Yahoo Tuning Groups Ultimate Backup tuning On the Hindoo division of the octave

On Thu, Mar 31, 2011 at 11:58 PM, Jake Freivald <jdfreivald@...> wrote:
>
> John,
>
> Someone (Mike? Michael?) recently talked about people tolerating sharp
> tones better than flat ones. Being the empirical sort of guy that you
> are, you might consider looking into that: +7.2 cents might be
> tolerable, but -7.2 might not.

I don't ever remember saying anything like that. I'm also really tired
of these arbitrary +7 -7 whatever cent cutoffs.

12-tet's 300 cent minor third is 16 cents flat, but is very tolerable.
12-tet's 400 cent major third is 14 cents sharp, but is also
tolerable.

Furthermore, mistuning tolerance is clearly subject to some sort of
individual variation - you have people like Igs who don't mind
father-tempered fifths that are in the 730 cents range, and then you
have folks like Gene on the other extreme who don't like 17-tet for
the 13-limit.

> Also, when you're putting chords together, have you considered the
> overall tolerances of the various intervals? In other words, if your
> major third is 380 cents and your fifth is 708 cents, each is within the
> tolerance, but the minor third between the 3 and the 5 is 708-380 = 328
> cents, a full 13 cents sharp. Throw in a seventh or ninth and things get
> more complicated.

Paul Erlich would have you flogged for doing anything less.

-Mike

🔗akjmicro <aaron@...>

Hey Michael,

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> Indeed 22EDO does have very strong fourths and fifths. It's the > tritone and major sixth where, IMVHO, it goes bad. 19EDO beats it
> in my book: it has a strong major sixth...the only thing I see as
> weak in 19TET is the tri-tone (which, bear in mind, 12TET is also
> terrible at).

Huh? It depends on *which* tritone you are talking about. Some folks prefer the 1\2 octave that is available in *any* even-numbered EDO....it's actually in some respects (geometrically) a simple interval. Sqrt(2)!

> Not to say every scale has to have a good major/minor and or
> neutral (which can serve as either major/minor) version of all
> common practice interval classes...but it sure seems to help and
> 31EDO seems to be the lowest EDO with virtually all major classes of > interval within 7 cents or so of perfectly just.
>

31 is great, but then again, the EDOs with moderate or even high errors compared to classic JI are still colorful in their own right. Usefulness, artistic merit and expressivity of a temperament have zilch to do with whether it measures up to JI, right?

AKJ

🔗lobawad <lobawad@...>

It's the structure of the interval system as a whole, and the way this structure is accessed/implemented (ie, modality) that matter most.

Specific close approximations to rational intervals don't have magical powers, and may even be irritating factors in context.

What's good about the "regular temperament paradigm" is that it runs backwards from what seems to be the usual contemporary conception. With 12-tET so ubiquitous, it is understandable that people assume that an equal division of the octave is some kind of "natural" starting point, which of course it is not.

Rather than starting with a grid (an equal division of an octave) and searching for rational intervals and structures within, the "regular temperament paradigm" names the desired intervals by constructive ingredient (primes) and constructs, not a tuning, but a deliberate and purposeful system of interals which can be tuned to varying degrees of accuracy.

This is radically, utterly, different from seeking approximations to rational intervals within equal divisions of the octave.

Without a system of intervals in mind, and specific musical standards, approximation cutoffs are indeed arbitrary. If our desired pure fifth is "beatless for all practical purposes", 7 cents is an absurd cutoff. With a fifth defined as "beatless", that's not even the same interval. Whereas if our fifth is defined as "moveable Sol", we can be even more generous in error tolerance, no problem (QED, just look at how out of tune diatonic melodies can be and still be completely recognizable and even aesthetically pleasing).

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Thu, Mar 31, 2011 at 11:58 PM, Jake Freivald <jdfreivald@...> wrote:
> >
> > John,
> >
> > Someone (Mike? Michael?) recently talked about people tolerating sharp
> > tones better than flat ones. Being the empirical sort of guy that you
> > are, you might consider looking into that: +7.2 cents might be
> > tolerable, but -7.2 might not.
>
> I don't ever remember saying anything like that. I'm also really tired
> of these arbitrary +7 -7 whatever cent cutoffs.
>
> 12-tet's 300 cent minor third is 16 cents flat, but is very tolerable.
> 12-tet's 400 cent major third is 14 cents sharp, but is also
> tolerable.
>
> Furthermore, mistuning tolerance is clearly subject to some sort of
> individual variation - you have people like Igs who don't mind
> father-tempered fifths that are in the 730 cents range, and then you
> have folks like Gene on the other extreme who don't like 17-tet for
> the 13-limit.
>
> > Also, when you're putting chords together, have you considered the
> > overall tolerances of the various intervals? In other words, if your
> > major third is 380 cents and your fifth is 708 cents, each is within the
> > tolerance, but the minor third between the 3 and the 5 is 708-380 = 328
> > cents, a full 13 cents sharp. Throw in a seventh or ninth and things get
> > more complicated.
>
> Paul Erlich would have you flogged for doing anything less.
>
> -Mike
>

🔗Michael <djtrancendance@...>

>"Huh? It depends on *which* tritone you are talking about. Some folks
prefer the 1\2 octave that is available in *any* even-numbered
EDO....it's actually in some respects (geometrically) a simple interval.
Sqrt(2)!"

Right, the problem is, so far as rational numbered fractions go, it is complex.
So I still can see why in the 18th century they called it a Devil's Interval of sorts. To me, it and the semitone are perhaps the two most obvious reasons certain chords in common practice music sound sour. Of course there are "stable sounding" chords with such intervals...but what virtually all "bad" chords (the ones you hear as bad from someone who, say, has never played piano before) involve the semitone and/or sqrt(2) tri-tone.

>"31 is great, but then again, the EDOs with moderate or even high errors
compared to classic JI are still colorful in their own right.
Usefulness, artistic merit and expressivity of a temperament have zilch
to do with whether it measures up to JI, right?"

I'd say, both yes and no.
The merit, I've found, of things like 14EDO is that intervals are far enough off they can be coaxed into functioning as intervals above and below themselves more easily IE a sqrt(2) semitone can often be a 7/5 or a 10/7. The other merit, is since most intervals are often "equally weak", there's a sense of softness in consistency which leads to a different kind of relaxation. And this actually seems to lead to a scale's being "un/non-just" across virtually all dyads as being an advantage...the problem is when a few intervals are very Just and the rest are terribly off just.

A flip side is...at least to me, gearing up my mind to listen to intervals "flip function" in things like 14EDO...is not for the faint of ear...many listeners simply can't follow it. Personally, I can listen to odd EDO temperaments with some effort in a sitting...but if I listened to them while driving, I would probably lose some concentration and crash my car.
The other thing is that things like large chords, even with the flipping, seem a lot more accessible in composition in something like 31EDO than 14 and it seems a lot easier to keep the chords sounding balanced (IE not too much consonance or dissonance on the average).

🔗Michael <djtrancendance@...>

Jake> > Someone (Mike? Michael?) recently talked about people tolerating sharp

> > tones better than flat ones. Being the empirical sort of guy that you

> > are, you might consider looking into that: +7.2 cents might be

> > tolerable, but -7.2 might not.

> I don't ever remember saying anything like that. I'm also really tired

> of these arbitrary +7 -7 whatever cent cutoffs.

Alas, I mentioned I am pretty sure tolerance is asymmetrical. And to complicate matters, some ratios have a very small tolerance (IE 9/5, where even more than a few cents above makes it sound like a sour 20/11) and the fifth appears to have a very large tolerance above itself (IE 50/33 actually sounds quite strong to me as an alternative to the pure fifth..and it's about 15 or so cents off!) Just don't try that trick by making something 15 cents or so under 3/2...it will sting!

I still like the 7 cent limit (though by 7 I mean anything under 8 cents) as a general guide...simply because if you are over 7, no matter how flexible the interval is, in most cases you are in trouble. Meanwhile if you are under 7, if you aren't good you are at least within a couple of cents of good. But sometimes you'll need more like 5 cents error and, in other extreme cases, 13 or even 15 cents off can still work.

🔗john777music <jfos777@...>

--- In tuning@yahoogroups.com, Jake Freivald <jdfreivald@...> wrote:
>
> John,
>
> Someone (Mike? Michael?) recently talked about people tolerating sharp
> tones better than flat ones. Being the empirical sort of guy that you
> are, you might consider looking into that: +7.2 cents might be
> tolerable, but -7.2 might not.

If you are tempering the higher note in a just interval, in most timbres, the interval will sound slightly better when the higher note is sharpened slightly instead of flattening it slightly. This idea is called 'stretch tuning'. See chapter 14 of my book.

>
> Also, when you're putting chords together, have you considered the
> overall tolerances of the various intervals? In other words, if your
> major third is 380 cents and your fifth is 708 cents, each is within the
> tolerance, but the minor third between the 3 and the 5 is 708-380 = 328
> cents, a full 13 cents sharp. Throw in a seventh or ninth and things get
> more complicated.

When it comes to creating chords I'm pretty strict. Every dyad in the chord must be within 6.776 cents (256/255) of a "good" interval. Over a one octave range my good intervals are...

1/1, 9/8, 8/7, 7/6, 6/5, 5/4, 9/7, 4/3, 11/8, 7/5, 10/7, 3/2, 11/7, 8/5, 5/3, 12/7, 7/4, 9/5, 11/6, 13/7 and 2/1.

See page 49 of my book which lists wider intervals that I consider good.

John.
>
> Regards,
> Jake
>
>
> > In 22EDO the Perfect Fourths and Fifths are only 7.136 cents out of tune which is as near as dammit to my limit of 6.776 cents. This means another bonus, the Fourths and Fifths in 22EDO should be tolerable. In light of this I'll work out the good tetrads and triads (and maybe 5 or higher note chords) that occur in 22EDO within an accuracy of 7.2 cents.
> >
> > John.
>

🔗Carl Lumma <carl@...>

🔗john777music <jfos777@...>

🔗Chris Vaisvil <chrisvaisvil@...>

🔗Michael <djtrancendance@...>

Carl>"Please stop advertising your book here"

Sounds like a double standard to me you are posing against John. Carl, you regularly tell people "you really should look at X book" or "you really should look at X paper", where often the books/papers are sold...and now you're saying "don't look at John's book, he's trying to sell it".

It seems to me like, plain and simple, you don't like John's book, and you are making up reasons why it's different/worse that aren't really there.
As Chris said " I honestly don't understand the problem here...especially when it seems John has passed out so many copies for free he can't possibly be making any money to speak of from it."

Shouldn't we be either
A) Helping publicize each others publications
OR
B) If you don't think a publication is worth publicizing, explain in detail WHY so the author can get a fair chance to improve his/her work.
?

--- On Fri, 4/1/11, Chris Vaisvil <chrisvaisvil@...> wrote:

From: Chris Vaisvil <chrisvaisvil@...m>
Subject: Re: [tuning] Re: On the Hindoo division of the octave
To: tuning@yahoogroups.com
Date: Friday, April 1, 2011, 5:13 PM

Just a thought - isn't this a *good* place to talk about a microtonal theory book?

I honestly don't understand the problem here....
especially when it seems John has passed out so many copies for free he can't possibly be making any money to speak of from it.

Chris

On Fri, Apr 1, 2011 at 7:01 PM, Carl Lumma <carl@...> wrote:

--- In tuning@yahoogroups.com, "john777music" <jfos777@...> wrote:

> See chapter 14 of my book.

Please stop advertising your book here.

-Carl

🔗Mike Battaglia <battaglia01@...>

🔗Carl Lumma <carl@...>

🔗Michael <djtrancendance@...>

MikeB>"Have you been reading the list at all? John has gotten numerous reviews on his book, and they are almost unanimously poor. What else do you want?"

Where are such unanimously poor reviews from? I recall reading Chris Vaisvil and Neil Haverstick liked the book. And yes, I've also heard a good few people don't like it. Thing I have noticed is, the people who don't like it often go on and on and on complaining...and the people who do like it praise it a few times and then let of it.

I figure either we have a problem which John is dealing out information in non-debatable form and/or people are trying to censor John out so he can't debate in the first place. If we have the second problem, we can't exactly blame John for the first...

>"The 256/255 cutoff for mistuning "because powers of two are probably involved"

makes less sense than that every interval has a Gaussian-weighted error function and that simpler intervals have greater fields of attraction than more complex ones."

I agree it's a dumb reason...but agree with John the end result/limit is a fair one. Gene, I recall, also has said in the past that about 7 cents is a good general cut-off point...and Monzo's online guide uses 7 cents in his definition of "pseudo-JI" as a fairly accurate rounding/error limit. Are we really that concerned with the math that we will take it over our own ears plus a fair deal of other people's?!

>the "these intervals are good because I consider them good" argument makes less sense than "there is a varying spectrum of consonance and dissonance with simpler intervals

tending to be more consonant."

You seem to be indirectly saying that "my ears consistently like these intervals (most of which are simpler, but with a few exceptions to my ears)" is somehow mark-ably worse than saying "simpler intervals tend to be more consonant". In many ways, both statements say the same thing...I'd even vouch to say the 'with a few exceptions' version is more specific.

And if we did blindly accept the "simpler intervals tend" statement...we would basically, as I see it, limit us to "Tenney height or bust" and push us to stop asking good questions about exceptions to Tenney Height as if exceptions must be "personal hearing quirks".

>"And the idea that 23-EDO is the best equal temperament under 30 is absolutely insane."

Best temperament for...what exactly? Your take on things seems every bit as personally biased as John's supposed take on them. I don't think any temperament is a best temperament for anything that's not very very personally biased. Personally I like 31EDO, but that's because I like just dyads and can tolerate higher-limit chords so long as they are composed of low-limit dyads (and I realize many people can't tolerate them).

As for 23...it has some good estimates of 11/6, 11/7, 10/7, 12/7, 13/9, 7/6, 16/9, 12/11, 9/8, and 13/8 plus a good low-limit 6/5 and 5/3.
It seems like a strong "higher limit all-stars" tuning...for some of the lower-numbered ranges of higher limit intervals. So if 6:7:11:12 or 6:7:10:12 or 9:13:16 or 8:9:13 are tolerable chords to someone of they like the above dyads...I can see why they'd enjoy the tuning. But far as the range of chords it has, for example, I don't see why/how it's anything particularly special.

🔗Mike Battaglia <battaglia01@...>

On Sat, Apr 2, 2011 at 12:48 AM, Michael <djtrancendance@...> wrote:
>
> MikeB>"Have you been reading the list at all? John has gotten numerous reviews on his book, and they are almost unanimously poor. What else do you want?"
>
> Where are such unanimously poor reviews from? I recall reading Chris Vaisvil and Neil Haverstick liked the book. And yes, I've also heard a good few people don't like it. Thing I have noticed is, the people who don't like it often go on and on and on complaining...and the people who do like it praise it a few times and then let of it.

