We're Just a bunch of EDOISTS

Gene said that he is bored with music that sounds crap. Well the game's up. Yes, I admit it. I belong to a secret society of Edoists which started from around the time of Debussy who's sole purpose is to sabotage all music.

Sorry Gene, couldn't let that one go.

--- In tuning@yahoogroups.com, "rick" <rick_ballan@...> wrote:

> Sorry Gene, couldn't let that one go.
>

Is there nowhere in the world, not even the tuning list, safe from 12edo fanatics? I don't much like sqrt(2) as a musical interval. So sue me. I'm entitled to my own personal tastes in these matters.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "rick" <rick_ballan@> wrote:
>
> > Sorry Gene, couldn't let that one go.
> >
>
> Is there nowhere in the world, not even the tuning list, safe from 12edo fanatics? I don't much like sqrt(2) as a musical interval. So sue me. I'm entitled to my own personal tastes in these matters.
>
I just think that its beyond ridiculous to say that all music over the last century or two has been "boring crap", to use your expression. What, is everyone in the entire music industry misguided? This position seems quite reasonable to me and the opposite of fanaticism. And as for sqrt(2), it's the *only* interval with perfect symmetry, like it or ney. C is to F# what F# is to C. Therefore I will sue you for the sum of $sqrt(2).00.

On 16 Jul 2010, at 6:05 PM, rick wrote:

> . And as for sqrt(2), it's the *only* interval with perfect > symmetry, like it or ney. C is to F# what F# is to C. Therefore I > will sue you for the sum of $sqrt(2).00.
>

I don't see any symmetry: C-F# is augmented fourth, F#-C is diminished fifth. These two intervals are complementary, not symmetric.

Daniel Forro

>"What, is everyone in the entire music industry misguided?"
By music industry, are we talking all musicians or just the highly
advertised, major label crowd? Far as the major label crowd, I actually agree
with Gene...the way those musicians write music is the same way people charge a
fraction of the final cost and good tech support but only during an
"introductory period" for things like internet service: to encourage impulse
buys not long-term quality.
There's tons of great things going on via independent musician, the problem
is the barrier to entry between them and public awareness is so high.

Meanwhile so far as sqrt(2)...it's the only interval which has the symmetry
of being times itself equal to two (duh, that's the definition of a square
root). :-S Guess what, square root of 3 does the same for the tri-tave...but I
haven't heard much about research on that symmetry.
I figure, in music, there are many types of symmetry. Symmetry about the
octave, 5th, sectional/difference-tone symmetry (ALA the PHI/Golden Section
scale), additive symmetry ALA a straight harmonic series...and you almost always
need to give up perfection in obeying one type of symmetry to get another. So
in the end it comes down to a combination artistic preference along with the
technical/mathematical aspect knowing how the symmetry you want works.

--- In tuning@yahoogroups.com, Daniel Forró <dan.for@...> wrote:
>
>
> On 16 Jul 2010, at 6:05 PM, rick wrote:
>
> > . And as for sqrt(2), it's the *only* interval with perfect
> > symmetry, like it or ney. C is to F# what F# is to C. Therefore I
> > will sue you for the sum of $sqrt(2).00.
> >
>
>
> I don't see any symmetry: C-F# is augmented fourth, F#-C is
> diminished fifth. These two intervals are complementary, not symmetric.

More to the point, they are not required to have the same tuning, whatever the 12edo jihad thinks. In meantone, they are separated by a diesis.

I think the real problem with all these debates about the tuning of common-practice music is the fact that enharmonic equivalence has been taken for granted by 12-tET-era composers, and also that the possibility of enharmonic equivalence was not conceived of before the 12-tET-era. Unless a composer did not take enharmonic equivalence for granted and went out of his/her way to specify it or deny it, we'll never know if F# is intended to have the same pitch as Gb in a given piece or not. If enharmonics are intended to be equivalent, then 12-tET is the only tuning that will do; if they are intended to be distinct, then 12-tET will not do; if the composer had no intent one way or the other, the ambiguity is irreconcilable. Insisting that any one tuning is the only one that will do for common-practice music is putting words in composers' mouths that they never uttered, and no matter how compelling the arguments, they will never be conclusive, since there are a variety of interpretations capable of rendering the music consistently.

-Igs

--- In tuning@yahoogroups.com, "rick" <rick_ballan@...> wrote:

> I just think that its beyond ridiculous to say that all music over the last century or two has been "boring crap", to use your expression. What, is everyone in the entire music industry misguided? This position seems quite reasonable to me and the opposite of fanaticism. And as for sqrt(2), it's the *only* interval with perfect symmetry, like it or ney. C is to F# what F# is to C. Therefore I will sue you for the sum of $sqrt(2).00.
>

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:

>If enharmonics are intended to be equivalent, then 12-tET is the only tuning that will do

What nonsense. Forgotten about circulating temperaments? Forgotten that on most instruments, tuning is adjustable?

>Insisting that any one tuning is the only one that will do for common-practice music is putting words in composers' mouths that they never uttered

This is why God gave us musicologists. Do you think the huge advances in knowledge in this field are based on no data?

--- In tuning@yahoogroups.com, Daniel Forró <dan.for@...> wrote:
>
>
> On 16 Jul 2010, at 6:05 PM, rick wrote:
>
> > . And as for sqrt(2), it's the *only* interval with perfect
> > symmetry, like it or ney. C is to F# what F# is to C. Therefore I
> > will sue you for the sum of $sqrt(2).00.
> >
>
>
> I don't see any symmetry: C-F# is augmented fourth, F#-C is
> diminished fifth. These two intervals are complementary, not symmetric.
>
> Daniel Forro
>
1. Just because C is at the bottom doesn't mean it is necessarily the tonic. It could be F# tonic to C b5 inverted.
2. This insistence on naming notes alphabetically completely misses the point of symmetrical equivalence, which is why some serial composers try to avoid it. By Mod(12), 12 = 0 so 6-12 == 6-0 and has same interval content as 0-6. Of course, this is not unique to 12 EDO but applies to any even EDO in general. For 16 EDO it would be 8-0, 22 EDO would be 11-0 etc...

1. ??? Tritone is F#-B#, not F#-Cb. And if it's just jazz chord
spelling (as I suppose) I would reserve it only for discussion about
jazz chords.

2. Sorry, you were the first one using those names and talking about
symmetry in this connection. I just reacted... :-)

When I compose 12tone music, I use often numbers, but as for me more
interesting are intervals and their directions, usually I use numbers
for intervals (including "+" and "-" for directions). It's better for
composition (as intervals are more important for music than note
order) and for intervallic analysis:

0 +4 +2 -1 -2 -4 rather than 0-4-6-5-3-11.

From the second row it's not clear that there are two symmetric
three-tone (trichord) groups, subsets.

But of course absolute numbering is also useful sometimes.

