graham@m... wrote:
> In-Reply-To: <ant1ke+3bj6@e...>
> wallyesterpaulrus wrote:
>
> > [perhaps, then, the linear temperament defined by 225:224 and
> > 32805:32768 would be a good fit -- can anyone remind me what
system
> > that is, by working out the appropriate wedgies or whatever?]
>
> Is that some kind of rhetorical question, or have you really
forgotten?

i forgot for a second, and then remembered that schismic does banish
the 225:224. i didn't see the harm in it being brought up again.

> See <http://x31eq.com/schismic.htm>.

this is how helmholtz and groven arranged things, for anyone
following along.

Hi Daniel,

François:
>>IMHO claim that 12ET represents a sort of natural perfection is
>>disproved by a simple fact: 12ET thirds are nearly impossible to
sign
>>in harmony! In cadential context, when there is enough time to
settle
>>a perfect chord, even average amateur singers are strongly attracted
>>to JI third.
>>
>>Try this very simple experiment, play any note on a piano, sustain
it,
>>sign the third, sustain it for a few seconds, then play the third on
>>the piano. Result: most people are too low (by some 15 cents) wrt to
>>piano. That works nearly all the time for nearly anybody with
minimal
>>musical training.

Daniel:
>Yes, but amateur singers are more likely to get it wrong ;-)

>To be honest, you make a strong case, and as I have said previously,
I'm st=
>ill not 100% sure.
>Now these are only theories, so don't jump on them, but:

>A: Maybe the singers used in any experiment were 'wavering', and they
presu=
>med that they were hitting 1.25 instead of 1.259 (perhaps by taking
the 'tro=
>ugh' of the pitch instead of the middle or peak). These two pitches
are very=
>close, so it can be very hard to tell.

I took a few measurements of final major chords of professional a
capella ensemble,
(renaissance music, so to be honest, there may be a bias in the style
of the
performers). The major third is definitely around 385 cents more or
less a few
cents (the accuracy limit of my measures), and not around let say 375
or 415.

>B: Also, it could've been that maybe the singer was (mistakingly)
/aiming/ =
>for chords which didn't beat rather than for what actually sounded
best.

What singers aim to, isn't what sound the best (to them at least)?
Furthermore,
I initially tought that the search of beatless sound was the key to a
capella JI.
Then I realised that for signing voices, the higher harmonics are
relatively
blunt (compared to fixed tuning instruments) for harmonics higher
than, let say
third or fourth. This is probably due to vibrato (even the slightest
one) and/or
the softness of vocal tract tissues. Whatever is the reason, this
makes the
beating of voices very difficult to detect directly and unlikely to be
the primary clue
to JI or not JI.

>C: Thirdly, as I've said in reply to Prophecyspirit, they might be
hitting =
>this beatless pitch to be in harmony with the (imo) faulty harmonic
overtone=
>s that certain instruments produce - rather than in harmony with the
fundame=
>ntal pitch. This could certainly be plausible.

Attraction to JI third exists for a capella singing and probably for
any
instrument capable of pitch adaptation. Further, even the most
reputedly inharmonic instrument, the piano, is not THAT inharmonic in
the mid
range: not enough (IMHO) to make account of the "missing" 15 cents of
song thirds.

>D: Due to the acoustic properties of both the human voice and
instrument in=
>question, maybe there's a quasi-mathematical 'sound effect' (like
some kind=
>of subtle 'wowowow') that enhances the interval if sung in Just
(1.25). Thi=
>s though is more of an side-effect, and I guess this 'sound effect'
could be=
>mathematically synthesized and added to the 1.259 interval too if
necessary=
>- then you would have the best of both worlds.

>E: Finally, perhaps the singers involved didn't quite hit the exact
pitch t=
>hat they should have done anyway - especially if they were 'trained'
to hit =
>1.25 - or even 'not trained enough' to hit 1.259

Amateur singers I know are not trained to sign this kind or this other
kind of third.
Nearly none of them are even aware that there is some other interval
than those found
on the piano. They usually rehearse with a piano, but just thirds pop
out naturally
when in proper condition (a capella, decent room accoustic, long
triadic chords)

What I have observed (measured in fact, I do not have such good ear)
for
a capella ensemble is that the initial value of thirds is often
near ET third, but given some time (up to few seconds depending of the
skill of the
signers) for the chord to settle, the third shrinks toward 385 cents.

That suggest that the mental image of the chord, before utterance, is
ET
(due IMHO to cultural pervasiveness of ET), then, performers settle to
more "natural" interval.

Obviously, this is probably not true for any genre. Some kind of
roughness
may be seeked, and so, deviation from JI is part of the style. I read
somewhere
that it may occur that even octave are purposedly not just "to show
that
it is an octave".

>It could be one of these...or any mix of these.

yours truly

François Laferrière

In a message dated 10/8/02 10:31:23 PM Central Daylight Time,
wallyesterpaulrus@yahoo.com writes:

> the promotion of
> microtemperaments has not met with the warmest of responses around
> here in the past.

Pianos aren't tuned exactly to theoretical 12-ET. I know some want pitch
exactness, but nature doesn't support such an idea. Neither does actual
tuning practice of acoustic instruments.

> i'm not sure this effect is quite what some people would accept for,
> say, renaissance or baroque music. which pitches exactly would you
> use?
>
My scale will play music composed for tempered scales. It just needs more
than one keyboard to do it. Trained organists have no problem chaning
imanuals, or playing two at once.

> so something like 16:19:24, or is the "just" premise abandoned here?

A-C-E theoretically is 54-64-81.

>
> > The 520-cent interval between E and A in the C scale is used.
>
> could i entreat of you to spell out the full progression, say in
> cents or something?

C-C-E-G > A >G; G-B-D-G > 7F

> i thought you were going to play existing, tonal, music, as written
> (?)

The "different note" is the same note with a sligh pitch differece to
maintain smoothness. I'd have to play the chord to know for sure. I see mroe
theory here than practicality.

> some note combinations will cover slight undulation.
>
> in the melody? still, didn't you say you worked out some full
> transcriptions of substantial pieces of western repertoire?
>
One can't play and unmarked score in JI or JT at sight. One has to test
different notes to see which is the best or right one till one is used to
playing. Yes a slight undulation of one note in a triad is covered by the
other notes in microtemperament.

Pauline

--- In tuning@y..., prophecyspirit@a... wrote:
> In a message dated 10/8/02 10:31:23 PM Central Daylight Time,
> wallyesterpaulrus@y... writes:
>
>
> > i'm not sure this effect is quite what some people would accept
for,
> > say, renaissance or baroque music. which pitches exactly would
you
> > use?
> >
> My scale will play music composed for tempered scales. It just
needs more
> than one keyboard to do it. Trained organists have no problem
chaning
> imanuals, or playing two at once.

you didn't answer the question.
>
> > so something like 16:19:24, or is the "just" premise abandoned
here?
>
> A-C-E theoretically is 54-64-81.

aren't those numbers too high to evoke any "justness"?

> > > The 520-cent interval between E and A in the C scale is used.
> >
> > could i entreat of you to spell out the full progression, say in
> > cents or something?
>
> C-C-E-G > A >G; G-B-D-G > 7F

i don't see cents or anything equivalent. can you be more explicit
here? i don't even see the chords i specified -- this sure is some
strange shorthand you're using.

> > i thought you were going to play existing, tonal, music, as
written
> > (?)
>
> The "different note" is the same note with a sligh pitch differece
to
> maintain smoothness.

you were talking about using different inversions of chords! please
try to follow the threads of discussion -- that's why i include
quotes.

> I'd have to play the chord to know for sure. I see mroe
> theory here than practicality.

huh? i'm asking you for the practical realization.

> > some note combinations will cover slight undulation.
> >
> > in the melody? still, didn't you say you worked out some full
> > transcriptions of substantial pieces of western repertoire?
> >
> One can't play and unmarked score in JI or JT at sight.

of course not -- that's why i said "worked out". so i'd like to see
one of the progressions i mentioned "worked out". i also mentioned a
5-part chord.

--- In tuning@y..., graham@m... wrote:
> In-Reply-To: <anteg5+k3bi@e...>
> wallyesterpaulrus wrote:
>
> > last year on the tuning-math list, gene ward smith derived the
> > optimal generators for this temperament, given a just octave of
1200
> > cents. they are:
> >
> > 699.812912 cents and
> > 384.171625 cents
>
> I don't know how these where chosen.

to minimize the sum-of-squared errors, i presume. gene?

> However I look at it, Pauline's tuning is a compromise between a
225:224
> planar temperament and strict JI.
> You may be able to tweak a specific
> planar temperament to get within 1 cent, but I'm not sure. I don't
think
> that's how she worked it out, anyway,

she did say she thought of it as being generated by 700-cent fifths
and 384-cent major thirds. but she also mentioned some 30/17 ratios,
so she may be tweaking certain things in specific places.

"wallyesterpaulrus" <wallyesterpaulrus@yahoo.com> writes

> > > last year on the tuning-math list, gene ward smith derived the
> > > optimal generators for this temperament, given a just octave of
> 1200
> > > cents. they are:
> > >
> > > 699.812912 cents and
> > > 384.171625 cents
> >
> > I don't know how these where chosen.
>
> to minimize the sum-of-squared errors, i presume. gene?

Yes; I ran the program again, and again got those values for least error.
You can add a 7/4
of 967.969074 to the mix, and 225/224 goes away.

I can't answer all yoru questions away from my organ, which at the moment
isn't playable, as I'm getting the bugs out of it.

But I know it'll play any common chords written for compositions with a
key-signature center.

Aso for 54-64-81, that's simply 906-0-408 broken down to it's lowest cents.

Pauline

In a message dated 10/9/02 1:48:37 PM Central Daylight Time,
wallyesterpaulrus@yahoo.com writes:

> she did say she thought of it as being generated by 700-cent fifths
> and 384-cent major thirds. but she also mentioned some 30/17 ratios,
> so she may be tweaking certain things in specific places.
>
The major 3rds are 700-cent generated as well, jsut tuned higher to 384 cents
to start with. 30/17 is the interval betweed 17/16 Db 105 and 30/16 (15/8) B
1088. It's thevonly interval ratio used. And that may only be temporary tillI
can get mroe tone generators.

Pauline

"wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>

> i forgot for a second, and then remembered that schismic does banish
> the 225:224. i didn't see the harm in it being brought up again.

Lots of linear temperaments banish 225/224, but the pure pauline planar
temperament is likely to be significantly better in tune. Here are
examples of 22-tone 5-limit Fokker blocks, each of which adds a hefty
dose of 7-limit
harmony if we temper 225/224 out, and which further increases its count,
but at the expense of the tuning, with a suitable linear temperament.

! scj22_a.scl
<3125/3072 250/243> Fokker block
! 225/224 ^ 15625/15552 = [6,5,22,37,-18,-6] catakleismic
22
!
25/24
16/15
10/9
9/8
144/125
6/5
5/4
32/25
4/3
864/625
25/18
36/25
3/2
25/16
8/5
5/3
125/72
16/9
9/5
15/8
48/25
2/1

Twelve major and thirteen minor triads, increasing to fifteen each for
catakleismic. Three major, three minor,
five subminor, and five Superman tetrads from pauline, with an additional
supermajor tetrad in catakleismic. Also, six subminor and six supermajor
triads in pauline, with an additional supermajor triad (simply part of
the additional supermajor tetrad) in catakleismic.

! scj22b.scl
<2048/2025 250/243> Fokker block
! 5120/5103 ^ 225/224 = [1,-8,-14,-10,25,-15] schismic candidate
22
!
25/24
16/15
10/9
9/8
32/27
6/5
5/4
32/25
4/3
27/20
64/45
40/27
3/2
25/16
8/5
5/3
27/16
16/9
9/5
15/8
48/25
2/1

This has thirteen major and thirteen minor JI triads; pauline adds five
major and five minor tetrads. We also have six subminor and six
supermajor triads, each of which extends to a complete tetrad. None of
this uses schismic! We do get an extra 7/5 and 7/4 from schismic, but we
may well wonder if it's worth it.

! scj22c.scl
<2048/2025 3125/3072> Fokker block
! 225/224 ^ 65625/65536 = [7,-3,827,7,-21] orwell candidate
22
!
25/24
16/15
10/9
9/8
75/64
6/5
5/4
32/25
4/3
512/375
45/32
375/256
3/2
25/16
8/5
5/3
128/75
16/9
9/5
15/8
48/25
2/1

Twelve major and twelve minor JI triads. Pauline adds seven each of
major, minor, subminor and supermajor tetrads, and nine each of subminor
and supermajor triads. We get two extra 7/6 and 7/4 each from orwell, but
again we may wonder if it's worth it.

Hi all,

Yet another multi-post about the view that only the 12-equal
temperament is needed for all the best music.

-----------

Hi Pauline,

>>This is really getting complicated now that overtone harmonics come
into the equation :)

>Since musical instruments and their natural harmonic
>partials came millennia before the ET scale was
>invneted, it stands to reason a proper scale
>should be based on the harmonic spectrum, rather
>tthan make a scale first and then force instruments
>conform to it.

I wouldn't say the 12-eT scale was invented - more 'discovered'.
Newton's theory of gravity made more sense before Einstein came along
and overthrew it.
I see your point, but 'natural' doesn't always mean 'best'. Due to
the complex mathematical interactions on air, traditional instruments
have a great sound quality, but obviously it's a limitation that
their natural harmonics can't be altered so easily.

-----------------------------------

Hi George,

>> But maybe this could be explained by the 'tolerance margin' that
>> one can bu=
>> ild up over time. To myself, Just intervals grate - not 12- eT.
>> Also, the oth=
>> er possiblity could be thanks to point C in my previous reply.
>> Interesting story btw.

>Since we were trying to convince you that 12-ET is not "best", it is
>only necessary to establish that there is something "better"; whether
>this might be JI or another temperament is secondary. Since you have
>an objection to JI, I was trying to direct your attention to meantone
>temperament or 31-ET (its virtual equivalent), which I don't think
>anyone has ever described as harsh or grating (as long as you avoid
>the wolf).
>
>The point that I was attempting to make is that, while I was very
>shocked when I again used 12-ET after several weeks of playing
>exclusively in meantone, I had a very delightful experience when I
>first played in meantone temperament after years of playing
>exclusively in 12-ET. Surely this must say that something other than
>a "tolerance margin" would be the primary consideration here.

Fair enough. Like you say, 'Tolerance' would seem to have little or
nothing to do with it. The only other possiblities then, might be
something to do with some kind of timbre phenomenon (possibly
specific to your keyboard) - or maybe the fact that your ears
simply 'prefer' mean-toned temperament. Also, if the overtone
harmonics of the instrument timbre was (unavoidably) strongly tuned
towards JI, then this could make them clash with the fundamental
tones or with each other.

>> Maybe I'm mistaken, but I think I recall someone in this group
>> saying how for /melodic/ purposes, 12-eT is perfect, whilst
>> harmonically it isn't perfect (well, he got one of those
right ;)...

>There is considerable evidence to suggest that raising the leading
>tone tends to improve the effect of its resolution to the tonic, both
>melodically *and* harmonically(!). (I wrote an article which was
>accepted for publication in the next issue of Xenharmonikon in which
>I elaborate on the effectiveness of a harmonically dissonant leading
>tone.)

Interesting.

>I was thinking of an experiment in which you were to *listen* to what
>you were *playing* so that you could try out as many different things
>as possible in the new tuning. (The problem with today's digital
>electronic instruments is that you have to have one that allows you
>to retune the notes individually.) But if you're only going to
>listen to something and not do the actual playing, then try to listen

It wouldn't be too easy to retune my keyboard (if at all possible),
but I would assume it's better to concentrate just by listening -
rather than playing aswell.

>to a number of things in the same tuning (I suggested meantone
>temperament) for a number of times over a period of a couple of weeks
>before you go back and listen to the *same thing(s)* (in the same
>timbres) in 12-ET.

I have done exactly this =) See below for details.

-----------------------------------------

Hi wallyesterpaulrus,

>> In the mean time, do you know of a comparison anywhere on the web
>> which demonstrates a good (say... classical) tune with examples of
>> 12-eT vs Just tuning? I should imagine the web is filled with
>> such comparisons - all waiting to prove me wrong! ;D

>it's obvious that you'll always prefer the 12-equal versions, because
>your brain has been "tuned", you might say, to the 12-equal pitches.

I should hope that's because they are /best/ tuned that way ;)

>but here goes anyway. this is adaptive tuning, not just, but it tries
>to make the chords as just as possible within themselves. spend a lot
>of time with these before commenting:
>
>http://bellsouthpwp.net/j/d/jdelaub/jstudio.htm

As I write this letter, I'm listening to the examples presented on
the page. In fact I've been been doing this for the past couple of
weeks - with as minimal 'exposure' to 12-eT as possible (quite hard
in this day and age one might find ;)

As expected, I found it off-tune at first, but I'll see if I can
really get to prefer it. I somehow still suspect that I won't, but
I'm going to keep an open mind about this - since obviously many seem
to think otherwise. I'll be posting the results here soon.

>and yes, wonderful things, such as the hammond organ, have been
>acheived by simply retuning the overtones to 12-equal. even 11- equal
>and 13-equal, which are extremely far from just intonation, have been
>made to sound "smooth", by Bill Sethares and Jacky Ligon, among
>others -- by tuning the overtones, as well as fundamentals, to the
>equal tuning in question.

If this is true, then /not/ tuning the overtones to 12-equal is what
I really think half (or possibly all) the problem is - with the claim
that 12-eT isn't perfect.
About 11 and 13 equal.... ermm - I'll leave that argument for another
day... ;D

>on the other hand, as a musical being i *know* that all sorts of
>weird-ass scales can come to sound "perfect", in the right musical
>contexts, and from that point of view the idea of one "perfect"
>musical scale is both absurd and very sad from the point of view of
>diminishing musical richness.

Not necessarily - music is based on 'limits' all the time.
There are so many possibilities in 12-eT unexplored. I would say
music so far has really only begun to scratch the surface, as even in
the best classical symphonies (for example), there are subtle
chord 'mistakes' and continuations in the melody/arrangement that
could be improved further.
Taking this to the extreme, theoretically, the best music would be
tailored right down to the wave - and the individual 0.001
second 'nuggets' that ultimately make all music up.

---------------------------------------------------------

Hi Francois,

>I took a few measurements of final major chords of professional a
>capella ensemble, (renaissance music, so to be honest, there may be
>a bias in the style of the performers). The major third is definitely
>around 385 cents more or less a few cents (the accuracy limit of my
>measures), and not around let say 375 or 415.

Fair enough. For an accurate and objective measurement, I take it
there wasn't much vibrato in their voices at the time?