I didn't like it, Carl didn't like it, Igs didn't like it. If we go on
and on and on complaining, that's only because the author of the book
has gone on and on and on reiterating the same defunct points without
addressing them.

> I figure either we have a problem which John is dealing out information in non-debatable form and/or people are trying to censor John out so he can't debate in the first place. If we have the second problem, we can't exactly blame John for the first...

Oh, right, it's all about censorship. You got it.

> >"The 256/255 cutoff for mistuning "because powers of two are probably involved"
> makes less sense than that every interval has a Gaussian-weighted error function and that simpler intervals have greater fields of attraction than more complex ones."
>
> I agree it's a dumb reason...but agree with John the end result/limit is a fair one. Gene, I recall, also has said in the past that about 7 cents is a good general cut-off point...and Monzo's online guide uses 7 cents in his definition of "pseudo-JI" as a fairly accurate rounding/error limit. Are we really that concerned with the math that we will take it over our own ears plus a fair deal of other people's?!

Who cares what anyone "says?" We are talking about a book called "The
Mathematics of Music." Not "My Personal Musical Preferences."

> >the "these intervals are good because I consider them good" argument makes less sense than "there is a varying spectrum of consonance and dissonance with simpler intervals
> tending to be more consonant."
>
> You seem to be indirectly saying that "my ears consistently like these intervals (most of which are simpler, but with a few exceptions to my ears)" is somehow mark-ably worse than saying "simpler intervals tend to be more consonant". In many ways, both statements say the same thing...I'd even vouch to say the 'with a few exceptions' version is more specific.

The latter is a statement that applies to everyone. The former is a
statement that applies only to John. As you've noticed, 12-EDO fails
John's acid test for 5-limit harmony, and the entire world uses it;
hence his formula doesn't seem to apply to the majority of the world.
How can a formula fail any more than that?

> And if we did blindly accept the "simpler intervals tend" statement...we would basically, as I see it, limit us to "Tenney height or bust" and push us to stop asking good questions about exceptions to Tenney Height as if exceptions must be "personal hearing quirks".

You don't have to blindly accept anything. Go do the tests yourself
and critique it and try and contribute something to the field.

> >"And the idea that 23-EDO is the best equal temperament under 30 is absolutely insane."
>
> Best temperament for...what exactly? Your take on things seems every bit as personally biased as John's supposed take on them. I don't think any temperament is a best temperament for anything that's not very very personally biased. Personally I like 31EDO, but that's because I like just dyads and can tolerate higher-limit chords so long as they are composed of low-limit dyads (and I realize many people can't tolerate them).

If you hate the concept of "best temperament," then you should be
rioting in the streets over the concept of there being "good
intervals."

-Mike

🔗Chris Vaisvil <chrisvaisvil@...>

Mike and Carl,

Mike wrote a number of points here, and I choose one to tie back to the
issue for continuity.

From my vantage the problem isn't self-promotion, the problem is a number of
people disagree with John's work. Certainly asking for some substance to
back an idea floated in the list is good and necessary as Mike B pointed
out. Even I, who gave a generally positive review, noted the title of the
book seemed to be a misnomer.

However, I personally don't like the feeling I get that was have yet another
person heading down the road towards being banned or chased away for having
differing ideas, however wrong they may be from other points of view.

As for the self promotion idea - anyone who has a point of view is
self-promoting that point of view, such as how I am with this email right
now. There is a difference between having a point of view and talking and
working from that point of view and SPAM which I'd define as advertisements.
And even some of that we tolerate under special circumstances - such as an
announcement for a new CD someone is *selling*.

Chris

On Sat, Apr 2, 2011 at 12:55 AM, Mike Battaglia <battaglia01@...>wrote:

>
>
>
>
> I didn't like it, Carl didn't like it, Igs didn't like it. If we go on
> and on and on complaining, that's only because the author of the book
> has gone on and on and on reiterating the same defunct points without
> addressing them.
>
>
>

🔗cityoftheasleep <igliashon@...>

I'm with Chris on this one. I don't think John's out of line at all. Especially considering that he seems game to give the book away to anyone here who wants it, despite the fact that he is losing money to do that. He also seems more than willing to listen to criticisms and suggestions and try out other approaches. I've never once seen him stray off topic or descend into flame territory. So what if he refers to his own book a lot? He probably just doesn't want to repeat what he's already written before.

-Igs

--- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> Mike and Carl,
>
> Mike wrote a number of points here, and I choose one to tie back to the
> issue for continuity.
>
> From my vantage the problem isn't self-promotion, the problem is a number of
> people disagree with John's work. Certainly asking for some substance to
> back an idea floated in the list is good and necessary as Mike B pointed
> out. Even I, who gave a generally positive review, noted the title of the
> book seemed to be a misnomer.
>
> However, I personally don't like the feeling I get that was have yet another
> person heading down the road towards being banned or chased away for having
> differing ideas, however wrong they may be from other points of view.
>
> As for the self promotion idea - anyone who has a point of view is
> self-promoting that point of view, such as how I am with this email right
> now. There is a difference between having a point of view and talking and
> working from that point of view and SPAM which I'd define as advertisements.
> And even some of that we tolerate under special circumstances - such as an
> announcement for a new CD someone is *selling*.
>
> Chris
>
> On Sat, Apr 2, 2011 at 12:55 AM, Mike Battaglia <battaglia01@...>wrote:
>
> >
> >
> >
> >
> > I didn't like it, Carl didn't like it, Igs didn't like it. If we go on
> > and on and on complaining, that's only because the author of the book
> > has gone on and on and on reiterating the same defunct points without
> > addressing them.
> >
> >
> >
>

🔗john777music <jfos777@...>

Carl and Mike, you have obviously made up your minds about me and I doubt that there is anything I could say or argue now that will change that. One or two points I'd like to make...

It took me 14 years hard work to arrive at my formula for harmony in sine wave intervals. Then I used the formula in a sophisticated program to quantify the concordance of intervals with complex tones and 'regular' timbres. I don't think my approach was anything less than 'scientific'.

Why is it insane? I have posted a list of all the good dyads that occur in each EDO from 4 to 49. Just considering EDOs less than 30, 29EDO has 7 good dyads, 27EDO has 8, 23EDO has 7, 22EDO has 6 and 19EDO has only 3. The winner is 27EDO with 8 good dyads. In joint second place are 29EDO and 23EDO with 7 good dyads each. Seems like a reasonable proposition that 23EDO should be good. BTW I said that 23EDO was the best EDO less than 25, not 30.

I think I read somewhere in the last flurry of posts that Carl and Mike didn't like my book. Have ye actually read the book? When I joined the list in January 2010 I uploaded a PDF version of my book to the Files section. Is this the version of the book that ye read? If so then you would be right in knocking it because it contained many errors. These have been corrected in the published paperback version.

As regards the reviews I was very happy with all of them. There were a lot of criticisms but there was some praise in there as well.

John.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Sat, Apr 2, 2011 at 12:48 AM, Michael <djtrancendance@...> wrote:
> >
> > MikeB>"Have you been reading the list at all? John has gotten numerous reviews on his book, and they are almost unanimously poor. What else do you want?"
> >
> >    Where are such unanimously poor reviews from? I recall reading Chris Vaisvil and Neil Haverstick liked the book. And yes, I've also heard a good few people don't like it. Thing I have noticed is, the people who don't like it often go on and on and on complaining...and the people who do like it praise it a few times and then let of it.
>
> I didn't like it, Carl didn't like it, Igs didn't like it. If we go on
> and on and on complaining, that's only because the author of the book
> has gone on and on and on reiterating the same defunct points without
> addressing them.
>
> > I figure either we have a problem which John is dealing out information in non-debatable form and/or people are trying to censor John out so he can't debate in the first place. If we have the second problem, we can't exactly blame John for the first...
>
> Oh, right, it's all about censorship. You got it.
>
> > >"The 256/255 cutoff for mistuning "because powers of two are probably involved"
> > makes less sense than that every interval has a Gaussian-weighted error function and that simpler intervals have greater fields of attraction than more complex ones."
> >
> > I agree it's a dumb reason...but agree with John the end result/limit is a fair one. Gene, I recall, also has said in the past that about 7 cents is a good general cut-off point...and Monzo's online guide uses 7 cents in his definition of "pseudo-JI" as a fairly accurate rounding/error limit. Are we really that concerned with the math that we will take it over our own ears plus a fair deal of other people's?!
>
> Who cares what anyone "says?" We are talking about a book called "The
> Mathematics of Music." Not "My Personal Musical Preferences."
>
> > >the "these intervals are good because I consider them good" argument makes less sense than "there is a varying spectrum of consonance and dissonance with simpler intervals
> > tending to be more consonant."
> >
> >    You seem to be indirectly saying that "my ears consistently like these intervals (most of which are simpler, but with a few exceptions to my ears)" is somehow mark-ably worse than saying "simpler intervals tend to be more consonant".   In many ways, both statements say the same thing...I'd even vouch to say the 'with a few exceptions' version is more specific.
>
> The latter is a statement that applies to everyone. The former is a
> statement that applies only to John. As you've noticed, 12-EDO fails
> John's acid test for 5-limit harmony, and the entire world uses it;
> hence his formula doesn't seem to apply to the majority of the world.
> How can a formula fail any more than that?
>
> > And if we did blindly accept the "simpler intervals tend" statement...we would basically, as I see it, limit us to "Tenney height or bust" and push us to stop asking good questions about exceptions to Tenney Height as if exceptions must be "personal hearing quirks".
>
> You don't have to blindly accept anything. Go do the tests yourself
> and critique it and try and contribute something to the field.
>
> > >"And the idea that 23-EDO is the best equal temperament under 30 is absolutely insane."
> >
> >    Best temperament for...what exactly? Your take on things seems every bit as personally biased as John's supposed take on them. I don't think any temperament is a best temperament for anything that's not very very personally biased. Personally I like 31EDO, but that's because I like just dyads and can tolerate higher-limit chords so long as they are composed of low-limit dyads (and I realize many people can't tolerate them).
>
> If you hate the concept of "best temperament," then you should be
> rioting in the streets over the concept of there being "good
> intervals."
>
> -Mike
>

🔗Carl Lumma <carl@...>

🔗Michael <djtrancendance@...>

Me> "I figure either we have a problem which John is dealing out
information in non-debatable form and/or people are trying to censor
John out so he can't debate in the first place. If we have the second
problem, we can't exactly blame John for the first..."

MikeB>"Oh, right, it's all about censorship. You got it."

Well put it this way. If you don't like what John says, why not simply ignore him? Surely if he has no followers, no one will take him up on his offers for explanations...and there thus wouldn't be a need to tell people to not listen to John.

>"Who cares what anyone "says?" We are talking about a book called "The Mathematics of Music." Not "My Personal Musical Preferences.""

And Harmonic Entropy is "The Mathematics of Music"?! Nothing is; it's a lousy book title, but John isn't bringing up the title or saying he has the "real/only" answer. You and others are the one making assumption his badly-chosen title has that meaning.

>"The latter is a statement that applies to everyone. The former is a statement that applies only to John. As you've noticed, 12-EDO fails John's acid test for 5-limit harmony, and the entire world uses it; hence his formula doesn't seem to apply to the majority of the world.

How can a formula fail any more than that?"

12TET has a 16/9, a 27/16, a tritone between 7/5 and 10/7, a major 7th just as near 19/10 as 15/8...it really isn't very 5-limit at all in the first place! Guess what...I'm quite sure 12TET fails any Harmonic Entropy or Tenney Height or even Odd-limit test for being 5-limit. So sure you can say John's theory "misses the mark" for gauging 12TET...but so do virtually all the others.
My question is...what WOULD possibly explain such things? Hence my discussions on error being possibly more acceptable for certain intervals than others other REGARDLESS of higher vs. lower Tenney Height and error generally being more tolerable over/sharp-of rather than being flat of intervals. Let's focus on answering the questions...and if someone's theory is truly weak, if will fall out within the questioning process...

>"You don't have to blindly accept anything. Go do the tests yourself and critique it and try and contribute something to the field."

You said yourself no one's theory should be censored out UNLESS someone can disprove it with actual examples and then said person should suggest an alternative. But now you are being a complete hypocrit....

So ok...what are my theories then? What about all the code I sent you and Gene concerning JI as contributions to the field that Igs and you both said were quite cool before?
Hmm...it seems just because you said I was contributing to the field THEN doesn't seem to mean you can't go back and say "oh yeah, I was just kidding, you contributed NOTHING" later.
Why not start a new thread in which I explain my theory and you try your best to poke holes in it? I'm game....

>"If you hate the concept of "best temperament," then you should be rioting in the streets over the concept of there being "good intervals.""

There are good intervals....for different causes. An interval that's consistently good for one cause may be consistently bad for another. One example: 12/11 is better than 15/14 with regards to critical band dissonance (as we have agreed before)...but an 22:24:27 chord is less tonal than an 14:15:17 chord. So which is the better interval? It depends which type of consonance (or lack of...if that's what the listener wants) you are going for. Which sends us back to the whole "Sethares vs. Harmonic Entropy theory camps" discussion we all had before... Which, yes, much comes down to the opinion of the listener: saying Sethares is valid does not mean saying HE must be "an arbitrary personal preference" or vice-versa.

Guess what?, music IS a whole lot about personal preferences. The only difference, I swear, is some preferences show up a lot more than others...and some show up so little they might as well be considered arbitrary whims. Now if you want to say John's ideas or mine are arbitrary whims...prepare to back them up with counter-examples...and prepare to allow others to make positive comments on the theories uncensored (if the theories are so bad....the only people making positive comments will be the authors of the theories and the theories will fail as a self-fulfilling prophecy).

🔗cityoftheasleep <igliashon@...>

🔗Chris Vaisvil <chrisvaisvil@...>

Dear Carl and Mike B.

The emails about John O'Sullivan from both of you is making what Michael S.
has been saying about the list seem correct. Is that what either of you
want?

I will agree with Mike B. that just page references leaves the people
without John's book in the dark though I can't possibly see this as vigorous
self-promotion. And I don't think I can agree with anything else written on
the subject by both of you.

I will let you guys in on a secret. The title of my first piece in one of
John's tunings was called Excluded by Peers because this is how I saw John
treated on this list.
His public rejection made certain that I was going to try that much harder
to give the man a fair shake. I will even admit I thought his calculator was
a bit off kilter, until I read his book.
I now understand why he created the calculator. I don't agree with all of
his book, point of view, or think his tuning is the solution to western
music's tuning quest.

But I do respect the huge amount of work he put into it.

His work can't really be considered scientific in the sense that he produced
unbiased results - by the nature of the method his results are biased to his
hearing and personality - and I said so in my review. However, this is no
crime. This is no reason to be negative to him. I think he deserves our
respect as a hard working colleague - even if you disagree with his methods
or conclusions. And Heaven knows we need as many people on this list willing
to discuss music and tuning instead of personality defects or petty dislikes
or displays delusional flights of ego as we can muster.