BTW I'm fascinated by symmetry since my childhood and use it last 20
years in almost all my New Music works in almost all music
parameters. Influences of the idea: Machaut, Renaissance and Baroque
polyphony, Skriabin, Schonberg, Hauer, Webern, Messiaen, my professor
Pinos (inventor of intervallic composition method, he was also the
first person, together with E. Herzog 60ies who found all 600^ all-
intervallic 12tone rows with computer program) and more... Czech
composer Miloslav Kabelac was a big fan of symmetry, too (try his 8th
symphony).

Daniel Forró

On 17 Jul 2010, at 10:24 PM, rick wrote:

>
>
> --- In tuning@yahoogroups.com, Daniel Forró <dan.for@...> wrote:
>>
>>
>> On 16 Jul 2010, at 6:05 PM, rick wrote:
>>
>>> . And as for sqrt(2), it's the *only* interval with perfect
>>> symmetry, like it or ney. C is to F# what F# is to C. Therefore I
>>> will sue you for the sum of $sqrt(2).00.
>>>
>>
>>
>> I don't see any symmetry: C-F# is augmented fourth, F#-C is
>> diminished fifth. These two intervals are complementary, not
>> symmetric.
>>
>> Daniel Forro
>>
> 1. Just because C is at the bottom doesn't mean it is necessarily
> the tonic. It could be F# tonic to C b5 inverted.
> 2. This insistence on naming notes alphabetically completely misses
> the point of symmetrical equivalence, which is why some serial
> composers try to avoid it. By Mod(12), 12 = 0 so 6-12 == 6-0 and
> has same interval content as 0-6. Of course, this is not unique to
> 12 EDO but applies to any even EDO in general. For 16 EDO it would
> be 8-0, 22 EDO would be 11-0 etc...

There are 267 distinct all-interval 12-tone rows if you eliminate inversion, retrograde, rotation, transposition.

I've got a useful, searchable list if anyone is interested.

Any given 12-tone row can be located in the list with a simple Word search.

Caleb

On Jul 17, 2010, at 10:02 AM, Daniel Forró wrote:
> ...all 600^ all-
> intervallic 12tone rows with computer program) /...
>

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

> >"What, is everyone in the entire music industry misguided?"
By music industry, are we talking all musicians or just the highly advertised, major label crowd?"

Musicians. I actually dislike the term "music industry" because it turns art into consumer items in your local corner store.

Far as the major label crowd, I actually agree with Gene...the way those musicians write music is the same way people charge a fraction of the final cost...

Me too. Here in Australia laws were actually passed in 98' that basically required $120,000 "licenses" for live music. Yet having recorded music, a DJ, a TV for sporting results or poker machines were classified as a tax break. It took 10 years for these criminal laws to be repealed - we musicians spent all our time lobbying - but not after it destroyed the entire cultural economy. And now, most of the live music revival is just another crap scam, amateur kids with acoustic guitars singing about nothing. This is what to expect when musical education, the tradition of accumulated knowledge and experience, has also fallen by the wayside. And if you hear bad music and complain then you get accused of restricting their 'artistic freedom', probably the most insidious capitalistic scam of all. The constitution didn't take into account freedom of non-expression, the right to be ignorant, to not have an opinion but to follow the crowd, or the right to cover it all up in any way one wants...Sorry, I get angry just thinking about what the politicians allowed to happen here.

Meanwhile so far as sqrt(2)...it's the only interval which has the symmetry of being times itself equal to two (duh, that's the definition of a square root). :-S Guess what, square root of 3 does the same for the tri-tave...but I haven't heard much about research on that symmetry. I figure, in music, there are many types of symmetry...

There is a world of difference between something that is 'self evident' or 'goes without saying' and something that is 'taken for granted'. Kid's will naturally sing in 8ve's but no one will 'naturally' choose to sing in units of PHI. We could also take the sqrt PHI or any number we choose and 'mathematically' the same things will happen. However, I *have* found some physical evidence for 8ve equivalence. Adding 8ve's only changes the amplitude of the wave, not it's shape i.e. its pitch. It's the only interval that does this. This is why we say that a C-c are equivalent and not C-G or C-C*PHI.

-Rick

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, Daniel Forró <dan.for@> wrote:
> >
> >
> > On 16 Jul 2010, at 6:05 PM, rick wrote:
> >
> > > . And as for sqrt(2), it's the *only* interval with perfect
> > > symmetry, like it or ney. C is to F# what F# is to C. Therefore I
> > > will sue you for the sum of $sqrt(2).00.
> > >
> >
> >
> > I don't see any symmetry: C-F# is augmented fourth, F#-C is
> > diminished fifth. These two intervals are complementary, not symmetric.
>
> More to the point, they are not required to have the same tuning, whatever the 12edo jihad thinks. In meantone, they are separated by a diesis.
>
I'm talking about the properties that occur when they *are* equivalent which inadvertently brought a logic all of its own. It's not mutually exclusive with what you're saying here Gene but adds to one's artistic 'palette' (excusing the pretension). But on a more personal note, I used to get home from school, pick up my guitar and books and study and practice till sometimes all hours of the night. Every other hour I was painting or composing. The implication that all this hard work by me and other (proper) musicians is just some form of 'jihad', or that we've all been conned because we took the 12 tet system for granted, reeks of missionary zeal. Sure, most of the music out there is crap. But the source of this is the inevitable mass-ignorance created by hyper-capitalism and fake-advertising, of a system which rewards laziness under 'human rights' and the banner of 'hard work', not musicians with integrity just doing their thing. *This* is why the west is so down on itself and its own traditions. It knows it has no integrity and therefore no inner strength to fall back on (do you think that terrorism would have worked against the Romans?). But it's throwing the baby out with the bathwater. If we spoke of other cultures like we do about ourselves we would be called racist. In any case, if the 12 system was so out of tune it could never have taken hold in the first place. It's one solution to the problem of ET, one that takes advantage of another great western tradition, irrationals. Now how else is a person with my background to approach the topic of alternate tunings but to take what I know and move outwards from there? Knowledge is not a prejudice.

-Rick

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:
>
> I think the real problem with all these debates about the tuning of common-practice music is the fact that enharmonic equivalence has been taken for granted by 12-tET-era composers, and also that the possibility of enharmonic equivalence was not conceived of before the 12-tET-era. Unless a composer did not take enharmonic equivalence for granted and went out of his/her way to specify it or deny it, we'll never know if F# is intended to have the same pitch as Gb in a given piece or not. If enharmonics are intended to be equivalent, then 12-tET is the only tuning that will do; if they are intended to be distinct, then 12-tET will not do; if the composer had no intent one way or the other, the ambiguity is irreconcilable. Insisting that any one tuning is the only one that will do for common-practice music is putting words in composers' mouths that they never uttered, and no matter how compelling the arguments, they will never be conclusive, since there are a variety of interpretations capable of rendering the music consistently.
>
> -Igs

Yes exactly Igs. Also, unpredictable or serendipitous consequences are one of the most important legacies left to us by the ancient Greeks. Eg, who would have guessed that by inscribing regular sided polygons into a circle and taking the number of sides to infinity we would arrive at the number PI? So even if these symmetries and enharmonics were unintentional, it doesn't make them wrong.