>>B: Also, it could've been that maybe the singer was (mistakingly)
>>/aiming/ for chords which didn't beat rather than for what actually
sounded
>>best.
>
>What singers aim to, isn't what sound the best (to them at least)?
>Furthermore,
>I initially tought that the search of beatless sound was the key to a
>capella JI.
>Then I realised that for signing voices, the higher harmonics are
>relatively
>blunt (compared to fixed tuning instruments) for harmonics higher
>than, let say
>third or fourth. This is probably due to vibrato (even the slightest
>one) and/or
>the softness of vocal tract tissues. Whatever is the reason, this
>makes the beating of voices very difficult to detect directly and
>unlikely to be the primary clue to JI or not JI.

Interesting, but as faint as a singers' harmonic overtones are, I
would've thought many (including the singers) could tell if their
harmonic overtones are in 'tune' with each other - even if on a
subconscious level.
I would love to hear human voices sing in harmony, but with the
tones /and/ overtones tuned exactly to 12-equal :) This would then
avoid the 'roughness' that you mentioned is sometimes 'preferable' in
certain kinds of music.

>>C: Thirdly, as I've said in reply to Prophecyspirit, they might be
>>hitting
>>this beatless pitch to be in harmony with the (imo) faulty harmonic
>>overtones that certain instruments produce - rather than in harmony
>>with the fundamental pitch. This could certainly be plausible.

>Attraction to JI third exists for a capella singing and probably for
>any instrument capable of pitch adaptation. Further, even the most
>reputedly inharmonic instrument, the piano, is not THAT inharmonic in
>the mid range: not enough (IMHO) to make account of the "missing"
>15 cents of song thirds.

But possibly enough for the brain to (maybe subconsciously) recognise
a certain 'off-tune' sound when the sub-harmonics 'clash' against the
fundamentals/each other ('roughness')...?

>>D: Due to the acoustic properties of both the human voice and
>>instrument in question, maybe there's a quasi-mathematical 'sound
>>effect' (like some kind of subtle 'wowowow') that enhances the
>>interval if sung in Just (1.25). This though is more of an
>>side-effect, and I guess this 'sound effect' could be mathematically
>>synthesized and added to the 1.259 interval too if necessary -
>>then you would have the best of both worlds.
>>
>>E: Finally, perhaps the singers involved didn't quite hit the exact
>>pitch t=
>>hat they should have done anyway - especially if they were 'trained'
>>to hit =
>>1.25 - or even 'not trained enough' to hit 1.259

>Amateur singers I know are not trained to sign this kind or this
other
>kind of third. Nearly none of them are even aware that there is some
>other interval than those found
>on the piano. They usually rehearse with a piano, but just thirds pop
>out naturally
>when in proper condition (a capella, decent room accoustic, long
>triadic chords)
>
>What I have observed (measured in fact, I do not have such good ear)
>for
>a capella ensemble is that the initial value of thirds is often
>near ET third, but given some time (up to few seconds depending of
the
>skill of the signers) for the chord to settle, the third shrinks
toward 385 cents.
>
>That suggest that the mental image of the chord, before utterance, is
>ET (due IMHO to cultural pervasiveness of ET), then, performers
settle
>to more "natural" interval.

As well as the previous "overtones clashing with fundamentals"
or "subtle quasi-mathematical 'wowowow'" syndromes, this could be
explained by something else; Singing in Just intonation might be
easier for the 'singing' brain to cope with. However, to the final
ear, 12-eT might ultimately sound better.

Cheers,
Daniel (soundburst@lycos.com)

http://www.skytopia.com/project/rating.html
http://www.skytopia.com/soundburst/soundburst.html

--- In tuning@y..., "Daniel White" <soundburst@l...> wrote:

> As I write this letter, I'm listening to the examples presented on
> the page. In fact I've been been doing this for the past couple of
> weeks - with as minimal 'exposure' to 12-eT as possible (quite hard
> in this day and age one might find ;)

Have you listened to examples of music tuned in meantone or a well-temperament? If so, do they sound out of tune to you? That seems to me the place to start your listening experiments.

--- In tuning@y..., "Daniel White" <soundburst@l...> wrote:

/tuning/topicId_39089.html#39941

Hello Daniel!

I can see we're back to "White Bread" 12-tET again with you! :)

>
> Not necessarily - music is based on 'limits' all the time.
> There are so many possibilities in 12-eT unexplored. I would say
> music so far has really only begun to scratch the surface, as even
in
> the best classical symphonies (for example), there are subtle
> chord 'mistakes' and continuations in the melody/arrangement that
> could be improved further.
> Taking this to the extreme, theoretically, the best music would be
> tailored right down to the wave - and the individual 0.001
> second 'nuggets' that ultimately make all music up.
>

***I think, Daniel, you may be a bit optimistic about this. Many
people don't share this view. In fact, I was just reading an
interesting interview with composer Easley Blackwood... who is an
incredibly well-versed pianist/composer. Of course, he's also become
a *microtonalist* so that might "color" his view (literally) in your
opinion (Interview is with Bruce Duffie):

"BD: Is there any end to musical possibility?

EB: Oh, eventually there is, but we're not there yet. At this point,
I am persuaded that the tonal and harmonic resources of the 12 note
equal scale have, in fact, been discovered and exploited. And I think
that's something that only came true in about 1965 or 1970. After
that, it's been some kind of a rehash of what's been done before. So
the last frontier to be breached is the atonal polyrhythmic idiom,
and there's a vast repertoire in that idiom that begins somewhere
around 1948, just to pick a random year...

BD: But I thought you said that this was dead!

EB: Well, it's dead now. It went on till about 1965. There's a huge
repertoire written at that time and I'm a participator in that. I
remember being confident that the techniques that are needed to play
polyrhythms accurately would eventually be part of any good
professional musician's standard training. It did not happen."

Anyway, the entire interview is here:

http://www.bruceduffie.com/blackwood.html

And I recommend it heartily to anybody interested in this subject who
hasn't read it yet.

(Well, I take that back... it's worth "re-reading..." :)

J. Pehrson

--- In tuning@y..., "Daniel White" <soundburst@l...> wrote:

> Due to
> the complex mathematical interactions on air,

what in particular are you thinking of here?
> -----------------------------------------
>
> Hi wallyesterpaulrus,

hi daniel!

> >> In the mean time, do you know of a comparison anywhere on the web
> >> which demonstrates a good (say... classical) tune with examples
of
> >> 12-eT vs Just tuning? I should imagine the web is filled with
> >> such comparisons - all waiting to prove me wrong! ;D
>
> >it's obvious that you'll always prefer the 12-equal versions,
because
> >your brain has been "tuned", you might say, to the 12-equal
pitches.
>
> I should hope that's because they are /best/ tuned that way ;)

that would be kind of insulting and/or conceited to anyone that
doesn't inhabit the sphere of modern Western musical culture,
wouldn't it?
>
> >and yes, wonderful things, such as the hammond organ, have been
> >acheived by simply retuning the overtones to 12-equal. even 11-
equal
> >and 13-equal, which are extremely far from just intonation, have
been
> >made to sound "smooth", by Bill Sethares and Jacky Ligon, among
> >others -- by tuning the overtones, as well as fundamentals, to the
> >equal tuning in question.
>
> If this is true, then /not/ tuning the overtones to 12-equal is
what
> I really think half (or possibly all) the problem is - with the
claim
> that 12-eT isn't perfect.
> About 11 and 13 equal.... ermm - I'll leave that argument for
another
> day... ;D

well, it really part of the same argument. if just tuning has nothing
to do with it, but eliminating clashing partials does have something
to do with it, then you'd have no basis for preferring a 12-equal
tuning (of fundamentals _and_ overtones) to an 11-equal or 13-equal
tuning (again, of fundamentals _and_ overtones).

> >on the other hand, as a musical being i *know* that all sorts of
> >weird-ass scales can come to sound "perfect", in the right musical
> >contexts, and from that point of view the idea of one "perfect"
> >musical scale is both absurd and very sad from the point of view of
> >diminishing musical richness.
>
> Not necessarily - music is based on 'limits' all the time.
> There are so many possibilities in 12-eT unexplored.

even more in other tunings!

> I would say
> music so far has really only begun to scratch the surface, as even
in
> the best classical symphonies (for example), there are subtle
> chord 'mistakes' and continuations in the melody/arrangement that
> could be improved further.
> Taking this to the extreme, theoretically, the best music would be
> tailored right down to the wave - and the individual 0.001
> second 'nuggets' that ultimately make all music up.

right -- and clearly very few pieces created in such a way would
conform to a 12-equal grid!

>
> >>B: Also, it could've been that maybe the singer was (mistakingly)
> >>/aiming/ for chords which didn't beat rather than for what
actually
> sounded
> >>best.
> >
> >What singers aim to, isn't what sound the best (to them at least)?
> >Furthermore,
> >I initially tought that the search of beatless sound was the key
to a
> >capella JI.
> >Then I realised that for signing voices, the higher harmonics are
> >relatively
> >blunt (compared to fixed tuning instruments) for harmonics higher
> >than, let say
> >third or fourth. This is probably due to vibrato (even the
slightest
> >one) and/or
> >the softness of vocal tract tissues. Whatever is the reason, this
> >makes the beating of voices very difficult to detect directly and
> >unlikely to be the primary clue to JI or not JI.
>
> Interesting, but as faint as a singers' harmonic overtones are, I
> would've thought many (including the singers) could tell if their
> harmonic overtones are in 'tune' with each other - even if on a
> subconscious level.

maybe, but daniel, you need to look beyond beating and study up on
*combinational tones*. if you have helmholtz's book, you can read
some about them there. otherwise, do some web searches. please?

> I would love to hear human voices sing in harmony, but with the
> tones /and/ overtones tuned exactly to 12-equal :)

of course (i know you were joking but i'll go on) that's impossible,
because any physical musical instrument that produces a periodic
vibration (including the human voice, bowed strings, reeds, and brass
instruments, when producing a clear tone) has, by virtue of fourier's
theorem, a perfectly harmonic overtone spectrum.
>
> But possibly enough for the brain to (maybe subconsciously)
recognise
> a certain 'off-tune' sound when the sub-harmonics 'clash' against
the
> fundamentals/each other ('roughness')...?

what "sub-harmonics" are you speaking of? virtual pitches?

> As well as the previous "overtones clashing with fundamentals"
> or "subtle quasi-mathematical 'wowowow'" syndromes, this could be
> explained by something else; Singing in Just intonation might be
> easier for the 'singing' brain to cope with. However, to the final
> ear, 12-eT might ultimately sound better.

what if no one is listening but the singers? :)

--- In tuning@y..., "Joseph Pehrson" <jpehrson@r...> wrote:

> Anyway, the entire interview is here:
>
> http://www.bruceduffie.com/blackwood.html

thanks so much for this joseph!! i was unaware of this interview.

here are some quotes that i find especially interesting:

"I had discovered some chord progressions in 12 notes in the process
of looking at some of the other equal tunings, which, oddly enough,
were never exploited or used by composers between 1904 and 1915 when
they would have been idiomatic."

this is right up my alley. i think i'm going to *love* this music if
i ever get to hear it. of course, joe monzo's latest bingo-card
lattices of 12-equal would be the best way of visualizing these
progressions, if we can ever find out what they are!

"There is a faction of people who believe in the inevitability of the
acceptance of the so-called academic modern idiom who are very
annoyed at what I am doing. They are out and out hostile. They are
trying to make me stop. They are trying to demoralize me."

i think you and i, joseph, can perhaps both sympathize with this
predicament!

"I think the overall purpose of music is to entertain and
please . . . Nothing more, nothing less. It provides high class
entertainment to a relatively small audience of people who are tuned
into it."

as far as i'm concerned, blackwood has some BIG BALLS to come out and
say this. go easley!! NB: see thing about "subtlety" below.

"More likely the 5th Symphony, or the march in the 6th Symphony, or a
piece like Respighi's Feste Romani, or a Beethoven 7th. Usually, it's
a big splashy exciting piece, and they go on from there and work into
the subtleties and get into the less bombastic things. They get into
Brahms and Beethoven and Mozart. And then they find their way into
chamber music."

personally, i was *really* interested in chamber music as a young
kid, and only later grew to appreciate big splashy exciting pieces.

"EB: It certainly is helpful. But after teaching harmony for 35
years, I can hear the chord progressions. The other night, just for
fun, I switched on the radio and heard the slow movement of the
Jupiter Symphony of Mozart. I hadn't thought about the piece for
awhile, but I found that as I listened to it, I could identify every
chord as it went by. I could hear the piece go I, V of ii, V of v, V,
V of iv, perfectly clear knowing what it was. At an earlier time I
would've been able to figure it out. But as it was, it went by and I
heard it."

in this regard too, i think i developed in the opposite order -- i
could identify chord progressions before i had much aptitude for
melody or even rhythm!

"Now perhaps, having this ability at this point has kind of changed
my perspective on atonal music."

i guess it makes sense that someone like blackwood, who started out
with perfect pitch, would have been drawn to atonal music for a time.
but what of someone like me, with only *relative* pitch? could it be
that the whole serial/atonal premise is even less aesthetically
relavant for us "relative" underlings?

"BD: You don't want to be obvious?

EB: I don't want to be obvious. I want subtleties to be there.

BD: Do you want to give obvious pleasure?

EB: Yes, I do, but I want there to be subtleties above and beyond
that. If it gives obvious pleasure and there are no subtleties,
you've got a piece like Orff's "Carmina Burana."

BD: That one just hits you in the gut.

EB: It hits you in the gut and you listen to it 5 times and that's
the end.

BD: And yet, some people listen to it 500 times.

EB: I remember when I first heard it. I was absolutely swept off my
feet. This must have been about 1958. I listened to it immediately
again and then listened to it every day for four days and then that
was the end of it. Never heard it again. Never wanted to hear it
again.

BD: That was 35 years ago. Would you want to hear it again now?

EB: Oh sure. But it lost my attention at that time. There are no
subtleties in it. "

i know exactly what he means. in a way, that's why i like
improvisation. there's no danger of playing exactly the same thing
twice. unfortunately, i don't practice enough, or perhaps have enough
natural talent, or am still too young and inexperienced, to really
hit that transcendent subtlety more than say 15% of the time, but if
i can simply entertain the other 85% of the time, that's good enough
for me! . . .

maybe any more on this should go on "metatuning" . . .

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>

/tuning/topicId_39089.html#39949

wrote:
> --- In tuning@y..., "Joseph Pehrson" <jpehrson@r...> wrote:
>
> > Anyway, the entire interview is here:
> >
> > http://www.bruceduffie.com/blackwood.html
>
> thanks so much for this joseph!! i was unaware of this interview.
>

***You're welcome, Paul. Very hip interview...

>
> "There is a faction of people who believe in the inevitability of
the
> acceptance of the so-called academic modern idiom who are very
> annoyed at what I am doing. They are out and out hostile. They are
> trying to make me stop. They are trying to demoralize me."
>
> i think you and i, joseph, can perhaps both sympathize with this
> predicament!
>

***Absolutely!

>
> "Now perhaps, having this ability at this point has kind of changed
> my perspective on atonal music."
>
> i guess it makes sense that someone like blackwood, who started out
> with perfect pitch, would have been drawn to atonal music for a
time.
> but what of someone like me, with only *relative* pitch? could it
be
> that the whole serial/atonal premise is even less aesthetically
> relavant for us "relative" underlings?
>

***Personally, I believe it's a matter of *timing.* When *I* was in
college, serial and atonal music was still "the thing..."

Now it's dead, for the most part. Composers of *your* age group
seldom deal with it anymore, except for a few "reactionaries" here
and there. Most of them are currently *much* more interesting in
incorporating *pop* music in their efforts...

Any more on metatuning...

JP

--- In tuning@y..., "Joseph Pehrson" <jpehrson@r...> wrote:

> ***Personally, I believe it's a matter of *timing.* When *I* was
in
> college, serial and atonal music was still "the thing..."
>
> Now it's dead, for the most part. Composers of *your* age group
> seldom deal with it anymore,

hmm . . . composers of my age group deal *plenty* with atonal music,
particularly if they go to new england conservatory and interact with
joe maneri (see, this is on-topic again :) ) . . .

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>

/tuning/topicId_39089.html#39953

wrote:
> --- In tuning@y..., "Joseph Pehrson" <jpehrson@r...> wrote:
>
> > ***Personally, I believe it's a matter of *timing.* When *I* was
> in
> > college, serial and atonal music was still "the thing..."
> >
> > Now it's dead, for the most part. Composers of *your* age group
> > seldom deal with it anymore,
>
> hmm . . . composers of my age group deal *plenty* with atonal
music,
> particularly if they go to new england conservatory and interact
with
> joe maneri (see, this is on-topic again :) ) . . .

***I guess you're right... and Julia's about your age too, I
believe... Well, at least it's "out of tune" atonality... :)

JP

--- In tuning@y..., "Joseph Pehrson" <jpehrson@r...> wrote:

> ***I guess you're right... and Julia's about your age too, I
> believe... Well, at least it's "out of tune" atonality... :)
>
> JP

hey -- lots of "underground electronica", drum & bass and the like,
is pretty much *atonal* as far as i can tell . . . interesting-
sounding bloops and bleeps, pitch relationships really don't matter,
it's the *rhythm* that is the main concern in this music . . .

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>

/tuning/topicId_39089.html#39958

wrote:
> --- In tuning@y..., "Joseph Pehrson" <jpehrson@r...> wrote:
>
> > ***I guess you're right... and Julia's about your age too, I
> > believe... Well, at least it's "out of tune" atonality... :)
> >
> > JP
>
> hey -- lots of "underground electronica", drum & bass and the like,
> is pretty much *atonal* as far as i can tell . . . interesting-
> sounding bloops and bleeps, pitch relationships really don't
matter,
> it's the *rhythm* that is the main concern in this music . . .

****Hmmm. Well, that sounds interesting. I thought I
liked "electronica..." at least what I've heard of it...

(metatuning...)

JP

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>

/tuning/topicId_39089.html#39949

wrote:
> --- In tuning@y..., "Joseph Pehrson" <jpehrson@r...> wrote:
>
> > Anyway, the entire interview is here:
> >
> > http://www.bruceduffie.com/blackwood.html
>
> thanks so much for this joseph!! i was unaware of this interview.
>

***I just ordered his "Microtonal Etudes..." More on that when I get
the CD...

Joseph P.

In a message dated 10/23/02 2:14:34 PM Central Daylight Time,
soundburst@lycos.com writes:

> Yet another multi-post about the view that only the 12-equal
> temperament is needed for all the best music.
>
The best argument agaisnt 12-ET, or any other kind of ET, is such scales are
out of tune with the harmonic partials the notes in the intervals used are
made of.

In 12-ET E 400 is 14 cents large out of tune with the 5th partial E 386.314.
The two pitches in any octave beat strongly with each other!

Pauline

Hi Pauline,

> The best argument agaisnt 12-ET, or any other kind of ET, is such scales are out of tune with the harmonic
> partials the notes in the intervals used are made of.

