Yahoo Tuning Groups Ultimate Backup tuning Michael Sheiman's harmonic derived scale.

Sorry for asking such unpleasant questions and destroy your toys, but I wonder:
- which synthesizer can set tuning with such accuracy
- which person can hear tuning with such accuracy (in the case there's a machine capable to play it)

Very often I see here in messages a big distance between nice looking theories and calculations on the paper (oops, on the screen of course) and their solution in real life. Could you please describe your solution?

Daniel Forro

On 29 Jan 2009, at 1:33 PM, vaisvil wrote:

>
> Michael sent me a microtonal scale he was working on and I improvised
> using it. I midi recorded the improvisation, cleaned it up, sped it
> up, and added z3ta+ synth 4 times to it.
>
> The scale contains parts of the harmonic series a fifth apart. He
> would be able to talk about it much more intelligently then I. This
> will be cross-posted to MMM.
>
> !e:\Music\harmonicious scale.scl
> !
> Harmonicious 12-tone scale
> 12
> !
> 203.91000173
> 291.51301613
> 386.31371386
> 470.78090733
> 551.3179423647566
> 628.2743472684155
> 701.9550008653874
> 772.6274277296696
> 905.8650025961624
> 1049.3629100223864
> 1145.0355724642502
> 2/1
>
> http://clones.soonlabel.com/mp3/harmonioussynth.mp3
>
> and as piano for completeness - the microtonal scale is much more
> apparent.
>
> http://clones.soonlabel.com/mp3/harmoniouspiano.mp3
>

🔗Petr Pařízek <p.parizek@...>

Daniel Forró wrote:

> Sorry for asking such unpleasant questions and destroy your toys, but
> I wonder:
> - which synthesizer can set tuning with such accuracy
> - which person can hear tuning with such accuracy (in the case
> there's a machine capable to play it)

First of all, from my own experience, very often the number of decimal places is just a matter of the way a particular program sends the numbers to the „output stream“ rather than the accuracy with which the scale is intended to be played. I know what I’m saying because some years ago I was making some scales with a calculator which showed the results with an accuracy of 12 decimal places and I always left them like that even though I didn’t know about any device tunable with this degree of accuracy.

Second, for some weird reason which I don’t understand, Chris has written interval sizes in cents even for the intervals which could be more understandable in the form of linear factors. Programs like Scala allow input data like „5/4“ and can distinguish them from sizes in cents (just for your information, Chris, it would be much clearer what you mean if you wrote 5/4 instead of 386.3137138 cents -- both mean the same interval).

And finally, don’t know if this is the case, but many times, I have found myself in a situation when I needed to work with very tiny intervals and preserve their sizes regardless of whether someone is listening to them or not. For example, if I’m making a scale which should temper out a very small interval or if I’m calculating beat rates for tempered intervals, it’s often important to preserve the interval sizes sometimes even as accurate as to 1000ths of a cent despite the fact there’s probably no device that can be tuned so accurately. The point here is that the accuracy has essentially nothing to do with our hearing but it allows us to better trace the method which was used to find that tuning/scale, which is often important for analyzing and comparing temperaments.

Petr

🔗Cameron Bobro <misterbobro@...>

--- In tuning@yahoogroups.com, Daniel Forro <dan.for@...> wrote:
>
> Sorry for asking such unpleasant questions and destroy your toys,
>but
> I wonder:

Revealing your ignorance isn't going to destroy anybody's toys, I
wouldn't think.

> - which synthesizer can set tuning with such accuracy

Software synthesizers can be tuned with extreme accuracy. If I recall
correctly, Hz to six decimal places would be most usual, but in 64-
bit Csound for example, I don't know to how many decimal places
everything is calculated.

Of course in that case it is more accurate to use ratios and formulas
and let the program worry about decimal places. In the specific cases
where the tuning, sound design, and actual method of sound production
are "as one", anything short of extreme accuracy in all parameters
can result in audible artifacts so it's a moot point whether you can
consciously hear such tiny differences or not because anyone can hear
the limitations of the quantized system suddenly revealed.

(Consider that in the virtual world, we can sculpt things in many
dimensions and even travel backwards in time. Any discontinuity
between dimensions gives you an audible click. Analog with its
"infinitely fine-grained" control voltages is actually better but I
don't have a 1000 dollars for single Cyndustries Zeroscillator
module. :-) )

> - which person can hear tuning with such accuracy (in the case
> there's a machine capable to play it)

Noone knows where the limits do or do not lie. They may claim to
know, but there's no way to really test these things, even if you
went about testing honestly rather than "setting it up to prove a
point", which is how allegedly "scientific" test usually are in this
case.

Sinewaves in headphones, what a joke. As much as I enjoy such tests,
and tend to do rather well on them, I know that they aren't "real
life".

>
> Very often I see here in messages a big distance between nice
>looking
> theories and calculations on the paper (oops, on the screen of
> course) and their solution in real life.

"Noone can tell the difference between a carefully drawn circle and
one drawn with a compass, you sure are childish for using a compass!"

>Could you please describe
> your solution?

Using a compass where applicable.

Does this preclude also tuning in the most organic and (maybe) "least
accurate" way of all, which is by ear in real time? Not at all, in
fact the two methods compliment each other very well. Working in the
outer space environment of "supernaturally" accurately tuned and even
"inaudible" synthesized sound, even if the final music presented
isn't tuned that accurately at all, or doesn't include sub- and
super- sonic vibrations, does strange and fascinating things.

Not necessarily good things of course, as you can make physically
sickening sounds and tunings as well.

But the irony of your smug and childish comment is this: noone would
blink seeing "4/3", even though "4/3" is infinitely more accurate
than "1.333333333333333"!

"LOL".

-Cameron Bobro

>
> Daniel Forro
>
> On 29 Jan 2009, at 1:33 PM, vaisvil wrote:
>
> >
> > Michael sent me a microtonal scale he was working on and I
improvised
> > using it. I midi recorded the improvisation, cleaned it up, sped
it
> > up, and added z3ta+ synth 4 times to it.
> >
> > The scale contains parts of the harmonic series a fifth apart. He
> > would be able to talk about it much more intelligently then I.
This
> > will be cross-posted to MMM.
> >
> > !e:\Music\harmonicious scale.scl
> > !
> > Harmonicious 12-tone scale
> > 12
> > !
> > 203.91000173
> > 291.51301613
> > 386.31371386
> > 470.78090733
> > 551.3179423647566
> > 628.2743472684155
> > 701.9550008653874
> > 772.6274277296696
> > 905.8650025961624
> > 1049.3629100223864
> > 1145.0355724642502
> > 2/1
> >
> > http://clones.soonlabel.com/mp3/harmonioussynth.mp3
> >
> > and as piano for completeness - the microtonal scale is much more
> > apparent.
> >
> > http://clones.soonlabel.com/mp3/harmoniouspiano.mp3
> >
>

🔗Daniel Forro <dan.for@...>

Yes, Peter, I understand scientific attitude, nothing against.
I don't know what you mean with "particular program sending output
stream", I was asking about converting such theoretical numbers with
many decimal points to practice of tuning MIDI instrument.

My questions has also nothing to do with fraction/decimal numbers
notation. You can write in binary, hex or septimal system, this is
just a way of writing the number. But basic problem is always here:
how to convert it to real world, that means sound, interval, acoustic
or electronic instrument, and even when converted with high accuracy,
who will be able to recognize it?