-Rick

> --- In tuning@yahoogroups.com, "rick" <rick_ballan@> wrote:
>
> > I just think that its beyond ridiculous to say that all music over the last century or two has been "boring crap", to use your expression. What, is everyone in the entire music industry misguided? This position seems quite reasonable to me and the opposite of fanaticism. And as for sqrt(2), it's the *only* interval with perfect symmetry, like it or ney. C is to F# what F# is to C. Therefore I will sue you for the sum of $sqrt(2).00.
> >
>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@> wrote:
>
> >If enharmonics are intended to be equivalent, then 12-tET is the only tuning that will do
>
> What nonsense. Forgotten about circulating temperaments? Forgotten that on most instruments, tuning is adjustable?
>
> >Insisting that any one tuning is the only one that will do for common-practice music is putting words in composers' mouths that they never uttered
>
> This is why God gave us musicologists. Do you think the huge advances in knowledge in this field are based on no data?
>
Musicologists are like historians; too afraid to make it themselves!

Do you think that conducting experiments in a laboratory is how one learns or understands music, by collecting data? And yet it took me only 6 months to bring into serious doubt the cherished theory of virtual pitch, a theory which took focus away from waves and merely relegated musical harmony to everything we *don't* understand about the brain, a theory which merely expressed the views of the the experimenters themselves, that it is 'subjective'. But to me this is just another excuse for *not practising one's scales*.

-Rick

--- In tuning@yahoogroups.com, "rick" <rick_ballan@...> wrote:
> Musicologists are like historians; too afraid to make it themselves!

George Bernard Shaw said a musicologist was someone who could read music but couldn't hear it.

--- In tuning@yahoogroups.com, "rick" <rick_ballan@...> wrote:

> The implication that all this hard work by me and other (proper) musicians is just some form of 'jihad', or that we've all been conned because we took the 12 tet system for granted, reeks of missionary zeal.

There was no such implicatiopn in anything I said, and the missionary zeal has all been coming from you. I said found the 4edo chord to be boring, and you thought that opinion was not to be tolerated, even though it is based on comparative listening with similar chords. Your intolerance is what reeks of missionary zeal.

>Now how else is a person with my background to approach the topic of alternate tunings but to take what I know and move outwards from there? Knowledge is not a prejudice.

And this group would be the perfect place to do this, but you don't. Instead, you not only ignore the history of Western music, which has not always been a 12edo deal, you ignore the huge number of alternative possibilities and give long lectures on how things are done in 12edo based jazz, as if that defined all of music.

--- In tuning@yahoogroups.com, "jonszanto" <jszanto@...> wrote:
>
> --- In tuning@yahoogroups.com, "rick" <rick_ballan@> wrote:
> > Musicologists are like historians; too afraid to make it themselves!
>
> George Bernard Shaw said a musicologist was someone who could read music but couldn't hear it.
>

"I played over the music of that scoundrel Brahms. What a giftless bastard! It annoys me that this self-inflated mediocrity is hailed as a genius." - GBS

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

> "I played over the music of that scoundrel Brahms. What a giftless bastard! It annoys me that this self-inflated mediocrity is hailed as a genius." - GBS
>

Sorry, misattribution, that was a quote from Tchaikovsky. But Shaw did make fun of him.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> --- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@> wrote:
>
> >If enharmonics are intended to be equivalent, then 12-tET is the only tuning that will do
>
> What nonsense. Forgotten about circulating temperaments? Forgotten that on most instruments, tuning is adjustable?
>

My bad. I did indeed forget about circulating temperaments. They are strange beasts that follow a logic quite unfamiliar to me. But as to the adjustability of tuning on most instruments, I'm not sure what implication that has to enharmonic equivalence. Can you clarify?

> >Insisting that any one tuning is the only one that will do for common-practice music is putting words in composers' mouths that they never uttered
>
> This is why God gave us musicologists. Do you think the huge advances in knowledge in this field are based on no data?
>

Re-read my sentence. Was there some consensus among the composers whose work defines "common practice" regarding a "one true tuning"? Have not the musicologists been discovering that the opposite was the case, that in fact a large variety of tunings were proposed and used throughout the era?

-Igs

--- In tuning@yahoogroups.com, "cityoftheasleep" <igliashon@...> wrote:

> My bad. I did indeed forget about circulating temperaments. They are strange beasts that follow a logic quite unfamiliar to me. But as to the adjustability of tuning on most instruments, I'm not sure what implication that has to enharmonic equivalence. Can you clarify?

An interval which is theoretically supposed to be sqrt(2) is likely to vary quite a bit depending on the harmonic and melodic context.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> An interval which is theoretically supposed to be sqrt(2) is
> likely to vary quite a bit depending on the harmonic and melodic
> context.

I don't get it. Any temperament that sends 50/49 to zero is
liable to have a sqrt(2) in its tuning. What do you have against
this poor interval?

-Carl

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

> I don't get it. Any temperament that sends 50/49 to zero is
> liable to have a sqrt(2) in its tuning.

Any pure-octaves regular temperament which does so must have sqrt(2) in it.

> What do you have against
> this poor interval?

I find it annoying. The highly regular chords of 2edo, 3edo and 4 edo all grate on me, they have a particular quality I don't like if you sustain them. And recommending sqrt(2) on the basis of a comma as large as 50/49 is not very convincing.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> I find it annoying.

I find people who perform music in white tie and tails, full of bogus pomp, annoying. And I'm frequently one of them. Life is full of such conundrums.

--- In tuning@yahoogroups.com, "jonszanto" <jszanto@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> > I find it annoying.
>
> I find people who perform music in white tie and tails, full of bogus pomp, annoying. And I'm frequently one of them. Life is full of such conundrums.

Am I alone in finding these completely symmetrical chords annoying?

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

> > What do you have against
> > this poor interval?
>
> I find it annoying. The highly regular chords of 2edo, 3edo and
> 4 edo all grate on me, they have a particular quality I don't
> like if you sustain them.

Fair enough.

> And recommending sqrt(2) on the basis
> of a comma as large as 50/49 is not very convincing.

Paul Erlich argued vigorously that it was the only acceptable
tuning for the tritone substitution. 50/49 is a pretty
important comma, though it may not suit your personal taste
for high accuracy.

-Carl

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> Am I alone in finding these completely symmetrical chords annoying?

Really, Gene, think of the odds: there *must* be at least one other person.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
> Am I alone in finding these completely symmetrical chords annoying?

Most or all of them are magic chords, which again, Paul argued
are more consonant than any just tuning thereof. He also argued
that the ability to invert them without changing their quality
was an important and desirable effect.

-Carl

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
> Most or all of them are magic chords, which again, Paul argued
> are more consonant than any just tuning thereof. He also argued
> that the ability to invert them without changing their quality
> was an important and desirable effect.

That doesn't necessarily mean they aren't annoying.