The more I learn about the history of the alternate tunings list the more I
morn for what the list used to be. If we ever will have vitality like that
again it will take a healthy dose of tolerance and respect for reasonable
people to have reasonable disagreements so there is an atmosphere of being
able to discuss new ideas. There are a lot of people in this world - and
just as many points of view. I don't see John hurting anyone, disrupting
anything, so I don't see why this is even an issue.

Sincerely,

Chris

On Sat, Apr 2, 2011 at 12:34 PM, Carl Lumma <carl@...> wrote:

>
>
> --- In tuning@yahoogroups.com, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> > From my vantage the problem isn't self-promotion, the problem
> > is a number of people disagree with John's work.
>
> Chris- John is a vigorous self-promoter who ignores feedback
> from the list. -C.
>
>
>

🔗Mike Battaglia <battaglia01@...>

On Sat, Apr 2, 2011 at 11:57 AM, john777music <jfos777@...> wrote:
>
> Carl and Mike, you have obviously made up your minds about me and I doubt that there is anything I could say or argue now that will change that. One or two points I'd like to make...

I have made up my mind about your existing theory, which is that it
could be improved.

> <the "these intervals are good because I consider them good" argument makes less sense than "there is a varying spectrum of consonance and dissonance with simpler intervals tending to be more consonant.">
>
> It took me 14 years hard work to arrive at my formula for harmony in sine wave intervals. Then I used the formula in a sophisticated program to quantify the concordance of intervals with complex tones and 'regular' timbres. I don't think my approach was anything less than 'scientific'.

It's hardly scientific to say that the maximum threshold for mistuning
an interval is 6.775 cents, because that happens to be 256/255, and
"powers of two are important."

> <And the idea that 23-EDO is the best equal temperament under 30 is absolutely insane.>
>
> Why is it insane? I have posted a list of all the good dyads that occur in each EDO from 4 to 49. Just considering EDOs less than 30, 29EDO has 7 good dyads, 27EDO has 8, 23EDO has 7, 22EDO has 6 and 19EDO has only 3. The winner is 27EDO with 8 good dyads. In joint second place are 29EDO and 23EDO with 7 good dyads each. Seems like a reasonable proposition that 23EDO should be good. BTW I said that 23EDO was the best EDO less than 25, not 30.

Because your theory has failed to predict that 19 and 22 are
exceptionally "good" EDOs under 25.

> I think I read somewhere in the last flurry of posts that Carl and Mike didn't like my book. Have ye actually read the book? When I joined the list in January 2010 I uploaded a PDF version of my book to the Files section. Is this the version of the book that ye read? If so then you would be right in knocking it because it contained many errors. These have been corrected in the published paperback version.

I haven't read your book. I am commenting on the theories that you are
posting publicly to this list. If you aren't posting the full theory
here because you want people to buy your book, then don't post it
here.

-Mike

🔗Mike Battaglia <battaglia01@...>

🔗Michael <djtrancendance@...>

MikeB>"Because your theory has failed to predict that 19 and 22 are exceptionally "good" EDOs under 25."

As if that is fact? Personally I think 19EDO is exceptional, but not 22. And if I look online far as popularity, it seems fairly obvious 19EDO has the advantage. And then we get 31TET, which is numerically much more accurate at 5-limit than 12TET.

Then again, is 12TET even remotely 5-limit or competitive in that sense except for the 3/2, 5/4 and 4/3 in it?... A great deal of intervals in 12TET aren't even vaguely near 5-limit ones (16/9 and 9/8? 7/5? 10/7? 27/16?...)

The amazing thing in all this so-called science...is just how much contradiction is in so-called expert studies.

In order to disprove John's theory...I swear, the only way to do it is to get a large group of people to sample intervals and intervals different errors away from them. It's a Plomp and Llevelt type of theory requiring a similar sort of test....and, for the record, I find it hard to believe the way P&L tested is anything less than scientific.

🔗Mike Battaglia <battaglia01@...>

On Sun, Apr 3, 2011 at 10:28 PM, Michael <djtrancendance@...> wrote:
>
> MikeB>"Because your theory has failed to predict that 19 and 22 are exceptionally "good" EDOs under 25."
>
> As if that is fact? Personally I think 19EDO is exceptional, but not 22. And if I look online far as popularity, it seems fairly obvious 19EDO has the advantage. And then we get 31TET, which is numerically much more accurate at 5-limit than 12TET.

Whether you "like it," or whether it's "popular," is besides the
point, which is that numerically speaking, they have exceptionally low
error compared to the ETs around them.

> Then again, is 12TET even remotely 5-limit or competitive in that sense except for the 3/2, 5/4 and 4/3 in it?... A great deal of intervals in 12TET aren't even vaguely near 5-limit ones (16/9 and 9/8? 7/5? 10/7? 27/16?...)

12TET can handle the 5-limit, yes.

> The amazing thing in all this so-called science...is just how much contradiction is in so-called expert studies.

Like what?

> In order to disprove John's theory...I swear, the only way to do it is to get a large group of people to sample intervals and intervals different errors away from them. It's a Plomp and Llevelt type of theory requiring a similar sort of test....and, for the record, I find it hard to believe the way P&L tested is anything less than scientific.

I don't see people disliking major triads in 12-TET, but they aren't
"good" in John's theory.

-Mike

🔗Michael <djtrancendance@...>

MikeB>"I have tried to suggest ways to tie his research into what has already been done, but I haven't gotten much of a positive response."

Yet, some theories can't be tied into "what has already been done". I respect John's work...but I will admit it's not tied to anything I've heard of far as prominent theories in psychoacoustics.
And maybe that's how it's best meant to be... For example, what Plomp and Llevelt did was no more than a listening test trying to find a consistent pattern of "personal preferences"...only for some bizarre reason it gets the benefit of the doubt as being "scientific". If they can get a chance to do that...shouldn't John as well?

To put it shortly...I think John deserves the opportunity to have his theory tested on a fairly large population (say, at least 25 people or so, and of the general population rather than the "pre-opinionated toward certain interval experts" on this list)...and only if it fails under such a situation denounced as "nothing more than a personal opinion".

Sadly...what's been going on (especially in Mike and Carl's corner) seems to hint that either something references past experiments or is popular with them or an leading expert (think Paul Erlich)... or it must somehow be a "personal opinion, built out of ego rather than honest thirst for progress". With that type of attitude...no wonder so many things are going nowhere.

BTW, does anyone actually HAVE any ideas how to rate intervals that go beyond Tenney Height of around 70 without using a sound sample test among a general population? And if not...why complain/ what's the point of doing something that does not lead to positive/productive new alternatives?

🔗Michael <djtrancendance@...>

MikeB>"Whether you "like it," or whether it's "popular," is besides the point, which is that numerically speaking, they have exceptionally low error compared to the ETs around them."

You seem to be taking two contradicting opinions here: one being that what people like John and I say must be just "personal opinion" (implying not valid among a larger public, just among oneself)...and on the other hand saying if something is not personal opinion and is valid among a larger public...that STILL doesn't count.

Then you say something about low-error being the point. This seems to say numerology is more important than how people, on the average, actually think something sounds...which I believe is a terrible mis-prioritization.

Me>"The amazing thing in all this so-called science...is just how much contradiction is in so-called expert studies."

MikeB>"Like what?"

Like the idea of 12TET as a 5-limit tuning when such a huge chunk of it is not 5-limit. The side point, again, is that people are constantly (EVEN IN 12TET!) made to deal with intervals above Tenney Height of 70 (again; 16/9, 27/16, 7/5, near 19/10....) and, for crying out loud, why won't people try to come up with a solution for analyzing such intervals instead of saying something along the lines of either "use Tenney Height for them" or "they just don't occur normally" (which is an obvious lie).

>"I don't see people disliking major triads in 12-TET, but they aren't "good" in John's theory."
Agreed, there is a common pattern in people favoring major triads (IE it's not 'just a personal opinion').
But where in John's theory are major triads disfavored? The only thing I can think of...is that the dyads on a 12TET triad are more than a 255/254-ish error off pure.

Then again...John's theory, as I understand it, covers dyads NOT triads. Now if you took a set of any three dyads rated as good by John's theory and made a chord of them...would the chord be rated "good" by most people? I figure it would be a good test to try out and actually for once, gasp, get some results that have nothing to do with ego-contests.

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:
>
> MikeB>"Because your theory has failed to predict that 19 and 22 are exceptionally "good" EDOs under 25."
>
> As if that is fact?

It's a fact that 19 and 22 are the lowest-error 5-limit systems until you hit 31. If you take the sum of the absolute values of the errors for 3, 5, and 5/3, for instance, from 12 to 34, then in order you get 34, 31, 19, 22, 27, 12 (and 24). Other error measurements give similar results. If you don't like stopping at the 5-limit you can go higher.

> Personally I think 19EDO is exceptional, but not 22.

And that's a personal opinion, not a fact.

And if I look online far as popularity, it seems fairly obvious 19EDO has the advantage. And then we get 31TET, which is numerically much more accurate at 5-limit than 12TET.
>
> Then again, is 12TET even remotely 5-limit or competitive in that sense except for the 3/2, 5/4 and 4/3 in it?... A great deal of intervals in 12TET aren't even vaguely near 5-limit ones (16/9 and 9/8? 7/5? 10/7? 27/16?...)

Amd your complaint with 9/8, 16/9, and 27/16 is...?

> The amazing thing in all this so-called science...is just how much contradiction is in so-called expert studies.

The amazing thing about ignoring so-called science is that you end up complaining about how 12et does a bad job of approximating 9/8 when that isn't even true.

> In order to disprove John's theory...I swear, the only way to do it is to get a large group of people to sample intervals and intervals different errors away from them.

A great plan. Also, a lot of work.

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

On Sun, Apr 3, 2011 at 10:39 PM, Michael <djtrancendance@...> wrote:
>
> MikeB>"I have tried to suggest ways to tie his research into what has already been done, but I haven't gotten much of a positive response."
>
> Yet, some theories can't be tied into "what has already been done".

Yeah right.

> I respect John's work...but I will admit it's not tied to anything I've heard of far as prominent theories in psychoacoustics.
> And maybe that's how it's best meant to be... For example, what Plomp and Llevelt did was no more than a listening test trying to find a consistent pattern of "personal preferences"...only for some bizarre reason it gets the benefit of the doubt as being "scientific". If they can get a chance to do that...shouldn't John as well?

John hasn't done a listening test to try and find a consistent pattern
of personal preferences. He claims that his formula simply states what
he, personally, as one human being, likes. If he goes and tests his
formula and finds a consistent pattern of personal preferences in the
general population, it certainly would be scientific. Saying "I
guessed that 256/255 was the maximum cutoff and that's what sounds
good to me" is not scientific.

> To put it shortly...I think John deserves the opportunity to have his theory tested on a fairly large population (say, at least 25 people or so, and of the general population rather than the "pre-opinionated toward certain interval experts" on this list)...and only if it fails under such a situation denounced as "nothing more than a personal opinion".

He is obviously free to go test his theory on whomever he wishes. Why
would you need me to approve of that beforehand? That makes no sense.

> Sadly...what's been going on (especially in Mike and Carl's corner) seems to hint that either something references past experiments or is popular with them or an leading expert (think Paul Erlich)... or it must somehow be a "personal opinion, built out of ego rather than honest thirst for progress". With that type of attitude...no wonder so many things are going nowhere.

I like things that make sense. I don't think his formula makes sense.
You can keep twisting the situation into some Marxist tuning list
class struggle with fascist undertones as much as you want, but that's
about all there is to it.

> BTW, does anyone actually HAVE any ideas how to rate intervals that go beyond Tenney Height of around 70 without using a sound sample test among a general population? And if not...why complain/ what's the point of doing something that does not lead to positive/productive new alternatives?

Use a model like HE or devise your own.

-Mike

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

On Sun, Apr 3, 2011 at 10:57 PM, Michael <djtrancendance@...> wrote:
>
> MikeB>"Whether you "like it," or whether it's "popular," is besides the point, which is that numerically speaking, they have exceptionally low error compared to the ETs around them."
>
> You seem to be taking two contradicting opinions here: one being that what people like John and I say must be just "personal opinion" (implying not valid among a larger public, just among oneself)...and on the other hand saying if something is not personal opinion and is valid among a larger public...that STILL doesn't count.

We're now dealing with math, so nobody's opinion counts for anything.
19-TET and 22-TET have really low error in the 5-limit and remain
unchallenged until you get to 31 equal.

You are free to come up with better and better models to judge why you
might not like 22 over 19 or 19 over 22. John's model is to say that
if an interval "no longer counts" as a mistuning of a simpler interval
unless it's within 256/255 of it. I disagree, because 12-TET's major
third is out of that range, but people still use it and like it
anyway. I still haven't heard any refutation of this.

> Then you say something about low-error being the point. This seems to say numerology is more important than how people, on the average, actually think something sounds...which I believe is a terrible mis-prioritization.

This is an argument that you shouldn't be making, since 19-TET is
probably the most popular microtonal tuning after 12 and 24. That it
is not a good tuning in John's system is more totalitarian than
anything I've said so far. I also now remind you that I am being very
polite, and that you are not.

> Me>"The amazing thing in all this so-called science...is just how much contradiction is in so-called expert studies."
> MikeB>"Like what?"
>
> Like the idea of 12TET as a 5-limit tuning when such a huge chunk of it is not 5-limit.

Oh really?

The side point, again, is that people are constantly (EVEN IN 12TET!)
made to deal with intervals above Tenney Height of 70 (again; 16/9,
27/16, 7/5, near 19/10....) and, for crying out loud, why won't people
try to come up with a solution for analyzing such intervals instead of
saying something along the lines of either "use Tenney Height for
them" or "they just don't occur normally" (which is an obvious lie).

What exactly about those intervals do you want to analyze?

> >"I don't see people disliking major triads in 12-TET, but they aren't "good" in John's theory."
> Agreed, there is a common pattern in people favoring major triads (IE it's not 'just a personal opinion').
> But where in John's theory are major triads disfavored? The only thing I can think of...is that the dyads on a 12TET triad are more than a 255/254-ish error off pure.

The 12-TET major triads is disfavored because it isn't "good."

> Then again...John's theory, as I understand it, covers dyads NOT triads. Now if you took a set of any three dyads rated as good by John's theory and made a chord of them...would the chord be rated "good" by most people? I figure it would be a good test to try out and actually for once, gasp, get some results that have nothing to do with ego-contests.

I'm not sure what ego-contests have to do with anything here.