I wonder as a composer and performer why you worked with intervals
which nobody can recognize. In my opinion it has no practical sense.
If we make music, there are some practical limitations in interval
size, which of course differ and depend on listener's experience with
microtonality and musical education. Exact size of such smallest
recognizable interval in musical practice is thing of discussion, but
for sure there is some limit. For me personally it's 5 Cents, I'm not
interested to make music with more steps in octave then 240 (in the
case of ET). To cross a border in the direction to smaller intervals
is a pure game with numbers far from reality. Nothing against game with numbers, I like, too. But music itself is more important for me
than some numbers. Even very nice and well calculated numbers on the
input can have poor musical result. Anyway, thay are just numbers,
and good music has something more inside.

I just asked how Chris or others solve this in musical practice, and
with MIDI instruments with limited accuracy. OK, I answer to myself:
it's necessary to work with hardware we have, so only approximation
is possible and we have to round numbers. Which is not necessarily a
problem, as for melody 5 Cents accuracy is good enough for common
ears, even for experienced ones, and for chords Yamaha's 1.171895
Cent unfortunately must be good enough, too... Such compromises must
be terribly painful for all of us with scientific approach, am I
right? Despite the fact that nobody can hear a difference :-)

Daniel Forro

On 29 Jan 2009, at 4:05 PM, Petr Pařízek wrote:

> Daniel Forró wrote:
>
> > Sorry for asking such unpleasant questions and destroy your toys,
> but
> > I wonder:
> > - which synthesizer can set tuning with such accuracy
> > - which person can hear tuning with such accuracy (in the case
> > there's a machine capable to play it)
>
> First of all, from my own experience, very often the number of decimal
> places is just a matter of the way a particular program sends the
> numbers to
> the „output stream“ rather than the accuracy with which the
> scale is
> intended to be played. I know what I’m saying because some years
> ago I was
> making some scales with a calculator which showed the results with an
> accuracy of 12 decimal places and I always left them like that even
> though I
> didn’t know about any device tunable with this degree of accuracy.
>
> Second, for some weird reason which I don’t understand, Chris has
> written
> interval sizes in cents even for the intervals which could be more
> understandable in the form of linear factors. Programs like Scala
> allow
> input data like „5/4“ and can distinguish them from sizes in
> cents (just for
> your information, Chris, it would be much clearer what you mean if
> you wrote
> 5/4 instead of 386.3137138 cents -- both mean the same interval).
>
> And finally, don’t know if this is the case, but many times, I
> have found
> myself in a situation when I needed to work with very tiny
> intervals and
> preserve their sizes regardless of whether someone is listening to
> them or
> not. For example, if I’m making a scale which should temper out a
> very small
> interval or if I’m calculating beat rates for tempered intervals,
> it’s often
> important to preserve the interval sizes sometimes even as accurate
> as to
> 1000ths of a cent despite the fact there’s probably no device that
> can be
> tuned so accurately. The point here is that the accuracy has
> essentially
> nothing to do with our hearing but it allows us to better trace the
> method
> which was used to find that tuning/scale, which is often important for
> analyzing and comparing temperaments.
>
> Petr
>

🔗Daniel Forro <dan.for@...>

OK, thanks for your nice explanation :-)

Daniel Forro

On 29 Jan 2009, at 4:27 PM, Cameron Bobro wrote:

> --- In tuning@yahoogroups.com, Daniel Forro <dan.for@...> wrote:
> >
> > Sorry for asking such unpleasant questions and destroy your toys,
> >but
> > I wonder:
>
> Revealing your ignorance isn't going to destroy anybody's toys, I
> wouldn't think.
>
> > - which synthesizer can set tuning with such accuracy
>
> Software synthesizers can be tuned with extreme accuracy. If I recall
> correctly, Hz to six decimal places would be most usual, but in 64-
> bit Csound for example, I don't know to how many decimal places
> everything is calculated.
>
> Of course in that case it is more accurate to use ratios and formulas
> and let the program worry about decimal places. In the specific cases
> where the tuning, sound design, and actual method of sound production
> are "as one", anything short of extreme accuracy in all parameters
> can result in audible artifacts so it's a moot point whether you can
> consciously hear such tiny differences or not because anyone can hear
> the limitations of the quantized system suddenly revealed.
>
>
Yes, then we hear side effect of approximation, not the difference in tuning itself.

🔗chrisvaisvil@...

I fed Mike's scale into z3ta+ I would assume the scale gets truncated after X decimals. However I fail to see the importance of your point. Its like throwing out a Stephen King book because you found a mis spelled word and those decimals mean even less of an error than that.

Sent via BlackBerry from T-Mobile

-----Original Message-----
From: Daniel Forro <dan.for@tiscali.cz>

Date: Thu, 29 Jan 2009 14:49:17
To: <tuning@yahoogroups.com>
Subject: Re: [tuning] Michael Sheiman's harmonic derived scale.

Sorry for asking such unpleasant questions and destroy your toys, but
I wonder:
- which synthesizer can set tuning with such accuracy
- which person can hear tuning with such accuracy (in the case
there's a machine capable to play it)

Very often I see here in messages a big distance between nice looking
theories and calculations on the paper (oops, on the screen of
course) and their solution in real life. Could you please describe
your solution?

Daniel Forro

On 29 Jan 2009, at 1:33 PM, vaisvil wrote:

🔗chrisvaisvil@...

Petr, I cut and pasted the scala file I used for the improvisation.
Sent via BlackBerry from T-Mobile

-----Original Message-----
From: Petr Pařízek <p.parizek@chello.cz>

Date: Thu, 29 Jan 2009 08:05:36
To: <tuning@yahoogroups.com>
Subject: [tuning] Re: Michael Sheiman's harmonic derived scale.

Daniel Forró wrote:

First of all, from my own experience, very often the number of decimal
places is just a matter of the way a particular program sends the numbers to
the „output stream“ rather than the accuracy with which the scale is
intended to be played. I know what I’m saying because some years ago I was
making some scales with a calculator which showed the results with an
accuracy of 12 decimal places and I always left them like that even though I
didn’t know about any device tunable with this degree of accuracy.

Second, for some weird reason which I don’t understand, Chris has written
interval sizes in cents even for the intervals which could be more
understandable in the form of linear factors. Programs like Scala allow
input data like „5/4“ and can distinguish them from sizes in cents (just for
your information, Chris, it would be much clearer what you mean if you wrote
5/4 instead of 386.3137138 cents -- both mean the same interval).

And finally, don’t know if this is the case, but many times, I have found
myself in a situation when I needed to work with very tiny intervals and
preserve their sizes regardless of whether someone is listening to them or
not. For example, if I’m making a scale which should temper out a very small
interval or if I’m calculating beat rates for tempered intervals, it’s often
important to preserve the interval sizes sometimes even as accurate as to
1000ths of a cent despite the fact there’s probably no device that can be
tuned so accurately. The point here is that the accuracy has essentially
nothing to do with our hearing but it allows us to better trace the method
which was used to find that tuning/scale, which is often important for
analyzing and comparing temperaments.

Petr

🔗Daniel Forro <dan.for@...>

🔗chrisvaisvil@...

Dan,

I agree that practicality is important. In science its wrapped in the concept of significant figures. But I didn't make the scale and I'd think Mike was trying aproximate fractions with decimals.

Thanks for liking the piece. Actually the scale is a little odd mapped on the regular keyboard. Sometimes 5ths are connsonant sometimes tritones are. But even its "off" intervals are musical. In general I've not followed up on my microtonal improves - yet.