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> >
> > Am I alone in finding these completely symmetrical chords annoying?
>
> Most or all of them are magic chords, which again, Paul argued
> are more consonant than any just tuning thereof.

Actually, if you adopt the theory that you need to get within seven cents or so for it to count, they aren't magic chords. But some other tunings *are*. This, in fact, may be what I'm reacting to. 7/5 and 10/7 are seventeen and a half cent away from sqrt(2); too far. 24/17 and 17/12 are much closer, but that's 17 limit. We all know the dismal tale of how badly 5/4 and 6/5 are tuned by 400 and 300 cents, and considering those as 9/7 or 7/6 instead just makes it much worse. So no, I don't think "magic chords" work in favor of the totally equal chords as opposed to the nearly equal chords. Meanwhile, the nearly equal chords I mentioned are all easily within the seven cent tolerance.

He also argued
> that the ability to invert them without changing their quality
> was an important and desirable effect.

Once again, this doesn't work, as the inversion of a nearly equal 3, 4 or 5 note chord is again such a chord. Or 6 notes, for that matter, but I don't think that really works as a chord any more.

So this argument is a bust, suggesting that what is wanted are the nearly equal chords of starling, marvel, and gamelismic temperaments.

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

> > Most or all of them are magic chords, which again, Paul argued
> > are more consonant than any just tuning thereof.
>
> Actually, if you adopt the theory that you need to get within
> seven cents or so for it to count, they aren't magic chords.

What theory is that? sqrt(2) clearly functions as a 7/5 in
the dominant 7th chord in 12-ET.

> But some other tunings *are*. This, in fact, may be what I'm
> reacting to. 7/5 and 10/7 are seventeen and a half cent away
> from sqrt(2); too far. 24/17 and 17/12 are much closer, but
> that's 17 limit. We all know the dismal tale of how badly 5/4
> and 6/5 are tuned by 400 and 300 cents, and considering those
> as 9/7 or 7/6 instead just makes it much worse. So no, I don't
> think "magic chords" work in favor of the totally equal chords
> as opposed to the nearly equal chords. Meanwhile, the nearly
> equal chords I mentioned are all easily within the seven cent
> tolerance.

Now we're talking about the dim7 I suppose. The argument
there is that you have a stack of 6/5s adding up to a 5/3,
which is otherwise impossible.

> > He also argued
> > that the ability to invert them without changing their quality
> > was an important and desirable effect.
>
> Once again, this doesn't work, as the inversion of a nearly
> equal 3, 4 or 5 note chord is again such a chord.

I don't know how nearly equal you mean -- max dyadic error 7
cents? There aren't JI equivalents in that range. In many
cases the perfectly equal version is slightly less than
optimal -- you yourself provided planar tunings for some of
these, once upona. I can't tell if you're denying magic
chords altogether or just crying over the lack of 7-cent
perturbations.

> Or 6 notes, for that matter, but I don't think that really
> works as a chord any more.

Hexads clearly work as chords in jazz and elsewhere, but
generally not in a single octave.

-Carl

Thanks Daniel, I'll check out some of those composers I haven't heard yet.

-Rick

--- In tuning@yahoogroups.com, Daniel Forró <dan.for@...> wrote:
>
> 1. ??? Tritone is F#-B#, not F#-Cb. And if it's just jazz chord
> spelling (as I suppose) I would reserve it only for discussion about
> jazz chords.
>
> 2. Sorry, you were the first one using those names and talking about
> symmetry in this connection. I just reacted... :-)
>
> When I compose 12tone music, I use often numbers, but as for me more
> interesting are intervals and their directions, usually I use numbers
> for intervals (including "+" and "-" for directions). It's better for
> composition (as intervals are more important for music than note
> order) and for intervallic analysis:
>
> 0 +4 +2 -1 -2 -4 rather than 0-4-6-5-3-11.
>
> From the second row it's not clear that there are two symmetric
> three-tone (trichord) groups, subsets.
>
> But of course absolute numbering is also useful sometimes.
>
> BTW I'm fascinated by symmetry since my childhood and use it last 20
> years in almost all my New Music works in almost all music
> parameters. Influences of the idea: Machaut, Renaissance and Baroque
> polyphony, Skriabin, Schonberg, Hauer, Webern, Messiaen, my professor
> Pinos (inventor of intervallic composition method, he was also the
> first person, together with E. Herzog 60ies who found all 600^ all-
> intervallic 12tone rows with computer program) and more... Czech
> composer Miloslav Kabelac was a big fan of symmetry, too (try his 8th
> symphony).
>
> Daniel Forró
>
>
> On 17 Jul 2010, at 10:24 PM, rick wrote:
>
> >
> >
> > --- In tuning@yahoogroups.com, Daniel Forró <dan.for@> wrote:
> >>
> >>
> >> On 16 Jul 2010, at 6:05 PM, rick wrote:
> >>
> >>> . And as for sqrt(2), it's the *only* interval with perfect
> >>> symmetry, like it or ney. C is to F# what F# is to C. Therefore I
> >>> will sue you for the sum of $sqrt(2).00.
> >>>
> >>
> >>
> >> I don't see any symmetry: C-F# is augmented fourth, F#-C is
> >> diminished fifth. These two intervals are complementary, not
> >> symmetric.
> >>
> >> Daniel Forro
> >>
> > 1. Just because C is at the bottom doesn't mean it is necessarily
> > the tonic. It could be F# tonic to C b5 inverted.
> > 2. This insistence on naming notes alphabetically completely misses
> > the point of symmetrical equivalence, which is why some serial
> > composers try to avoid it. By Mod(12), 12 = 0 so 6-12 == 6-0 and
> > has same interval content as 0-6. Of course, this is not unique to
> > 12 EDO but applies to any even EDO in general. For 16 EDO it would
> > be 8-0, 22 EDO would be 11-0 etc...
>

--- In tuning@yahoogroups.com, "jonszanto" <jszanto@...> wrote:
>
> --- In tuning@yahoogroups.com, "rick" <rick_ballan@> wrote:
> > Musicologists are like historians; too afraid to make it themselves!
>
> George Bernard Shaw said a musicologist was someone who could read music but couldn't hear it.
>
Nice one. And who was it that said "He has an ear for music like Van Gogh?"

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "rick" <rick_ballan@> wrote:
>
> > The implication that all this hard work by me and other (proper) musicians is just some form of 'jihad', or that we've all been conned because we took the 12 tet system for granted, reeks of missionary zeal.
>
> There was no such implicatiopn in anything I said, and the missionary zeal has all been coming from you. I said found the 4edo chord to be boring, and you thought that opinion was not to be tolerated, even though it is based on comparative listening with similar chords. Your intolerance is what reeks of missionary zeal.
>
> >Now how else is a person with my background to approach the topic of alternate tunings but to take what I know and move outwards from there? Knowledge is not a prejudice.
>
> And this group would be the perfect place to do this, but you don't. Instead, you not only ignore the history of Western music, which has not always been a 12edo deal, you ignore the huge number of alternative possibilities and give long lectures on how things are done in 12edo based jazz, as if that defined all of music.
>
Yes but Gene, you must remember that playing guitar for someone like me is as second nature as speaking. And when I'm composing well it's the same. So it's not a question that I deliberately ignore other possible tunings - I'm here aren't I? - but that years of number crunching and countless false leads made me actually appreciate what I seemed to know in the first place. Only after years of trying to turn music into JI could I appreciate what an eloquent solution the 12 EDO system really was, how it balanced simplicity of use against making small harmonic sacrifices etc...It also taught me that there is a commonality to all tunings which I've been trying to capture ever since.