-Mike

🔗Mike Battaglia <battaglia01@...>

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:

John's theory works out much differently for triads. At least, if I made no mistake there aren't any John-good triads, but loads of dyads. Here's what I get for number of John-good triads from 1 to 34:

1: 0
2: 0
3: 0
4: 0
5: 0
6: 0
7: 2
8: 2
9: 3
10: 0
11: 2
12: 3
13: 1
14: 4
15: 4
16: 4
17: 15
18: 8
19: 5
20: 2
21: 8
22: 13
23: 0
24: 17
25: 5
26: 10
27: 17
28: 6
29: 31
30: 7
31: 46
32: 18
33: 14
34: 51

The three John-good 12edo triads, in case you were wondering, are 1-4/3-3/2, 1-4/3-17/9 and 1-17/12-17/9. This may not be strictly John-approved, since I tossed in the octave inversions of each of the "good" intervals, giving me 56 in total. So for instance 17/9 is "good", but 18/17 actually isn't. And I ignored whether 18/17 is too close to 1 also. But at least 1-4/3-3/2 is a clear John-good triad.

First edo to have a "good" 5-limit triad? 31. But you knew that, right?

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

On Mon, Apr 4, 2011 at 1:05 AM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> > John's theory works out much differently for triads. At least, if I made no mistake there aren't any John-good triads, but loads of dyads.
>
> In 23edo.

He claims that there are a few John-good triads in 23-EDO. See here:

/tuning/topicId_97458.html#97458

I guess that 23-EDO can make for a pretty good no-3 subgroup
temperament, especially if you ignore 7/4 and 11/8 but look at other
intervals involving primes 7 and 11.

I'm not sure that John did his own approach right, however, as one of
the triads listed is 1-16-21, which seems to approximate 7:11:13 in
23-EDO. However, I don't think he supports 13-limit intervals to begin
with.

Actually, I just realized what's going on: 78/77 has foiled things
here. 1-16-21 made the list because John defines a good triad as one
in which all three of the dyads are individually good. So although the
nearest approximation for 1-16-21 is 7:11:13, in this case we have
7-11 is 783 cents, or about 11/7, 11-13 is 261 cents or about 7/6, and
7-13 is 1043 cents or about 11/6. So we have a 1/1-11/7-11/6 triad
that's also pretty close to 7:11:13 because 23-EDO eliminates 78/77.

-Mike

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> He claims that there are a few John-good triads in 23-EDO. See here:

Yeah, it occurred to me that I needed to change my program after I posted that.

> /tuning/topicId_97458.html#97458
>
> I guess that 23-EDO can make for a pretty good no-3 subgroup
> temperament, especially if you ignore 7/4 and 11/8 but look at other
> intervals involving primes 7 and 11.

One reason I was wondering about that result was that I'd already taken the trouble to explain here:

http://xenharmonic.wikispaces.com/23edo

that 23 works just like 46 on the subgroup 2.9.15.21.33.13.17. And you can look at that as a chord; some of it has to pass the John test. How does a 26-30-32-33-34-36-42 chord grab you, though? Seems kind of mashed in.

> I'm not sure that John did his own approach right, however, as one of
> the triads listed is 1-16-21, which seems to approximate 7:11:13 in
> 23-EDO. However, I don't think he supports 13-limit intervals to begin
> with.

Well, he actually does.

🔗Mike Battaglia <battaglia01@...>

🔗genewardsmith <genewardsmith@...>

🔗Mike Battaglia <battaglia01@...>

On Mon, Apr 4, 2011 at 3:37 AM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > > Yeah, it's a bit rough - I prefer 3-30-42-47-51-58-73. That works for me.
>
> A 73-limit man, eh?

Wait, was your original chord in 23-tet or in JI? When you said
26-30-32-33-34-36-42 with dashes instead of colons, I thought you
meant in 23-tet. The chord I gave was also in 23-tet.

> > Maybe for a subgroup like the above it would make more sense to view
> > it as supporting two complementary hexads rather than as supporting
> > one huge and convoluted heptad. Whether this approach will actually
> > work or what those hexads will be I can't say, but it may be worth a
> > shot.
>
> One thing to do with it to start out with is divide the whole thing by 3: 2/3.3.5.7.11.13/3.17/3. From that you can see the 3.5.7.11 chord and the 4/3.13/3.17/3 chord, which makes a lot more sense. So you have, say, an 8-13-17 chord and a 3-5-7-11 chord for starters. The 3-5-7-11 chord is obvious pretty crucial, and if you boot the 5 the 3-7-11 triad is within the O'S bound.
>
> Anyway, these are just otonal chords; the proposed chord system also includes utonal and magic chords.

OK, I see we're using dashes for JI chords now. When you say "magic"
chords, what do you mean? I thought the "magic" moniker referred to a
chord like 12-tet's augmented chord.

-Mike

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> Wait, was your original chord in 23-tet or in JI? When you said
> 26-30-32-33-34-36-42 with dashes instead of colons, I thought you
> meant in 23-tet. The chord I gave was also in 23-tet.

I suppose I need to start using colons, though it's bad notation.
The reason I say "bad" is that 3:2 means 3/2, and 2:3 means 2/3, and people here do accept that, most of the time. Then they use 2:3:5:7 to mean 1-3/2-5/2-7/2, and this supposedly makes sense! Apparently it does to everyone but me, but I stopped being confused by it ten years ago, so... Meanwhile, in the rest of the world, you might say a quadrilateral had sides in a proportion 2:3:5:7, which just gives the relative sizes, so maybe you can look at it like that, and not as a sequence of ascending ratios.

> > One thing to do with it to start out with is divide the whole thing by 3: 2/3.3.5.7.11.13/3.17/3. From that you can see the 3.5.7.11 chord and the 4/3.13/3.17/3 chord, which makes a lot more sense. So you have, say, an 8-13-17 chord and a 3-5-7-11 chord for starters. The 3-5-7-11 chord is obvious pretty crucial, and if you boot the 5 the 3-7-11 triad is within the O'S bound.
> >
> > Anyway, these are just otonal chords; the proposed chord system also includes utonal and magic chords.
>
> OK, I see we're using dashes for JI chords now. When you say "magic"
> chords, what do you mean? I thought the "magic" moniker referred to a
> chord like 12-tet's augmented chord.

Exactly. Why couldn't there be any of those? You've got all of these commas like 91/90 and 154/153 etc etc to play with.

🔗Chris Vaisvil <chrisvaisvil@...>

As far as I understand from what he wrote John did do a large number of
listening tests. And then he used these tests to devise a number of
mathematical models. Then he went back and tested the models for consistency
against his hearing and discarded the model that did not perform well.

Mike, perhaps you should ask John if he'd be willing to give you a copy of
the book? His first offer was "you can have a copy if you write a review" -
not a bad trade.

Chris

On Sun, Apr 3, 2011 at 11:49 PM, Mike Battaglia <battaglia01@...>wrote:

> "personal preferences"...only for some bizarre reason it gets the benefit
> of the doubt as being "scientific". If they can get a chance to do
> that...shouldn't John as well?
>
> John hasn't done a listening test to try and find a consistent pattern
> of personal preferences. He claims that his formula simply states what
> he, personally, as one human being, likes. If he goes and tests his
> formula and finds a consistent pattern of personal preferences in the
> general population, it certainly would be scientific. Saying "I
> guessed that 256/255 was the maximum cutoff and that's what sounds
> good to me" is not scientific.
>
>
>

🔗Mike Battaglia <battaglia01@...>

On Mon, Apr 4, 2011 at 10:25 AM, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> As far as I understand from what he wrote John did do a large number of listening tests. And then he used these tests to devise a number of mathematical models. Then he went back and tested the models for consistency against his hearing and discarded the model that did not perform well.

I believe he said he did the listening tests on only himself. There
are also plenty of listening tests that have been done on this list.
Carl just linked to a huge spreadsheet by Dave Keenan on the matter.
In one case, we saw that there was a conflict between Tenney Height
and John's formula, and the four of us who responded preferred the TH
intervals.

> Mike, perhaps you should ask John if he'd be willing to give you a copy of the book? His first offer was "you can have a copy if you write a review" - not a bad trade.

I don't really have time to go through an entire book right now. But
the point isn't to review his book anyway - I am simply putting my
thoughts out there on what of his formula he has posted to the list.

-Mike

🔗Michael <djtrancendance@...>

> MikeB>"Because your theory has failed to predict that 19 and 22 are exceptionally "good" EDOs under 25."

>
Me> As if that is fact?
Gene>"It's a fact that 19 and 22 are the lowest-error 5-limit systems until you hit 31. "

But does lowest error mean "good"?! That's the part, I'm saying, which is an opinion. Saying "19 and 22EDO are the best tuning systems under 31 so far as approximating 5-limit intervals" would make it fact...but that's not what was say.

>"And your complaint with 9/8, 16/9, and 27/16 is...?"
They are 9 or 27 odd-limit...there's nothing 5-limit about them. Not to mention the 7/5 and 10/7 semitone. ...And yet 12EDO (which contains all of those them) is formally considered a 5-limit tuning (bizarre)...
That seems to imply to say 5/4, 4/3, and 3/2 are the only 5-limit intervals that really matter and everything else doesn't: it gives a very biased weight to certain 5-limit intervals (of which there are not many). I assume this goes back to historical bias for giving major thirds and/or perfect fifths in meantone precedence for accuracy over other intervals.
Now what if someone considers a good accuracy 8/5 or 6/5 important? Actually many people may: for example, many electronica genres purposefully use minor chords more prolifically than major ones. Then the person is likely to consider 12TET not much of a 5-limit tuning.
In fact I'd say it's much more of a 9-limit tuning than a 5-limit one: the only thing 5-limit about it is that no EDO near it contains nearly as many 5-limit intervals.
Far as nailing everything in 5-limit...I'd say 19 is mark-ably better than 12EDO and 31EDO is darn close to perfect for all but the most picky listeners.

Me> In order to disprove John's theory...I swear, the only way to do
it is to get a large group of people to sample intervals and intervals
different errors away from them.

Gene>A great plan. Also, a lot of work.

And as such, I'm not saying the plan "has to be achieved" because, indeed making it happen could be a very long arduous task. On the other hand, as of now, I think it's fair to say John's theory is neither proven nor disproven...and there is nothing wrong with that.

🔗Mike Battaglia <battaglia01@...>

On Mon, Apr 4, 2011 at 10:46 AM, Michael <djtrancendance@...> wrote:
>
> > MikeB>"Because your theory has failed to predict that 19 and 22 are exceptionally "good" EDOs under 25."
> >
> Me> As if that is fact?
> Gene>"It's a fact that 19 and 22 are the lowest-error 5-limit systems until you hit 31. "
>
> But does lowest error mean "good"?! That's the part, I'm saying, which is an opinion. Saying "19 and 22EDO are the best tuning systems under 31 so far as approximating 5-limit intervals" would make it fact...but that's not what was say.

They should be "good" for writing harmonic music. If you're a
serialist, atonal composer, you might not like 19 and 22 as much.

> >"And your complaint with 9/8, 16/9, and 27/16 is...?"
> They are 9 or 27 odd-limit...there's nothing 5-limit about them. Not to mention the 7/5 and 10/7 semitone. ...And yet 12EDO (which contains all of those them) is formally considered a 5-limit tuning (bizarre)...

You are taking odd-limit and sticking it where prime-limit should be.
12-EDO is a decent 5-prime-limit tuning.

> That seems to imply to say 5/4, 4/3, and 3/2 are the only 5-limit intervals that really matter and everything else doesn't: it gives a very biased weight to certain 5-limit intervals (of which there are not many). I assume this goes back to historical bias for giving major thirds and/or perfect fifths in meantone precedence for accuracy over other intervals.
> Now what if someone considers a good accuracy 8/5 or 6/5 important? Actually many people may: for example, many electronica genres purposefully use minor chords more prolifically than major ones. Then the person is likely to consider 12TET not much of a 5-limit tuning.

What...? Where did anyone ever say that 6/5 isn't a 5-limit interval?
How is the accuracy of 5/4 and the accuracy of 8/5 any different in
12-TET? I don't understand where you're coming from at all now.

I recommend responding to this post again with the awareness that the
phrase "12-TET is a decent 5-limit tuning" refers to the prime-limit.

> Me> In order to disprove John's theory...I swear, the only way to do it is to get a large group of people to sample intervals and intervals different errors away from them.
> Gene>A great plan. Also, a lot of work.
>
> And as such, I'm not saying the plan "has to be achieved" because, indeed making it happen could be a very long arduous task. On the other hand, as of now, I think it's fair to say John's theory is neither proven nor disproven...and there is nothing wrong with that.

What do you mean it isn't disproven? His theory predicts that 12-equal
isn't a "good" tuning for 5-limit harmony. Meanwhile, in a listening
test I just did, the results show that most of the human population on
planet earth use 12-TET and really seem to enjoy it. What else do you
want?

Why don't you just admit that the formula could use a bit of polishing?

-Mike

🔗Chris Vaisvil <chrisvaisvil@...>

What is the problem if he did the listening tests only on himself? This has
been noted by *everyone*.

And if you don't have the time to read a very short book (paperback size
around 100 pages) then I don't see how you can argue about how he derived
his formula. If his formula doesn't work for you then it simply doesn't
work.

As I mentioned in an earlier post I would not call his investigation
"scientific" because the nature of the method has built in bias. BUT his
method is totally valid for *his* hearing and the model related to *his*
hearing and unless he was exceptionally different hearing his conclusions
has some percentage of validity for most people. I say this because in even
an earlier post yet I noted that psycho-acoustics is (rationally) based on
probabilistic models and cann never be 100% right or 100% wrong for 100% of
the population. Its probably best to describe the conclusions as trends and
tendencies, and in terms of typical and atypical.

Chris

On Mon, Apr 4, 2011 at 10:34 AM, Mike Battaglia <battaglia01@...>wrote:

>
>
> On Mon, Apr 4, 2011 at 10:25 AM, Chris Vaisvil <chrisvaisvil@gmail.com>
> wrote:
> >
> > As far as I understand from what he wrote John did do a large number of
> listening tests. And then he used these tests to devise a number of
> mathematical models. Then he went back and tested the models for consistency
> against his hearing and discarded the model that did not perform well.
>
> I believe he said he did the listening tests on only himself. There
> are also plenty of listening tests that have been done on this list.
> Carl just linked to a huge spreadsheet by Dave Keenan on the matter.
> In one case, we saw that there was a conflict between Tenney Height
> and John's formula, and the four of us who responded preferred the TH
> intervals.
>
>
> > Mike, perhaps you should ask John if he'd be willing to give you a copy
> of the book? His first offer was "you can have a copy if you write a review"
> - not a bad trade.
>
> I don't really have time to go through an entire book right now. But
> the point isn't to review his book anyway - I am simply putting my
> thoughts out there on what of his formula he has posted to the list.
>
> -Mike
>
>

🔗Michael <djtrancendance@...>

Use a model like HE or devise your own.