> In 12-ET E 400 is 14 cents large out of tune with the 5th partial E 386.314. The two pitches in any octave
> beat strongly with each other!

Yes, and if you say that 12-et is the only true tuning, as some do, it means that the partials of say a 'cello
in a 'cello concerto are out of tune, and the instrument should be rebuilt somehow to have a timbre with 12-et
partials - surely! Or maybe all the 12-et recordings we have should be electronically manipulated to have only
12-et pitches in the ;-).

- the "out of tune" 'cello partials such as even the seventh partial can be louder than many of the accompanying
instruments in a 'cello concerto - but you have to listen pretty carefully to hear them - maybe in sustained
notes, because we tend to hear it as a single timbre rather than a multitude of separate instruments.

12-et as a fine tuning, indeed, and a vibrant one. Has a lot of energy in it - wakes one up!
(Though it may possibly be somewhat of a twentieth century aquired taste, otherwise why didn't the
musicians of Bach's time go for it when they could have easily retuned their harpsichords to match their
lutes etc.).

My little 'cello drone midi clip exercise at
http://tunesmithy.netfirms.com/tunes/tunes.htm#Newbie_notes
may make a few think? Those notes are at the correct relative volumes
for the partials at least as measured on my 'cello voice here
on the SB Live S/W synth.

Also this exercise with the highland bagpipes
http://www-personal.umich.edu/~emacpher/pipes/acoustics/psychodrone.html
which brings them out more clearly. Maybe someone should do that
with the 'cello too - would be quite striking.

Robert

--- In tuning@y..., prophecyspirit@a... wrote:
> In a message dated 10/23/02 2:14:34 PM Central Daylight Time,
> soundburst@l... writes:
>
>
> > Yet another multi-post about the view that only the 12-equal
> > temperament is needed for all the best music.
> >
> The best argument agaisnt 12-ET, or any other kind of ET, is such scales are
> out of tune with the harmonic partials the notes in the intervals used are
> made of.

I thought you maintained, reasonably enough, that being out of tune by a cent or two did not really count as "out of tune".

In a message dated 10/24/02 12:16:53 AM Central Daylight Time,
robertwalker@ntlworld.com writes:

> why didn't the
> musicians of Bach's time go for it when they could have easily retuned
> their harpsichords to match their
> lutes etc.).
>
Robert,

While ET was known and used in Bach's day, it took till 1800 for it to catch
on "universially" in Germany,and till 1850 for it to catch on in England, and
eve later in America. that speaks volumes in itself about its iinadequacies,
despite its convenience!

While percussion instruments have a different partial series than other
instruments, the partials are still in harmony with each other within just
temperament limitations. For example in the regular harmonic partials the
11th harmonid at 551 cents, while it doesn't form part of a harmonious chord,
is nonetheless beat free when played with a chord. The 13th at 841 cents is
the same.

Pauline

In a message dated 10/24/02 5:24:14 AM Central Daylight Time,
genewardsmith@juno.com writes:

> I thought you maintained, reasonably enough, that being out of tune by a
> cent or two did not really count as "out of tune".
>
That's a far cry from being 14 cents our of tune with the major 3rd, as ET
is! And the minor 7th is 31 cents large out of tune.

Also, back when ET was 1st advocated, musicians played at a much lower pitch
usually than today. Lower pitches don't sound as out of tune to the ear as do
a higher pitch. That's why the low-pitched guitar is so much mroe popular
than similar plucked instrumetns at higher pitch.

Pauline

--- In tuning@y..., "Daniel White" <soundburst@l...> wrote:
> Hi all,
>
> Yet another multi-post about the view that only the 12-equal
> temperament is needed for all the best music.
>
> -----------
>
> Hi George,
>
> >> But maybe this could be explained by the 'tolerance margin' that
> >> one can bu=
> >> ild up over time. To myself, Just intervals grate - not 12- eT.
> >> Also, the oth=
> >> er possiblity could be thanks to point C in my previous reply.
> >> Interesting story btw.
>
> >Since we were trying to convince you that 12-ET is not "best", it
is
> >only necessary to establish that there is something "better";
whether
> >this might be JI or another temperament is secondary. Since you
have
> >an objection to JI, I was trying to direct your attention to
meantone
> >temperament or 31-ET (its virtual equivalent), which I don't think
> >anyone has ever described as harsh or grating (as long as you avoid
> >the wolf).
> >
> >The point that I was attempting to make is that, while I was very
> >shocked when I again used 12-ET after several weeks of playing
> >exclusively in meantone, I had a very delightful experience when I
> >first played in meantone temperament after years of playing
> >exclusively in 12-ET. Surely this must say that something other
than
> >a "tolerance margin" would be the primary consideration here.
>
> Fair enough. Like you say, 'Tolerance' would seem to have little or
> nothing to do with it. The only other possiblities then, might be
> something to do with some kind of timbre phenomenon (possibly
> specific to your keyboard)

I've heard many different tunings over many years on two different
retunable electronic organs I owned and also on two different kinds
of Scalatrons and have used many sorts of timbres (all with harmonic
partials) on them, and I think I can safely say that my impressions
are pretty much the same, regardless of the timbre.

> - or maybe the fact that your ears
> simply 'prefer' mean-toned temperament.

My ears also prefer 19-ET, 22-ET, and 41-ET (to mention a few) over
12-ET, and my preference is closely correlated with the ability of
the tuning to approximate just intervals. So I prefer 31 or 41-ET to
19 or 22-ET.

You have to realize, however, that there are things you can do in 19
or 22 that can't be done in other systems, and each one has its own
combination of capabilities and limitation. So the choice a composer
may make is not necessarily only a matter of one system sounding
harmonically "better" than another. As we discussed below, there is
also the melodic element to take into consideration.

> Also, if the overtone
> harmonics of the instrument timbre was (unavoidably) strongly tuned
> towards JI, then this could make them clash with the fundamental
> tones or with each other.

The partials of most musical instruments are either exact or nearly
exact multiples (or harmonics) of the fundamental frequency, so you
have pointed out what happens when intervals are not in (or very
close to) just intonation. In 12-ET they clash much more strongly
than they do in those other divisions I mentioned, and in just
intonation the clashing (if you can even hear it) is minimal.

> >> Maybe I'm mistaken, but I think I recall someone in this group
> >> saying how for /melodic/ purposes, 12-eT is perfect, whilst
> >> harmonically it isn't perfect (well, he got one of those
> right ;)...
>
> >There is considerable evidence to suggest that raising the leading
> >tone tends to improve the effect of its resolution to the tonic,
both
> >melodically *and* harmonically(!). (I wrote an article which was
> >accepted for publication in the next issue of Xenharmonikon in
which
> >I elaborate on the effectiveness of a harmonically dissonant
leading
> >tone.)
>
> Interesting.

Just intonation doesn't preclude the possibility of making use of
this effect, since, given enough tones, you could have more than one
size of major third, for example, or you could have different sizes
in different keys. A different-size third would probably be
considerably more dissonant than a just 4:5, but the objective would
not be to avoid dissonance, but rather to maximize the total range of
consonance to dissonance -- something that JI does better than any ET
below 100 tones.

> >I was thinking of an experiment in which you were to *listen* to
what
> >you were *playing* so that you could try out as many different
things
> >as possible in the new tuning. (The problem with today's digital
> >electronic instruments is that you have to have one that allows you
> >to retune the notes individually.) But if you're only going to
> >listen to something and not do the actual playing, then try to
listen
>
> It wouldn't be too easy to retune my keyboard (if at all possible),
> but I would assume it's better to concentrate just by listening -
> rather than playing aswell.

If you're playing, you can sustain any chord as long as you want, but
if you're just listening to a recording, it may go by too fast for
your purposes. The best of both worlds would be to have someone else
play while you listen.

> >to a number of things in the same tuning (I suggested meantone
> >temperament) for a number of times over a period of a couple of
weeks
> >before you go back and listen to the *same thing(s)* (in the same
> >timbres) in 12-ET.
>
> I have done exactly this =) See below for details.

> > [Paul Erlich's recommendation:]
> >http://bellsouthpwp.net/j/d/jdelaub/jstudio.htm
>
> As I write this letter, I'm listening to the examples presented on
> the page. In fact I've been been doing this for the past couple of
> weeks - with as minimal 'exposure' to 12-eT as possible (quite hard
> in this day and age one might find ;)
>
> As expected, I found it off-tune at first, but I'll see if I can
> really get to prefer it. I somehow still suspect that I won't, but
> I'm going to keep an open mind about this - since obviously many
seem
> to think otherwise. I'll be posting the results here soon.

I see that this is adaptive JI, which may or may not sound a little
too dry (i.e., beatless) for your taste. It would be good also to
find something in both 12-ET and meantone temperament as well, after
you've spent sufficient time with this.

Doesn't anyone out there have any music more than a few seconds in
length in both 12-ET and meantone temperament in exactly the same
timbre?

--George

--- In tuning@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:
> --- In tuning@y..., prophecyspirit@a... wrote:
> > In a message dated 10/23/02 2:14:34 PM Central Daylight Time,
> > soundburst@l... writes:
> >
> >
> > > Yet another multi-post about the view that only the 12-equal
> > > temperament is needed for all the best music.
> > >
> > The best argument agaisnt 12-ET, or any other kind of ET, is such
scales are
> > out of tune with the harmonic partials the notes in the intervals
used are
> > made of.
>
> I thought you maintained, reasonably enough, that being out of tune
>by a cent or two did not really count as "out of tune".

and also (if i might chime in, pauline), again quite reasonably, that
combinational tones are of great importance here.

--- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:

> but the objective would
> not be to avoid dissonance, but rather to maximize the total range
of
> consonance to dissonance -- something that JI does better than any
ET
> below 100 tones.

i am curious as to how you arrived at that figure. reply on tuning-
math if appropriate.

> Doesn't anyone out there have any music more than a few seconds in
> length in both 12-ET and meantone temperament in exactly the same
> timbre?

of course -- herman miller, on both his pavane for a warped princess
page, and pachelbel's warped canon page, provides versions in 12-
equal and many other tunings, including several varieties of meantone.

--- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:

> Doesn't anyone out there have any music more than a few seconds in
> length in both 12-ET and meantone temperament in exactly the same
> timbre?

If not, I can easily create some examples. Where would I put them?

In a message dated 10/24/02 1:26:36 PM Central Daylight Time,
gdsecor@yahoo.com writes:

> Just intonation doesn't preclude the possibility of making use of
> this effect, since, given enough tones, you could have more than one
> size of major third, for example,

My Phillips scale has an ascending scale and a descending scale. The 3rds
size depends on where the are in these scale. One can play whatever one needs
to do regarding 3rd size, whether in Beethoven, which someone mentioned, or
any other composer for tempered scales.

Pauline

In a message dated 10/24/02 1:29:03 PM Central Daylight Time,
wallyesterpaulrus@yahoo.com writes:

> > I thought you maintained, reasonably enough, that being out of tune
> >by a cent or two did not really count as "out of tune".
>
> and also (if i might chime in, pauline), again quite reasonably, that
> combinational tones are of great importance here.

Combinationa tones are left intact so long as the temperament is no mroe
thatn +/- 3 cents the intervals theoretical value in cents. My Phillips scale
perfectly reporduces these. Admittedly, in perfect JI produced electronicly
they're a bit storniger. But that's an unnatural way to create tones of any
kind. Electronic-organ firms have done their best in quality instruments to
avoid intervals being locked in phase. As no pipe organ has such.

Paualine

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>
wrote:
> --- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
>
> > but the objective would
> > not be to avoid dissonance, but rather to maximize the total
range
> of
> > consonance to dissonance -- something that JI does better than
any
> ET
> > below 100 tones.
>
> i am curious as to how you arrived at that figure. reply on tuning-
> math if appropriate.

Sorry this reply took so long -- I've been very busy this past week
(and still am, so I need to keep this brief).

It's just a round number that could be higher. By it I mean that no
ET below 100 really matches the high consonance of JI, and I don't
mean 5 or 7-limit JI (in which case maybe I could have said below 99
tones). When your consonances are exact (or nearly so), the
dissonance of intervals that aren't small-number ratios (such as
those false by a comma) stand out in sharpest contrast.

When I was first looking for a good 13-limit tuning, I concluded that
no ET that I considered practical had intonation good enough to give
me a sound that was close enough to JI. To get a reasonable amount
of modulation, I ended up with a microtemperament of 29 tones. (I'll
have to post it someday.)

--George

--- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
> --- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>
> wrote:
> > --- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
> >
> > > but the objective would
> > > not be to avoid dissonance, but rather to maximize the total
> range
> > of
> > > consonance to dissonance -- something that JI does better than
> any
> > ET
> > > below 100 tones.
> >
> > i am curious as to how you arrived at that figure. reply on
tuning-
> > math if appropriate.
>
> Sorry this reply took so long -- I've been very busy this past week
> (and still am, so I need to keep this brief).
>
> It's just a round number that could be higher. By it I mean that
no
> ET below 100 really matches the high consonance of JI, and I don't
> mean 5 or 7-limit JI (in which case maybe I could have said below
99
> tones). When your consonances are exact (or nearly so), the
> dissonance of intervals that aren't small-number ratios (such as
> those false by a comma) stand out in sharpest contrast.

agreed (thus my recent comments to julia) but you didn't say how many
pitches, let along which pitches, you would include when you
said "JI". an infinite number? it wasn't a clear comparison you were
making.

--- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:

> When I was first looking for a good 13-limit tuning, I concluded that
> no ET that I considered practical had intonation good enough to give
> me a sound that was close enough to JI.

How close is close enough?

To get a reasonable amount
> of modulation, I ended up with a microtemperament of 29 tones.

I still like 311 as a sort of universal temperament, or 494 for the 13-limit if 311 isn't quite good enough. As for practical, I'm a terrible violinist and never worry about such issues. :)

--- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>
wrote:
> --- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
> > --- In tuning@y..., "wallyesterpaulrus" <wallyesterpaulrus@y...>
> > wrote:
> > > --- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
> > >
> > > > but the objective would
> > > > not be to avoid dissonance, but rather to maximize the total
> > range
> > > of
> > > > consonance to dissonance -- something that JI does better
than
> > any
> > > ET
> > > > below 100 tones.
> > >
> > > i am curious as to how you arrived at that figure. reply on
> tuning-
> > > math if appropriate.
> >
> > Sorry this reply took so long -- I've been very busy this past
week
> > (and still am, so I need to keep this brief).
> >
> > It's just a round number that could be higher. By it I mean that
> no
> > ET below 100 really matches the high consonance of JI, and I
don't
> > mean 5 or 7-limit JI (in which case maybe I could have said below
> 99
> > tones). When your consonances are exact (or nearly so), the
> > dissonance of intervals that aren't small-number ratios (such as
> > those false by a comma) stand out in sharpest contrast.
>
> agreed (thus my recent comments to julia) but you didn't say how
many
> pitches, let along which pitches, you would include when you
> said "JI". an infinite number? it wasn't a clear comparison you
were
> making.

I was speaking in generalities, so I had an indefinite number of
pitches in mind when I said "JI".

I have gotten the impression that JI isn't too popular around here,
so let me take this opportunity to put in a few good words for it.

One of the strengths of JI is that it's an open or "expandable"
approach. You can start with a modest number of tones at such and
such a prime limit, and if you want to increase your capabilities
later, you can just add more tones. If you don't increase the prime
limit, then you get more modulation, but if you do, then you get more
kinds of harmonic material (or you can do both). Having done this,
whatever JI instruments you have built are compatible with whatever
new ones you might build, since they have a subset of tones from the
new (larger) set.

Contrast this with someone who has started with 19-ET (for example)
and decides later to use a different ET. Unless a specially built
instrument is retunable (or otherwise adaptable), it is necessary to
build a new instrument for the new system. An exception is going to
72-ET from one of its subsets (including 12), but I wouldn't be as
happy with this as I would be with a JI subset.

Some Middle Path tunings also have the advantage of compatible
expandability. A good example is the Miracle tuning: if you start
with Blackjack, you have the option of going on to Canasta and Stud-
Loco later on.

But with JI your options are much less limited.

--George

In a message dated 10/29/02 9:47:59 AM Central Standard Time,
gdsecor@yahoo.com writes:

> One of the strengths of JI is that it's an open or "expandable"
> approach. You can start with a modest number of tones at such and
> such a prime limit, and if you want to increase your capabilities
> later, you can just add more tones.

George,

When I studied piano, I learned about what was called "passing notes."
Howeer, when experimenting with JI on my organ, I found most so-called
passing notes were really parts of complex chords whose harmonic numbers were
up into say the 20s ro 30s, or even beyond! Helmholtz's book lists together
the odd harmonics up to 63. And the even ones go way beyond that. Thus a
common hymn can have very high chord numbers.

My all-key JI scale has a 19 odd limit. But the even numbers are very much
higher--F having the highest number in five figures--10935! Thus
theoretically, the harmonic numbers in JI are seemingy endless.

Pauline

--- In tuning@y..., "Gene Ward Smith" <genewardsmith@j...> wrote:
> --- In tuning@y..., "gdsecor" <gdsecor@y...> wrote:
>
> > When I was first looking for a good 13-limit tuning, I concluded
that
> > no ET that I considered practical had intonation good enough to
give
> > me a sound that was close enough to JI.
>
> How close is close enough?

No consonance within the harmonic limit would have an error more than
4 cents. (For 2:3 & 3:4 this would not be greater than 2 cents,
since 8:9 would be double that.)

> To get a reasonable amount
> > of modulation, I ended up with a microtemperament of 29 tones.

My microtemperament has a max error of <3.25 cents for 6 otonal
ogdoads in a 29-tone constant structure. (There's also a 17-tone CS
version with 3 otonal ogdoads, of which 14 tones are a subset of the
29.)

> I still like 311 as a sort of universal temperament, or 494 for the
13-limit if 311 isn't quite good enough. As for practical, I'm a
terrible violinist and never worry about such issues. :)

And I think that 494 is superb even at the 17 limit, and 311
certainly comes "close enough", as I answered above. The problem is
finding something that's "practical". With a microtemperament I can
have much better intonation than with an ET and more modulation than
with JI, given that each option has about the same number of tones).

--George

Hi all, sorry I've taken so long with this 'multi-post' - been so
busy lately! For all those not in the know, I'm firmly of the opinion
that only 12-tET (as opposed to JI or meantone) is needed for all the
best music...

---------------------

Hi J. Pehrson,

>I can see we're back to "White Bread" 12-tET again with you! :)

lol :)

>> Not necessarily - music is based on 'limits' all the time.
>> There are so many possibilities in 12-eT unexplored. I would say
>> music so far has really only begun to scratch the surface, as even
in
>> the best classical symphonies (for example), there are subtle
>> chord 'mistakes' and continuations in the melody/arrangement that
>> could be improved further.
>> Taking this to the extreme, theoretically, the best music would be
>> tailored right down to the wave - and the individual 0.001
>> second 'nuggets' that ultimately make all music up.