Therefore I don't buy your statement that it's how things are done in 12EDO "jazz", which is just a marketing/pigeon holing word, because I hear exactly the same things like guide tones and diminished chords all the way through diatonic classical music (Just today I went to hear Vaughn William's Sea Symph and every crashing wave was built by a dim7). Its the way things are done in the vast majority of cases. Trying to retune these using whole-numbers is not impossible by any means so long as one distinguishes between tonal and passing intervals and noting where they appear in a composition.

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
>
> > > Most or all of them are magic chords, which again, Paul argued
> > > are more consonant than any just tuning thereof.
> >
> > Actually, if you adopt the theory that you need to get within
> > seven cents or so for it to count, they aren't magic chords.
>
> What theory is that?

The "theory" is more an observation, that if you don't get within 7 cents you've got a pretty piss-poor approximation for musical purposes.

sqrt(2) clearly functions as a 7/5 in
> the dominant 7th chord in 12-ET.

I wouldn't say "clearly", because the 7 in the dom7 in 12et is not completely clear. And yes, I think it does function as a 7/5; if 12 is a little murky, 22 is clear. But it is a terrible approximation, and saying I shouldn't find it annoying on the grounds that it is a good one is nonsense.

> Now we're talking about the dim7 I suppose. The argument
> there is that you have a stack of 6/5s adding up to a 5/3,
> which is otherwise impossible.

That is the crap sound I don't like. The "nearly equal" version has a stack of 6/5s adding up to 12/7, and I think that sounds better. It's certainly in better tune by the numbers. It's 126/125 as a comma, 13.8 cents, rather than 648/625, 62.6 cents. Guess which works better.

> > > He also argued
> > > that the ability to invert them without changing their quality
> > > was an important and desirable effect.
> >
> > Once again, this doesn't work, as the inversion of a nearly
> > equal 3, 4 or 5 note chord is again such a chord.
>
> I don't know how nearly equal you mean -- max dyadic error 7
> cents?

Yes. Distribute the 13.8 cent comma between three 6/5s and one 7/6, and you are easily less than 7 cents off, as you've got 3.45 cents on average to spread around. Distribute 62.6 cents four ways and you are in crap city, the same somewhat dubious minor third we all enjoy in 12et, and tritones even worse.

There aren't JI equivalents in that range. In many
> cases the perfectly equal version is slightly less than
> optimal -- you yourself provided planar tunings for some of
> these, once upona.

Wake up and smell the coffee! That is, of course, what this is about.

I can't tell if you're denying magic
> chords altogether or just crying over the lack of 7-cent
> perturbations.

No, I'm saying the completely equal versions aren't very good. It's not rocket science--look at the numbers. If they need to be good for the magic chord effect to work its hypothetical magic, then it's no wonder they don't *sound* good. Why would anyone expect them to?

> > Or 6 notes, for that matter, but I don't think that really
> > works as a chord any more.
>
> Hexads clearly work as chords in jazz and elsewhere, but
> generally not in a single octave.

Well, the nearly-equal hexad is this nifty 5-limit chord which spreads
32805/32768, which we all know is less than two cents, around on five 9/8s and one 10/9. And yeah, voicing is clearly the key here.

--- In tuning@yahoogroups.com, "rick" <rick_ballan@...> wrote:

> Therefore I don't buy your statement that it's how things are done in 12EDO "jazz", which is just a marketing/pigeon holing word, because I hear exactly the same things like guide tones and diminished chords all the way through diatonic classical music

And yet, when I compared guide tones to Baroque continuo, you ridiculed me. That sort of thing is why I get the idea you are very narrow minded.

It's hard to gage exactly how many on the List are presently concerned with
retuning 12 equal into JI. The myriad of historical tunings that were in
use - that were non-12 equal - make this expedition murky at best.

La Monte Young once generously explained to me how he adapted his 12 equal
"Sarabande" into a just intonation piece. The key to its success,
according to the composer and theorist, is to place the fundamental extremely
low...beyond human hearing. La Monte then chose a specific array, found in the
higher realms of the overtone series, to finalize a set of his preferred
relationships. In his aesthetic, this would mean no 5/4 major
thirds....ever!

Johnny

On Sat, Jul 17, 2010 at 11:34 AM, rick <rick_ballan@...> wrote:
>
> Do you think that conducting experiments in a laboratory is how one learns or understands music, by collecting data? And yet it took me only 6 months to bring into serious doubt the cherished theory of virtual pitch, a theory which took focus away from waves and merely relegated musical harmony to everything we *don't* understand about the brain, a theory which merely expressed the views of the the experimenters themselves, that it is 'subjective'. But to me this is just another excuse for *not practising one's scales*.

Argh.

-Mike

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

> The "theory" is more an observation, that if you don't get
> within 7 cents you've got a pretty piss-poor approximation
> for musical purposes.

The only limit to accuracy is the desire to remove commas.
With adaptive JI, one can have his cake and eat it too.
Throw in a little adaptive timbre to help with the larger
commas and there really isn't a reason we all can't be living
in musical utopia. Incidentally, while you were gone I
figured out that the optimal tuning for using a temperament
adaptively (as a melodic temperament) is the one which
minimizes the largest *difference* between dyadic errors,
preserving signs and when the unison is included as a dyad:

http://lumma.org/music/theory/AdaptiveShift.txt

> sqrt(2) clearly functions as a 7/5 in
> > the dominant 7th chord in 12-ET.
//
> But it is a terrible approximation, and saying I shouldn't
> find it annoying on the grounds that it is a good one
> is nonsense.

No one can tell you not to find something annoying, or not to
use that as inspiration.

> > I can't tell if you're denying magic
> > chords altogether or just crying over the lack of 7-cent
> > perturbations.
>
> No, I'm saying the completely equal versions aren't very good.
> It's not rocket science--look at the numbers. If they need to
> be good for the magic chord effect to work its hypothetical
> magic, then it's no wonder they don't *sound* good. Why would
> anyone expect them to?

I'm not arguing the equal versions are best, I simply said
that they are magic chords and that is one thing they have
going for them. Jeez. In case you forgot, here are the two
chords in question:

http://lumma.org/music/theory/sss/4-ET.mid
http://lumma.org/music/theory/sss/dim-planar.mid

-Carl

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Sat, Jul 17, 2010 at 11:34 AM, rick <rick_ballan@...> wrote:
> >
> > Do you think that conducting experiments in a laboratory is how
> > one learns or understands music, by collecting data? And yet it
> > took me only 6 months to bring into serious doubt the cherished
> > theory of virtual pitch,

Wow, missed this. The mind boggles.