Mine, as of now, is a sort of averaged Tenney Height, dividing either the numerator or denominator by the prime of 3 for values where the TH is over 70.

For example...for 15/11.

1) 15 is divisible by 3 five times (making it 5/11).
2) So we take ((TH of 15/11 = 165) + (TH 5/11 = 55)) / 2.0 = 110.
----------------
And for 16/11.....
1) 16 is NOT divisible by 3, so we take Tenney Height normally

2) TH of 16/11 = 176

-----------------------------------
And for 13/9
1) 9 is divisible by 3

2) So we take ((TH of 13/9 = 117) + (TH 13/3 = 39)) / 2.0 = 78.
----------------------------
And for 11/9
1) 9 is divisible by 3
2) TH of 11/9 = 99 and TH of 11/3 = 33...(33 + 99) / 2 = >>>66<<<<. Seems not unreasonably bad considering the major 3rd is TH = 20...and the minor third is TH = 30.
---------------------------

If anything, this form of TH still seems to unfavorable to me for 11-limit...but it sure seems to be a large step forward from standard Tenney Height, which seems to say virtually all of 11-limit and 13-limit is garbage. Using Carl's convention IE sqrt(TH) could improve results further...

Any other ideas how to come up with something that calculates the TH for 11-limit and above well?

🔗Michael <djtrancendance@...>

🔗Mike Battaglia <battaglia01@...>

On Mon, Apr 4, 2011 at 11:01 AM, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> What is the problem if he did the listening tests only on himself? This has been noted by *everyone*.

Chris, I don't understand where you're coming from. I really don't!

My only goal on this list is to continue to research how music works.
As you know, I myself have a number of qualms with the status quo, in
that the existing theory hasn't accomplished its primary aim of making
it easy to write music in other tunings. So, I spent some of my free
time trying to contribute things here about periodicity buzz and
MODMOS's and the like. At one point, I spent weeks trying to come up
with an optimization for Harmonic Entropy, told everyone that I had it
all figured out, and then discovered I screwed up a single line early
on in the derivation of my optimization that caused weeks of work to
be wasted. I still haven't fixed that one.

When I posted stuff, I got critical feedback on it. I didn't always
like the feedback that I was being given, because I thought that it
was given in an impolite manner. So I resolved to be more polite when
I give feedback.

In this case, John, who has obviously worked very hard on his formula,
came onto the tuning list and told everyone about his book, titled
"The Mathematics Of Music," and proclaimed that under his system 6.776
was the maximum threshold of mistuning, that 12-TET couldn't handle
5-limit harmony, etc. I think that this is absurd because most of the
world uses a tuning system in which most of the intervals are at least
twice as mistuned as that. However, I think his model is headed in an
interesting direction in that it's a simple average of critical band
dissonance and harmonic complexity, and with a bit of tweaking could
be a useful rule of thumb to evaluate tuning systems and chords
quickly. And I've said this a number of times, offered him some
constructive criticism, etc. I do not claim to be perfect, and if my
suggestions were refuted with some kind of logic then I'd have dropped
my suggestions completely and rethought things, which I've done
publicly on this list a number of times now. But I haven't.

So, I sought, politely, to give some feedback, make some suggestions
to refine the model, etc. I have not gotten much of a positive
response. And I noticed that when new people join the forum, John
seeks to promote his book right off the bat before they know any
better. Likewise, I want to promote what I think is the truth as well,
and make sure that I chime in when I see things being asserted that I
know aren't true. I have always given reasons behind my arguments, I
have never made it personal, and I have never threatened to "censor"
John or anything like that. I'm not going to ban him either. But the
point is that I am not Carl, who has not been as polite lately, and I
would like you to not confuse me with him.

So surely you admit that the criticism that I'm trying to "stifle" or
"censor" anyone is a bit off base. But when somebody claims that
256/255 is a magic interval that happens to be the maximum threshold
of mistuning of any just interval, and says that to newcomers on the
list before they know any different, then I am going to chime in and
claim that it is not.

> As I mentioned in an earlier post I would not call his investigation "scientific" because the nature of the method has built in bias. BUT his method is totally valid for *his* hearing and the model related to *his* hearing and unless he was exceptionally different hearing his conclusions has some percentage of validity for most people. I say this because in even an earlier post yet I noted that psycho-acoustics is (rationally) based on probabilistic models and cann never be 100% right or 100% wrong for 100% of the population. Its probably best to describe the conclusions as trends and tendencies, and in terms of typical and atypical.

He's perfectly allowed to come up with formulas that accurately
describe his hearing. I don't think that the 256/255 cutoff accurately
describes *my* hearing. And, if you look around you on planet Earth,
where people somehow derive spiritual meaning out of music that's
written in 12-TET, I don't think it accurately describes *their*
hearing either. However, 12-TET major and minor chords are not "good"
in John's formula.

And if his formula is only supposed to describe John's personal quirks
and preferences, then I really don't want to buy his book. Why would
I? That doesn't make any sense.

-Mike

🔗Michael <djtrancendance@...>

>"You are taking odd-limit and sticking it where prime-limit should be. 12-EDO is a decent 5-prime-limit tuning."

Fair enough. Although I believe we've discussed in the past...that odd-limit means much more than prime limit so far as accurately depicting consonance. I mean we could say 99/66 is 5 prime limit. I (for once) will lean toward what I recall Carl said a long time ago in that prime limit rating quite often means very little...and, far as the example, am quite under the impression 12EDO succeeds because the way it is designed just happens to give a fair (though not good) range of 5-odd-limit intervals...and that happening is not necessarily an artifact of it being a 5-prime-limit scale. Or...can you directly prove otherwise?

>"What...? Where did anyone ever say that 6/5 isn't a 5-limit interval?"
I never said that. What I said is 12EDO's 6/5 is, let's say, pretty far from ideal.

>"What do you mean it isn't disproven? His theory predicts that 12-equal isn't a "good" tuning for 5-limit harmony. "

Where on earth does he say that? And even if he did...to an extent, I agree: 12EDO is "barely fair" and certainly not "good". 19 and 31 are both superb for 5-limit harmony (at least numerically speaking) over 12EDO by a large degree. Far as why people like 12EDO well...how many of them have had the chance/privilege to hear 19EDO in comparison?! ;-)

>"Why don't you just admit that the formula could use a bit of polishing?"

Of course, it can use a LOT of polishing. But so can Tenney Height.
However, for some bizarre reason, Tenney Height is put on a pedastal over EVERYTHING here. This list seems to have such a stigma against improving and/or opposing Tenney Height that they'd rather sit in an un-drained Port-A-Potty for months eating food through a hole in the roof until they drown in their own....

🔗Mike Battaglia <battaglia01@...>

🔗Michael <djtrancendance@...>

>"He's perfectly allowed to come up with formulas that accurately describe his hearing. I don't think that the 256/255 cutoff accurately describes *my* hearing. And, if you look around you on planet Earth, where people somehow derive spiritual meaning out of music that's written in 12-TET, I don't think it accurately describes *their* hearing either. "

To perhaps over-summarize: I think John's system excels at ensuring NEW tuning systems sound good to most people, rather than explaining established EDO systems. As you said, his system ties together critical band dissonance and harmonic entropy.
So if a new system DOES comply with his perhaps overly strict 256/255 limit, you can be pretty sure it will sound good to most people (IE, for sure, quarter comma meantone, which has tons of good chords by his system, would likely work...as would irregular temperaments with many of his dyads made to be in tune within about 7 cents).

Granted, I think John went out on a limb trying to categorize temperaments/EDO's by his system...as that is something not only his system seems to fail at, but also leading many systems IE look at Igs's comments about HE/critical-band-dissonance...failing to accurately describe what he hears in EDOs.

Now back to perhaps some productive discussion...how do you all think John's formula MAY be able to be used productively and/or improved far as making new scales?

🔗Mike Battaglia <battaglia01@...>

On Mon, Apr 4, 2011 at 11:27 AM, Michael <djtrancendance@...> wrote:
>
> >"You are taking odd-limit and sticking it where prime-limit should be. 12-EDO is a decent 5-prime-limit tuning."
>
> Fair enough. Although I believe we've discussed in the past...that odd-limit means much more than prime limit so far as accurately depicting consonance. I mean we could say 99/66 is 5 prime limit. I (for once) will lean toward what I recall Carl said a long time ago in that prime limit rating quite often means very little...and, far as the example, am quite under the impression 12EDO succeeds because the way it is designed just happens to give a fair (though not good) range of 5-odd-limit intervals...and that happening is not necessarily an artifact of it being a 5-prime-limit scale. Or...can you directly prove otherwise?

Yeah. Major chords with added seconds are used often. So are sus
chords. So are major 7 chords. These all sound great. They are also
not 5-odd-limit chords.

> >"What...? Where did anyone ever say that 6/5 isn't a 5-limit interval?"
> I never said that. What I said is 12EDO's 6/5 is, let's say, pretty far from ideal.

But it's still "good" enough to inspire people all around the world.

> >"What do you mean it isn't disproven? His theory predicts that 12-equal isn't a "good" tuning for 5-limit harmony. "
>
> Where on earth does he say that? And even if he did...to an extent, I agree: 12EDO is "barely fair" and certainly not "good". 19 and 31 are both superb for 5-limit harmony (at least numerically speaking) over 12EDO by a large degree. Far as why people like 12EDO well...how many of them have had the chance/privilege to hear 19EDO in comparison?! ;-)

He also doesn't think that 19EDO is a good 5-limit tuning either. See here:

/tuning/topicId_97118.html#97118
/tuning/topicId_97458.html#97458

> >"Why don't you just admit that the formula could use a bit of polishing?"
>
> Of course, it can use a LOT of polishing. But so can Tenney Height.
> However, for some bizarre reason, Tenney Height is put on a pedastal over EVERYTHING here. This list seems to have such a stigma against improving and/or opposing Tenney Height that they'd rather sit in an un-drained Port-A-Potty for months eating food through a hole in the roof until they drown in their own....

Thanks for the colorful analogy. This is pure fiction. Harmonic
Entropy improves on Tenney Height. And as you know, improving on
Harmonic Entropy is big business these days. I don't think that John's
formula improves on it.

-Mike

🔗Michael <djtrancendance@...>

Me>"The side point, again, is that people are constantly (EVEN IN 12TET!) made to deal with intervals above Tenney Height of 70 (again; 16/9, 27/16, 7/5, near 19/10....) and, for crying out loud, why won't people try to come up with a solution for analyzing such intervals instead of saying something along the lines of either "use Tenney Height for

them" or "they just don't occur normally" (which is an obvious lie).

MikeB>"What exactly about those intervals do you want to analyze?"

Which ones can be use prominently/frequently in composition without sounding sour to most people. Say we, just for a second, got off the "maximize perfect fifths, fourths, and major 3rds" bus of meantone-related tuning history...and thought about alternatives.

Such as

A) "could people be just as happy with good 9-limit IE 16/9, 14/9 and 7-limit IE 7/5, 10/7, 12/7, 7/6...intervals given precedence for purity instead of 5-limit ones?" After all, many such intervals they are already familiar with from 12EDO...

B) How about 11-limit? Granted, there is no 11-limit in 12EDO, so this one is more out on a limb far as familiarity.
Of course (as I've been alluding to)...at least mathematically that this would involve something more advanced than Tenney Height...the classical example in my mind being 22/15 vs. 16/11 given to me by Igs ages ago (we both agreed the 22/15, despite the much higher TH, sounds much better). We'd need something that could say, for example, a 15-odd-limit interval can be decent while an 11-limit interval can be bad...and that there are "good" and "bad" intervals within 11-limit...that they aren't merely in order of best to worst as you go up in Tenney Height.

🔗Mike Battaglia <battaglia01@...>

On Mon, Apr 4, 2011 at 11:37 AM, Michael <djtrancendance@...> wrote:
>
> >"He's perfectly allowed to come up with formulas that accurately describe his hearing. I don't think that the 256/255 cutoff accurately describes *my* hearing. And, if you look around you on planet Earth, where people somehow derive spiritual meaning out of music that's written in 12-TET, I don't think it accurately describes *their* hearing either. "
>
> To perhaps over-summarize: I think John's system excels at ensuring NEW tuning systems sound good to most people, rather than explaining established EDO systems. As you said, his system ties together critical band dissonance and harmonic entropy.

Not harmonic entropy; his system ties together critical band
dissonance and something kind of like Tenney Height. If it were
harmonic entropy, the 256/255 cutoff would be replaced with something
more like a smooth gradient that's shaped like a normal distribution
on either side.

> So if a new system DOES comply with his perhaps overly strict 256/255 limit, you can be pretty sure it will sound good to most people (IE, for sure, quarter comma meantone, which has tons of good chords by his system, would likely work...as would irregular temperaments with many of his dyads made to be in tune within about 7 cents).

Except that the O'Sullivan formula predicts that 19-EDO has no "good"
triads, and that 23-EDO does. It also predicts that 22-EDO is the best
EDO under 30, I believe, which I thought you said you disagreed with,
and that you liked 19-EDO a lot more than 22.

> Granted, I think John went out on a limb trying to categorize temperaments/EDO's by his system...as that is something not only his system seems to fail at, but also leading many systems IE look at Igs's comments about HE/critical-band-dissonance...failing to accurately describe what he hears in EDOs.

The whole reason that we're doing so much research is because we know
the current theory is NOT perfect. That is the point. That doesn't
mean that 256/255 is a magical mistuning vector that we all need to
follow, and that every other competing theory is correct.

It's also not just about coming up with a system that blindly just
"works," it's about understanding the cognitive and psychoacoustic
roots of music to begin with. Even if 256/255 did happen to be a
decent cutoff for mistuning, that still wouldn't say anything special
about 256/255, other than that it's kind of in the ballpark.

I once again recommend you take some time to go through the tonalsoft
encyclopedia and the xenwiki so you can yourself understand the
current theory before you criticize it.

> Now back to perhaps some productive discussion...how do you all think John's formula MAY be able to be used productively and/or improved far as making new scales?

I think that he should widen the 256/255 mistuning threshold, and I
think he should ditch the concept of 256/255 being some kind of
special mistuning interval because it's a power of 2. I think that he
should consider having a mistuning threshold that varies with the
interval such that more complex intervals are less sensitive to
mistuning than less complex intervals (or more sensitive, if you see
it Igs' way). I think that he might want to consider replacing the 1/x
+ 1/y term with x*y, because it's simpler and will probably work
better in certain cases. I think that his formula might have some nice
applications in the subgroup search. That's all.

-Mike

🔗lobawad <lobawad@...>

Parsimony does not favor the inclusion of ratios based on the fifth partial into the reason for the musical success of (strict) 12-tET. 12-tET is a superb Pythagorean system based on the 2nd and 3rd partials- amazingly closing in a mere dozen slight temperings of pure intervals. There's no reason to insist on working in higher partials in vague smeary forms to account for the harmonic (in a literal sense) validity of 12-tET.