-----Original Message-----
From: Daniel Forro <dan.for@tiscali.cz>

Date: Thu, 29 Jan 2009 22:14:25
To: <tuning@yahoogroups.com>
Subject: Re: [tuning] Michael Sheiman's harmonic derived scale.

Thanks for polite explanation without personal arrogant and
aggressive attacks.

Yes, that's exactly my point, those decimals are not necessary in
musical practice. Music will sound same with or without such
accuracy, that's important.

Your first impro reminds me a little bit athmosphere of some synth
soloing of Keith Emerson from ELP, his big Moog system was always out
of tune :-) And narrow chords in piano sounds well. Nice! You should
make a composition from it.

Daniel Forro

On 29 Jan 2009, at 9:38 PM, chrisvaisvil@gmail.com wrote:

> I fed Mike's scale into z3ta+ I would assume the scale gets
> truncated after X decimals. However I fail to see the importance of
> your point. Its like throwing out a Stephen King book because you
> found a mis spelled word and those decimals mean even less of an
> error than that.
>

🔗djtrancendance@...

I can't quite tell if you are asking this to me or Chris. I don't know much about tuning synthesizers; I do all my testing via software (IE OpenMPT, an open-source tracker which supports micro-tonal natively)

But my theory:
A) started with just the harmonic scale IE the ratios
9/8 10/9 11/10 12/11 13/12 14/13 15/14
B) I experimented with my ears to find out how I could use fractions that both fit the harmonic series, fit the octave, and sounded good. After much testing I came up with
9/8 10/8 11/8 12/8 (one harmonic series) ||| 10/9 11/10 12/11 (a second series)...oddly enough this sounded as good to my ears as the series itself.
C) I then picked another 5 notes by ear to accompany those 7 notes. Then I noticed most of those notes were just a continuation of the 2 harmonic series
and interpolated. Thus, while the harmonic series is "tonal", this tuning is "bi-tonal".

So, it turns out, my ears AND theory worked together on this one, no one method dominated and I was always asking the questions "can finding new notes by ear sound better than theory?" or "will theory sound better than figuring out notes by ear"? In the end of the day, they both more or less led to the same place.

-Michael

--- On Wed, 1/28/09, Daniel Forro <dan.for@...> wrote:

From: Daniel Forro <dan.for@tiscali.cz>
Subject: Re: [tuning] Michael Sheiman's harmonic derived scale.
To: tuning@yahoogroups.com
Date: Wednesday, January 28, 2009, 9:49 PM

Sorry for asking such unpleasant questions and destroy your toys, but

I wonder:

- which synthesizer can set tuning with such accuracy

- which person can hear tuning with such accuracy (in the case

there's a machine capable to play it)

Very often I see here in messages a big distance between nice looking

theories and calculations on the paper (oops, on the screen of

course) and their solution in real life. Could you please describe

your solution?

Daniel Forro

On 29 Jan 2009, at 1:33 PM, vaisvil wrote:

> Michael sent me a microtonal scale he was working on and I improvised

> using it. I midi recorded the improvisation, cleaned it up, sped it

> up, and added z3ta+ synth 4 times to it.

> The scale contains parts of the harmonic series a fifth apart. He

> would be able to talk about it much more intelligently then I. This

> will be cross-posted to MMM.

> !e:\Music\harmonici ous scale.scl

> !

> Harmonicious 12-tone scale

> 12

> !

> 203.91000173

> 291.51301613

> 386.31371386

> 470.78090733

> 551.3179423647566

> 628.2743472684155

> 701.9550008653874

> 772.6274277296696

> 905.8650025961624

> 1049.3629100223864

> 1145.0355724642502

> 2/1

> http://clones. soonlabel. com/mp3/harmonio ussynth.mp3

> and as piano for completeness - the microtonal scale is much more

> apparent.

> http://clones. soonlabel. com/mp3/harmonio uspiano.mp3

🔗Michael Sheiman <djtrancendance@...>

Hehehe...
I can't believe how much talk is going on here about the accuracy/truncation issue that has so little to do with the scale.
Seriously, after about 4 decimal places I can't even hear a difference with any such "truncation". If the harmonic distortion in the series occur at 200.05hz instead of 200hz virtually no one could tell the difference.

Argh...is there any way we can get back to discussing/criticizing/grilling/etc. the actual scale in question musically instead of debating how well some guy's synth(s) can handle it? Chris seems to have figured out how to get away with loading it into a synth almost overnight...it can't be rocket science.

-Michael
--- On Thu, 1/29/09, chrisvaisvil@... <chrisvaisvil@...> wrote:

From: chrisvaisvil@... <chrisvaisvil@...>
Subject: Re: [tuning] Michael Sheiman's harmonic derived scale.
To: tuning@yahoogroups.com
Date: Thursday, January 29, 2009, 4:38 AM

Sent via BlackBerry from T-MobileFrom: Daniel Forro
Date: Thu, 29 Jan 2009 14:49:17 +0900
To: <tuning@yahoogroups. com>
Subject: Re: [tuning] Michael Sheiman's harmonic derived scale.
Sorry for asking such unpleasant questions and destroy your toys, but
I wonder:
- which synthesizer can set tuning with such accuracy
- which person can hear tuning with such accuracy (in the case
there's a machine capable to play it)

Very often I see here in messages a big distance between nice looking
theories and calculations on the paper (oops, on the screen of
course) and their solution in real life. Could you please describe
your solution?

Daniel Forro

On 29 Jan 2009, at 1:33 PM, vaisvil wrote:

>
> Michael sent me a microtonal scale he was working on and I improvised
> using it. I midi recorded the improvisation, cleaned it up, sped it
> up, and added z3ta+ synth 4 times to it.
>
> The scale contains parts of the harmonic series a fifth apart. He
> would be able to talk about it much more intelligently then I. This
> will be cross-posted to MMM.
>
> !e:\Music\harmonici ous scale.scl
> !
> Harmonicious 12-tone scale
> 12
> !
> 203.91000173
> 291.51301613
> 386.31371386
> 470.78090733
> 551.3179423647566
> 628.2743472684155
> 701.9550008653874
> 772.6274277296696
> 905.8650025961624
> 1049.3629100223864
> 1145.0355724642502
> 2/1
>
> http://clones. soonlabel. com/mp3/harmonio ussynth.mp3
>
> and as piano for completeness - the microtonal scale is much more
> apparent.
>
> http://clones. soonlabel. com/mp3/harmonio uspiano.mp3
>

🔗Michael Sheiman <djtrancendance@...>

---But I didn't make the scale and I'd think Mike was trying aproximate fractions with ---decimals.
Scala doesn't take fractions, does it?

First I handed the scale to Chris in (often repeating) decimal form up to about 6 decimal digits accuracy, but he wanted something scala could except, so I decided to render to cents (which I know scala excepts) and my cents calculator rendered 9+ decimal places.

I know for a fact at least 90% of the notes in the scale can be reduced to fractions up to about 25/17 (nothing with factors over 25 or so for sure)...BTW this accuracy issue is NOT supposed to be a critical part of the scale. :-)

--- On Thu, 1/29/09, chrisvaisvil@... <chrisvaisvil@...> wrote:

From: chrisvaisvil@... <chrisvaisvil@...>
Subject: Re: [tuning] Michael Sheiman's harmonic derived scale.
To: tuning@yahoogroups.com
Date: Thursday, January 29, 2009, 5:41 AM

Dan,

I agree that practicality is important. In science its wrapped in the concept of significant figures. But I didn't make the scale and I'd think Mike was trying aproximate fractions with decimals.