-Carl

Carl>"Throw in a little adaptive timbre to help with the larger
commas and there really isn't a reason we all can't be living
in musical utopia."

A few concerns for adaptive JI, "even" with Setharesian timbres

A) At least from what adaptive JI implementations I've seen, adaptive JI ignores
neutral seconds, the 11/6 seventh, and several other more exotic intervals and
instead concentrates on common practice intervals. On the other hand of course,
in theory adaptive JI COULD include such intervals.

B) Same goes for letting the composer choose between slight variations of a
chord IE things like the comma-like difference between 13/8 and 18/11. How many
JI programs will actually ask you "here are the possible ways to tune chords
that sound like the chord you made...now which one do you want?"

C) I also have seen adaptive JI lack choice for how many notes are counted as in
a chord. If there are 7 notes sustained at once..I assume an adaptive JI
program would most likely make a 4-note JI chord and give up on the other tones
and make them neighboring tones. However (at the cost of having higher limit
chords, in many cases) it would be nice to have an option to have 5, 6, or even
7 notes pushed into a lowest-possible-limit JI chord.

D) I think in many ways the starting scale still matters a LOT in JI. It
determines which dyads, triads, etc. you are nearest to and thus what the
program tries to "round" you chord to. Thus a good scale for adaptive JI, I
figure, would have most possible notes within 10 if not 7 cents of perfect
intervals and commatic "shift" would often be too small to notice.

E) What would be a good way to figure out which chords could be considered JI
under the Setharesian method but not the standard "harmonic only" timbre method?

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "Carl Lumma" <carl@> wrote:
>
> > I don't get it. Any temperament that sends 50/49 to zero is
> > liable to have a sqrt(2) in its tuning.
>
> Any pure-octaves regular temperament which does so must have sqrt(2) in it.
>
> > What do you have against
> > this poor interval?
>
> I find it annoying. The highly regular chords of 2edo, 3edo and 4 edo all grate on me, they have a particular quality I don't like if you sustain them. And recommending sqrt(2) on the basis of a comma as large as 50/49 is not very convincing.
>
Then don't sustain them. That's the whole point of passing chords. You won't understand what I'm saying by listening to them completely out of harmonic context. One of my favourite V7 chords in a ballad is the 7(#9)-> 7(b9) voiced so that the #9 (aka 'minor third') and major third are semitones apart eg G-F-A#-B to G-F-Ab-B to Cmaj7. Another one is the 13(b9) which is like an E maj triad over a G7. The temporary clashing creates a dreamy quality. But hold any one of these too long and they will indeed become very annoying.

By retuning all of these clashes kind of misses the point. Music constantly moves forward and knowing how to deal with 'dissonance' is an important part of the art.

--- In tuning@yahoogroups.com, "jonszanto" <jszanto@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> > Am I alone in finding these completely symmetrical chords annoying?
>
> Really, Gene, think of the odds: there *must* be at least one other person.
>
*Everyone* will find them annoying if treated in the wrong way. Again, what I find annoying is the belief that the art of musical composition can be circumvented by a 'science' that takes only a small part of the bigger picture and tests the crap out of it. When Pythagoras discovered that ratio = harmony he is said to have exclaimed "Everything is logos!", which is the Greek word for order, ratio, measure. It became the root of our word 'logic' and the suffix '...ology'. Therefore, 'musicology' is a complete tautology. Hardly 'scientific' or 'historically accurate. Forget about white shirts and tails. The true pompous posturing is found in the idea that music could ever be reduced to a 'science' when it is really just bad science.

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@> wrote:
> >
> > Am I alone in finding these completely symmetrical chords annoying?
>
> Most or all of them are magic chords, which again, Paul argued
> are more consonant than any just tuning thereof. He also argued
> that the ability to invert them without changing their quality
> was an important and desirable effect.
>
> -Carl
>
It doesn't surprise me that Paul said it right. He more than anybody understands that 'consonance' is largely context based.

--- In tuning@yahoogroups.com, "Carl Lumma" <carl@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >
> > On Sat, Jul 17, 2010 at 11:34 AM, rick <rick_ballan@> wrote:
> > >
> > > Do you think that conducting experiments in a laboratory is how
> > > one learns or understands music, by collecting data? And yet it
> > > took me only 6 months to bring into serious doubt the cherished
> > > theory of virtual pitch,
>
> Wow, missed this. The mind boggles.
>
> -Carl
>
Complex waves contain extrema at the GCD's between the convergents/semi-convergents of their component frequencies, the most prominent of which correspond to the VP. What's so 'boggling' about that? It's proven and is going to be published. End of story.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Sat, Jul 17, 2010 at 11:34 AM, rick <rick_ballan@...> wrote:
> >
> > Do you think that conducting experiments in a laboratory is how one learns or understands music, by collecting data? And yet it took me only 6 months to bring into serious doubt the cherished theory of virtual pitch, a theory which took focus away from waves and merely relegated musical harmony to everything we *don't* understand about the brain, a theory which merely expressed the views of the the experimenters themselves, that it is 'subjective'. But to me this is just another excuse for *not practising one's scales*.
>
> Argh.
>
> -Mike
>
Argh! I said that VP could possibly be explained by the fact that the GCD's of JI intervals remain after the wave has been significantly detuned. This has now been proved, will be published, and your and Carl's opinion is now just that, an opinion.

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
>
>
>
> --- In tuning@yahoogroups.com, "rick" <rick_ballan@> wrote:
>
> > Therefore I don't buy your statement that it's how things are done in 12EDO "jazz", which is just a marketing/pigeon holing word, because I hear exactly the same things like guide tones and diminished chords all the way through diatonic classical music
>
> And yet, when I compared guide tones to Baroque continuo, you ridiculed me. That sort of thing is why I get the idea you are very narrow minded.
>
I've never ridiculed you about this Gene. Sorry if it came across this way (I was more trying to be funny). I just meant to say that the identification of guide tones 3rds-7ths as *the* important intervals seems to be something unique to the 20th century, though its presence can be felt in earlier tonal music. And I'm not narrow minded. I like allot of music, including xentonality. But I don't think that things have to be mutually exclusive.

In my opinion exactly this is the most banal and primitive, and overused chord progression since the Baroque times. In any tonal piece, including jazz an pop.

I personally started to be allergic on it many years ago. It destroyed lot of nice melodies which could live well without such harmonization.

One of the ugliest and the most boring cliche in music at all.

The most important, for sure not. The most used, yes. Quantity, yes, but quality is missing. It's not possible to develop it or to derive anything creative from it. There's only one chance - stop using it. Now.