Not only is doing so not parsimonious, it is also damaging to sturdy understanding of psychoacoustic tempering "realities". Hunting for reasons to justify the assumption that intervals clearly and unequivicabley based on partials 3 and 2 somehow "are" based on the 5th partial is not scientific.

At the same time, it is important to understand that "12-tET" does not in actual practice refer to 12-tEt in the same manner we would assume that, say 22-edo refers to a consistent and accurately tuned equal division of the octave into 22 parts. "12-tEt", as can be easily verified by listening to various performances, refers to "pretty much, roughly, 12-tET" as well. We can hear harmonic ratios based on the 5th and 7th partial in NOMINALLY 12-tET music- and these renditions are sometimes far clearer than vague approximations.

This abilitiy of a nomnial 12-tET system to embrace even accurate approximations of the 5th and 7th partial ratios does not mean that a strictly tuned 12-tET system represents these ratios well. The reality may be quite the contrary- it may very well be that the very poorness and vagueness, as far as identifiability in terms of the harmonic series, of the approximations offered by 12-tET is what
enables nominal 12-tET to be so flexible, and the mind to interpret these intervals in different ways as well.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Mon, Apr 4, 2011 at 10:46 AM, Michael <djtrancendance@...> wrote:
> >
> > > MikeB>"Because your theory has failed to predict that 19 and 22 are exceptionally "good" EDOs under 25."
> > >
> > Me>    As if that is fact?
> > Gene>"It's a fact that 19 and 22 are the lowest-error 5-limit systems until you hit 31. "
> >
> > But does lowest error mean "good"?! That's the part, I'm saying, which is an opinion. Saying "19 and 22EDO are the best tuning systems under 31 so far as approximating 5-limit intervals" would make it fact...but that's not what was say.
>
> They should be "good" for writing harmonic music. If you're a
> serialist, atonal composer, you might not like 19 and 22 as much.
>
> > >"And your complaint with 9/8, 16/9, and 27/16 is...?"
> > They are 9 or 27 odd-limit...there's nothing 5-limit about them. Not to mention the 7/5 and 10/7 semitone. ...And yet 12EDO (which contains all of those them) is formally considered a 5-limit tuning (bizarre)...
>
> You are taking odd-limit and sticking it where prime-limit should be.
> 12-EDO is a decent 5-prime-limit tuning.
>
> > That seems to imply to say 5/4, 4/3, and 3/2 are the only 5-limit intervals that really matter and everything else doesn't: it gives a very biased weight to certain 5-limit intervals (of which there are not many). I assume this goes back to historical bias for giving major thirds and/or perfect fifths in meantone precedence for accuracy over other intervals.
> >    Now what if someone considers a good accuracy 8/5 or 6/5 important? Actually many people may: for example, many electronica genres purposefully use minor chords more prolifically than major ones. Then the person is likely to consider 12TET not much of a 5-limit tuning.
>
> What...? Where did anyone ever say that 6/5 isn't a 5-limit interval?
> How is the accuracy of 5/4 and the accuracy of 8/5 any different in
> 12-TET? I don't understand where you're coming from at all now.
>
> I recommend responding to this post again with the awareness that the
> phrase "12-TET is a decent 5-limit tuning" refers to the prime-limit.
>
> > Me> In order to disprove John's theory...I swear, the only way to do it is to get a large group of people to sample intervals and intervals different errors away from them.
> > Gene>A great plan. Also, a lot of work.
> >
> >     And as such, I'm not saying the plan "has to be achieved" because, indeed making it happen could be a very long arduous task. On the other hand, as of now, I think it's fair to say John's theory is neither proven nor disproven...and there is nothing wrong with that.
>
> What do you mean it isn't disproven? His theory predicts that 12-equal
> isn't a "good" tuning for 5-limit harmony. Meanwhile, in a listening
> test I just did, the results show that most of the human population on
> planet earth use 12-TET and really seem to enjoy it. What else do you
> want?
>
> Why don't you just admit that the formula could use a bit of polishing?
>
> -Mike
>

🔗Michael <djtrancendance@...>

🔗Chris Vaisvil <chrisvaisvil@...>

Yes you have been more polite than Carl to John, however you seem to
agree with Carl's point about promotion.

Yet I don't remember one soul complaining about Cris Foster's book
being promoted.

My suggestion was that you asked for a copy of John's book for the
price of a review.

On Mon, Apr 4, 2011 at 11:23 AM, Mike Battaglia <battaglia01@...> wrote:
>
>
>
> And I noticed that when new people join the forum, John
> seeks to promote his book right off the bat before they know any
> better. Likewise, I want to promote what I think is the truth as well,
> and make sure that I chime in when I see things being asserted that I
> know aren't true. I have always given reasons behind my arguments, I
> have never made it personal, and I have never threatened to "censor"
> John or anything like that. I'm not going to ban him either. But the
> point is that I am not Carl, who has not been as polite lately, and I
> would like you to not confuse me with him.
>
> So surely you admit that the criticism that I'm trying to "stifle" or
> "censor" anyone is a bit off base. But when somebody claims that
> 256/255 is a magic interval that happens to be the maximum threshold
> of mistuning of any just interval, and says that to newcomers on the
> list before they know any different, then I am going to chime in and
> claim that it is not.
>
> > As I mentioned in an earlier post I would not call his investigation "scientific" because the nature of the method has built in bias. BUT his method is totally valid for *his* hearing and the model related to *his* hearing and unless he was exceptionally different hearing his conclusions has some percentage of validity for most people. I say this because in even an earlier post yet I noted that psycho-acoustics is (rationally) based on probabilistic models and cann never be 100% right or 100% wrong for 100% of the population. Its probably best to describe the conclusions as trends and tendencies, and in terms of typical and atypical.
>
> He's perfectly allowed to come up with formulas that accurately
> describe his hearing. I don't think that the 256/255 cutoff accurately
> describes *my* hearing. And, if you look around you on planet Earth,
> where people somehow derive spiritual meaning out of music that's
> written in 12-TET, I don't think it accurately describes *their*
> hearing either. However, 12-TET major and minor chords are not "good"
> in John's formula.
>
> And if his formula is only supposed to describe John's personal quirks
> and preferences, then I really don't want to buy his book. Why would
> I? That doesn't make any sense.
>
> -Mike
>

🔗Michael <djtrancendance@...>

MikeB>"Except that the O'Sullivan formula predicts that 19-EDO has no "good"

triads, and that 23-EDO does. It also predicts that 22-EDO is the best

EDO under 30, I believe, which I thought you said you disagreed with,

and that you liked 19-EDO a lot more than 22."

You two seem going off on two different tangents. He seems to be talking about good among ALL limit ratios, while you are saying good among 5-limit ones. And I DO think 19 is fairly ideal...for 5-limit. If you said for up to 9-limit, I'd prefer 22. It's a whole different ballgame...

>"I once again recommend you take some time to go through the tonalsoft

encyclopedia and the xenwiki so you can yourself understand the

current theory before you criticize it."

Ah ok wise Mike?! :-S What is obvious, as I have said above, is that you are simply misunderstanding the goals John and I are going for....specifically by assuming we are going for 5-limit...and then turning around and saying "you need to learn more about 5-limit and theories good at it IE Tenney Height". For the record, I think it's fair to say the thrust of much of what John and I both do is to try to get a picture beyond 5-limit...no wonder we don't weight 5-limit as heavily as someone like you does...

>"I think that he should consider having a mistuning threshold that varies with the

interval such that more complex intervals are less sensitive to

mistuning than less complex intervals (or more sensitive, if you see

it Igs' way)."

Agreed...and I DO see it Igs's way in this case and agree scalable would be ideal.
But I still think 7 cents is a good general ballpark figure even though it varies in "width" by ratio...just like people often say the critical band is near 17/16 (fairly accurate between 261 and 440 hz IE the general instrument "middle c" octave range) when, in reality, it gets wider than that at low frequencies and narrower at high ones.
Now let's say we curved "error scalability" by the Harmonic Entropy curve. The would make pretty good sense for, say, 9/7 and 5/4...but go to hell with 11/6 and fairly strong higher-limit intervals the HE curve virtually ignores. And why does the HE curve ignore them? Well the Tenney Height rating it derives them from is so weak...of course. So, again, if we want to fix this issue, we need to come up with something that weighs higher limits more fairly than Tenney Height.

🔗Jake Freivald <jdfreivald@...>

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:

> >"And your complaint with 9/8, 16/9, and 27/16 is...?"
> They are 9 or 27 odd-limit...there's nothing 5-limit about them.

They are 3-limit, which is included in 5-limit in the prime limit sense. In the odd-limit sense, 9/8 is 9-limit. What's wrong with that?

> Not to mention the 7/5 and 10/7 semitone. ...And yet 12EDO (which contains all of those them) is formally considered a 5-limit tuning (bizarre)...

"Formally considered" makes no sense unless you actually do formally consider. To formally consider it to be anything, I think the clearest way is to give a val or subgroup val.

I'm not sure if anyone ever said any such thing. Most theorists, even the ones opposed to rational number consonance considerations in general, treat 2 as an interval that matters.

> I assume this goes back to historical bias for giving major thirds and/or perfect fifths in meantone precedence for accuracy over other intervals.

Meantone practice does not in fact do that.

> In fact I'd say it's much more of a 9-limit tuning than a 5-limit one: the only thing 5-limit about it is that no EDO near it contains nearly as many 5-limit intervals.

Use of 12et evolved from meantone by way of circulating temperaments in a gradual process, and however bad you feel it is as a 5-limit system, anything before 12 is much worse. 7 can't tell the difference between a major and a minor third.

> Far as nailing everything in 5-limit...I'd say 19 is mark-ably better than 12EDO and 31EDO is darn close to perfect for all but the most picky listeners.

Well, join the vast crowds of people who think the same. Those are close to the tunings originally used for 5-limit music.

🔗genewardsmith <genewardsmith@...>

🔗Carl Lumma <carl@...>

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, Michael <djtrancendance@...> wrote:

> Fair enough. Although I believe we've discussed in the past...that odd-limit means much more than prime limit so far as accurately depicting consonance. I mean we could say 99/66 is 5 prime limit.

99/66 is 3-limit, which makes it 5-limit.

> I (for once) will lean toward what I recall Carl said a long time ago in that prime limit rating quite often means very little.

Probably because it's not a rating at all, and has never been used as one.

..and, far as the example, am quite under the impression 12EDO succeeds because the way it is designed just happens to give a fair (though not good) range of 5-odd-limit intervals...and that happening is not necessarily an artifact of it being a 5-prime-limit scale. Or...can you directly prove otherwise?

You seem to be suggesting that it could be that it's good in the 5-limit inconsistently, which as it happens is false. You need to go to higher edos to get one which has good, inconsistent mappings and if you did, I fail to see it proves anything.

> However, for some bizarre reason, Tenney Height is put on a pedastal over EVERYTHING here.

By whom? Name names and cite quotes.

🔗genewardsmith <genewardsmith@...>

🔗Chris Vaisvil <chrisvaisvil@...>

No Carl, I'm not defending John. That is changing the subject.
I'm saying that am dismayed at your objections. I've said so in my first
post on this matter.
This is not like the case of Marcel who, from all appearances, willfully
insulted everyone and anyone.

"No! Bias effects all results, jeez."

What do you mean by this? Do you mean there are no unbiased scientific
studies?

-C

On Mon, Apr 4, 2011 at 3:03 PM, Carl Lumma <carl@...> wrote:

>
>
> Chris wrote:
>
> > And if you don't have the time to read a very short book
>
> You're talking about a guy who 'published' and is selling a
> book without having done a single google search in 14 years
> on the thing he was writing about. You're defending such
> behavior?
>
>
> > As I mentioned in an earlier post I would not call his
> > investigation "scientific" because the nature of the method
> > has built in bias. BUT his method is totally valid for *his*
> > hearing and the model related to *his* hearing
>
> No! Bias effects all results, jeez.
>
> -Carl
>
>
>

🔗genewardsmith <genewardsmith@...>

🔗Carl Lumma <carl@...>

🔗genewardsmith <genewardsmith@...>

--- In tuning@yahoogroups.com, "lobawad" <lobawad@...> wrote:
>
> Parsimony does not favor the inclusion of ratios based on the fifth partial into the reason for the musical success of (strict) 12-tET.

But history unequivocally does, which derails your whole argument. Historically, 12 was considered elsewhere as a Pythagorean system, but evolved in the West out of a 5-limit system as a matter of historical fact. 53 likewise has been looked at in theory from both points of view.

> This abilitiy of a nomnial 12-tET system to embrace even accurate approximations of the 5th and 7th partial ratios does not mean that a strictly tuned 12-tET system represents these ratios well.

No, but it also makes sense in terms of the evolution of 12et from tuning systems which do a much better job for these ratios.

> The reality may be quite the contrary- it may very well be that the very poorness and vagueness, as far as identifiability in terms of the harmonic series, of the approximations offered by 12-tET is what
> enables nominal 12-tET to be so flexible, and the mind to interpret these intervals in different ways as well.

It's true that some common practice music is hard to convert with full success to meantone, but generally more can be done along those lines than most people seem to think. I'm not saying try it on Messiaen, but you might be surprised by the extent to which it works on Brahms or Wagner.

🔗genewardsmith <genewardsmith@...>

🔗Michael <djtrancendance@...>

🔗Carl Lumma <carl@...>

🔗Mike Battaglia <battaglia01@...>

Lump sum response:

On Mon, Apr 4, 2011 at 3:05 PM, genewardsmith
<genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > However, I think his model is headed in an
> > interesting direction in that it's a simple average of critical band
> > dissonance and harmonic complexity
>
> You keep saying that. I'd like an explanation of why you think so.

From his website:

> (2 + 1/x + 1/y - diss(x,y) ) / 2
>
> x and y are integers, x >= y , x <256 and y <256. x/y is simplified is possible.
> If y/x is less than or equal to 0.9375 then the formula for 'diss(x,y)' is simply: y/x.
> If y/x is greater than 0.9375 then the formula for 'diss(x,y)' is: (1 - y/x)*15.
> The 2 on the left hand side of the formula is the sum of the strength values of two notes if each has a value of 1.
> The 1/x + 1/y has to do with periodicity (see my book).
> The diss(x,y) has to do with dissonance (beats/beating).
> The /2 on the right is an average.

If we cut out all of the weighting and so forth, then the basic
essence of his formula is

1/x + 1/y - y/x

Which is the same as

(x+y)/(x*y) - y/x

Which is, effectively

complexity(x,y) - size(x,y)

Where he just so happens to be using a different metric for complexity
than usual. The metric is set up so that higher values represent more
consonant intervals. So we can see that as x*y increases, the
complexity term will go down, meaning the consonance score takes a
hit. Also, we can see that as x/y gets smaller and smaller, into
critical band roughness territory, then y/x gets larger and larger,
asymptotically approaching 1. So the consonance score takes a hit if
the interval is really complex or really small.