>***I think, Daniel, you may be a bit optimistic about this. Many
>people don't share this view. In fact, I was just reading an

>"BD: Is there any end to musical possibility?
>
>EB: Oh, eventually there is, but we're not there yet. At this point,
>I am persuaded that the tonal and harmonic resources of the 12 note
>equal scale have, in fact, been discovered and exploited. And I think

I disagree. Consider how many different melodies there can be. The
thing I've noticed is even if certain chord patterns are similar, if
the timing and the contrapuntal melodies are in any way different,
this really makes it a whole new tune.

I've noticed that the same chord progression can have many
different 'flavours' according to not only what chords came
before/after, but also in the implementation. Yes, there is a
fundamental limit to how many melodies can be composed, but combined
with the timbre (timbric?) and rhythmic permutations, this number is
getting so ridiculously high, that for all intents and purposes it
might as well be infinite :)
I think also what makes people say 12-equal has been exhausted is the
fact that there's so little good music around these days anyway, so
the temptation is great...

------------

Hi wallyesterpaulrus,

> Due to
> the complex mathematical interactions on air,
>
>what in particular are you thinking of here?

Well, I simply meant the inner design of instruments - and how they
affect the air to produce a certain timbre.

>> >> In the mean time, do you know of a comparison anywhere on the
web
>> >> which demonstrates a good (say... classical) tune with examples
of
>> >> 12-eT vs Just tuning? I should imagine the web is filled with
>> >> such comparisons - all waiting to prove me wrong! ;D
>> >>
>> >
>> >it's obvious that you'll always prefer the 12-equal versions,
because
>> >your brain has been "tuned", you might say, to the 12-equal
pitches.
>>
>> I should hope that's because they are /best/ tuned that way ;)

>that would be kind of insulting and/or conceited to anyone that
>doesn't inhabit the sphere of modern Western musical culture,
>wouldn't it?

It's my opinion, and one I think might actually be ultimately correct
for many reasons. Remember, I think that I could be wrong too. I'm
not saying for certain that I'm absolutely right :)

>> If this is true, then /not/ tuning the overtones to 12-equal is
>> what
>> I really think half (or possibly all) the problem is - with the
>> claim
>> that 12-eT isn't perfect.
>> About 11 and 13 equal.... ermm - I'll leave that argument for
>> another day... ;D

>well, it really part of the same argument. if just tuning has nothing
>to do with it, but eliminating clashing partials does have something
>to do with it, then you'd have no basis for preferring a 12- equal
>tuning (of fundamentals _and_ overtones) to an 11-equal or 13- equal
>tuning (again, of fundamentals _and_ overtones).

I'm not sure I quite follow here, but basically I think the number 12
is very special for some reason. I can't see any contradiction in
eliminating clashing partials and keeping only to 12-equal.
I doubt any amount of cultural conditioning could convince people 11
or 13 equal is better than 12 equal even if everyone started out
using 11 or 13 equal in the first place.

>> Not necessarily - music is based on 'limits' all the time.
>> There are so many possibilities in 12-eT unexplored.

>even more in other tunings!

Yes, but I meant /good/ possibilities ;-)

>> Taking this to the extreme, theoretically, the best music would be
>> tailored right down to the wave - and the individual 0.001
>> second 'nuggets' that ultimately make all music up.

>right -- and clearly very few pieces created in such a way would
>conform to a 12-equal grid!

Yes, but only in the same way that there are about 100,000 possible
bad melodies to every good one :D

>> Interesting, but as faint as a singers' harmonic overtones are, I
>> would've thought many (including the singers) could tell if their
>> harmonic overtones are in 'tune' with each other - even if on a
>> subconscious level.

>maybe, but daniel, you need to look beyond beating and study up on
>*combinational tones*. if you have helmholtz's book, you can read
>some about them there. otherwise, do some web searches. please?

I tried, but didn't find too much. I think I possibly understand
without realising it anyway, but if you could concisely explain it in
a paragraph or two, I would be grateful :)

>> I would love to hear human voices sing in harmony, but with the
>> tones /and/ overtones tuned exactly to 12-equal :)

>of course (i know you were joking but i'll go on) that's impossible,
>because any physical musical instrument that produces a periodic
>vibration (including the human voice, bowed strings, reeds, and brass
>instruments, when producing a clear tone) has, by virtue of fourier's
>theorem, a perfectly harmonic overtone spectrum.

Which is why only a synthesizer could produce the aforementioned
overtones - yep.

>> But possibly enough for the brain to (maybe subconsciously)
recognise
>> a certain 'off-tune' sound when the sub-harmonics 'clash' against
the
>> fundamentals/each other ('roughness')...?

>what "sub-harmonics" are you speaking of? virtual pitches?

Umm... just replace 'sub-harmonics' with 'overtones'. I didn't need
to add another term.

>> As well as the previous "overtones clashing with fundamentals"
>> or "subtle quasi-mathematical 'wowowow'" syndromes, this could be
>> explained by something else; Singing in Just intonation might be
>> easier for the 'singing' brain to cope with. However, to the final
>> ear, 12-eT might ultimately sound better.

>what if no one is listening but the singers? :)

lol :)
Umm.. one other thought is that maybe the effect with singers is that
singing in JI will increase some physical vibration near their
ear/brain - and that this is a good 'feeling' (similar to how a
computer's case will 'buzz' if the cooling fan inside is spinning at
a certain frequency, or the phenomenon of how shorter buildings can
topple more easily than taller buildings in a hurricane - if the
frequency is adjusted to that building).
A singer might be biased to 'look' for this frequency instead of the
(in my opinion) natural 12-equal pitch.
In this sense, I would argue that it's the listener's ears which are
more accurate.

-------------

Hi Pauline,

>The best argument agaisnt 12-ET, or any other kind
>of ET, is such scales are out of tune with the
>harmonic partials the notes in the intervals used
>are made of.
>
>In 12-ET E 400 is 14 cents large out of tune with the
>5th partial E 386.314. The two pitches in any octave
>beat strongly with each other!

I think you must have missed my earlier point how if the partials are
also tuned to 12-et, then one can have the best of both worlds :)
Also remember that the 'evolving' type sound you get when combining
JI partials with 12-equal intervals might be preferred, but this
isn't anything to do with the Just ratios in particular; it could be
any 'offset' from the original 12-eT that would create this
evolving 'chorus' (roughness?) effect.
Example: 400 cents played together with 414 cents would create
aformentioned chorus effect, just like 400 cents and 386.314 cents
does (or 393c and 407c for that matter).

------------

Hi Robert,

>> In 12-ET E 400 is 14 cents large out of tune with the 5th partial
E 386.314.
>> The two pitches in any octave
>> beat strongly with each other!

>Yes, and if you say that 12-et is the only true tuning, as some do,
it means
>that the partials of say a 'cello
>in a 'cello concerto are out of tune, and the instrument should be
rebuilt
>somehow to have a timbre with 12-et
>partials - surely! Or maybe all the 12-et recordings we have should
be
>electronically manipulated to have only 12-et pitches in the ;-).

Yes! I concur! :D

>12-et as a fine tuning, indeed, and a vibrant one. Has a lot of
energy in it -
>wakes one up!
>(Though it may possibly be somewhat of a twentieth century aquired
taste,
>otherwise why didn't the
>musicians of Bach's time go for it when they could have easily
retuned their
>harpsichords to match their lutes etc.).

Good question and one I am tempted to explore the background of to
find out more.

>My little 'cello drone midi clip exercise at
>http://tunesmithy.netfirms.com/tunes/tunes.htm#Newbie_notes
>may make a few think? Those notes are at the correct relative volumes
>for the partials at least as measured on my 'cello voice here
>on the SB Live S/W synth.

A very good example of showing the overtones in a sound - welldone :)

------------------

Hi Dave,

>I cannot see how it can logically be claimed that 12- equal is
>all that's needed for a music which lives up to its potential.
>To many of us, musical passages performed in 12-eqt sound very
>different and have a very different psychological impact than
>musical passages which, excepting for the tuning, are identical
>but which are performed in just intonation. The just passages

This could be a timbre phenomenon maybe? Is there any way you prefer
it in 12 equal, or is JI/MT better in every way?

>But there are people who very much dislike the sound of music
>in just intonation, and for those people, just intonation, even
>thought it sounds different, doesn't have much to offer. But there
>are others of us - over 25% at least - who contrariwise like the
>sound of the just versions better, finding their emotional impact
>to be more pleasing and intense. Should we be left out?

Ummm... no I guess not :) Maybe you 25% lot are right and I'm wrong,
but I'm wondering if there's the /chance/ that the 75% (including me
it would seem!) are right :)
At this point in time, I won't bother arguing about the possiblity
that we're both right in different ways.
Obviously, even if the 75% are right, it would make sense to
(sometimes) have music performed in Just/Mean-tone for the benefit of
those who prefer it that way - even if they are wrong to prefer it
that way ;)

>There will always be people who initially react strongly against
>something which clashes with what they are used to hearing - the fact
>that it sounds "different" becomes psychologically equivalent to
>sounding "off" or "funny" or just "wrong" to them.

It doesn't just sound different to me - it really does sound off. And
it's not just initially, I've really tried to get used to Just/Mean-
tone - for longer lengths of time that most people would dream of! :)

------------

Hi Ed Foote,

>12 ET may wake one up, at first, but there is an inuring effect that
>comes with it. Ultimately, it begins to dull the senses at a
particularly
>organic level. Et can desensitize the nervous system in a sadly
insidious
>way.
>When all like intervals are the same tempered size, the ear begins to
>accept the dissonance as the standard harmonic quality, and stops
listening
>for the textural sensations that comes from juxtaposing tempered vs.
Just
>intervals. (We may liken this to weather. After a few weeks of
perfect 70

Very interesting if you're actually right, but of course I completely
disagree. If you were right, then agreed - it would be very sad how
so many people are 'brainwashed' by 12-eT. But going by experience,
it would seem brainwashing has little to do with it. It would seem
different minds are simply geared (whether rightly or wrongly) to JI
or 12-eT.
I would be very interested to know - Do any people in this group like
Just intonation and 12-equal equally as much?

>degree, sunny weather in the South Pacific islands, I began to wish
for the
>excitement of a passing thunderstorm. Unchanging qualities dull our
senses
>in one way or another).

You're probably right in one way or another, but I don't think the
analogy is too relevant here =P

>So it is with 12 ET. All thirds are the same and they are all busy,
but
>after a while, that busy-ness becomes less and less stimulative. We
just
>stop paying attention to the physical quality of the interval.
Compare this

Perhaps you're right, but this is where vibrato and the chorus effect
come in. 12-eT is still the base though from which pitch should be
altered from.

12-equal + vibrato + chorus effect + pitch slides + sound effects are
all that's needed for the best music concerning anything outside 12
equal I believe.

-------------

Hi Johnny,

>I've used Scala to hear Joe Pehrson play some
>Beethoven in KII and it sounds rather
>revelatory. But now that I can sing on my own
>the opening of Symphony #5, I still miss the
>embossed equal tempered opening descending
>major thirds. I readily admit only considering
>400 cent interval for this opening, which is
>mostly thought of for its rhythm, tempo, and
>length of silence. Try imagining the openings
>in 386 cents just. Quite soft in comparison
>to the moderns.
>
>I'm trying to loosen up my expectations.

Hehe - at last - someone in this group who might possibly prefer 12-
et ;)
Another perfect example of a tune to compare temperaments with is
Eine Kleine Nachtmusik.
The amount of thirds in that would be torture for Just intonation (or
even mean-tone ;)

------------------

Hi George,

>I've heard many different tunings over many years on two different
>retunable electronic organs I owned and also on two different kinds
>of Scalatrons and have used many sorts of timbres (all with harmonic
>partials) on them, and I think I can safely say that my impressions
>are pretty much the same, regardless of the timbre.

>> - or maybe the fact that your ears
>> simply 'prefer' mean-toned temperament.

>My ears also prefer 19-ET, 22-ET, and 41-ET (to mention a few) over
>12-ET, and my preference is closely correlated with the ability of
>the tuning to approximate just intervals. So I prefer 31 or 41- ET to
>19 or 22-ET.

Yes, but those are chosen to effectively emulate JI, so it's one and
the same.

>> > [Paul Erlich's recommendation:]
>> >http://bellsouthpwp.net/j/d/jdelaub/jstudio.htm
>>
>> As I write this letter, I'm listening to the examples presented on
>> the page. In fact I've been been doing this for the past couple of
>> weeks - with as minimal 'exposure' to 12-eT as possible (quite hard
>> in this day and age one might find ;)
>>
>> As expected, I found it off-tune at first, but I'll see if I can
>> really get to prefer it. I somehow still suspect that I won't, but
>> I'm going to keep an open mind about this - since obviously many
>> seem to think otherwise. I'll be posting the results here soon.

>I see that this is adaptive JI, which may or may not sound a little
>too dry (i.e., beatless) for your taste. It would be good also to

Well, about the results of that experiment, as I expected I didn't
really prefer it any more than I did originally after trying
for /days/ to prefer it. It wasn't just beatless or dry - it really
did sound 'off' to me.

>find something in both 12-ET and meantone temperament as well, after
>you've spent sufficient time with this.

OK doke, see below...

--------------

>> Doesn't anyone out there have any music more than a few seconds in
>> length in both 12-ET and meantone temperament in exactly the same
>> timbre?

>of course -- herman miller, on both his pavane for a warped princess
>page, and pachelbel's warped canon page, provides versions in 12-
>equal and many other tunings, including several varieties of
meantone.

I looked at this page, and tried many of the example tunes - all
sounded to me fractionally worse than the original 12-eT version.
However, there are quite a few, so perhaps you can direct me to
trying out one version in particular so I can listen for (sigh....)
an extended period of time....?

Pages are:
http://www.io.com/~hmiller/music/pavane.html
http://www.io.com/~hmiller/music/warped-canon.html

>Hmm, how about a Steinway concert piano in Meantone, Well-
Temperament,
>and Equal? Maybe Mozart?
>try this: www.uk-piano.org/edfoote/well_tempered_piano.html

The acid test would be Eine Kleine Nachtmusik as mentioned above >;)
If someone could do a midi of that in the most 'accepted' mean-tone
temperament and 12-eT for comparison, I would be more than happy to
put up a poll on my site along with the sound test I already have.

---------------

That's it - phew! :)

Cheers,
Daniel

Daniel,

Just out of curiousity: how many languages do you speak fluently? I mean, really conversant and literately eloquent in them. If you only speak English, just let me know that.

This isn't a facetious question at all. Your entire premise is that everything that can be considered music (or as you put it "the best music") can be translated to 12tET. I want to examine that premise in greater detail and context.

Cheers,
Jon

--- In tuning@yahoogroups.com, "Daniel White <soundburst@l...>"
<soundburst@l...> wrote:

> Another perfect example of a tune to compare temperaments with is
> Eine Kleine Nachtmusik.

ok, sure.

> The amount of thirds in that would be torture for Just intonation
(or
> even mean-tone ;)

mozart himself taught his violin students some 20 different pitches
within the octave. because he used a form of meantone tuning (similar
to a subset of 55-equal), G# was not the same as Ab, etc.

now along comes daniel white, saying that the tuning mozart himself
taught is not the correct tuning for mozart's own music, but 12-equal
is.

RIIIGHT . . .

--- In tuning@yahoogroups.com, "Daniel White <soundburst@l...>" <soundburst@l...> wrote:
> It's my opinion, and one I think might actually be ultimately correct
> for many reasons.

How could you possibly prove such an opinion either correct or not correct? In your opinion, the question "which tuning is the abolute best" makes sense. In my opinion, the question is nonsensical.

hi Daniel,

> From: <wallyesterpaulrus@yahoo.com>
> To: <tuning@yahoogroups.com>
> Sent: Monday, December 16, 2002 3:00 PM
> Subject: [tuning] Re: 12-equal Vs. Just tuning
>
>
> --- In tuning@yahoogroups.com, "Daniel White <soundburst@l...>"
> <soundburst@l...> wrote:
>
> > Another perfect example of a tune to compare
> > temperaments with is Eine Kleine Nachtmusik.
>
> ok, sure.
>
> > The amount of thirds in that would be torture
> > for Just intonation (or even mean-tone ;)
>
> mozart himself taught his violin students some
> 20 different pitches within the octave. because
> he used a form of meantone tuning (similar to a
> subset of 55-equal), G# was not the same as Ab, etc.
>
> now along comes daniel white, saying that the
> tuning mozart himself taught is not the correct
> tuning for mozart's own music, but 12-equal is.
>
> RIIIGHT . . .

paul mentioned exactly the same thing i intended to
write in response to you.

i don't have a retuned example of _Eine Kleine Nachtmusik_,
but i do have the beginning of Mozart's famous 40th Symphony
(G-minor) tuned to the subset of 55edo mentioned by paul.
it opens with my webpage _Mozart's tuning: 55-EDO,
and its close relative, 1/6-comma meantone_:

http://sonic-arts.org/monzo/55edo/55edo.htm

i don't have a 12edo version of the Mozart Symphony, but
you can get one from Classical MIDI Archives:

http://www.classicalarchives.com/mozart.html

scroll down to about halfway down the page for the
12edo MIDI's ... your guess is as good as mine as to
what tuning appears on the live-performance mp3's! ;-)

in my opinion, the 55edo/meantone version of
Mozart's 40th sounds way better than the 12edo version.
... and after all, it *is* the tuning Mozart intended
for the piece.

-monz

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:

> in my opinion, the 55edo/meantone version of
> Mozart's 40th sounds way better than the 12edo version.
> ... and after all, it *is* the tuning Mozart intended
> for the piece.

Here's someone who thinks it is the best all-around solution for tuning Western music of the 17th and 18th centuries:

http://www-midischool.cwru.edu/Duffin/Vallotti/

Joe,

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
> i don't have a retuned example of _Eine Kleine Nachtmusik_,
> but i do have the beginning of Mozart's famous 40th Symphony
> (G-minor) tuned to the subset of 55edo mentioned by paul.
> it opens with my webpage _Mozart's tuning: 55-EDO,
> and its close relative, 1/6-comma meantone_:
>
> http://sonic-arts.org/monzo/55edo/55edo.htm

With all due respect, retuned MIDI files aren't going to convince anyone of a superiority of a tuning, at least when what we're talking about is an orchestral piece. If someone can compare recordings of an orchestra playing in the two different intonations, then I'd call it a valid test of preferences.

The difference between a good orchestra recording and a MIDI rendition is far greater, aesthetically, than the difference between 12tET and 55edo. There has to be a better way to illustrate for the uninitiated.