Daniel Forro

On 19 Jul 2010, at 7:57 PM, rick wrote:

>
>
> --- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> > wrote:
>>
>>
>>
>> --- In tuning@yahoogroups.com, "rick" <rick_ballan@> wrote:
>>
>>> Therefore I don't buy your statement that it's how things are >>> done in 12EDO "jazz", which is just a marketing/pigeon holing >>> word, because I hear exactly the same things like guide tones and >>> diminished chords all the way through diatonic classical music
>>
>> And yet, when I compared guide tones to Baroque continuo, you >> ridiculed me. That sort of thing is why I get the idea you are >> very narrow minded.
>>
> I've never ridiculed you about this Gene. Sorry if it came across > this way (I was more trying to be funny). I just meant to say that > the identification of guide tones 3rds-7ths as *the* important > intervals seems to be something unique to the 20th century, though > its presence can be felt in earlier tonal music. And I'm not narrow > minded. I like allot of music, including xentonality. But I don't > think that things have to be mutually exclusive.

--- In tuning@yahoogroups.com, "rick" <rick_ballan@...> wrote:

> It doesn't surprise me that Paul said it right. He more than anybody understands that 'consonance' is largely context based.
>

You keep talking about consonance and dissonance, which I never mentioned. The words I used, if you will recall, are "boring" and "annoying". Of course you scientific types can't understand that, so you put on your white lab coats and talk about consonance and dissonance instead.

On 19.07.2010, at 11:57, rick wrote:
> I just meant to say that the identification of guide tones 3rds-7ths > as *the* important intervals seems to be something unique to the > 20th century, though its presence can be felt in earlier tonal music.

the treatment of 7th as guide tone (stepwise resolution etc.) is discussed in most classical theories of harmony, not something 20th century at all (quite the opposite, starting with end 19th century 7th were treated differently). The guide tone qualities of the 3rds are also discussed in detail earlier, e.g., in 19th century treatises such as Riemann.

Best wishes,
Torsten

--
Torsten Anders
Interdisciplinary Centre for Computer Music Research
University of Plymouth
Office: +44-1752-586219
Private: +44-1752-558917
http://strasheela.sourceforge.net
http://www.torsten-anders.de

On Mon, Jul 19, 2010 at 6:38 AM, rick <rick_ballan@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > On Sat, Jul 17, 2010 at 11:34 AM, rick <rick_ballan@...> wrote:
> > >
> > > Do you think that conducting experiments in a laboratory is how one learns or understands music, by collecting data? And yet it took me only 6 months to bring into serious doubt the cherished theory of virtual pitch, a theory which took focus away from waves and merely relegated musical harmony to everything we *don't* understand about the brain, a theory which merely expressed the views of the the experimenters themselves, that it is 'subjective'. But to me this is just another excuse for *not practising one's scales*.
> >
> > Argh.
> >
> > -Mike
> >
> Argh! I said that VP could possibly be explained by the fact that the GCD's of JI intervals remain after the wave has been significantly detuned. This has now been proved, will be published, and your and Carl's opinion is now just that, an opinion.

LOL. I wasn't aware that when something is published, it becomes an
undeniable fact.

We've been over this about a thousand times, and every time it
resolves the same way: I explain that the term "virtual pitch" is just
a terminology that for some reason offends you, and you say "ok, I
understand that." Then, a few weeks later, you start up again with the
"I have singlehandedly disproven virtual pitch by finding a
mathematical way to generate the virtual pitch." And then we do it all
again.

At this point I'm convinced that you simply have some weird kind of
fetish for finding "glory," or however you view these things.

-Mike

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

> LOL. I wasn't aware that when something is published, it becomes an
> undeniable fact.

I wasn't aware that when something is submitted to a refereed journal (if that is what he has done) it's the same as being published.

--- In tuning@yahoogroups.com, "rick" <rick_ballan@...> wrote:

> Complex waves contain extrema at the GCD's between the
> convergents/semi-convergents of their component frequencies,

Huh? Wait, don't answer that.

> the most prominent of which correspond to the VP. What's so
> 'boggling' about that?

The fact that you think you've "called VP into doubt" is
boggling, Rick.

> It's proven and is going to be published.

Whoopie.

-Carl

Also, if I remember correctly, didn't your model basically crap out
for 10 steps out of 12? It kept alternating between 7/4, 16/9, and
9/5, or something like that?

-Mike

On Mon, Jul 19, 2010 at 11:49 AM, Mike Battaglia <battaglia01@...> wrote:
> On Mon, Jul 19, 2010 at 6:38 AM, rick <rick_ballan@...> wrote:
>>
>> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>> >
>> > On Sat, Jul 17, 2010 at 11:34 AM, rick <rick_ballan@...> wrote:
>> > >
>> > > Do you think that conducting experiments in a laboratory is how one learns or understands music, by collecting data? And yet it took me only 6 months to bring into serious doubt the cherished theory of virtual pitch, a theory which took focus away from waves and merely relegated musical harmony to everything we *don't* understand about the brain, a theory which merely expressed the views of the the experimenters themselves, that it is 'subjective'. But to me this is just another excuse for *not practising one's scales*.
>> >
>> > Argh.
>> >
>> > -Mike
>> >
>> Argh! I said that VP could possibly be explained by the fact that the GCD's of JI intervals remain after the wave has been significantly detuned. This has now been proved, will be published, and your and Carl's opinion is now just that, an opinion.
>
> LOL. I wasn't aware that when something is published, it becomes an
> undeniable fact.
>
> We've been over this about a thousand times, and every time it
> resolves the same way: I explain that the term "virtual pitch" is just
> a terminology that for some reason offends you, and you say "ok, I
> understand that." Then, a few weeks later, you start up again with the
> "I have singlehandedly disproven virtual pitch by finding a
> mathematical way to generate the virtual pitch." And then we do it all
> again.
>
> At this point I'm convinced that you simply have some weird kind of
> fetish for finding "glory," or however you view these things.
>
> -Mike
>

--- In tuning@yahoogroups.com, "genewardsmith" <genewardsmith@...> wrote:
> .... 7/5 and 10/7 are seventeen and a half cent away from sqrt(2);
> too far. 24/17 and 17/12 are much closer, but that's 17 limit....

Hi Gene,

historically there are even more archaic interpretations:
http://www.medieval.org/emfaq/harmony/tritone.html
"
...augmented fourth equal to precisely three 9:8 whole-tones, or 729:512, e.g. f-b) as one of the 13 basic intervals, and also proposes as a distinct 14th interval the "semitritonus" or diminished fifth of 1024:729, which he finds somewhat less discordant....
"
so far about the good-old Pythagorean 3-limit concept of the tritone.

Here some coeval funny illustrations by master Bosch:
http://solomonsmusic.net/Bosch_Music.htm

Additional Wiki includes the corresponding higher 7 & 5-limit variants:
http://en.wikipedia.org/wiki/Tritone
[attend the sound-examples]
"
ratios:"...7:5, 10:7, 25:18, 45:32, 729:512..."with theirs approxs in
in ~Cents: "... 583, 617, 569, 590, 612..."