I apologize if I seemed terse. I pasted a scale from someone else so its like - what do I say? And practicality is by nature situational. I thought the thread title was kind of clear. Sent via BlackBerry from T-MobileFrom: Daniel Forro
Date: Thu, 29 Jan 2009 22:14:25 +0900
To: <tuning@yahoogroups. com>
Subject: Re: [tuning] Michael Sheiman's harmonic derived scale.
Thanks for polite explanation without personal arrogant and
aggressive attacks.

Yes, that's exactly my point, those decimals are not necessary in
musical practice. Music will sound same with or without such
accuracy, that's important.

Daniel Forro

On 29 Jan 2009, at 9:38 PM, chrisvaisvil@ gmail.com wrote:

🔗Graham Breed <gbreed@...>

🔗Daniel Forro <dan.for@...>

Nice idea to combine theory with practice this way, scientific and empirical attitude, and balance it so well. I often use similar method for music composition.

Daniel Forro

On 29 Jan 2009, at 11:49 PM, djtrancendance@... wrote:

>
> I can't quite tell if you are asking this to me or Chris. I > don't know much about tuning synthesizers; I do all my testing via > software (IE OpenMPT, an open-source tracker which supports micro-> tonal natively)
>
> But my theory:
> A) started with just the harmonic scale IE the ratios
> 9/8 10/9 11/10 12/11 13/12 14/13 15/14
> B) I experimented with my ears to find out how I could use > fractions that both fit the harmonic series, fit the octave, and > sounded good. After much testing I came up with
> 9/8 10/8 11/8 12/8 (one harmonic series) ||| 10/9 11/10 12/11 (a > second series)...oddly enough this sounded as good to my ears as > the series itself.
> C) I then picked another 5 notes by ear to accompany those 7 > notes. Then I noticed most of those notes were just a continuation > of the 2 harmonic series and interpolated. Thus, while the > harmonic series is "tonal", this tuning is "bi-tonal".
>
> So, it turns out, my ears AND theory worked together on this > one, no one method dominated and I was always asking the questions > "can finding new notes by ear sound better than theory?" or "will > theory sound better than figuring out notes by ear"? In the end of > the day, they both more or less led to the same place.
>
> -Michael

🔗Daniel Forro <dan.for@...>

- Why accuracy issue has so little to do with the scale? Scale is made from intervals and frequencies, so of course it is important. When somebody invented some scale, for sure it has some reason why this or that interval of certain accuracy was selected. We can discuss how much Cents (or Hz) differences can be still recognized.

- Yes, it's quite easy to convert Cent table to SysEx data for any hardware synth with microtonal feature, but it's necessary to round the numbers, which can lead to approximation errors +/-1 or 2 Cents or so maximally. That was my point. I don't have experience how software synths handle it, but we have experts here saying it works with high accuracy. So far so good.

- Interval/tuning/scale accuracy is of course important part of discussion. Which sense would be in inventing some scale or tuning system, and then not keeping the rules which we invented because of not enough accuracy? My point is which "unfocussing" from original values is still acceptable, in other words when we start to hear differences are so big that there's different scale. There are also practical limits of our hearing system, and another limits based on music education or musical culture (OK, it's not necessary to go so far).

Daniel Forro

On 29 Jan 2009, at 11:56 PM, Michael Sheiman wrote:

>
> Hehehe...
> I can't believe how much talk is going on here about the accuracy/> truncation issue that has so little to do with the scale.
> Seriously, after about 4 decimal places I can't even hear a > difference with any such "truncation". If the harmonic distortion > in the series occur at 200.05hz instead of 200hz virtually no one > could tell the difference.
>
> Argh...is there any way we can get back to discussing/> criticizing/grilling/etc. the actual scale in question musically > instead of debating how well some guy's synth(s) can handle it? > Chris seems to have figured out how to get away with loading it > into a synth almost overnight...it can't be rocket science.
>
> -Michael

🔗djtrancendance@...

---My point is which "unfocussing" from original
---values is still acceptable, in other words when we start to hear
---differences are so big that there's different scale.
Good point! Whereas I figure 1-2 cents off the original probably won't matter, If people kept on estimating my tuning (or anyone else's) based on estimates, and people estimated their estimates...the end result could well be a completely different scale.
Later today I will make a notation of the tuning in pure fractional form for this reason.

-Michael

--- On Thu, 1/29/09, Daniel Forro <dan.for@...> wrote:

From: Daniel Forro
<dan.for@...>
Subject: Re: [tuning] Michael Sheiman's harmonic derived scale.
To: tuning@yahoogroups.com
Date: Thursday, January 29, 2009, 8:28 AM

- Why accuracy issue has so little to do with the scale? Scale is

made from intervals and frequencies, so of course it is important.

When somebody invented some scale, for sure it has some reason why

this or that interval of certain accuracy was selected. We can

discuss how much Cents (or Hz) differences can be still recognized.

- Yes, it's quite easy to convert Cent table to SysEx data for any

hardware synth with microtonal feature, but it's necessary to round

the numbers, which can lead to approximation errors +/-1 or 2 Cents

or so maximally. That was my point. I don't have experience how

software synths handle it, but we have experts here saying it works

with high accuracy. So far so good.

- Interval/tuning/ scale accuracy is of course important part of

discussion. Which sense would be in inventing some scale or tuning

system, and then not keeping the rules which we invented because of

not enough accuracy? My point is which "unfocussing" from original

values is still acceptable, in other words when we start to hear

differences are so big that there's different scale. There are also

practical limits of our hearing system, and another limits based on

music education or musical culture (OK, it's not necessary to go so

far).

Daniel Forro

On 29 Jan 2009, at 11:56 PM, Michael Sheiman wrote:

> Hehehe...

> I can't believe how much talk is going on here about the accuracy/

> truncation issue that has so little to do with the scale.

> Seriously, after about 4 decimal places I can't even hear a

> difference with any such "truncation" . If the harmonic distortion

> in the series occur at 200.05hz instead of 200hz virtually no one

> could tell the difference.

> Argh...is there any way we can get back to discussing/

> criticizing/ grilling/ etc. the actual scale in question musically

> instead of debating how well some guy's synth(s) can handle it?

> Chris seems to have figured out how to get away with loading it

> into a synth almost overnight... it can't be rocket science.

> -Michael

🔗djtrancendance@...

Hehehe....

Actually (assuming you indeed used all 12 notes in my "tuning" as a scale) it still sounds pretty good to me...I'm amazed you got something that emotional considering I haven't even really gotten down to explaining how to make scales within that tuning (or asking other people if they have suggestions since I am still working out the theory myself).

However the not-so-even harmonics on the piano seem to do some damage (a flaw with my tuning not your playing), and reveal a fault in the tuning in forcing such an instrument to stick to such tight intervals (it seems "clean harmonic-ed" acoustic guitar sounds are much better for avoiding this, btw).
********************************************************
My much much shorter and less detailed example is on
http://geocities.com/djtrancendance/micro/duality.mp3

But, of course, I cheat. :-)
I use the 1st, 2nd, 4th 5th, 6th,7th, 8th, 10th, and 12th notes of the scale only.
For some reason beyond my comprehension...only about up to 9 notes at once can sound "in the same mood" in my scale...that and
the extra spacing helps prevent beating in tight areas.
***************************************************
BTW, another good scale to use (that's more consonant) is the 7-tone scale using the
1st, 2nd,4th,6th,8th,10th, and 11th note of the tuning.