Cheers,
Jon

--- In tuning@yahoogroups.com, "Daniel White <soundburst@l...>"

/tuning/topicId_39089.html#41510

<soundburst@l...> wrote:
> Hi all, sorry I've taken so long with this 'multi-post' - been so
> busy lately! For all those not in the know, I'm firmly of the
opinion that only 12-tET (as opposed to JI or meantone) is needed
for all the best music...
>
> ---------------------
>
> Hi J. Pehrson,
>
> >I can see we're back to "White Bread" 12-tET again with you! :)
>
> lol :)
>

***Hello Daniel!

You're kinda turning into the H.L.Mencken of the Tuning List. Well,
you're a good "foil" so no harm in that!

Actually, some of your arguments seem to "hold water..." For
instance, you're viewpoint that it *still* is possible to write music
in 12-equal, I believe is confirmed by certain fine composers around
still doing it, although they *do* tend to use *lots* of "special
effects" in the categories of variations of timbre and so forth, or
in novel use of metrics, timing or instrumentation. Mostly, I
believe these "special effects" are used to offset the 12-equal
scale, which has been so thoroughly explored...

There is nothing all that magical about the number 12, despite its
being an unusually harmonic and versatile scale with a limited number
of pitches, but if I understand my history correctly, we might just
as easily chosen a 19-equal scale, as emulating a fair number of
harmonic series partials, without too many more notes.

I understand that you believe emulating partials is not all that
important a process, but I believe you would have to explain why our
*Western* music spent all its time in the Renaissance using parallel
octaves and fifths (2nd and 3rd partials) and then spent so much time
evolving meantone systems that would handle the 5th partial as a new
practice, starting with "Faux Bourdon" in England and so on...

So, history seems to show that the pursuit of these partials had a
*lot* to do with what we have, over a period of time,
called "music..." much of which involves the lower integer ones, and
which led, ironically looking at *your* viewpoint, to 12-equal, which
does a remarkable job of emulating them. I think it's pretty clear
that this search for the emulation of partials lead both to
*meantone* and to your favorite 12-equal.

I believe Paul's point, if I have it correct, is that the significant
beating in 12-equal means it really *is* an imperfect system for
emulating partials, although certainly not on the scale of the
dissonant 13-equal... Which is, of course, a usable scale, just much
different...

So essentially, you've put the "cart before the horse" or put your
accustomization to 12-equal before the history that selected it! In
a sense 12-equal is a splendid *compromise* that has worked well for
a long time, but not as long as the *meantone* tuning that preceded
it... I'm sure that if you lived in the "heyday" of meantone you
would have proclaimed that the "only way" as well... :)

Since you're working *backwards* at least in *my* thinking, the idea
of taking the natural overtone series and creating 12-equal partials
seems particularly curious. It's even more curious when we think
about the fact that even a single *musical* tone, or what we commonly
define as music, with a recognizable pitch, is distinguised
from "noise" just by the recurring periodic nature of it's
simultaneous just overtones...

I rather wish somebody would do your experiment with 12-equal partial
timbres, since, personally, I believe the results would sound pretty
terrible and would set to rest the notion that we should, somehow, go
in *that* direction, rather than the other way: trying to create
systems that emulate the harmonic series as much as possible which I
think we can *conclusively* state is what Western history has been
trying to do...

Joseph Pehrson

hello Daniel

> I think you must have missed my earlier point how if the partials
are
> also tuned to 12-et, then one can have the best of both worlds :)

On acoustical instrument, "tuning the partials" makes no sense at all.
An instrument is
either (nearly) harmonic (most of them) or (downright) inharmonic
according to the laws of physics that
governs its vibration modes.

With electronic instrument, it is possible, in principle, to "tune
partials". Thus
you propose instead of having partials to

f0
2*f0
3*f0
4*f0
5*f0
6*f0
7*f0
8*f0
9*f0
10*f0

have them "tuned" to

f0
f0 * 2
f0 * 2^(19/12)
f0 * 4
f0 * 2^(14/6)
f0 * 2^(31/12)
- (being ambiguous in 12ET, 7th harmonics does not deserves to exist)
f0 * 8
etc.

No simple physical object may practically display such spectrum, so it
is
very unlikely to sound very different from an array of out of tune
sine generators.

Further, this argument cannot be used to advocate 12ET because this
can be done (or at least imagined)
for ANY tuning. Furthermore, having a set of inharmonic tones that
never beat or
produce any kind of roughness when combined would probably be boring
to death...

> Umm.. one other thought is that maybe the effect with singers is
that
> singing in JI will increase some physical vibration near their
> ear/brain - and that this is a good 'feeling' (similar to how a
> computer's case will 'buzz' if the cooling fan inside is spinning at
> a certain frequency, or the phenomenon of how shorter buildings can
> topple more easily than taller buildings in a hurricane - if the
> frequency is adjusted to that building).
> A singer might be biased to 'look' for this frequency instead of the
> (in my opinion) natural 12-equal pitch.
> In this sense, I would argue that it's the listener's ears which are
> more accurate.

If the singers are not qualified to sing "correctly" because singing
is a biased processed, then should we not exclude song voice from
the realm of "correct music"!! Come on!! that is a very specious
argument (to say the less)!

yours truly

François Laferrière

Hi Jon,

>Just out of curiousity: how many languages do you speak fluently? I
mean,
>really conversant and literately eloquent in them. If you only speak
English,
>just let me know that.

I do only speak English - having seen no real need (as yet) to learn
another language. May I enquire as to why you asked? :)

>This isn't a facetious question at all. Your entire premise is that
everything
>that can be considered music (or as you put it "the best music") can
be
>translated to 12tET. I want to examine that premise in greater
detail and
>context.

I would be interested to know how you would go about this.

-------------

Hi Gene,

>How could you possibly prove such an opinion either correct or not
correct? In
>your opinion, the question "which tuning is the abolute best" makes
sense. In
>my opinion, the question is nonsensical.

I'm not trying to prove 100% either way. I am instead trying to show
there's a /chance/ that either way (12eT in particular ;) - could be
right (and the other way wrong). It just happens to be the side of 12
equal I'm on :)

Also, isn't it your opinion that there is a 'best' tuning, but that
it should be tailored to each piece of music?

-------------

Hi Paul,

>> The amount of thirds in that would be torture for Just intonation
(or
>> even mean-tone ;)

>mozart himself taught his violin students some 20 different pitches
>within the octave. because he used a form of meantone tuning (similar
>to a subset of 55-equal), G# was not the same as Ab, etc.
>
>now along comes daniel white, saying that the tuning mozart himself
>taught is not the correct tuning for mozart's own music, but 12-equal
>is.
>
>RIIIGHT . . .

I'm not sure why Mozart chose a form of meantone tuning instead of 12-
tET - and it's something I'd need to research of to find out more.
However, bear in mind that even Mozart could be mistaken in what
temperament he chose for his own music, just in the same way others
(including myself) /could/ be mistaken for choosing 12-eT for their
own music.

-----------

Hi Monz,

>i don't have a retuned example of _Eine Kleine Nachtmusik_,
>but i do have the beginning of Mozart's famous 40th Symphony
>(G-minor) tuned to the subset of 55edo mentioned by paul.
>it opens with my webpage _Mozart's tuning: 55-EDO,
>and its close relative, 1/6-comma meantone_:
>
>http://sonic-arts.org/monzo/55edo/55edo.htm

I compared the two versions and guess what? ;)
They are quite close, but once again, I think the 12-eT version is
fractionally preferable to the 55edo version both melodically and
harmonically. Nice piece by the way!

Maybe you could you do a version but at the same tempo as the one at
classicalarchives.com?

------------

I've just noticed some more posts in the group. I'll be responding to
these soon.

Cheers,
Daniel (soundburst@lycos.com)
--
http://www.skytopia.com/project/scale.html

--- In tuning@yahoogroups.com, "Daniel White <soundburst@l...>" <soundburst@l...> wrote:

> Also, isn't it your opinion that there is a 'best' tuning, but that
> it should be tailored to each piece of music?

I start with the tuning and then write music for it, but that's just me. One could argue the best tuning for a given piece of music is the one the composer intended, I suppose.

Hello Daniel,

First off: it *really* would be helpful if you could reply to each individual question/post. While it may seem like more work, what we risk is having the various threads of thought intermingling until it is impossible to tell who is saying what!

The small investment in will reward you (and us) with a more clear 'education' in our topics...

--- In tuning@yahoogroups.com, "Daniel White <soundburst@l...>" <soundburst@l...> wrote:
> I do only speak English - having seen no real need (as yet) to
> learn another language. May I enquire as to why you asked? :)

Absolutely. You are approaching music in the same way as language: you see no need for anything else. In doing so, you are making a critical error, one that I attribute to youth, inexperience, hubris, or simple human nature - one size does not fit all.

There are centuries of writings in other languages that were written by authors speaking their native tongue. And there are endless pieces of prose and poetry that all their charm, passion, anger, intent, thrust if translated into another language (such as English). If you haven't travelled to 'foreign lands', then you haven't experiences - first hand - the reality of "it must lose something in the translation".

This is a real-world parallel to what you are asking anyone to believe: that every piece of music would be best in 'one language'. And it is your narrowness of vision that is disallowing you from imagining musics that not only wouldn't be 'improved' - that, in fact, they would either be harmed or that it would be impossible!

You owe it to yourself to consider your question again, in two parallel but equally important ways:

1. What musics of the world have I *not* taken careful account and study of? Have I exposed myself to as much of the music of the world that does *not* use 12tet as I possibly can, to determine why it either isn't or whether or not it could be 'translated'?

2. In what ways, in a more deeply aesthetic sense, could art forms fit one mold? How can I (Daniel) ignore the possibility that, with the incredible creativity embodied in humanity, expect that art forms would gravitate towards one, undeniable mode of construction, instead of spreading out in a myriad of approaches, limited only by the imagination of the individual?

Your premise belies an extremely narrow or thinly informed view of not only music but human artistic creativity (not to mention the physics of sound and musical history). For one to look for "best" systems ignores our basic needs for a variety in life. I would never be happy in a life that, in effect, "McDonlad's-izes" everything into musical hamburgers that are the same the world over.

> I'm not sure why Mozart chose a form of meantone tuning instead of
> 12- tET - and it's something I'd need to research of to find
> out more.

Yes, we *do* expect you to do some more study...

> However, bear in mind that even Mozart could be mistaken in what
> temperament he chose for his own music

Daniel, are you a composer? Do you have any idea about making the personal choices for one's own music? Based on what you have written so far, my money is on Mozart knowing which end is up - you've got a heavy, heavy burden of proof on your shoulders to come up to his standards!

Look, I mean this in all good intent. ASCII is awful at portraying feelings, so don't take any 'mean-ness' in my writing. But I'll be honest and say forthrightly that you have a *lot* to learn about all these issues before you'll ever make headway in convincing intelligent musicians that 12 is the end-all, be-all.

Cheers,
Jon

Daniel,

There was an editorial goof in my last reply. Please note the words marked off in asterisks:

"There are centuries of writings in other languages that were
written by authors speaking their native tongue. And there are endless pieces of prose and poetry that *would lose* all their charm, passion, anger, intent, thrust if translated into another language (such as English)."

Sorry for the lax typing!

Cheers,
Jon

----- Original Message -----
From: <JSZANTO@ADNC.COM>

> Look, I mean this in all good intent. ASCII is awful at
> portraying feelings, so don't take any 'mean-ness' in my
> writing. But I'll be honest and say forthrightly that you have
> a *lot* to learn about all these issues before you'll ever make
> headway in convincing intelligent musicians that 12 is the end-all,
be-all.

Particularly on this list.

* David Beardsley
* http://biink.com
* http://mp3.com/davidbeardsley

hi Daniel,

> From: <soundburst@lycos.com>
> To: <tuning@yahoogroups.com>
> Sent: Tuesday, December 17, 2002 8:28 AM
> Subject: [tuning] Re: 12-equal Vs. Just tuning
>
>
> Hi Monz,
>
> >i don't have a retuned example of _Eine Kleine Nachtmusik_,
> >but i do have the beginning of Mozart's famous 40th Symphony
> >(G-minor) tuned to the subset of 55edo mentioned by paul.
> >it opens with my webpage _Mozart's tuning: 55-EDO,
> >and its close relative, 1/6-comma meantone_:
> >
> >http://sonic-arts.org/monzo/55edo/55edo.htm
>
> I compared the two versions and guess what? ;)
> They are quite close, but once again, I think the 12-eT
> version is fractionally preferable to the 55edo version
> both melodically and harmonically. Nice piece by the way!
>
> Maybe you could you do a version but at the same tempo as the one at
> classicalarchives.com?

nah ... the one at classicalarchives.com is "straight off
the page", all at one (rather fast) tempo.

the excerpt i made has subtle nuances of tempo, and
overall is rather slower than the "straight" version,
and that's the way i like the piece.

if i were going to bother, i'd do it the other way
around, and just eliminate all the pitch-bends from
my version, keeping the tempo changes in the 12edo version.

perhaps it's the tempo which causes you to prefer the
classicalarchives.com 12edo version?

to me, the subtle harmonic and melodic nuances of
the 55edo version are far preferable to the bland,
colorless 12edo version.

i feel the same way about many of my own pieces which
were originally written in 12edo then retuned to either
real JI or adaptive-JI. the 12edo versions are so
bland that after i get used to hearing the JI versions,
i never want to listen to the 12edo versions again.

one example from my own work is _3 Plus 4_,
which you can find in both 12edo (MIDI) and JI (mp3),
about 1/4 of the way down this page:

http://sonic-arts.org/monzo/worklist/worklist.htm

for some reason, the 12edo version is coming out
with the wrong percussion sounds when i transform
it into a .wav (in preparation for an .mp3), and
even the MIDI plays incorrectly under QuickTime.
sorry about that, but i haven't been able to figure
out what's wrong.

-monz

--- In tuning@yahoogroups.com, "Joseph Pehrson <jpehrson@r...>"
<jpehrson@r...> wrote:

> I believe Paul's point, if I have it correct, is that the
significant
> beating in 12-equal means it really *is* an imperfect system for
> emulating partials, although certainly not on the scale of the
> dissonant 13-equal... Which is, of course, a usable scale, just
much
> different...

hmm . . . what i was saying about 13-equal was very different from
this.

daniel had proposed, as a remedy for the beating of the 12-equal
consonances, electronically retuning the partials of all the
instruments/timbres to themselves be in 12-equal -- hence no beating.

i pointed out that one could easily do the same thing in 11-equal or
13-equal, and eliminate beating in *those* tunings as well -- as has
been evidenced quite nicely by our friends Bill Sethares and Jacky
Ligon, among others, on the MakeMicroMusic list.

so, simply from the point of view of eliminating beating, daniel has
no basis to claim that his proposal of 12 is in any way superior to
an analogous situation with 11 or 13.

moving on . . .

if daniel chooses to go ahead and study combinational tones, he'll
see that even this all-partials-in-12 world will produce many "out-of-
the-system", clashing notes due to the non-linear response of the ear-
brain system. these combinational tones are typically quiet and
typically musicians learn to filter them out (subconsciously) in the
course of their training, but they happen to be very much "in-the-
system" in just intonation, and become a pleasing part of the overall
effect in JI, often coinciding exactly with chord tones.. which is
one reason why JI-immersed people are so loathe to go back to 12 --
those clashing combinational tones, often a quartertone or more off
of where they would be in JI, suddenly stick out like a sore thumb
and a hand full of sore fingers.

> So essentially, you've put the "cart before the horse" or put your
> accustomization to 12-equal before the history that selected it!

clearly this line of argument isn't working with daniel . . . he
claims that history was wrong and 12 was really the goal all along!
which, incidentally, is the same thing balzano implies, though at
least balzano allows for the possibility of other equal tunings (20,
32 . . .) for microtonality . . .

> I rather wish somebody would do your experiment with 12-equal
>partial
> timbres,

it's been done -- ask bill sethares.

> since, personally, I believe the results would sound pretty
> terrible

actually, the result is quite nice -- the hammond organ, for example,
operates pretty much on this principle.

--- In tuning@yahoogroups.com, "Daniel White <soundburst@l...>"

/tuning/topicId_39089.html#41519
> >mozart himself taught his violin students some 20 different pitches
> >within the octave. because he used a form of meantone tuning
(similar
> >to a subset of 55-equal), G# was not the same as Ab, etc.
> >
> >now along comes daniel white, saying that the tuning mozart himself
> >taught is not the correct tuning for mozart's own music, but 12-
equal
> >is.
> >
> >RIIIGHT . . .
>
> I'm not sure why Mozart chose a form of meantone tuning instead of
12- tET - and it's something I'd need to research of to find out more.
> However, bear in mind that even Mozart could be mistaken in what
> temperament he chose for his own music, just in the same way others
> (including myself) /could/ be mistaken for choosing 12-eT for their
> own music.
>

***My impression, Daniel, is that 12-equal hadn't been used much yet,
at least in the West... with I guess the exception of some lute
tablature... so I don't believe it would be a "natural" choice...

Glad you think you might be "wrong" in always composing in 12-equal.
Why not try something else, just for a change, and forget that you
think it sounds "wrong..."? Just find some kind of new "rightness"
about it!

If after writing the pieces and listening, if you're "not having fun
yet" go back to your old 12-equal standby.

However, your posts to, particularly, this list, reveal your
curiosity, even if you're taking the "devils advocate" position...!

J. Pehrson

--- In tuning@yahoogroups.com, "francois_laferriere
<francois.laferriere@o...>" <francois.laferriere@o...> wrote:

> f0
> f0 * 2
> f0 * 2^(19/12)
> f0 * 4
> f0 * 2^(14/6)
> f0 * 2^(31/12)
[...]
> f0 * 8
> etc.
>
> No simple physical object may practically display such spectrum, so
it
> is
> very unlikely to sound very different from an array of out of tune
> sine generators.

that all depends on the amplitude envelope(s) involved. if you start
with a synthesized timbre that sounds like a single note, and retune
the partials as above, in all likelihood the result will still sound
like a single note, just a bit "noisier" or "wobblier". if you don't
believe me, you absolutely must obtain a copy of bill sethares' book
and CD.

> Further, this argument cannot be used to advocate 12ET because this
> can be done (or at least imagined)
> for ANY tuning.

exactly -- though the further the partials are moved from a harmonic
series, the less realistic and more wobbly/noisy the timbre becomes.
12-equal (including the 7th harmonic) is not too bad at all in this
respect.

> Furthermore, having a set of inharmonic tones that
> never beat or
> produce any kind of roughness when combined would probably be boring
> to death...

this is far from true for what daniel is proposing. all the
traditional dissonances of 12-equal are still dissonant in this
arrangement!

> If the singers are not qualified to sing "correctly" because singing
> is a biased processed, then should we not exclude song voice from
> the realm of "correct music"!! Come on!! that is a very specious
> argument (to say the less)!
>
> yours truly
>
> François Laferrière

i agree with you there, francois!