He also flips the calculation such that if the interval is wide
enough, it also takes a hit if it's too wide, but I glossed over that
at the time. But it's not really a bad formula in theory, and if a
more sensible mistuning cutoff were picked it would probably be pretty
hand to have around.

-Mike

🔗Mike Battaglia <battaglia01@...>

🔗Chris Vaisvil <chrisvaisvil@...>

Yes, please go back and read my message. I *did* say it was biased - to his
own sensory perception.

You seem to be agruing about if its a given John's system will work for
John. If his system to be self-consistent it will work for John. I'm pretty
sure it is. The problem for discussing his system on this list is - does it
work for other people? I contended that statistics says it will work for
some slice of the general population who have sensory and psychological
perceptions close enough to John's to allow it to work within some
statistically defined degree. Since no one else is John, no one else,
excepting maybe a twin, is likely to share 100% John's perception of sensory
input. I'll be surprised if you take issue with that. And go back - I've
been saying that for a while.

As for the problem of extrapolating personal sensory perception to the
population as a whole - no need to discus this yet again. It doesn't work as
an absolute.

On Mon, Apr 4, 2011 at 4:11 PM, Carl Lumma <carl@...> wrote:

>
>
> --- Chris Vaisvil <chrisvaisvil@...> wrote:
>
> > "No! Bias effects all results, jeez."
> >
> > What do you mean by this?
>
> Self-experimenters must contend with both subject and
> experimenter expectation bias at the same time, and...
> this is why self-experimentation is avoided in the sciences
> whenever possible. If anything, you're actually less
> likely to discover your own true preferences than you are
> someone else's.
>
> -Carl
>
>
>

🔗Chris Vaisvil <chrisvaisvil@...>

Mike,

You are making my points out to be unreasonable when they were not to begin
with.

My point was that John is talking about his method / book / point of view
within the context of on topic posts for this forum.
I see nothing wrong with it. Can't you and Carl just deal with it?

I see my point about Marcel was cut out of your quotation of my response. If
John were acting like Marcel it would be different.
But he is not. If you and John can't see eye to eye (i.e. he won't take your
suggestions) I sympathize but he is not doing "wrong".

This is interesting - do I read in your reply that Cris Foster's promotion
of his book was ok because it was tangential to this list were as John's
promotion of a very on topic book is not ok?

*blinks eyes*.

Did I read that right?

Chris

On Mon, Apr 4, 2011 at 4:19 PM, Mike Battaglia <battaglia01@...>wrote:

>
>
> On Mon, Apr 4, 2011 at 12:40 PM, Chris Vaisvil <chrisvaisvil@...>
> wrote:
> > Yes you have been more polite than Carl to John, however you seem to
> > agree with Carl's point about promotion.
> >
> > Yet I don't remember one soul complaining about Cris Foster's book
> > being promoted.
>
> It wasn't being promoted constantly, and his book is tangential to the
> main point of the list.
>
>
> > My suggestion was that you asked for a copy of John's book for the
> > price of a review.
>
> Chris, this is unreasonable. It can't be that someone comes onto a
> message board with a decade and a half of prior research on it, makes
> claims that contradict both the research and common sense, and then
> demands that I read 100 pages of material before commenting on said
> claims. I don't have the time. That being said, I still don't think
> that 256/255 is the maximum cutoff for mistuning an interval.
>
> -Mike
>
>

🔗Mike Battaglia <battaglia01@...>

On Mon, Apr 4, 2011 at 4:54 PM, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> Mike,
>
> You are making my points out to be unreasonable when they were not to begin with.
>
> My point was that John is talking about his method / book / point of view within the context of on topic posts for this forum.
> I see nothing wrong with it. Can't you and Carl just deal with it?

Then there's also nothing wrong with myself providing critical
feedback on his method and point of view within the context of on
topic posts for this forum either.

> I see my point about Marcel was cut out of your quotation of my response. If John were acting like Marcel it would be different.
> But he is not. If you and John can't see eye to eye (i.e. he won't take your suggestions) I sympathize but he is not doing "wrong".

And I will continue to criticize his work.

> This is interesting - do I read in your reply that Cris Foster's promotion of his book was ok because it was tangential to this list were as John's promotion of a very on topic book is not ok?
>
> *blinks eyes*.
>
> Did I read that right?

This is a forum about tuning. If someone, every so often, mentions
that they have written a book on a subject that comes up once in a
blue moon as a somewhat related discussion to tuning, that's one
thing. It is quite another for someone else to advertise their book
repeatedly which is written about the very subject that we are trying
to publicly discuss for free. And to demand that someone buy and read
the whole book before passing judgment on the sweeping generalized
claims that are being made is adding insult to injury.

-Mike

🔗Chris Vaisvil <chrisvaisvil@...>

Nothing wrong with you being critical - that is the scientific method -
which to whatever degree it is applicable to our work I'm all for.

But.... point me to

"It is quite another for someone else to advertise their book
repeatedly"

I have seen no ads. Can you show them to me? I've only a post with page
number references.

" which is written about the very subject that we are trying
to publicly discuss for free."

True, we are trying to discuss this on an equal basis. All for it. Should be
free - after all look at the price we pay putting up with each other ;-)

"And to demand that someone buy and read
the whole book before passing judgment on the sweeping generalized
claims that are being made is adding insult to injury."

I have not seen such a demand. If you would be so kind as to point that out
I will see your (and I think Carl's) point of view.
I will freely admit I do not completely read every tuning related post - so
if I missed this post it is crucial in my understanding of what is happening
here.

The last I saw John was still offering the book to be sent for the price of
a review.

Chris

🔗Mike Battaglia <battaglia01@...>

On Mon, Apr 4, 2011 at 5:33 PM, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> "It is quite another for someone else to advertise their book
> repeatedly"
>
> I have seen no ads. Can you show them to me? I've only a post with page number references.

Every post John's made since he's been here is about "his" tuning
system, which is in "his" book, and what he thinks is good in "his"
system. Now, I have never threatened to "censor," or "moderate," or
"ban" anyone, so you and Michael can stop throwing the slippery slope
fascist strawmen at me, please.

But you know what? I do think that this is all in poor taste. I do
think that it's in poor taste to join a community of researchers with
a decade and a half of ongoing research on it, make no effort to learn
what research that they have done or understand the existing paradigm,
make claims about how music works but then ignore feedback from the
other researchers who have been here before, invent your own
terminology for things that have already been developed and try to
push that, and then continue to promote "your" system to newcomers to
the list. I think that given the "open source" music theory community
that we have, it's in poor taste. I likewise think it's in poor taste
to "patent" a scale.

I am not going to ban or censor him, and I wish him the best with his
book. In fact, I think if he'd take the suggestions that have been
offered to him, he'd have a really good book and a good model. But
that's how I feel about it.

> "And to demand that someone buy and read
> the whole book before passing judgment on the sweeping generalized
> claims that are being made is adding insult to injury."
>
> I have not seen such a demand. If you would be so kind as to point that out I will see your (and I think Carl's) point of view.

I don't know if he himself has made a demand. I was more referring to
you and Michael implying that I can't review his work unless I read
his book. My response to that is that I shouldn't have to read 100
pages of material before discounting an idea that was posted publicly.

> I will freely admit I do not completely read every tuning related post - so if I missed this post it is crucial in my understanding of what is happening here.
>
> The last I saw John was still offering the book to be sent for the price of a review.

You know what, I'll review it. If he sends me a free copy, I will
review his book and post it up here, complete with psychoacoustic
analysis, comparisons to other facets of music theory, etc. I will be
as fair-minded as I have been when I suggested ways for him to back up
his existing model with proven aspects of psychoacoustics. If he's
game, then I will review it. I can't promise I'll finish it in a day
or two, as this is hell week for me, but I will review it in as best
of a timely fashion as I am able and post my review.

-Mike

🔗Carl Lumma <carl@...>

Gene wrote:

> Now that's interesting. How does HE sort out the other comparisons
> at s=1%? If HE matches my choices perfectly, I'll start to feel
> pretty good about it.

Why don't you actually, you know, have a look at some
harmonic entropy values? I've updated my spreadsheet for
your enjoyment!

http://lumma.org/music/theory/DyadicEntropy.xls

By the way, since TH of 13/7 and 11/8 is > 70, it's really
borderline to say it ranks one above the other.

Recently I said TH is good for about 150 ratios, but SPAN
takes that down to about 50. And here there are, sorted
by size:

8/7 7/6 6/5 5/4 9/7 4/3 7/5 10/7 3/2 8/5 5/3 7/4 9/5 11/6 2
11/5 9/4 7/3 12/5 5/2 13/5 8/3 11/4 14/5 3
13/4 10/3 7/2 11/3 15/4 4
17/4 13/3 9/2 14/3 5
16/3 11/2 17/3 6
19/3 13/2 20/3 7
22/3 15/2 23/3 8

and sorted by Tenney height:

2 3 4 5 3/2 6 7 8 5/2 4/3 7/2 5/3 9/2 5/4 7/3 11/2 8/3
13/2 7/4 6/5 10/3 15/2 11/3 7/5 9/4 13/3 8/5 7/6 14/3
11/4 9/5 16/3 17/3 13/4 11/5 8/7 19/3 12/5 15/4 20/3 9/7
13/5 11/6 22/3 17/4 23/3 10/7 14/5

And that's really all it is.

-Carl

🔗genewardsmith <genewardsmith@...>

🔗Carl Lumma <carl@...>

🔗genewardsmith <genewardsmith@...>

🔗Carl Lumma <carl@...>

🔗genewardsmith <genewardsmith@...>

🔗Carl Lumma <carl@...>

🔗genewardsmith <genewardsmith@...>

🔗Carl Lumma <carl@...>

🔗genewardsmith <genewardsmith@...>

🔗Carl Lumma <carl@...>

🔗genewardsmith <genewardsmith@...>

🔗lobawad <lobawad@...>

It seems to me that in order to support the claim the 23-edo is the "best" equal division of the octave under 25 divisions, you'd have to create music in 23-edo to demonstrate that the system is indeed "good".

--- In tuning@yahoogroups.com, "john777music" <jfos777@...> wrote:
>
> Carl and Mike, you have obviously made up your minds about me and I doubt that there is anything I could say or argue now that will change that. One or two points I'd like to make...
>
> <the "these intervals are good because I consider them good" argument makes less sense than "there is a varying spectrum of consonance and dissonance with simpler intervals tending to be more consonant.">
>
> It took me 14 years hard work to arrive at my formula for harmony in sine wave intervals. Then I used the formula in a sophisticated program to quantify the concordance of intervals with complex tones and 'regular' timbres. I don't think my approach was anything less than 'scientific'.
>
> <And the idea that 23-EDO is the best equal temperament under 30 is absolutely insane.>
>
> Why is it insane? I have posted a list of all the good dyads that occur in each EDO from 4 to 49. Just considering EDOs less than 30, 29EDO has 7 good dyads, 27EDO has 8, 23EDO has 7, 22EDO has 6 and 19EDO has only 3. The winner is 27EDO with 8 good dyads. In joint second place are 29EDO and 23EDO with 7 good dyads each. Seems like a reasonable proposition that 23EDO should be good. BTW I said that 23EDO was the best EDO less than 25, not 30.
>
> I think I read somewhere in the last flurry of posts that Carl and Mike didn't like my book. Have ye actually read the book? When I joined the list in January 2010 I uploaded a PDF version of my book to the Files section. Is this the version of the book that ye read? If so then you would be right in knocking it because it contained many errors. These have been corrected in the published paperback version.
>
> As regards the reviews I was very happy with all of them. There were a lot of criticisms but there was some praise in there as well.
>
> John.
>
>
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > On Sat, Apr 2, 2011 at 12:48 AM, Michael <djtrancendance@> wrote:
> > >
> > > MikeB>"Have you been reading the list at all? John has gotten numerous reviews on his book, and they are almost unanimously poor. What else do you want?"
> > >
> > >    Where are such unanimously poor reviews from? I recall reading Chris Vaisvil and Neil Haverstick liked the book. And yes, I've also heard a good few people don't like it. Thing I have noticed is, the people who don't like it often go on and on and on complaining...and the people who do like it praise it a few times and then let of it.
> >
> > I didn't like it, Carl didn't like it, Igs didn't like it. If we go on
> > and on and on complaining, that's only because the author of the book
> > has gone on and on and on reiterating the same defunct points without
> > addressing them.
> >
> > > I figure either we have a problem which John is dealing out information in non-debatable form and/or people are trying to censor John out so he can't debate in the first place. If we have the second problem, we can't exactly blame John for the first...
> >
> > Oh, right, it's all about censorship. You got it.
> >
> > > >"The 256/255 cutoff for mistuning "because powers of two are probably involved"
> > > makes less sense than that every interval has a Gaussian-weighted error function and that simpler intervals have greater fields of attraction than more complex ones."
> > >
> > > I agree it's a dumb reason...but agree with John the end result/limit is a fair one. Gene, I recall, also has said in the past that about 7 cents is a good general cut-off point...and Monzo's online guide uses 7 cents in his definition of "pseudo-JI" as a fairly accurate rounding/error limit. Are we really that concerned with the math that we will take it over our own ears plus a fair deal of other people's?!
> >
> > Who cares what anyone "says?" We are talking about a book called "The
> > Mathematics of Music." Not "My Personal Musical Preferences."
> >
> > > >the "these intervals are good because I consider them good" argument makes less sense than "there is a varying spectrum of consonance and dissonance with simpler intervals
> > > tending to be more consonant."
> > >
> > >    You seem to be indirectly saying that "my ears consistently like these intervals (most of which are simpler, but with a few exceptions to my ears)" is somehow mark-ably worse than saying "simpler intervals tend to be more consonant".   In many ways, both statements say the same thing...I'd even vouch to say the 'with a few exceptions' version is more specific.
> >
> > The latter is a statement that applies to everyone. The former is a
> > statement that applies only to John. As you've noticed, 12-EDO fails
> > John's acid test for 5-limit harmony, and the entire world uses it;
> > hence his formula doesn't seem to apply to the majority of the world.
> > How can a formula fail any more than that?
> >
> > > And if we did blindly accept the "simpler intervals tend" statement...we would basically, as I see it, limit us to "Tenney height or bust" and push us to stop asking good questions about exceptions to Tenney Height as if exceptions must be "personal hearing quirks".
> >
> > You don't have to blindly accept anything. Go do the tests yourself
> > and critique it and try and contribute something to the field.
> >
> > > >"And the idea that 23-EDO is the best equal temperament under 30 is absolutely insane."
> > >
> > >    Best temperament for...what exactly? Your take on things seems every bit as personally biased as John's supposed take on them. I don't think any temperament is a best temperament for anything that's not very very personally biased. Personally I like 31EDO, but that's because I like just dyads and can tolerate higher-limit chords so long as they are composed of low-limit dyads (and I realize many people can't tolerate them).
> >
> > If you hate the concept of "best temperament," then you should be
> > rioting in the streets over the concept of there being "good
> > intervals."
> >
> > -Mike
> >
>

🔗Michael <djtrancendance@...>

>:Now, I have never threatened to "censor," or "moderate," or

"ban" anyone, so you and Michael can stop throwing the slippery slope

fascist strawmen at me, please."