This scale explains where I got the basis for the 12-note scale from.
The ratios between notes 1,2,4,6, and 8 are 9/8,10/9,11/10,12/11 (straight from overtones on the harmonic series)! Note: the 8th note is a perfect 5th.

And then between the 8th,10th,11th and octave the ratios are 10/9, 11/10, and 12/11 (again, straight from the series...only this time we are starting from the 5th).

Now what do we do with, say, the first note times 7/8,6/8...from the first harmonic and all the other parts of the series we miss? We multiply them by 2,4,1/2,1/4...(or 1
if they already fit within the octave)...to push them back into the octave....and then use them to create the other 5 notes of the 12 note scale (only keeping the ones that don't fall too close to existing notes to help avoid critical-band/beating related problems).

   So, in many ways....this is a dead simple scale, certainly nothing like the complex magic of MOS scales. But, I hope, what is simple to create will also come across to many people as simple to listen to and maybe even understandable to those not naturally interested in micro-tonal music.
********************************************************
    BTW, for those of you who are really hard-core about it :-)....I am working on a 14-tone version of the tuning which has the two closest notes set at about 1.04-times each other minimum (about 67 cents) in closeness instead of about 1.05-times each other minimum (about 84 cents). BTW, I have
managed to get 10-note scales (meaning 10 notes that fit within the same "mood") from that tuning instead of the 9-note maximum I could get out of my 12-note scale.
   The 14-note version obviously
beats a bit more but gives an extra 2 notes of freedom and still beats harmonically so much of the "periodic consonance" is still maintained. If anyone is interested please ask and I will gladly post the 14-note version.

Enjoy....

--- On Wed, 1/28/09, vaisvil <chrisvaisvil@...> wrote:

From: vaisvil <chrisvaisvil@...>
Subject: [tuning] Michael Sheiman's harmonic derived scale.
To: tuning@yahoogroups.com
Date: Wednesday, January 28, 2009, 8:33 PM

Michael sent me a microtonal scale he was working on and I improvised

using it. I midi recorded the improvisation, cleaned it up, sped it

up, and added z3ta+ synth 4 times to it.

The scale contains parts of the harmonic series a fifth apart. He

would be able to talk about it much more intelligently then I. This

will be cross-posted to MMM.

!e:\Music\harmonici ous scale.scl

Harmonicious 12-tone scale

203.91000173

291.51301613

386.31371386

470.78090733

551.3179423647566

628.2743472684155

701.9550008653874

772.6274277296696

905.8650025961624

1049.3629100223864

1145.0355724642502

2/1

http://clones. soonlabel. com/mp3/harmonio ussynth.mp3

and as piano for completeness - the microtonal scale is much more

apparent.

http://clones. soonlabel. com/mp3/harmonio uspiano.mp3

🔗Carl Lumma <carl@...>

🔗chrisvaisvil@...

🔗Carl Lumma <carl@...>

🔗Michael Sheiman <djtrancendance@...>

Note, this scale is an odd case.

You know how in the harmonic series no two notes played together are sour, to some extent? In other words, you know how you don't worry about which notes you need to play together to make a "clear chord" in the harmonic series?

Well, I believe the same goes for my tuning for the most part. Except, that some notes are "out of mood" and playing too many notes too close together sounds "bumpy" though not "out of key" far as dissonance goes, hence why I suggest 7-9 tones at once and not the full 12.

At least by design, my tuning should be an odd case where finding the chord and perfect intervals are NOT of importance since everything is designed to be at least very close to perfect intervals (again, agreed, it's a rational scale, and perhaps overly so).

But....don't worry....I will re-post this understandably rational tuning as fractions for sake of easier understanding and easier comparison with existing scale systems, among other things.

-Michael

--- On Thu, 1/29/09, Carl Lumma <carl@...> wrote:

From: Carl Lumma <carl@lumma.org>
Subject: [tuning] Re: Michael Sheiman's harmonic derived scale.
To: tuning@yahoogroups.com
Date: Thursday, January 29, 2009, 11:52 AM

--- In tuning@yahoogroups. com, chrisvaisvil@ ... wrote:

> Sure, makes sense from a scale format, but is of no practical

> importance to me as a performer (except understanding the math

> of what I'm using_)

It's of high importance to performers, if they want to be

know where chords are in the scale.

-Carl

🔗Chris Vaisvil <chrisvaisvil@...>

🔗Michael Sheiman <djtrancendance@...>

--Microtonal tuning has a fairly steep learning curve, especially when
people start throwing --around harmonic series partial numbers.
Intellectually, sure I know what it is - but its not --concrete for me at
all.
Again, a good technique is just pick 7-9 notes out of my tuning that sound good to you and stick with those. Also again, there are really no "non-chords" in the harmonic series or my scale which is based on them (though some combinations of note sound a tad rougher than others, of course). It might be a better idea to worry about moods than chords for that reason: there is no real "equivalent" between chords in my scale and matching any "only use pure-intervals" structure/goal because virtually everything is a pure interval of sorts.

Modulation/transposition is another story...I will have to work on that...if you expect most people to be able to get something that sounds as good as what you wrote purely "by ear" instead of using scale of 7-9 notes, for sure that expectation increases the learning curve a lot. I don't expect other people to do that kind of thing either...which is why I believe it's so important to start looking for scales within my tuning.

If anyone messing with my tuning trying to find good sub-sets IE "scales" (like I am myself) finds some great 7-9 note scales I would appreciate you share them here.:-)

-Michael

--- On Thu, 1/29/09, Chris Vaisvil <chrisvaisvil@...> wrote:

From: Chris Vaisvil <chrisvaisvil@...>
Subject: Re: [tuning] Re: Michael Sheiman's harmonic derived scale.
To: tuning@yahoogroups.com
Date: Thursday, January 29, 2009, 1:32 PM

Ok, you got a point - its the same way I use my music theory - to sift through things quicker.

At this point though I'm blissfully doing it all by ear, which is what I meant by my comment.

Microtonal tuning has a fairly steep learning curve, especially when people start throwing around harmonic series partial numbers. Intellectually, sure I know what it is - but its not concrete for me at all.

On Thu, Jan 29, 2009 at 2:52 PM, Carl Lumma <carl@...> wrote:

--- In tuning@yahoogroups. com, chrisvaisvil@ ... wrote:

> Sure, makes sense from a scale format, but is of no practical

> importance to me as a performer (except understanding the math

> of what I'm using_)

It's of high importance to performers, if they want to be

know where chords are in the scale.

-Carl

🔗Daniel Forro <dan.for@...>

🔗Carl Lumma <carl@...>

🔗Chris Vaisvil <chrisvaisvil@...>

Please do post your improv!!

What controller are you using? I've not yet had luck with using the MS2000
for that purpose despite all the nice knobs - but I've not read much on how
to do it either.