--- In tuning@yahoogroups.com, "Daniel White <soundburst@l...>"
<soundburst@l...> wrote:

> However, bear in mind that even Mozart could be mistaken in what
> temperament he chose for his own music, just in the same way others
> (including myself) /could/ be mistaken for choosing 12-eT for their
> own music.

reading this today, it is my opinion that this is complete nonsense.
was renoir mistaken in the colors he chose for his paintings? when i
sign my name, am i using the wrong handwriting? . . .

Hi Jon,

>First off: it *really* would be helpful if you could reply to each
individual
>question/post. While it may seem like more work, what we risk is
having the
>various threads of thought intermingling until it is impossible to
tell who is
>saying what!

Fair enough. I usually precede each comment with the author who wrote
that portion though. Perhaps I should be asking for people to always
include the author name like I do.

>> I do only speak English - having seen no real need (as yet) to
>> learn another language. May I enquire as to why you asked? :)

>Absolutely. You are approaching music in the same way as language:
you see no
>need for anything else. In doing so, you are making a critical
error, one that

I somewhat expected this kind of reply :) You make good points that
really do apply to language and poetry in a way, but the point is:
music really is a universal language.....

>I attribute to youth, inexperience, hubris, or simple human nature -
one size
>does not fit all.
>There are centuries of writings in other languages that were written
by authors
>speaking their native tongue. And there are endless pieces of prose
and poetry
>that all their charm, passion, anger, intent, thrust if translated
into another
>language (such as English). If you haven't travelled to 'foreign
lands', then
>you haven't experiences - first hand - the reality of "it must lose
something
>in the translation".

I readily admit to certain aspects in other languages being
preferable to English. What one appreciates in each language is all
the different tones and forms of expression. Even the subtleties in
the pronounciation of words are obviously more than just trivial. My
point rests again - music is a universal language - and this is why
people can appreciate 'different' music from the other side of the
globe. This doesn't mean there isn't an ideal or incentive to aim for
though. Of course, there is /great/ room for variety and creativity,
but I ultimately believe there's a reason why a certain piece of
music is good - and that this completely transcends culture and could
even be mathematical and/or spiritual.

>This is a real-world parallel to what you are asking anyone to
believe: that
>every piece of music would be best in 'one language'. And it is your
narrowness
>of vision that is disallowing you from imagining musics that not
only wouldn't
>be 'improved' - that, in fact, they would either be harmed or that
it would be
>impossible!

As I have said in the article on my site concerning aesthetics, I
certainly believe that sometimes, adding something good to a tune
will also necessarily take something away. This isn't always the case
though since certain 'tune nuggets' (for example) and chord sequences
are recognised as being better than others. It all depends on the
context of the tune - and is a million times more complex than anyone
one of us could imagine.
It just so happens that I believe 12-eT is one of the main 'common
denominators' around which all music should be built.

>You owe it to yourself to consider your question again, in two
parallel but
>equally important ways:
>
>1. What musics of the world have I *not* taken careful account and
study of?
>Have I exposed myself to as much of the music of the world that does
*not* use
>12tet as I possibly can, to determine why it either isn't or whether
or not it
>could be 'translated'?

Well, of course I've studied music of all 'types' and will continue
to do so. As well as the differences in each, there are also many
similarities - but also bear in mind that bad taste in music is found
all around the sphere and in /every/ 'type' of music. You only have
to turn on the TV to find this out ;)

>2. In what ways, in a more deeply aesthetic sense, could art forms
fit one
>mold? How can I (Daniel) ignore the possibility that, with the
incredible
>creativity embodied in humanity, expect that art forms would
gravitate towards
>one, undeniable mode of construction, instead of spreading out in a
myriad of
>approaches, limited only by the imagination of the individual?

There must be a massive (unknown) hierarchy of quality to chords,
melody, construction and ultimately to each individual tune. The
amazing and truly profound thing is - the ones at the top (best) are
incredibly varied I believe!

>Your premise belies an extremely narrow or thinly informed view of
not only
>music but human artistic creativity (not to mention the physics of
sound and
>musical history). For one to look for "best" systems ignores our
basic needs
>for a variety in life. I would never be happy in a life that, in
effect,
>"McDonlad's-izes" everything into musical hamburgers that are the
same the
>world over.

lol - well it's a funny analogy for many interesting possibilities -
if not entirely relevant or accurate in this situation =P

>> I'm not sure why Mozart chose a form of meantone tuning instead of
>> 12- tET - and it's something I'd need to research of to find
>> out more.

>Yes, we *do* expect you to do some more study...

As we all do. :)

>> However, bear in mind that even Mozart could be mistaken in what
>> temperament he chose for his own music

>Daniel, are you a composer?

You betcha :) If you're actually interested in hearing some of the
music I compose, you might like to check out the URL I've pasted at
the end of this post. Perhaps try 'Grand Finale' first if you wish -
as that's my favourite.

>Do you have any idea about making the personal
>choices for one's own music?

When composing music, one should aim to discover the best chord
patterns, melodies, structures, and continuations etc.. Someone who's
got good taste in music will appreciate those things best, even if
they aren't the ones who wrote the music in the first place :)

>Based on what you have written so far, my money is
>on Mozart knowing which end is up - you've got a heavy, heavy burden
of proof
>on your shoulders to come up to his standards!

I feel myself going through deja vu here ;) - but I'll say the same
thing I said to someone else some time ago; Mozart is of course a
brilliant composer, but that doesn't mean he's going to be right
about /every/ choice in music. And why should this include the
temperament he chose for his own music?

>Look, I mean this in all good intent. ASCII is awful at portraying
feelings, so
>don't take any 'mean-ness' in my writing. But I'll be honest and say

np :) It's always a good thing to present the other view - if only so
one can see exactly what I'm arguing against ;)

>forthrightly that you have a *lot* to learn about all these issues
before
>you'll ever make headway in convincing intelligent musicians that 12
is the
>end-all, be-all.

Music is so complex, that it'll be some time before any opinions are
proved either right or wrong. Hopefully, humanity is progressing
towards what might resemble the truth though! :)

Thanks,
Daniel (soundburst@lycos.com)

http://www.skytopia.com/soundburst/soundburst.html

--- In tuning@yahoogroups.com, "wallyesterpaulrus

/tuning/topicId_39089.html#41525

<wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:
> --- In tuning@yahoogroups.com, "Joseph Pehrson <jpehrson@r...>"
> <jpehrson@r...> wrote:
>
> > I believe Paul's point, if I have it correct, is that the
> significant
> > beating in 12-equal means it really *is* an imperfect system for
> > emulating partials, although certainly not on the scale of the
> > dissonant 13-equal... Which is, of course, a usable scale, just
> much
> > different...
>
> hmm . . . what i was saying about 13-equal was very different from
> this.
>
> daniel had proposed, as a remedy for the beating of the 12-equal
> consonances, electronically retuning the partials of all the
> instruments/timbres to themselves be in 12-equal -- hence no
beating.
>
> i pointed out that one could easily do the same thing in 11-equal
or
> 13-equal, and eliminate beating in *those* tunings as well -- as
has
> been evidenced quite nicely by our friends Bill Sethares and Jacky
> Ligon, among others, on the MakeMicroMusic list.
>
> so, simply from the point of view of eliminating beating, daniel
has
> no basis to claim that his proposal of 12 is in any way superior to
> an analogous situation with 11 or 13.
>

***Hi Paul!

Oh... I see what he's getting at. However, eliminating beating among
lower-integer ratio intervals in a scale doesn't have anything to do
with the dissonances in the scale, yes, where beats *can't* be
eliminated, right?? And there is a great difference in the number of
such dissonances in a scale such as 13-equal as opposed to 12-equal,
right? So the comparison doesn't hold, even if the beating on the
lower-interger ones can be eliminated??

Thanks!

Joseph

--- In tuning@yahoogroups.com, "Daniel White <soundburst@l...>"
<soundburst@l...> wrote:

> Music is so complex, that it'll be some time before any opinions
are
> proved either right or wrong. Hopefully, humanity is progressing
> towards what might resemble the truth though! :)
>
> Thanks,
> Daniel (soundburst@l...)

daniel, let's say you're confronted with an arabic musician. modern
synthesizers in the arabic world normally have an option to lower all
the E and B keys by a quarter-tone, so that the white keys correspond
with what is often known as the "arabic diatonic scale".

as the great light of truth, revealer of 12-equal as universal ideal,
it seems you have four options to "correct" the arabic musician. the
two pitches, according to you, should be

1. E and B
2. Eb and B
3. E and Bb
4. Eb and Bb

since you say you're so well versed with all styles of music from all
over the sphere, surely you've already determined the answer to this
dilemma.

so what do you tell the arabic musician to do, o wise one?

--- In tuning@yahoogroups.com, "Joseph Pehrson <jpehrson@r...>"
<jpehrson@r...> wrote:

> However, eliminating beating among
> lower-integer ratio intervals in a scale doesn't have anything to
do
> with the dissonances in the scale, yes, where beats *can't* be
> eliminated, right??

hmm . . . well, yeah, i guess that's right, if by "low-integer ratio
intervals" you really mean "intervals between low-numbered partials",
because in these scales, there are no low-integer ratios (except
2:1), instead there is equal division of the octave, and we're
talking about a situation in which the partials themselves are
quantized to these same divisions.

> And there is a great difference in the number of
> such dissonances in a scale such as 13-equal as opposed to 12-
equal,
> right?

assuming i interpreted the above correctly, the answer is no!

> So the comparison doesn't hold, even if the beating on the
> lower-interger ones can be eliminated??

it sure does seem to hold!

looks like you have to brush up on your sethares again, joseph!

(the thing is, sethares seems to overestimate the extent to which
dissonance is caused by beating/roughness -- there are other factors
involved, such that 13-equal can never truly be as consonant no
matter *how* you tune the partials -- but that's veering a bit
outside the premises of this present scenario . . .)

--- In tuning@yahoogroups.com, "wallyesterpaulrus

/tuning/topicId_39089.html#41533

<wallyesterpaulrus@y...>" <wallyesterpaulrus@y...> wrote:
> --- In tuning@yahoogroups.com, "Joseph Pehrson <jpehrson@r...>"
> <jpehrson@r...> wrote:
>
> > However, eliminating beating among
> > lower-integer ratio intervals in a scale doesn't have anything to
> do
> > with the dissonances in the scale, yes, where beats *can't* be
> > eliminated, right??
>
> hmm . . . well, yeah, i guess that's right, if by "low-integer
ratio
> intervals" you really mean "intervals between low-numbered
partials",
> because in these scales, there are no low-integer ratios (except
> 2:1), instead there is equal division of the octave, and we're
> talking about a situation in which the partials themselves are
> quantized to these same divisions.
>
>
> > And there is a great difference in the number of
> > such dissonances in a scale such as 13-equal as opposed to 12-
> equal,
> > right?
>
> assuming i interpreted the above correctly, the answer is no!
>
> > So the comparison doesn't hold, even if the beating on the
> > lower-interger ones can be eliminated??
>
> it sure does seem to hold!
>
> looks like you have to brush up on your sethares again, joseph!
>

***Oh sure, that's right... he's the guy who can make a minor ninth
sound like an octave! I admit it's time for a "reread..." So I
guess practically *any* interval can be made consonant, if you mess
around with the partials in a certain way...

> (the thing is, sethares seems to overestimate the extent to which
> dissonance is caused by beating/roughness -- there are other
factors
> involved, such that 13-equal can never truly be as consonant no
> matter *how* you tune the partials -- but that's veering a bit
> outside the premises of this present scenario . . .)

***Well, I think this is a bit what I was getting at... when showing
Daniel White how we arrived at his "magic" number 12...

JP

Daniel,

--- In tuning@yahoogroups.com, "Daniel White <soundburst@l...>" <soundburst@l...> wrote:
> I somewhat expected this kind of reply :) You make good points that
> really do apply to language and poetry in a way, but the point is:
> music really is a universal language.....

Wrong. Completely wrong. You're really showing how little you know about the musics of the world, and the reactions of people from differing cultures to other 'musics'. Sound might be universal, aspects of rhythm certainly, even certain fundamental tuning and scalar 'melodicles' (pentatonic melodies abound over the world, etc.). But 'music', as you are portraying it (a "tune", chord progressions, etc) is not universal. And certainly 12tet isn't, and I hope it never becomes such.

> I readily admit to certain aspects in other languages being
> preferable to English. What one appreciates in each language is all
> the different tones and forms of expression. Even the subtleties in
> the pronounciation of words are obviously more than just trivial.

That is an extraordinary parallel example to microtonal tunings! How do you think the inflections of speech (for example, many of the Asian languages and dialects) are managed? Not just through volume and sound attributes, but extremely suble *pitch* alterations?

Ever wonder if composers, feeling trapped by the huge distance of 100 cents between intervals, longed for a more natural way to set speech, so that a 'song' more closely paralleled the lovely intonations of the actual language?

(Note: I know at least one very important composer who has...)

> music is a universal language - and this is why
> people can appreciate 'different' music from the other side of the
> globe.

Next time you throw a party, try and entertain people with Korean Pansori epics or some good ol' Chinese Opera (and not the Grand Ol Opry). Tell my how 'universally' it was enjoyed...

> but I ultimately believe there's a reason why a certain piece of
> music is good

Good? How can an art form meet some overall value of "good"? (Gad, we're getting pretty far from tuning...)

> and that this completely transcends culture and could
> even be mathematical and/or spiritual.

If it's mathmatical, it is going to entail a lot more than 12. And spirituality in music is a very deep subject.

> As I have said in the article on my site concerning aesthetics

... I apologize for not going to your site - I'll take a look tonight.

> It all depends on the context of the tune

You know, there *are* valid musics that don't necessarily revolve around the concept of 'tune'.

> It just so happens that I believe 12-eT is one of the main 'common
> denominators' around which all music should be built.

Why have a common denominator? I don't want any art form that aspires to be "common".

> Well, of course I've studied music of all 'types' and will continue
> to do so.

Then you know that trying to emulate gamelans - both Balinese and Javanese - in 12tet would be both ludicrous and completely destructive to the music. Much the same with many traditional forms of Near and Far Eastern musics.

> As we all do. :)

Sure, but as you've seen from most all of the responses, the respondents seem to know more about 12tet than you seem to know about the wide world of musics *outside* of the dreaded black-and-white.

> Perhaps try 'Grand Finale' first if you wish - as that's my
> favourite.

I'll start there.

> When composing music, one should aim to discover the best chord
> patterns

Iiiiiiiiiiiiyyyyyyyy! What about music that doesn't follow chord patterns??? How Western can you get?!

> Mozart is of course a
> brilliant composer, but that doesn't mean he's going to be right
> about /every/ choice in music. And why should this include the
> temperament he chose for his own music?

Because it's HIS creation. It is absurd and arrogant to assume you would know better about his choices (not to mention the lenghty explanation from a previous poster that explained about the history of meantone, temperaments, and 12tet evolution...).

> np :)

Cool.

Cheers,
Jon

--- In tuning@yahoogroups.com, "Daniel White <soundburst@l...>"

/tuning/topicId_39089.html#41529

>
> http://www.skytopia.com/soundburst/soundburst.html

***Hi Daniel!

I listened to your "Grand Finale" and it's clear that you have
competent MIDI chops. I think your music could be enhanced, though,
by expanding the concept a bit, both in rhythm and timbre. Keep this
stuff for lucrative jingle jangle...

I would visit Jon Szanto's MakeMicroMusic site where such practical
pieces are posted, and maybe you can join the discussion. I think
you will be accepted since you may have the *intention* of writing
microtonal music, or at least haven't totally dismissed the notion:

/makemicromusic/

You might also want to listen to pieces on the "Tuning Punks..."
There are several nice alternately-tuned pieces over there:

http://artists.mp3s.com/artists/72/the_tuning_punks.html

Your website is fun. Good luck...

Joe Pehrson

hello Paul, Daniel and others

I have not read yet the book of sethares. Nevertheless I read his
original
article on the web ("relating tuning and timbre"). To say the truth, I
overlooked
the section "from scale to timbre".

> Paul
> that all depends on the amplitude envelope(s) involved. if you start
> with a synthesized timbre that sounds like a single note, and retune
> the partials as above, in all likelihood the result will still sound
> like a single note, just a bit "noisier" or "wobblier". if you don't
> believe me, you absolutely must obtain a copy of bill sethares' book
> and CD.

I do believe you, I won't challenge your hands-on experience of such
timbre.
I suppose that it is not sufficiently deviant from harmonic sound to
fall out of the cognitive category "harmonic sounds"; no surprise it
may
be perceived as slighly weird single note.

Is there really a "wobble" perceived ?? If so this may means that
there is a totally virtual beat between a pseudo-harmonics and a
"virtual" harmonics placed where there would have been an harmonics.
This is really facinating!

> Francois:
> Further, this argument cannot be used to advocate 12ET because this
> can be done (or at least imagined) for ANY tuning.

> Paul:
> exactly -- though the further the partials are moved from a harmonic
> series, the less realistic and more wobbly/noisy the timbre becomes.
> 12-equal (including the 7th harmonic) is not too bad at all in this
> respect.

It is pleasure to know that we agree from time to time

> François:
> Furthermore, having a set of inharmonic tones that
> never beat or produce any kind of roughness when combined would
probably be boring
> to death...

Paul:
> this is far from true for what daniel is proposing. all the
> traditional dissonances of 12-equal are still dissonant in this
> arrangement!

Again, I do not challenge your auditory experience that is far greater
than mine. I suppose that traditionnal dissonaces still exists because
the retuned timbre are not that far from being harmonic. What I mean
is that, no combination of tone produces beating pseudo-harmonics
because all pseudo-harmonics are arbitrarily tuned to perfecly
overlaps. So if there is any roughness, it is contained in
individual tone, and not much by combination of tones.

It is like if every single note contained the whole set of interval of
the 12ET scale.
For me it is like putting all the spices you have in every ingredient
to be used in any recipies. I suspect (but again, I need to hear music
in such strange tuning) that this shall narrow the palette.

yours truly

François Laferrière

Hi Paul,

> daniel, let's say you're confronted with an arabic musician. modern
> synthesizers in the arabic world normally have an option to lower
all
> the E and B keys by a quarter-tone, so that the white keys
correspond
> with what is often known as the "arabic diatonic scale".
>
> as the great light of truth, revealer of 12-equal as universal
ideal,
> it seems you have four options to "correct" the arabic musician.
the
> two pitches, according to you, should be
>
> 1. E and B
> 2. Eb and B
> 3. E and Bb
> 4. Eb and Bb
>
> since you say you're so well versed with all styles of music from
all
> over the sphere, surely you've already determined the answer to
this
> dilemma.
>
> so what do you tell the arabic musician to do, o wise one?