Nope, you never did threaten to censor. You, however, have said "this part of John's theory IE the error margin is ridiculous"...among other things, without any counterproof other than "well it doesn't match any of the past 'expert' theories". That and you went ahead and claimed John was going out on a limb to promote his book (though not half so much as Carl did). You aren't "banning anyone", just rather saying "posting your own efforts, no matter how much honest work you put into them, will open you up to being repeatedly called a psuedoscientist by Carl and I....even if you NEVER mentioned it being scientific in the first place". News flash...music is an art...and the science in music is nothing more than matching what we hear with numbers: there is no way to escape some degree of bias because music is an art...all we can hope for is that musical patterns can be open to review by many people...which John seems quite open to
doing. So I don't see what the huge problem is...

> In fact, I think if he'd take the suggestions that have been offered to him
Given the suggestions involve simply cutting out parts of his theory without alternative ideas, I don't see how this is so easy. So you want a margin of error that's not fixed but works for different intervals? You suggested he either match it to HE (which has its own flaws and makes it copying on his part) or make a scaled model that differs in tolerance per interval on a different basis without even hinting what that basis could be.
The solution? How about a listening test, over a random population (just like the Strawberry Jam test) of a huge group of intervals (yes, including ones with Tenney Height over 70). Then we would get a curve (in the same way the Plomp and Llevelt curve was derived) and be able to summarize the curve in a mathematical formula that actually matches what most people hear. BTW, P&L's curve, DESPITE BEING GENERATED BY A LISTENING TEST, DIRECTLY REFLECTS PSYCHOACOUSTICS.

Then again...you seem gung-ho in saying listening test must be UNSCIENTIFIC (a small step from saying rating music by listening to it is a useless way to go about it)...which leaves people like John and Myself with no options other than copying existing theories or being ridiculed.

🔗Mike Battaglia <battaglia01@...>

On Tue, Apr 5, 2011 at 11:26 AM, Michael <djtrancendance@...> wrote:
>
> >:Now, I have never threatened to "censor," or "moderate," or
> "ban" anyone, so you and Michael can stop throwing the slippery slope
> fascist strawmen at me, please."
>
> Nope, you never did threaten to censor. You, however, have said "this part of John's theory IE the error margin is ridiculous"...among other things, without any counterproof other than "well it doesn't match any of the past 'expert' theories".

Those "expert" theories were subjected to numerous listening tests.
The results of one of them were posted in the last 24 hours. If you
think that nobody has ever tested the maximum degree of mistuning for
a JI interval, then you need to read more.

> > In fact, I think if he'd take the suggestions that have been offered to him
> Given the suggestions involve simply cutting out parts of his theory without alternative ideas, I don't see how this is so easy. So you want a margin of error that's not fixed but works for different intervals? You suggested he either match it to HE (which has its own flaws and makes it copying on his part) or make a scaled model that differs in tolerance per interval on a different basis without even hinting what that basis could be.

I've given a lot of suggestions. I suggested that he widen it, I
suggested he weight the "good" mistuning cutoff by complexity, I
suggested he drop the 256/255 numerology. In fact, I've posted exactly
what my suggestions have been in almost every single response to you
since this thread started, so now I'm convinced that you aren't
reading what I write at all.

> The solution? How about a listening test, over a random population (just like the Strawberry Jam test) of a huge group of intervals (yes, including ones with Tenney Height over 70). Then we would get a curve (in the same way the Plomp and Llevelt curve was derived) and be able to summarize the curve in a mathematical formula that actually matches what most people hear. BTW, P&L's curve, DESPITE BEING GENERATED BY A LISTENING TEST, DIRECTLY REFLECTS PSYCHOACOUSTICS.

Go ahead and organize it. mTurk is a good place to start.

> Then again...you seem gung-ho in saying listening test must be UNSCIENTIFIC (a small step from saying rating music by listening to it is a useless way to go about it)...which leaves people like John and Myself with no options other than copying existing theories or being ridiculed.

At this point, you seem to have no idea what I'm saying at all.

-Mike

🔗Michael <djtrancendance@...>

>"Those "expert" theories were subjected to numerous listening tests"

But I'm unconvinced, for example, that this fact means all theories in the future must match the closest expert theory. For example, what pattern in the HE curve explains how Middle Eastern music (which uses several intervals NOT at HE minima) works? You mentioned something about swapping parameter value, but never followed up with an example. My take: if an "expert theory" does NOT cover the ground of a certain type of music, this opens the door for new theories, "even" unrelated to older ones, to cover it...and for those new theories to be listening tested from scratch.

>"I suggested that he widen it, I suggested he weight the "good" mistuning cutoff by complexity"

The first suggestion sounds like giving up IE make the theory more true by making it less accurate. The second seems to say "directly copy how Tenney Height works" IE don't make a theory, simply copy it..the problem being that copying a theory without at least incremental changes means the implications of the "new" theory will be unchanged from the original one.

>"Go ahead and organize it. mTurk is a good place to start."

Funny, I thought the Mechanical Turk was reserved for only very serious physics/engineering/math problems and never art?
Anyhow, yes, I'll try a sound test on it. I'm specifically wondering how intervals like 11/6, 11/9, and 22/15 will fare...I'm betting the "order" from best to worst will be similar to Tenney Height in most cases (perhaps with a few exceptions, like 16/11)...but the degree to which such higher limit intervals are worst will be much less than expected by TH.

Me> Then again...you seem gung-ho in saying listening test must be
UNSCIENTIFIC (a small step from saying rating music by listening to it
is a useless way to go about it)...which leaves people like John and
Myself with no options other than copying existing theories or being
ridiculed.

MikeB>"At this point, you seem to have no idea what I'm saying at all."

Well then, what are you saying or, rather, what would you suggest? You seem to be suggesting John give up on many of the parts of his theory and instead copy those parts from existing theories. You do seem to say "you should try something else that's not part of an existing theory", but then not even hint what NEW alternatives may exist.

🔗Mike Battaglia <battaglia01@...>

Mike, this is my last reply to you on this, as we're now going in
circles. Everything you're saying is something I've already addressed.
Feel free to message me offlist if you'd like to talk more.

On Tue, Apr 5, 2011 at 12:01 PM, Michael <djtrancendance@...> wrote:
>
> >"Those "expert" theories were subjected to numerous listening tests"
>
> But I'm unconvinced, for example, that this fact means all theories in the future must match the closest expert theory.

All theories in the future should match the results of listening
tests. If they don't, then they don't accurately represent how music
works with human beings.

> For example, what pattern in the HE curve explains how Middle Eastern music (which uses several intervals NOT at HE minima) works?

Uh, it means that discordant intervals can have a use in music?

> You mentioned something about swapping parameter value, but never followed up with an example. My take: if an "expert theory" does NOT cover the ground of a certain type of music, this opens the door for new theories, "even" unrelated to older ones, to cover it...and for those new theories to be listening tested from scratch.

John's theory is not listening tested from scratch.

> >"I suggested that he widen it, I suggested he weight the "good" mistuning cutoff by complexity"
>
> The first suggestion sounds like giving up IE make the theory more true by making it less accurate.

Giving up on what? I didn't realize that the point of the theory was
just to say the opposite of what everyone else is saying.

> The second seems to say "directly copy how Tenney Height works" IE don't make a theory, simply copy it..the problem being that copying a theory without at least incremental changes means the implications of the "new" theory will be unchanged from the original one.

OK. Well, if the goal is to just establish "a theory" so that you can
have "your own theory," and make it totally separate from other
theories, then it's worth comparing them to see which is more
accurate. And my initial comparison the 256/255 maximum mistuning
cutoff is ridiculous.

> >"Go ahead and organize it. mTurk is a good place to start."
>
> Funny, I thought the Mechanical Turk was reserved for only very serious physics/engineering/math problems and never art?
> Anyhow, yes, I'll try a sound test on it. I'm specifically wondering how intervals like 11/6, 11/9, and 22/15 will fare...I'm betting the "order" from best to worst will be similar to Tenney Height in most cases (perhaps with a few exceptions, like 16/11)...but the degree to which such higher limit intervals are worst will be much less than expected by TH.

Go ahead, and please post the results.

> Me> Then again...you seem gung-ho in saying listening test must be UNSCIENTIFIC (a small step from saying rating music by listening to it is a useless way to go about it)...which leaves people like John and Myself with no options other than copying existing theories or being ridiculed.
>
> MikeB>"At this point, you seem to have no idea what I'm saying at all."
>
> Well then, what are you saying or, rather, what would you suggest? You seem to be suggesting John give up on many of the parts of his theory and instead copy those parts from existing theories. You do seem to say "you should try something else that's not part of an existing theory", but then not even hint what NEW alternatives may exist.

I suggested that he improve the 6.776 cent cutoff because IT IS
RIDICULOUS. Almost the entire world uses a tuning system that is out
of the 6.776 cent cutoff and loves every minute of it. I keep saying
this, and you haven't refuted it once - not once. The current formula
does not accurately reflect the musical perception of most of the
world's population. That means it could probably use some tweaking.

I have given reasons why it's ridiculous - that the most popular
tuning system in the world doesn't fit the criteria, that other
popular microtonal systems also don't fit the criteria (like
19-equal), that any old Joe can test and see that 400 cents is still
heard as 5/4 by playing around with a synth for 5 minutes, that there
hasn't been any decent explanation given for why 256/255 should be
significant as a mistuning interval. I have said this over and over
and over. I think it has some good points, which I have also said over
and over.

The suggestion that I have given, and I've given it repeatedly now, is
to widen the mistuning cutoff, which is the only possible suggestion
that you could give to improve a system with too strict a mistuning
cutoff. I suggested he possibly experiment with using a mistuning
tolerance value that is not constant but a function of the interval
being judged. I suggested he experiment with weighting the cutoff in
both directions, given Igs' recent suggestion to weight prime error in
the opposite direction to what's usually done.

The goal is not, at the end of the day, for everyone to have their own
proprietary theories. The goal is to figure out how music works. John
is free to take my suggestions and improve on them and give me no
credit whatsoever. I simply suggested a way to tweak the formula a
bit. That's it. Your criticism that my suggestions "are too similar to
the existing theory" is tantamount to saying that my suggestions are
in line with the best information that we currently have on how the
perception of consonance works. That's hardly a criticism at all.

-Mike

🔗genewardsmith <genewardsmith@...>

🔗Michael <djtrancendance@...>

Me>> "But I'm unconvinced, for example, that this fact means all theories in the future must match the closest expert theory."

MikeB>"All theories in the future should match the results of listening tests. If they don't, then they don't accurately represent how music works with human beings."

The new theories must match some sort of listening tests, but NOT past theories: that's my point. Past theories that are listening tested is not equal to the process of running listening tests on new theories and a new theory can agree with a new listening test without being the same as an old theory that was listening tested.

>> For example, what pattern in the HE curve explains how Middle
Eastern music (which uses several intervals NOT at HE minima) works?

>"Uh, it means that discordant intervals can have a use in music?

If you slap a sticker saying what's not low-limit JI must be discordant and don't question if certain higher-limit intervals can be concordant. I see a nice share of Middle Eastern music theory as a great example, in many cases, of higher limit concordance that Westerners often have simply proven ignorant of and unwilling to, ahem, listening test on fair grounds. Cameron, myself, Igs, and several others have noticed countless times where things like 11/9 and 11/6 can be quite concordant. And don't even get me started on Igs's "Map of the Internal Landscape", an album which threw even my fairly liberal attitude toward many high-limit intervals in a loop.

>"John's theory is not listening tested from scratch."

Listen again, I said " My take: if an "expert theory" does NOT cover the ground of a certain
type of music, this opens the door for new theories, "even" unrelated to
older ones, to cover it...and for those new theories to be listening
tested from scratch."

This implies we should open theories like John's FOR TESTING...I never said such theories were tested but, rather, am saying they deserve a fair chance TO be listening tested (and that they should be tested, specifically because they have not been).

>"Go ahead, and please post the results."

Cool...I already have a basic 13-or-so-interval survey on the Mechanical Turk (mainly debatable areas like neutral thirds, the area between 7/5 and 8/5, and different types of sevenths) and am just looking for a place to post the sound sample files (all samples done with the same guitar sample...NOT sine waves).

Does anyone have an ftp directory that translates to a website URL they are willing to open up for this?

>"I suggested that he improve the 6.776 cent cutoff because IT IS RIDICULOUS. Almost the entire world uses a tuning system that is out of the 6.776 cent cutoff and loves every minute of it."

True about "the entire world uses..."...and people regularly ALSO accept 18/17-ish semitones when they clearly violate the testing results of P&L's "scientifically derived" curve and "love every minute of it".
However, typically, I agree with John that around 7 cents or less or error is a "guarantee of safety" for virtually ANY type of interval you are trying to approximate while 14 cents, for example, only seems to work safely for very simple intervals IE 5/4.
John's limit clearly seems to aim for "what can always be considered safe for any interval" rather than "what's the greatest error that can EVER possibly work...even if it fails with more 'unsafe' intervals". You are obviously trying to solve a different problem than John...no wonder you disagree with his answer.

>"The goal is not, at the end of the day, for everyone to have their own proprietary theories. The goal is to figure out how music works."

No kidding. So, instead of repeatedly suggesting people change their goals to fit existing theories, or so it seems, why not merely help in the cause of getting together some listening tests? I'm doing one for my theory...why not suggest ideas for doing one for John's instead of griping how you 'know his theory is wrong'?

>"Your criticism that my suggestions "are too similar to the existing theory" is tantamount to saying that my suggestions are in line with the best information that we currently have on how the perception of consonance works."

If we knew how consonance works...we surely wouldn't have leading musical ambassador's like Igs and Chris finding gaping exceptions in 'leading' theories and surely would have found microtonal scales that work for the average listener and are "anything but just a personal opinion"...eh? But we haven't....and, rather than sitting around and pretending everything is fine and the theories we have already are near-perfect...IMVHO we should go out and seek new grounds, At least until we do break through. No, this does not mean outright crazy popularity (think "Nickelback"...ugh)...but rather for microtonal music to be as seriously accepted as a household art as any other type of music. We have a lot of work left to do (especially with listening tests on the general public) and little bragging rights with music (we may with math...but mathematicians aren't necessarily good musicians)...