On Thu, Jan 29, 2009 at 7:17 PM, Carl Lumma <carl@...> wrote:

> --- In tuning@...m <tuning%40yahoogroups.com>, Chris Vaisvil
> <chrisvaisvil@...> wrote:
> >
> > Ok, you got a point - its the same way I use my music theory - to
> > sift through things quicker.
> >
> > At this point though I'm blissfully doing it all by ear, which is
> > what I meant by my comment.
>
> That's right: for those performers doing absolutely everything
> by ear, the extra information carried by the ratios isn't useful.
> Note that this is a more extreme position in microtonal music
> than usual. Many guitarists do everything by ear, but they
> always do it in the same scale, and that scale happens to match
> everything they hear on the radio, etc. It's a lot harder
> when the scale could be anything.
>
> But that isn't to say the approach is invalid. In fact, an
> exercise I plan to undertake soon is to randomly assign every
> key on my MIDI controller a different pitch and then try to
> improvise. Another variant is to restrict that the pitches
> be ascending. Could be a lot of fun. I do seem to remember
> doing my best improvisations (in a sense, anyway) before I
> knew much theory...
>
> -Carl
>
>
>

🔗Daniel Forro <dan.for@...>

🔗Daniel Forró <dan.for@...>

You've got it. There must be some balance between theory and practice, intelect and emotion, strict order and chaos, performing prepared music or improvising... All theory is useless if the resulting music following it strictly is boring and uninteresting (whatever this means), and opposite: pure improvisation without any knowledge can lead to the same boring and uninteresting result.

Daniel Forro

On 30 Jan 2009, at 9:17 AM, Carl Lumma wrote:

> --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
> >
> > Ok, you got a point - its the same way I use my music theory - to
> > sift through things quicker.
> >
> > At this point though I'm blissfully doing it all by ear, which is
> > what I meant by my comment.
>
> That's right: for those performers doing absolutely everything
> by ear, the extra information carried by the ratios isn't useful.
> Note that this is a more extreme position in microtonal music
> than usual. Many guitarists do everything by ear, but they
> always do it in the same scale, and that scale happens to match
> everything they hear on the radio, etc. It's a lot harder
> when the scale could be anything.
>
> But that isn't to say the approach is invalid. In fact, an
> exercise I plan to undertake soon is to randomly assign every
> key on my MIDI controller a different pitch and then try to
> improvise. Another variant is to restrict that the pitches
> be ascending. Could be a lot of fun. I do seem to remember
> doing my best improvisations (in a sense, anyway) before I
> knew much theory...
>
> -Carl
>

🔗Daniel Forro <dan.for@...>

🔗Carl Lumma <carl@...>

🔗Chris Vaisvil <chrisvaisvil@...>

for those moments when the migration gets too intense try www.virtualbox.org

its free, which is a very nice price.

- I have an XP Pro install in a virtual machine in a Vista 64 installation
exclusively using a USB wireless adaptor running Netflix full screen video -
~30 - 35% cpu load doing that and its fast - it really runs as it it were
its own machine.

and if you don't like it - delete the virtual hard drive and *poof* its
gone.

On Thu, Jan 29, 2009 at 10:28 PM, Carl Lumma <carl@...> wrote:

> --- In tuning@yahoogroups.com <tuning%40yahoogroups.com>, Daniel Forro
> <dan.for@...> wrote:
> >
> > Hi, Carl,
> >
> > yes, it's great software and I have seen this feature, and want
> > to use it. Everything goes so slowly. Last year I finally
> > managed to switch to OS X and reconnect all MIDI in my studio
> > (since yesterday I have 864 MIDI channels, using about 350).
> > Now I try to decide which sequencer under OS X I will use in
> > the future, and the offer is not totally satisfying - Logic or
> > Digital Performer.
>
> Definitely Logic.
>
> > If I'm not satisfied, I will stay with good old Opcode Studio
> > Vision under OS 9 with all consequences. Still there's a lot of
> > work with conversion from older software.
>
> I feel your pain. I'm in the process of migrating from
> 32-bit to 64-bit Windows, and it's sucking my will to live.
>
> -Carl
>
>
>

🔗Daniel Forro <dan.for@...>

🔗Petr Pařízek <p.parizek@...>

Daniel Forró wrote:

> I don't know what you mean with "particular program sending output
> stream", I was asking about converting such theoretical numbers with
> many decimal points to practice of tuning MIDI instrument.

What I was saying in my previous post is that many calculators write the stored numbers very accurately, which some people may never find useful. But even though, this doesn’t mean we should remove the decimal places that we find meaningless. For example, if you make temperaments in Scala (I mean, for Vallotti/Young, for example, you tell the program to chain 6 fifths narrower by 1/6 of a Pyth. comma and 6 pure fifths) and save this into a „.scl“ file, the cent sizes contained in the file will be rounded to 5 decimal places (i.e. to the nearest ten-thousandth of a cent), which is obviously meaningless for converting to SysEx commands. But if the program has the ability to do it this way and is internally „set“ to do it like that, then there’s no reason for removing the unwanted numerals from the output file and it would just také your time to do that. Further more, if you leave them there, you can much more easily know the method which was used to get to the particular tuning. For example, in quarter-comma meantone, we know that 4 fifths minus 2 octaves should be ~386 cents, which means that 4 fifths should be ~2786 cents (assuming we want pure octaves). Splitting this value into 4 equal steps gives you 696.5 cents. If you then rounded all the interval sizes to the nearest cent, you would get a chain of alternating fifths of 696 and 697 cents and the temperament listing would lose its „regularity“. But if you preserve the original sizes, you’ll immediately realize that there’s nothing else going on here but a straight chain of fifths of one particular size, which really is the concept of meantone. Further more, don’t know if you have ever tried it, but if you compare a 697 cent fifth with a 696.5 cent fifth, it‘s just a different sound -- I can also demonstrate this, if you like.

> how to convert it to real world, that means sound, interval, acoustic
> or electronic instrument, and even when converted with high accuracy,
> who will be able to recognize it?

From my personal experience, even if highly accurate numbers are not of much use in music, they are of good use, for example, when making an electronic version of a „model“ temperament for later tuning on acoustic instruments, despite the fact that no acoustic instrument can be tuned so accurately and that harpsichord or piano strings may have slightly „mistuned“ overtones sometimes. AFAIK, Cool Edit rounds the input frequency data to the nearest „ten-millionth“ of a Hz, which, at a frequency of 16Hz (which is among the slowest frequencies you could possibly call a „tone“), is about a millionth of a cent. My small Qbasic utility from 2004 for making periodic sawtooth waves could handle the input frequencies with even better accuracy. In those years, I was often working with temperaments based on equal beat rates and I realized I could only do the job with very accurate numbers if I really wanted the beat rates to be equal. For example, suppose you make a temperament where both C-E and E-G beat 2 times per second. If you change the pitch of one of the tones by just a tenth of a cent, the beat rates change so remarcably that you can’t consider them equal anymore. Again, this is not something which should matter in actual music, but it does matter in the way a particular tuning/temperament is described.

> I wonder as a composer and performer why you worked with intervals
> which nobody can recognize. In my opinion it has no practical sense.