(All in my opinion), each case (or 'bit of tune') would need to be
looked at seperately before making 'judgements' of this kind. My
experience indicates that the answer to your question could be any of
them - 1, 2 3 & 4 could be appropriate. Or maybe even none of them
would be, since I would say the surrounding chords/melodies would
need to be tailored - so that Eb, Bb, E or B would fit it in and make
sense.

I like the cream of most styles of music including arabic music. But
I do believe some arabic pieces containing (in particular) long
sustaining quarter-tone notes could be improved if tweaked to 12-eT.
This might mean changing the structure of the surrounding melodies /a
bit/ to fit in, but in my opinion, it would be worthwhile.

Cheers, Daniel

Hi François,

--- In tuning@yahoogroups.com, "francois_laferriere
<francois.laferriere@o...>" <francois.laferriere@o...> wrote:
> hello Daniel
>
> > I think you must have missed my earlier point how if the partials
> are
> > also tuned to 12-et, then one can have the best of both worlds :)
>
> On acoustical instrument, "tuning the partials" makes no sense at
all.
> An instrument is
> either (nearly) harmonic (most of them) or (downright) inharmonic
> according to the laws of physics that
> governs its vibration modes.
>
> With electronic instrument, it is possible, in principle, to "tune
> partials". Thus
> you propose instead of having partials to
>
> f0
> 2*f0
> 3*f0
> 4*f0
> 5*f0
> 6*f0
> 7*f0
> 8*f0
> 9*f0
> 10*f0
>
> have them "tuned" to
>
> f0
> f0 * 2
> f0 * 2^(19/12)
> f0 * 4
> f0 * 2^(14/6)
> f0 * 2^(31/12)
> - (being ambiguous in 12ET, 7th harmonics does not deserves to
exist)
> f0 * 8
> etc.

Absolutely, but I think it can go one further than this. Imagine that
for every note played in a tune, the harmonic partials are tailored
for that moment in the instrument. This means the timbre of an
instrument would evolve throughout the tune according to what chords
are playing at the time. This would be incredibly unfeasible and
impractical, but maybe the best music would actually do this - who
knows! :)

> for ANY tuning. Furthermore, having a set of inharmonic tones that
> never beat or
> produce any kind of roughness when combined would probably be boring
> to death...

Not if also combined with clever use of vibrato, slides and other
slight pitch offsets I would imagine.

> If the singers are not qualified to sing "correctly" because singing
> is a biased processed, then should we not exclude song voice from
> the realm of "correct music"!! Come on!! that is a very specious
> argument (to say the less)!

Well obviously, singing is good and fun for many reasons. What I'm
saying isn't easy (if at all possible) by traditional means, but I'm
simply talking about an ideal here.

Cheers,
Daniel (soundburst@lycos.com)
http://www.skytopia.com

Daniel,

I'm going to reply a bit more to you on the strength of your music chops - yes, I did go listen to "Grand Finale" and some of the others. You've done a great job of MIDI orchestration and more than a passing talent with traditional musics. If it had been really lame I wouldn't bother! :)

--- In tuning@yahoogroups.com, "Daniel White <soundburst@l...>" <soundburst@l...> wrote:
> I like the cream of most styles of music including arabic music. But
> I do believe some arabic pieces containing (in particular) long
> sustaining quarter-tone notes could be improved if tweaked to 12-eT.
> This might mean changing the structure of the surrounding melodies
> /a bit/ to fit in, but in my opinion, it would be worthwhile.

You don't get it, do you? You are asking to take away the very elements that makes that music *special*, that actually gives it it's character! You want to rob the music of it's indentifiable and attractive features, simply because *your* ear doesn't like 1/4 tones as much as 12 giant divisions of the octave.

- You want to take away colors from Matisse, Stella, Titian (or add some 'brightners' to Rembrandt).
- You want to reduce the vocabulary of Tennyson, Blake, Li Po.
- You'd ask great French chefs to kindly use less ingredients in their creations ("can't you just put a burger between two buns? that's what everyone *likes*!").

Daniel, you've come into the home of people who cherish and revel in the wide pallette of intonations, who appreciate and celebrate the differences that differing tuning choices create in the great musics of the world (not to mention those just being developed). And you've done it not only without taking off your shoes, but you've tracked mud into the house.

You can keep posting, and you may get a few more reponses. But all you've done up to this point is "but really, I think it would sound better in 12", with no greater reasoning than that is what *you* would like to hear. A good number of people have shown you how important other tunings are to the rest of the world (outside of the staid, boring, Western-European genesis of 12tet).

When I went to your site I looked at your music preferences, and I've read carefully your comments here on the site. It does appear that you have NOT exposed yourself to any significant degree (i.e. other than casual listening) to the very musics you would rob of their individual charismas. That isn't a very nice thing to do.

Cheers,
Jon

Hi Monz,

> if i were going to bother, i'd do it the other way
> around, and just eliminate all the pitch-bends from
> my version, keeping the tempo changes in the 12edo version.
>
>
>
> perhaps it's the tempo which causes you to prefer the
> classicalarchives.com 12edo version?

Nope - I was just thinking of using the same tempo for a
possible 'comparison' for others maybe...

> to me, the subtle harmonic and melodic nuances of
> the 55edo version are far preferable to the bland,
> colorless 12edo version.
>
>
>
> i feel the same way about many of my own pieces which
> were originally written in 12edo then retuned to either
> real JI or adaptive-JI. the 12edo versions are so
> bland that after i get used to hearing the JI versions,
> i never want to listen to the 12edo versions again.
>
> one example from my own work is _3 Plus 4_,
> which you can find in both 12edo (MIDI) and JI (mp3),
> about 1/4 of the way down this page:
> http://sonic-arts.org/monzo/worklist/worklist.htm

I've just been hearing your song - 'As Long As We Live'. I like some
of the chords and melody! The section around 17 seconds has a
nice 'drone' sound to it too - nicely done.

I heard the '3 Plus 4' tune - sweet song :) The mp3 I like too even
with the microtonal pitches, but maybe you could also make an mp3 in
12-eT for the rest of us? ;)

I'll hear some of your other music too including some music at the
tuning punks site soon.

Cheers,
Daniel (soundburst@lycos.com)

hi Daniel,

> From: <soundburst@lycos.com>
> To: <tuning@yahoogroups.com>
> Sent: Thursday, December 19, 2002 9:32 AM
> Subject: [tuning] Re: 12-equal Vs. Just tuning
>
>
> I've just been hearing your song - 'As Long As We Live'.
> I like some of the chords and melody! The section
> around 17 seconds has a nice 'drone' sound to it
> too - nicely done.

thanks.

> I heard the '3 Plus 4' tune - sweet song :) The mp3 I
> like too even with the microtonal pitches, but maybe you
> could also make an mp3 in 12-eT for the rest of us? ;)

i guess by "the rest of us" you mean people who might
listen to my music who are not subscribers to this list.

:)

anyway, i've tried making .wav's and .mp3's of the 12edo
version of _3 Plus 4_ but the percussion parts are coming
out with the wrong timbres, and i haven't been able to
figure out why or how to fix it.

-monz

--- In tuning@yahoogroups.com, "Jon Szanto <JSZANTO@A...>"

/tuning/topicId_39089.html#41555

>
> You can keep posting, and you may get a few more reponses. But all
you've done up to this point is "but really, I think it would sound
better in 12", with no greater reasoning than that is what *you*
would like to hear. A good number of people have shown you how
important other tunings are to the rest of the world (outside of the
staid, boring, Western-European genesis of 12tet).
>

***It seems, from a *diplomatic* point of view, maybe it would have
been better if Daniel had simply asked:

"I like 12-equal. I don't understand why anybody would compose in
anything else and I remain unconvinced. Why do it??"

Or some such... the old adage "getting more flys with sugar, etc..."
rather than starting out with strong opposition right off.

I'm assuming he is interested in learning something about this. Why,
otherwise, would he be bothering with this list??

J. Pehrson

----- Original Message -----
From: <jpehrson@rcn.com>

> --- In tuning@yahoogroups.com, "Jon Szanto <JSZANTO@A...>"
>
> /tuning/topicId_39089.html#41555
>
> >
> > You can keep posting, and you may get a few more reponses. But all
> you've done up to this point is "but really, I think it would sound
> better in 12", with no greater reasoning than that is what *you*
> would like to hear. A good number of people have shown you how
> important other tunings are to the rest of the world (outside of the
> staid, boring, Western-European genesis of 12tet).
> >
>
> ***It seems, from a *diplomatic* point of view, maybe it would have
> been better if Daniel had simply asked:
>
> "I like 12-equal. I don't understand why anybody would compose in
> anything else and I remain unconvinced. Why do it??"
>
> Or some such... the old adage "getting more flys with sugar, etc..."
> rather than starting out with strong opposition right off.
>
> I'm assuming he is interested in learning something about this. Why,
> otherwise, would he be bothering with this list??

Troll?

* David Beardsley
* http://biink.com
* http://mp3.com/davidbeardsley

--- In tuning@yahoogroups.com, "francois_laferriere
<francois.laferriere@o...>" <francois.laferriere@o...> wrote:

> Is there really a "wobble" perceived ?? If so this may means that
> there is a totally virtual beat between a pseudo-harmonics and a
> "virtual" harmonics placed where there would have been an harmonics.
> This is really facinating!

francois, there are two phenomena involved.

the first is combinational tones. even a sine wave will be heard as
possessing a weak series of harmonics above it, since it produces
summation tones with itself!

the second is known as second-order beating.

please, if at all possible, borrow or purchase, and study, this book:

Physics And Psychophysics Of Music
By: Roederer, J. G.; Roederer, Juan G.
Published: November 1994
Springer-Verlag Telos
Language: English
ISBN: 0387943668

>
> > François:
> > Furthermore, having a set of inharmonic tones that
> > never beat or produce any kind of roughness when combined would
> probably be boring
> > to death...
>
> Paul:
> > this is far from true for what daniel is proposing. all the
> > traditional dissonances of 12-equal are still dissonant in this
> > arrangement!
>
> Again, I do not challenge your auditory experience that is far
greater
> than mine. I suppose that traditionnal dissonaces still exists
because
> the retuned timbre are not that far from being harmonic. What I mean
> is that, no combination of tone produces beating pseudo-harmonics
> because all pseudo-harmonics are arbitrarily tuned to perfecly
> overlaps.

not at all -- there will still be plenty of beating from 1-semitone
misses and even 2-semitone misses.

> So if there is any roughness, it is contained in
> individual tone, and not much by combination of tones.

think of a minor second, for example -- probably the most dissonant
interval in 12-equal. a minor second is just about equally dissonant,
whether the overtones are truly harmonic or quantized to 12-equal.

> It is like if every single note contained the whole set of interval
of
> the 12ET scale.

well, not the whole set -- typically the list of partials is
truncated after the 8th or 12th, with (as you guessed) the 7th and
11th omitted.

> For me it is like putting all the spices you have in every
ingredient
> to be used in any recipies. I suspect (but again, I need to hear
music
> in such strange tuning) that this shall narrow the palette.

there is nothing strange about 12-equal! to hear it with
(essentially) 12-equal partials, listen to the hammond organ -- if
you like jazz, check out jimmy smith or john medeski . . . if you
like rock, thijs van leer of focus and tony kaye of yes made nice use
of the hammond organ in the early 70s . . . other examples
abound . . . the hammond organ is typically played through a rotating
speaker, so any second-order beating in the timbres tends to be
drowned out in the resulting wash of harmonic fluctuation . . . the
effect is quite beautiful to my ears (my hammond organ has been sadly
neglected in my back room since my rotating speaker caught on
fire) . . .

Hi Joseph,

Thanks for your comments about my music (Jon too). I am always
looking for constructive criticism - you're probably right that it
could be improved with some extra rhythmic variety.

>***It seems, from a *diplomatic* point of view, maybe it would have
>been better if Daniel had simply asked:
>
>"I like 12-equal. I don't understand why anybody would compose in
>anything else and I remain unconvinced. Why do it??"

Maybe I chose the 'long way round' as it were, but there was always a
good reason for doing so (whether in answer to a question or a
response on an opinion etc.) and it brought up many interesting
discussions on things semi-related to the topic too. I apologise to
anyone if I was ever a bit 'blunt' or inconsiderate maybe - this was
never intended :(

>Or some such... the old adage "getting more flys with sugar, etc..."
>rather than starting out with strong opposition right off.
>
>I'm assuming he is interested in learning something about this. Why,
>otherwise, would he be bothering with this list??

Absolutely. I know I will get a more informed response here than
almost any other place. In the beginning, I was looking for a general
Yahoo group on music/scale theory, couldn't find one (at least not a
very active one), and found the tuning group.

As for composing microtonally, well it's certainly not totally out of
the question. If by any chance I do get to like microtonal music (and
I will listen to more from the tuning punks site - I promise), then
I'll certainly give it a shot. A few have suggested that I try to
compose music from the off in microtonal (choosing the scale first,
then playing around). When I get some more free time, I will consider
this too.

To be honset, I know I've been advocating 12-eT, but I think there
might even be a chance that Pythagoras' scale of fifths could even be
the 'right' scale too - since many of the pitches come close to Just
intonation such as Fb and 5/4 (which I don't agree with, but I could
be wrong on this). This way there would be (almost) JI pitches mixed
in with (almost) the 12-eT pitches.

As far as my points on harmonic partials go, does anyone have any
comments about the partials in an instrument changing dynamically to
fit the various chords throughout a tune? For example a very 'high
partial' (say... the 7th partial Bb, could be changed to B or A if
the background chord demanded it). It goes without saying a
synthesizer would be needed for this.

I'll add a couple more things. One thing I've noticed is how the
overall pitch of the partials are 'quieter' when the partials used
are Just (*1, *2, *3, *4, *5 etc). Naturally, this is because
of 'destructive interference' of the partials colliding upon each
other throughout the wave. I would be interested to know the relative
volumes of these - or are they are all quietened down equally?

Regards,
Daniel (soundburst@lycos.com)

--- In tuning@yahoogroups.com, "Daniel White <soundburst@l...>"

/tuning/topicId_39089.html#41562

>
> Absolutely. I know I will get a more informed response here than
> almost any other place. In the beginning, I was looking for a
general Yahoo group on music/scale theory, couldn't find one (at
least not a very active one), and found the tuning group.
>

***There aren't many interesting ones, certainly not on Yahoo... at
least that's been my experience. This is one of the most active
and "accelerated" music theory lists around...

HOWEVER, there is *one* good one, but it is only available in email
form, not as Web access. It's from the Society of Music Theory, and
you need to join the list here:

http://www.societymusictheory.org/mailman/listinfo/mto-list

I must admit I've been quite behind reading it, and find the Tuning
List quite a bit more interesting on the overall...

Joseph Pehrson

--- In tuning@yahoogroups.com, "Joseph Pehrson <jpehrson@r...>" <jpehrson@r...> wrote:

> HOWEVER, there is *one* good one, but it is only available in email
> form, not as Web access. It's from the Society of Music Theory, and
> you need to join the list here:
>
> http://www.societymusictheory.org/mailman/listinfo/mto-list

Now why hasn't anyone mentioned this before?

Gene,

--- In tuning@yahoogroups.com, "Gene Ward Smith <genewardsmith@j...>" <genewardsmith@j...> wrote:
> --- In tuning@yahoogroups.com, "Joseph Pehrson <jpehrson@r...>" <jpehrson@r...> wrote:
> > http://www.societymusictheory.org/mailman/listinfo/mto-list
>
> Now why hasn't anyone mentioned this before?

I believe Joe *has* brought up that group in conversations before. It may have first come up during the Isacoff jabber. I bet they're a pretty stuffy lot... :)

Cheers,
Jon

--- In tuning@yahoogroups.com, "Gene Ward Smith <genewardsmith@j...>"

/tuning/topicId_39089.html#41564

<genewardsmith@j...> wrote:
> --- In tuning@yahoogroups.com, "Joseph Pehrson <jpehrson@r...>"
<jpehrson@r...> wrote:
>
> > HOWEVER, there is *one* good one, but it is only available in
email
> > form, not as Web access. It's from the Society of Music Theory,
and
> > you need to join the list here:
> >
> > http://www.societymusictheory.org/mailman/listinfo/mto-list
>
> Now why hasn't anyone mentioned this before?

***Hi Gene,

Paul and I have *both* mentioned it on this very list. I don't know
about "stuffy," Jon unless that is synonymous with "dull" which it is
sometimes. Every now and then it picks up, but they don't have all
the lovable "wild and crazy guys" that we have on the Tuning List,
nor are most of the composers so interested in trying new things...
although a *few* there are...

J. Pehrson

--- In tuning@yahoogroups.com, "Joseph Pehrson <jpehrson@r...>"

/tuning/topicId_39089.html#41566

<jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, "Gene Ward Smith
<genewardsmith@j...>"
>
> /tuning/topicId_39089.html#41564
>
> <genewardsmith@j...> wrote:
> > --- In tuning@yahoogroups.com, "Joseph Pehrson <jpehrson@r...>"
> <jpehrson@r...> wrote:
> >
> > > HOWEVER, there is *one* good one, but it is only available in
> email
> > > form, not as Web access. It's from the Society of Music
Theory,
> and
> > > you need to join the list here:
> > >
> > > http://www.societymusictheory.org/mailman/listinfo/mto-list
> >
> > Now why hasn't anyone mentioned this before?
>
>
> ***Hi Gene,
>
> Paul and I have *both* mentioned it on this very list. I don't
know
> about "stuffy," Jon unless that is synonymous with "dull" which it
is
> sometimes. Every now and then it picks up, but they don't have all
> the lovable "wild and crazy guys" that we have on the Tuning List,
> nor are most of the composers so interested in trying new things...
> although a *few* there are...
>
> J. Pehrson

***I should also add that the MTO list is not as intellectually
rigorous as even this one, certainly not as rigorous as "Tuning Math"
and the posters also not as technologically adept as our
little "crew" on all the lists...

J. Pehrson

--- In tuning@yahoogroups.com, "Joseph Pehrson <jpehrson@r...>" <jpehrson@r...> wrote:
> I don't know about "stuffy," Jon unless that is synonymous with
> "dull" which it is sometimes.