If you are working with very small „commas“ which can get very widely distributed in a particular temperament, sooner or later, you may find that the amount of tempering can be even as small as a fraction of a cent. And in some very rare cases, even the comma itself can be smaller than a cent. One example of the former is the 5-limit schisma (i.e. 8 pure fourths minus 3 octaves minus a pure major third), which is just about 2 cents in size; an example of the latter can be the „ragisma“ (i.e. the semi-augmented second of 8/7 minus 3 pure fourths plus 4 pure minor thirds), which is just about 0.4 cents. As you can see, both the schisma and the ragisma have many many possibilities how they can be distributed among the mentioned intervals. If you make temperaments using these, they will definitely sound like JI because such tiny pitch alterations are not recognizable by our ear. But it is often useful to have these small interval sizes preserved because then you can easily spot how the particular temperament was made and therefore what are the target intervals we are trying to approximate in it. Further more, even though the schisma itself is about 2 cents in size, it can happily be distributed in such a way that one fifth will be only about 1/8th of a cent flat of pure, which is a far far better option than to have 7 or 8 pure fifths followed by one 2-cent flat fifth in the chain. If you use the „untempered“ version with one fifth 2 cents flat, then the one fifth’s slow beating can be (sometimes( audible when compared to the other fifths in the chain. On the other side, if you use the tempered version where each fifth is flattened by only about 1/8 of a cent, all the fifths will sound as if they were JI, even though they are not.

Petr

🔗Petr Pařízek <p.parizek@...>

🔗Carl Lumma <carl@...>

🔗Daniel Forro <dan.for@...>

Hi, Peter, thanks for a message.

On 30 Jan 2009, at 3:49 PM, Petr Pařízek wrote:

>
> Daniel Forró wrote:
>
> > I don't know what you mean with "particular program sending output
> > stream", I was asking about converting such theoretical numbers with
> > many decimal points to practice of tuning MIDI instrument.
>
> What I was saying in my previous post is that many calculators
> write the stored numbers very accurately, which some people may
> never find useful. But even though, this doesn’t mean we should
> remove the decimal places that we find meaningless. For example, if
> you make temperaments in Scala (I mean, for Vallotti/Young, for
> example, you tell the program to chain 6 fifths narrower by 1/6 of
> a Pyth. comma and 6 pure fifths) and save this into a „.scl“
> file, the cent sizes contained in the file will be rounded to 5
> decimal places (i.e. to the nearest ten-thousandth of a cent),
> which is obviously meaningless for converting to SysEx commands.
> But if the program has the ability to do it this way and is
> internally „set“ to do it like that, then there’s no reason
> for removing the unwanted numerals from the output file and it
> would just také your time to do that. Further more, if you leave
> them there, you can much more easily know the method which was used
> to get to the particular tuning. For example, in quarter-comma
> meantone, we know that 4 fifths minus 2 octaves should be ~386
> cents, which means that 4 fifths should be ~2786 cents (assuming we
> want pure octaves). Splitting this value into 4 equal steps gives
> you 696.5 cents. If you then rounded all the interval sizes to the
> nearest cent, you would get a chain of alternating fifths of 696
> and 697 cents and the temperament listing would lose its
> „regularity“. But if you preserve the original sizes, you’ll
> immediately realize that there’s nothing else going on here but a
> straight chain of fifths of one particular size, which really is
> the concept of meantone. Further more, don’t know if you have ever
> tried it, but if you compare a 697 cent fifth with a 696.5 cent
> fifth, it‘s just a different sound -- I can also demonstrate this,
> if you like.
>
So you meant "saving data", not stream...
You describe well what's necessary to do to correct approximation
errors when tuning hardware synth with limited resolution. This is
practical side of that problem, and of course there's no reason to
change original theoretical listing with high resolution.
Yes, if both notes of interval sound together, even small differences
can be heared, if we prepare a special test with enough long
sustained notes in suitable timbre and alternating both cases. But
again, in the stream of real music composition this can't happen.
Music is music, not simple testing pattern. It will be covered by
other notes vertically and horizontally, nobody will mention it.Music is much higher level of language, we feel complex stories,
articles and sentences, not individual phonems.
> > how to convert it to real world, that means sound, interval,
> acoustic
> > or electronic instrument, and even when converted with high
> accuracy,
> > who will be able to recognize it?
>
> From my personal experience, even if highly accurate numbers are
> not of much use in music, they are of good use, for example, when> making an electronic version of a „model“ temperament for later
> tuning on acoustic instruments, despite the fact that no acoustic
> instrument can be tuned so accurately and that harpsichord or piano
> strings may have slightly „mistuned“ overtones sometimes. AFAIK,
> Cool Edit rounds the input frequency data to the nearest „ten-
> millionth“ of a Hz, which, at a frequency of 16Hz (which is among
> the slowest frequencies you could possibly call a „tone“), is
> about a millionth of a cent. My small Qbasic utility from 2004 for
> making periodic sawtooth waves could handle the input frequencies
> with even better accuracy. In those years, I was often working with
> temperaments based on equal beat rates and I realized I could only
> do the job with very accurate numbers if I really wanted the beat
> rates to be equal. For example, suppose you make a temperament
> where both C-E and E-G beat 2 times per second. If you change the
> pitch of one of the tones by just a tenth of a cent, the beat rates
> change so remarcably that you can’t consider them equal anymore.
> Again, this is not something which should matter in actual music,
> but it does matter in the way a particular tuning/temperament is
> described.
>
Yes, this is scientific attitude. My original questions were directed
to dealing with this in practice.
> > I wonder as a composer and performer why you worked with intervals
> > which nobody can recognize. In my opinion it has no practical sense.
>
> If you are working with very small „commas“ which can get very
> widely distributed in a particular temperament, sooner or later,
> you may find that the amount of tempering can be even as small as a
> fraction of a cent. And in some very rare cases, even the comma
> itself can be smaller than a cent. One example of the former is the
> 5-limit schisma (i.e. 8 pure fourths minus 3 octaves minus a pure
> major third), which is just about 2 cents in size; an example of
> the latter can be the „ragisma“ (i.e. the semi-augmented second
> of 8/7 minus 3 pure fourths plus 4 pure minor thirds), which is
> just about 0.4 cents. As you can see, both the schisma and the
> ragisma have many many possibilities how they can be distributed
> among the mentioned intervals. If you make temperaments using
> these, they will definitely sound like JI because such tiny pitch
> alterations are not recognizable by our ear.
>
Yes, that's exactly what I wanted to hear - not recognizable. That's
real life.
> But it is often useful to have these small interval sizes preserved
> because then you can easily spot how the particular temperament was
> made and therefore what are the target intervals we are trying to
> approximate in it. Further more, even though the schisma itself is
> about 2 cents in size, it can happily be distributed in such a way
> that one fifth will be only about 1/8th of a cent flat of pure,> which is a far far better option than to have 7 or 8 pure fifths
> followed by one 2-cent flat fifth in the chain. If you use the
> „untempered“ version with one fifth 2 cents flat, then the one
> fifth’s slow beating can be (sometimes( audible when compared to
> the other fifths in the chain. On the other side, if you use the
> tempered version where each fifth is flattened by only about 1/8 of
> a cent, all the fifths will sound as if they were JI, even though
> they are not.
>
> Petr
>
Yes, this is scientific face of coin again. Audible when you dospecial test, not in running music.

Daniel Forro

🔗chrisvaisvil@...

🔗Kraig Grady <kraiggrady@...>

🔗Chris Vaisvil <chrisvaisvil@...>

Hi Dan,

The first text link is your original file and it has a .wps extention. -
this seems to be from microsoft works??

I translated it to .rtf - rich text file format which is more universal - it
looked the same to me.

If you could save your file in a more universal format it would be great.
In the extreme one could download open office (which is free) and save it as
a PDF file once you have it as you want it to look.

Thanks,

Chris

On Fri, Jan 30, 2009 at 10:26 PM, daniel_anthony_stearns <
daniel_anthony_stearns@...> wrote:

> hey there chris, thanks. unfortunately the first text link wouldn't
> open for me, and the second one skewed the little ascii note-naming
> chart rendering it unintelligible (well, that's acually fitting
> somehow) and the musical examples on their own are like the upper-
> harmonics of jazz chords to early interval naming church folk.....an
> ugly thing outside a compelling context!!!! BUT hey, I really
> actually do appreciate you going out of your way to this---->it's the
> kind of thing that makes me want to be a better person,no joke.so
> thanks again.
>
>
> --- In tuning@yahoogroups.com <tuning%40yahoogroups.com>, chrisvaisvil@...
> wrote:
> >
> > http://micro.soonlabel.com
> >
> > Dan's Work on 20Tet
> > Sent via BlackBerry from T-Mobile
> >
> > -----Original Message-----
> > From: "Carl Lumma" <carl@...>
> >
> > Date: Fri, 30 Jan 2009 07:14:18
> > To: <tuning@yahoogroups.com <tuning%40yahoogroups.com>>
> > Subject: [tuning] Re: Michael Sheiman's harmonic derived scale.
> >
> >
> > I've got multiple HDDs set up with XP, Vista, and 7.
> > Mainly I just need a clear weekend to work on it. -Carl
> >
> > --- In tuning@yahoogroups.com <tuning%40yahoogroups.com>, Chris Vaisvil
> <chrisvaisvil@> wrote:
> > >
> > > for those moments when the migration gets too intense try
> > > www.virtualbox.org
> > >
> > > its free, which is a very nice price.
> > >
> > > - I have an XP Pro install in a virtual machine in a Vista 64
> > > installation exclusively using a USB wireless adaptor running
> > > Netflix full screen video - ~30 - 35% cpu load doing that and
> > > its fast - it really runs as it it were its own machine.
> > >
> > > and if you don't like it - delete the virtual hard drive and
> > > *poof* its gone.
> > >
> >
>
>
>

🔗Dave Seidel <dave@...>

Here you go:

!
Harmonicious 12-tone scale (rational version)
12
!
9/8
58/49
5/4
21/16
11/8
23/16
3/2
25/16
27/16
11/6
31/16
2/1

It just took me a few minutes with this:
http://www.sengpielaudio.com/calculator-centsratio.htm
and this:
http://superspace.epfl.ch/approximator/

It is true for me as well that it I find it much more useful to see it in this form than in cents, which I never work with.

Here is Scala's default view of the scale:

|
Harmonicious 12-tone scale (rational version)
|
0: 1/1 0.000 unison, perfect prime
1: 9/8 203.910 major whole tone
2: 58/49 291.925
3: 5/4 386.314 major third
4: 21/16 470.781 narrow fourth
5: 11/8 551.318 undecimal semi-augmented fourth
6: 23/16 628.274 23rd harmonic
7: 3/2 701.955 perfect fifth
8: 25/16 772.627 classic augmented fifth
9: 27/16 905.865 Pythagorean major sixth
10: 11/6 1049.363 21/4-tone, undecimal neutral seventh
11: 31/16 1145.036 31st harmonic
12: 2/1 1200.000 octave

- Dave

Kraig Grady wrote:
> In general, it would have been expedient to publish the ratios instead > of two days of discussion. For one it would then be easy to compare it > to Canright's scale, Wilson's helixsongs, or my own Centaur tuning, and > i am sure numerous others. Actually it is best to put it out in a graph > cause that way one cannot reinvent something merely by mode.

--
~DaveSeidel = [
http://mysterybear.net,
http://daveseidel.tumblr.com,
http://twitter.com/DaveSeidel
];

🔗Michael Sheiman <djtrancendance@...>

Wow...thank you!
I honestly had no clue how to break, for example, the third note in the tuning into 58/49.

--- On Sat, 1/31/09, Dave Seidel <dave@superluminal.com> wrote:

From: Dave Seidel <dave@...>
Subject: Re: [tuning] Re: Michael Sheiman's harmonic derived scale.
To: tuning@yahoogroups.com
Date: Saturday, January 31, 2009, 6:30 AM

Here you go:

Harmonicious 12-tone scale (rational version)

9/8

58/49

5/4

21/16

11/8

23/16

3/2

25/16

27/16

11/6

31/16

2/1

It just took me a few minutes with this:

http://www.sengpiel audio.com/ calculator- centsratio. htm

and this:

http://superspace. epfl.ch/approxim ator/

It is true for me as well that it I find it much more useful to see it

in this form than in cents, which I never work with.

Here is Scala's default view of the scale:

Harmonicious 12-tone scale (rational version)

0: 1/1 0.000 unison, perfect prime

1: 9/8 203.910 major whole tone

2: 58/49 291.925

3: 5/4 386.314 major third

4: 21/16 470.781 narrow fourth

5: 11/8 551.318 undecimal semi-augmented fourth

6: 23/16 628.274 23rd harmonic

7: 3/2 701.955 perfect fifth

8: 25/16 772.627 classic augmented fifth

9: 27/16 905.865 Pythagorean major sixth

10: 11/6 1049.363 21/4-tone, undecimal neutral seventh

11: 31/16 1145.036 31st harmonic

12: 2/1 1200.000 octave

- Dave

Kraig Grady wrote:

> In general, it would have been expedient to publish the ratios instead

> of two days of discussion. For one it would then be easy to compare it

> to Canright's scale, Wilson's helixsongs, or my own Centaur tuning, and

> i am sure numerous others. Actually it is best to put it out in a graph

> cause that way one cannot reinvent something merely by mode.

~DaveSeidel = [

http://mysterybear. net,

http://daveseidel. tumblr.com,

http://twitter. com/DaveSeidel

];

🔗Daniel Forro <dan.for@...>

Thanks for sending it, and for useful links.

On 31 Jan 2009, at 11:30 PM, Dave Seidel wrote:

> Here you go:
>
> !
> Harmonicious 12-tone scale (rational version)
> 12
> !
> 9/8
> 58/49
> 5/4
> 21/16
> 11/8
> 23/16
> 3/2
> 25/16
> 27/16
> 11/6
> 31/16
> 2/1
>
> It just took me a few minutes with this:
> http://www.sengpielaudio.com/calculator-centsratio.htm
> and this:
> http://superspace.epfl.ch/approximator/
>
> It is true for me as well that it I find it much more useful to see it
> in this form than in cents, which I never work with.
>
>
I'm used to cents from the past as I work mainly with hardware synthesizers and cents differences can be easily set there. Cent table also tells me on the first sight how big are intervals between two adjacent steps, without need to count them with fractions.
> Here is Scala's default view of the scale:
>
> |
> Harmonicious 12-tone scale (rational version)
> |
> 0: 1/1 0.000 unison, perfect prime
> 1: 9/8 203.910 major whole tone
> 2: 58/49 291.925
> 3: 5/4 386.314 major third
> 4: 21/16 470.781 narrow fourth
> 5: 11/8 551.318 undecimal semi-augmented fourth
> 6: 23/16 628.274 23rd harmonic
> 7: 3/2 701.955 perfect fifth
> 8: 25/16 772.627 classic augmented fifth
> 9: 27/16 905.865 Pythagorean major sixth
> 10: 11/6 1049.363 21/4-tone, undecimal neutral seventh
> 11: 31/16 1145.036 31st harmonic
> 12: 2/1 1200.000 octave
>
> - Dave
>

Michael Sheiman's harmonic derived scale.

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