I use it as less perjorative than dull - sort of like dry and dusty as opposed to completely lifeless. :)

Cheers,
Jon

> From: <jpehrson@rcn.com>
> To: <tuning@yahoogroups.com>
> Sent: Friday, December 20, 2002 10:07 AM
> Subject: [tuning] Re: theory listmania
>
>
> > <genewardsmith@j...> wrote:
> > > --- In tuning@yahoogroups.com, "Joseph Pehrson <jpehrson@r...>"
> > > <jpehrson@r...> wrote:
> > >
> > > > HOWEVER, there is *one* good one, but it is only
> > > > available in email form, not as Web access. It's
> > > > from the Society of Music Theory, and you need to
> > > > join the list here:
> > > >
> > > > http://www.societymusictheory.org/mailman/listinfo/mto-list
> > >
> > > Now why hasn't anyone mentioned this before?
> >
> >
> > ***Hi Gene,
> >
> > Paul and I have *both* mentioned it on this very list.
> > I don't know about "stuffy," Jon unless that is synonymous
> > with "dull" which it is sometimes. Every now and then it
> > picks up, but they don't have all the lovable "wild and crazy
> > guys" that we have on the Tuning List, nor are most of the
> > composers so interested in trying new things... although
> > a *few* there are...
> >
> > J. Pehrson
>
>
> ***I should also add that the MTO list is not as intellectually
> rigorous as even this one, certainly not as rigorous as
> "Tuning Math" and the posters also not as technologically
> adept as our little "crew" on all the lists...
>
> J. Pehrson

i used to read MTO-talk, but gave up a long time ago, mostly
because i found it both dull *and* stuffy! :)

(... especially compared to these lists, as you point out, Joe.
remember the McLaren rants last year on crazy-music, with such
subject lines as "The arrogrant incometant ignoramous Arnold
Schoenberg"?)

-monz

--- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:

> (... especially compared to these lists, as you point out, Joe.
> remember the McLaren rants last year on crazy-music, with such
> subject lines as "The arrogrant incometant ignoramous Arnold
> Schoenberg"?)

I haven't seen McLaren around since he complained to me that Paul was too mathematical, a view I did not find myself in entire agreement with.

Hi Paul,

>francois, there are two phenomena involved.
>
>the first is combinational tones. even a sine wave will be heard as
>possessing a weak series of harmonics above it, since it produces
>summation tones with itself!

That's interesting. Isn't a sine wave a pure fundamental sound? Can
you explain more?

>the second is known as second-order beating.
>
>please, if at all possible, borrow or purchase, and study, this book:
>
>Physics And Psychophysics Of Music
>By: Roederer, J. G.; Roederer, Juan G.
>Published: November 1994
>Springer-Verlag Telos
>Language: English
>ISBN: 0387943668

I'll be looking out for that book too. :)

Cheers,
Daniel (soundburst@lycos.com)

--- In tuning@yahoogroups.com, "Gene Ward Smith <genewardsmith@j...>"

/tuning/topicId_39089.html#41570

<genewardsmith@j...> wrote:
> --- In tuning@yahoogroups.com, "monz" <monz@a...> wrote:
>
> > (... especially compared to these lists, as you point out, Joe.
> > remember the McLaren rants last year on crazy-music, with such
> > subject lines as "The arrogrant incometant ignoramous Arnold
> > Schoenberg"?)
>
> I haven't seen McLaren around since he complained to me that Paul
was too mathematical, a view I did not find myself in entire
agreement with.

***I can see there is still some humor on this list.

Signed,

Math dope

JP

Hi Jon,

>> I somewhat expected this kind of reply :) You make good points that
>> really do apply to language and poetry in a way, but the point is:
>> music really is a universal language.....

>Wrong. Completely wrong. You're really showing how little you know
about the
>musics of the world, and the reactions of people from differing
cultures to
>other 'musics'. Sound might be universal, aspects of rhythm
certainly, even
>certain fundamental tuning and scalar 'melodicles' (pentatonic
melodies abound
>over the world, etc.). But 'music', as you are portraying it
(a "tune", chord
>progressions, etc) is not universal. And certainly 12tet isn't, and
I hope it
>never becomes such.

(This is getting pretty far from tuning I guess, so I won't say much
more on the subject...)

But surely you think some chord combinations are better than others -
even outside of opinion? I'm not talking about ones which are
arguable - for no-one really knows for sure about those. But compare
a completely random/clashing chord sequence (say... made by a
computer with a randomised program),... with one that has been
constructed by a human composer thoughtfully. There's no doubt the
composer's sequence is better. Thus if one chord can be better than
another, then all chord sequences can have a 'quality rating'.
Wouldn't you agree?

Glad you think that certain aspects of rhythm and 'melodicles' might
be universal.

>Ever wonder if composers, feeling trapped by the huge distance of
100 cents
>between intervals, longed for a more natural way to set speech, so
that a
>'song' more closely paralleled the lovely intonations of the actual
language?
>
> (Note: I know at least one very important composer who has...)

Good point, and that's exactly why I think slides are fine in music -
as it's more of an 'effect'.

>> but I ultimately believe there's a reason why a certain piece of
>> music is good

>Good? How can an art form meet some overall value of "good"?

Try loading a windows exe program file as a raw sample into a sound
editor such as Sound Forge. Then listen to one Mozart's Symphony
No.40. There can be no doubt the symphony is the better piece of
music in every way - even outside of opinion. Thus all music can be
rated... surely?

> (Gad, we're getting pretty far from tuning...)

Hehe - yeah I guess so, but it is interesting :)

>> Mozart is of course a
>> brilliant composer, but that doesn't mean he's going to be right
>> about /every/ choice in music. And why should this include the
>> temperament he chose for his own music?

>Because it's HIS creation. It is absurd and arrogant to assume you
would know
>better about his choices

I'm not saying I do know better for sure - just there's a /chance/
that he may be wrong. Also, as someone else has already said,
meantone temperament was generally more prevalent around the time, so
this isn't so much a deliberate mistake anyway - more just following
what was 'ready at hand'.

Cheers,
Daniel (soundburst@lycos.com)

Hi Monz,

>i used to read MTO-talk, but gave up a long time ago, mostly
>because i found it both dull *and* stuffy! :)
>
>
>(... especially compared to these lists, as you point out, Joe.

This is another reason why I like to post on this list. It's
refreshing to see people /trying/ something new - even if I don't
always agree with everything :)

Cheers,
Daniel (soundburst@lycos.com)
http://www.skytopia.com

--- In tuning@yahoogroups.com, "Daniel White <soundburst@l...>"
<soundburst@l...> wrote:

> I'll add a couple more things. One thing I've noticed is how the
> overall pitch of the partials are 'quieter' when the partials used
> are Just (*1, *2, *3, *4, *5 etc). Naturally, this is because
> of 'destructive interference' of the partials colliding upon each
> other throughout the wave. I would be interested to know the
relative
> volumes of these - or are they are all quietened down equally?
>
> Regards,
> Daniel (soundburst@l...)

daniel,

in order to gauge the impact of any destructive interference that may
be occuring, we need to know the *phase relationships* of the tones
you are using. as i tried to explain to pauline, being *in phase* (or
in your case, being *out of phase*) is not the same thing as being
phase-locked.

perhaps you could provide a few more details of the setup you're
using and i could try to assess the acoustical and psychoacoustical
phenomena that are probably involved.

right now, my suspicion is that there is no actual destructive
interference involved, and what you're experiencing is a simple
manifestation of the virtual pitch phenomenon -- a set of *harmonic
partials*, evokes the sense of a single pitch, corresponding to the
fundamental (even if physically absent) -- while a set of *inharmonic
partials* will evoke a multiplicity of pitches, at all the near-fits
to a harmonic sub-fundamental that may fit the partials. so it would
follow that as you move the partials away from true harmonicity,
they'll stick out more as separate pitches (rather than as components
of the timbre of the fundamental), and thus you'll *think* that
they're getting louder.

make sense?

p.s. don't forget about combinational tones.

-paul

--- In tuning@yahoogroups.com, "Joseph Pehrson <jpehrson@r...>"
<jpehrson@r...> wrote:
> --- In tuning@yahoogroups.com, "Gene Ward Smith
<genewardsmith@j...>"
>
> /tuning/topicId_39089.html#41564
>
> <genewardsmith@j...> wrote:
> > --- In tuning@yahoogroups.com, "Joseph Pehrson <jpehrson@r...>"
> <jpehrson@r...> wrote:
> >
> > > HOWEVER, there is *one* good one, but it is only available in
> email
> > > form, not as Web access. It's from the Society of Music
Theory,
> and
> > > you need to join the list here:
> > >
> > > http://www.societymusictheory.org/mailman/listinfo/mto-list
> >
> > Now why hasn't anyone mentioned this before?
>
>
> ***Hi Gene,
>
> Paul and I have *both* mentioned it on this very list.

which paul was that?
wasn't me!

--- In tuning@yahoogroups.com, "Daniel White <soundburst@l...>"
<soundburst@l...> wrote:
> Hi Paul,
>
> >francois, there are two phenomena involved.
> >
> >the first is combinational tones. even a sine wave will be heard as
> >possessing a weak series of harmonics above it, since it produces
> >summation tones with itself!
>
> That's interesting. Isn't a sine wave a pure fundamental sound? Can
> you explain more?

the ear has a non-linear response to sound. therefore, even if a pure
sine wave is produced *in the air*, the ear-brain mechanism will add
a small amount of harmonic partial content into the sound.

the best explanation of how non-linear response creates harmonic
partials, difference tones, and summation tones, can be found in the
feynman lectures on physics. it's pretty simple trigonometry.

On 2002-12-20, wallyesterpaulrus <wallyesterpaulrus@yahoo.com> uttered to...:

>therefore, even if a pure sine wave is produced *in the air*, the
>ear-brain mechanism will add a small amount of harmonic partial content
>into the sound.

I would say "might add" -- there's a lot of evidence that our ears are
nonlinear, yes, but there's far less to show that the effect can be
modelled by anything approaching a simple, memoryless nonlinearity. It
isn't entirely sure one can generalize from difference tone experiments
and the like, then. I think one should rather directly test for
discrimination of said harmonics at a given SPL level before making a
judgment.

(My first post to the list, so a brief intro is probably a good idea. I'm
a 24-year old Finnish math student and an enthusiast in audio DSP -- I was
prodded to join this forum by someone on the music-dsp list. I've no
training in music theory, formal or otherwise; my interest in tunings is
half aesthetic, half mathy. At the moment I think I have a fair grasp of
the basics, like historical Western tunings/temperaments, but as for the
esoteric stuff, a lot remains to be learnt.)
--
Sampo Syreeni, aka decoy - mailto:decoy@iki.fi, tel:+358-50-5756111
student/math+cs/helsinki university, http://www.iki.fi/~decoy/front
openpgp: 050985C2/025E D175 ABE5 027C 9494 EEB0 E090 8BA9 0509 85C2

--- In tuning@yahoogroups.com, Sampo Syreeni <decoy@i...> wrote:
> On 2002-12-20, wallyesterpaulrus <wallyesterpaulrus@y...> uttered to...:

At the moment I think I have a fair grasp of
> the basics, like historical Western tunings/temperaments, but as for the
> esoteric stuff, a lot remains to be learnt.)

If you want to dive in off the deep end into the mathematics of tuning, I suggest the tuning-math list.

Gene,

--- In tuning@yahoogroups.com, "Gene Ward Smith <genewardsmith@j...>" <genewardsmith@j...> wrote:
> --- In tuning@yahoogroups.com, Sampo Syreeni <decoy@i...> wrote:
> > On 2002-12-20, wallyesterpaulrus <wallyesterpaulrus@y...> uttered to...:
>
> At the moment I think I have a fair grasp of
> > the basics, like historical Western tunings/temperaments, but as for the
> > esoteric stuff, a lot remains to be learnt.)
>
> If you want to dive in off the deep end into the mathematics of tuning, I suggest the tuning-math list.

Oh, great: he comes for pot, and you give him heroin! :)

Cheers,
Jon

Hi Paul,

add a couple more things. One thing I've noticed is how the
> > overall pitch of the partials are 'quieter' when the partials
used
> > are Just (*1, *2, *3, *4, *5 etc). Naturally, this is because
> > of 'destructive interference' of the partials colliding upon each
> > other throughout the wave. I would be interested to know the
> relative
> > volumes of these - or are they are all quietened down equally?
> >
> > Regards,
> > Daniel (soundburst@l...)
>
> daniel,
>
> in order to gauge the impact of any destructive interference that
may
> be occuring, we need to know the *phase relationships* of the tones
> you are using. as i tried to explain to pauline, being *in phase*
(or
> in your case, being *out of phase*) is not the same thing as being
> phase-locked.
>
> perhaps you could provide a few more details of the setup you're
> using and i could try to assess the acoustical and psychoacoustical
> phenomena that are probably involved.
>
> right now, my suspicion is that there is no actual destructive
> interference involved, and what you're experiencing is a simple
> manifestation of the virtual pitch phenomenon -- a set of *harmonic
> partials*, evokes the sense of a single pitch, corresponding to the
> fundamental (even if physically absent) -- while a set of
*inharmonic
> partials* will evoke a multiplicity of pitches, at all the near-
fits
> to a harmonic sub-fundamental that may fit the partials. so it
would
> follow that as you move the partials away from true harmonicity,
> they'll stick out more as separate pitches (rather than as
components
> of the timbre of the fundamental), and thus you'll *think* that
> they're getting louder.
>
> make sense?

Yep :) Very interesting too.

I think you guessed right on what setup I used. But just to clarify,
I program the sounds with pure sine waves starting at 0 degrees. I
can see why you said the pitches are apparently quieter - as opposed
to actually being quieter.

Thanks,
Daniel (soundburst@lycos.com)

--- In tuning@yahoogroups.com, Sampo Syreeni <decoy@i...> wrote:
> On 2002-12-20, wallyesterpaulrus <wallyesterpaulrus@y...> uttered
to...:
>
> >therefore, even if a pure sine wave is produced *in the air*, the
> >ear-brain mechanism will add a small amount of harmonic partial
content
> >into the sound.
>
> I would say "might add" -- there's a lot of evidence that our ears
are
> nonlinear, yes, but there's far less to show that the effect can be
> modelled by anything approaching a simple, memoryless nonlinearity.

i wasn't suggesting that it was simple at all! in fact, certain cubic
combinational tones do not follow the cubic dependence on amplitude
that one would expect from a simple, feynman-like model. but it's a
start.

> It
> isn't entirely sure one can generalize from difference tone
experiments
> and the like, then.

i don't think i was generalizing -- just stating a fact.

> I think one should rather directly test for
> discrimination of said harmonics at a given SPL level before making
a
> judgment.

this has been done; for example, see reiner plomp, _aspects of tone
sensation_, or check for more recent references in roederer.

>
> (My first post to the list, so a brief intro is probably a good
idea. I'm
> a 24-year old Finnish math student and an enthusiast in audio DSP --
I was
> prodded to join this forum by someone on the music-dsp list. I've no
> training in music theory, formal or otherwise; my interest in
tunings is
> half aesthetic, half mathy. At the moment I think I have a fair
grasp of
> the basics, like historical Western tunings/temperaments, but as
for the
> esoteric stuff, a lot remains to be learnt.)

don't forget to check out the tuning-math list!

--- In tuning@yahoogroups.com, "Daniel White <soundburst@l...>"
<soundburst@l...> wrote:

>
> Yep :) Very interesting too.
>
> I think you guessed right on what setup I used. But just to
clarify,
> I program the sounds with pure sine waves starting at 0 degrees.

then everything's actually "in phase", rather than "out of phase".
but this is probably immaterial -- since you're probably not creating
sets of sine waves with the *same* frequency, are you? if not,
there's no way to get a permanent state of constructive *or*
destructive interference.

Hi Paul,

>> Yep :) Very interesting too.
>>
>> I think you guessed right on what setup I used. But just to
clarify,
>> I program the sounds with pure sine waves starting at 0 degrees.

>then everything's actually "in phase", rather than "out of phase".
>but this is probably immaterial -- since you're probably not
creating
>sets of sine waves with the *same* frequency, are you? if not,
>there's no way to get a permanent state of constructive *or*
>destructive interference.

To go more in depth, I mixed all the below sine waves together to
make one final composite sound (a 'ramp' wave in actual fact).
F=frequency and V=volume. All start at 0 degrees.

F=1 V=1
F=2 V=0.5
F=3 V=0.333
F=4 V=0.25
F=5 V=0.2
etc. etc.

So I assume there's no destructive interference, and that
the 'quietening' of partials is only illusionary?

Cheers,
Daniel (soundburst@lycos.com)

--- In tuning@yahoogroups.com, "Daniel White <soundburst@l...>"
<soundburst@l...> wrote:
> Hi Paul,
>
> >> Yep :) Very interesting too.
> >>
> >> I think you guessed right on what setup I used. But just to
> clarify,
> >> I program the sounds with pure sine waves starting at 0 degrees.
>
> >then everything's actually "in phase", rather than "out of phase".
> >but this is probably immaterial -- since you're probably not
> creating
> >sets of sine waves with the *same* frequency, are you? if not,
> >there's no way to get a permanent state of constructive *or*
> >destructive interference.
>
> To go more in depth, I mixed all the below sine waves together to
> make one final composite sound (a 'ramp' wave in actual fact).
> F=frequency and V=volume. All start at 0 degrees.
>
> F=1 V=1
> F=2 V=0.5
> F=3 V=0.333
> F=4 V=0.25
> F=5 V=0.2
> etc. etc.
>
> So I assume there's no destructive interference, and that
> the 'quietening' of partials is only illusionary?

correct -- well, 'illusionary' or not, it's a product of the brain's
central pitch processor and its never-ending quest to locate
*pitches* in the information from the ears. *pitches*, though they
can correspond to single ("sine-wave")* frequency components, are
usually products of several frequency components, forming harmonic
series (or near-harmonic series). quite often the fundamental is
absent, and yet a *pitch* is present at the would-be fundamental of
the incomplete harmonic series. thus the phenomenon is known
as "virtual pitch".

given your quest, you would do well to study the articles related to
this phenomenon at

http://www.mmk.ei.tum.de/persons/ter.html

and, more up-to-date,

http://www.cariani.com/

*i put "sine-wave" in quotes because it's exceedingly difficult to
arrrange for any isolated fourier components ("sine waves"**) to make
it through to the auditory nerve without any overtone partners

**i put "sine waves" in quotes again because the interpretation of
this would have to be in terms of fourier theory, in which "sine
waves"*** form the basis of an infinite-dimensional vector space

***i put "sine waves" in quotes yet again because they're, more
generally, linear combinations of sine and cosine waves with the same
frequency.

On 2002-12-24, wallyesterpaulrus <wallyesterpaulrus@yahoo.com> uttered to...:

>correct -- well, 'illusionary' or not, it's a product of the brain's
>central pitch processor and its never-ending quest to locate *pitches*
>in the information from the ears.

I would complement the explanation by noting that if the fundamental is
high enough (say, 1kHz), upper partials will land in a frequency region
where equal loudness curves start to curve up -- above some 1-2kHz
progressively higher SPLs are need to give rise to an equivalent sensation
of loudness.
--
Sampo Syreeni, aka decoy - mailto:decoy@iki.fi, tel:+358-50-5756111
student/math+cs/helsinki university, http://www.iki.fi/~decoy/front
openpgp: 050985C2/025E D175 ABE5 027C 9494 EEB0 E090 8BA9 0509 85C2