An author in Wiki even accepts in his contribution,
much larger deviations of about an ~quarter-tone off from 600Cents:
"The 11:8 undecimal tritone is ~551.3 cents
and may be derived from the harmonic series as the interval between the eighth harmonic and the eleventh harmonic...."

In Switzerland that 11/8 -"tritone" is labeled as the 'alphorn-fa":
http://launch.dir.groups.yahoo.com/group/tuning/message/64344
"Remark: ~51.3 Cents leads to funny quartertones."

Here an composers statement about the functionality of the tritone:
"Any tendency for a tonality to emerge may be avoided by introducing a note three whole tones distant from the key note of that tonality."
Quote made by:
http://en.wikipedia.org/wiki/Reginald_Smith_Brindle

Hence, due to all the hitherto above mentioned and many other possibile interpretations of perception,
the tritone can be considered within 12-EDO dodecatonics as the most ambigious unstable interval against the unison-root.

Exclusively it even allows above all other intervals
to provoke some strange acoustical illusions,
especially alike the so called:

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

Further information, more en detail, including some sound-examples:
http://deutsch.ucsd.edu/psychology/deutsch_research6.php

Demonstrations by download-able *.mp3 file
http://philomel.com/musical_illusions/play.php?fname=Tritone_paradox
http://philomel.com/musical_illusions/tritone.php

University reseach-group:
https://ccrma.stanford.edu/realsimple/mus_illus/Tritone_Paradox.html

My colleague Ernst Terhard persents here in his view about that topic:
http://www.mmk.ei.tum.de/persons/ter/top/tritone.html

Against all that incertitude, Carl claimed by his 7-limit theory in
/tuning/topicId_91069.html#91153
"
sqrt(2) clearly functions as a 7/5 in the dominant 7th chord in 12-ET
"

I dare to doubt about that is the only feasable solution:

In order to fefute that par-example,
study Richard-Wagner's classical counter-example:
http://en.wikipedia.org/wiki/Tristan_chord
"The Tristan chord is a chord made up of the notes F, B, D# and G#. More generally, it can be any chord that consists of these same intervals: augmented fourth, augmented sixth, and augmented ninth above a root....

[see the note-score in the WIKI-link, and listen to the sound-file]

Analysis:
Although at the same time enharmonically sounding like the half-diminished chord F-Ab-Cb-Eb, it can also be interpreted as the suspended altered subdominant II: B-D#-F-G# (the G# being the suspension in the key of A minor)."

References to other musicological lectures about the T-chord in:
/tuning/topicId_58278.html#58413
http://mto.societymusictheory.org/issues/mto.95.1.1/mto.95.1.1.rothgeb.art

Hence, byond of that somehow doubious character of sqrt(2):
Personally I would'nt insist to restrict to the perticular meaning of sqrt(2) within 12-EDO so strictly to just that two given interpretations as the alone valid one.
The above given ratios do allow some other potential alternatives,
each depending of the chosen ratios.

All you can say of the interval-seize: ~sqrt(2)+-(~50 Cents)
without knowing any context in the evolution of melody and harmony,
is to localize the limits:
Somewhere inbetween the range of an: 4th and 5th.
in the case of lacking knowledge about the function of the interval.

In oder to determine it more precisely,
one needs more information:
How arised that 'tritone' within the progression of time,
that can be influenced by the factors:

1. Melodic-line,
2. Harmoic-progress
or even in some rare cases
3. Rhytmic-patterns
no to neglect
4. Listeners training, expectations and habits

There are many strategies and schools to find some
reasonable fitting ratios, depending on the personal preferences,
about the quest:
Could my present understanding of the interval-ratio
work as an apt eligible imagination for other listeners too?

Arrive the Conclusion:
{includes some slapping of 12-ET and its off-shot sqrt(2)}
Always try to take a broade view,
when argueing how to grasp about ~sqrt(2)'s possible meaning.
Expect that other people come to different resolutions as you-self.
Try to study carefully the context before the interval arises within time-progression.
Be aware:
The so yielding result depends on the personal consuetude
and habits: There are many ways of individual apprehension:
Just consider, when ~sqrt(2) occurs in 12-ET: "One seize fits all."
But i.m.h.o. meanwhile that tedious tritone-interval got used all to much up, so that it had become fully worn out to a needless nub.
Exhausted due to all to much overstraining.
Now it has become almost meaningless spent,
just as hackneyed as the boring 12-ET itself.
The sqrt(2) blunder arises from atonal 12-EDO.
Why using a stupid bunch of a dozen logarithimic-equidistant intervals?
Namely sqrt(2) can be considered as the worst among the twelf:
Shot-off, out of the target!

Now, my previous general rebuff of 12-ET: "Tears in my ears!"
can be substantiated more precisely into the refinded bottom line:

Quintessence:
Popping sqrt(2) results in my ear-canal an tear-dropping-flood,
skirls banal in the acoustic-meatus an whirl of high-water-flood,
No good!

bye
Andy

ok,

I'm being serious here.

Since some people hinge harmonic perception on virtual pitch playing a
significant role this suggests that you have a different way to explain the
perception of harmony.

Can you give me (us?) the brief version of this finding?

And not being serious

Guys - you have it wrong. Its not being published that establishes a fact -
all that has to happen is for it to be on the internet.

Chris

On Mon, Jul 19, 2010 at 11:49 AM, Mike Battaglia <battaglia01@...>wrote:

>
>
> On Mon, Jul 19, 2010 at 6:38 AM, rick <rick_ballan@...<rick_ballan%40yahoo.com.au>>
> wrote:
> >
> > --- In tuning@yahoogroups.com <tuning%40yahoogroups.com>, Mike Battaglia
> <battaglia01@...> wrote:
> > >
> > > On Sat, Jul 17, 2010 at 11:34 AM, rick <rick_ballan@...> wrote:
> > > >
> > > > Do you think that conducting experiments in a laboratory is how one
> learns or understands music, by collecting data? And yet it took me only 6
> months to bring into serious doubt the cherished theory of virtual pitch, a
> theory which took focus away from waves and merely relegated musical harmony
> to everything we *don't* understand about the brain, a theory which merely
> expressed the views of the the experimenters themselves, that it is
> 'subjective'. But to me this is just another excuse for *not practising
> one's scales*.
> > >
>

On Mon, Jul 19, 2010 at 4:03 PM, Chris Vaisvil <chrisvaisvil@...> wrote:
>
> Can you give me (us?) the brief version of this finding?

Rick has come up with an algorithm to estimate the fundamental
frequency for a complex waveform. It works entirely in the time domain
and doesn't involve an autocorrelation or anything like that. The end.

-Mike

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Mon, Jul 19, 2010 at 6:38 AM, rick <rick_ballan@...> wrote:
> >
> > --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> > >
> > > On Sat, Jul 17, 2010 at 11:34 AM, rick <rick_ballan@> wrote:
> > > >
> > > > Do you think that conducting experiments in a laboratory is how one learns or understands music, by collecting data? And yet it took me only 6 months to bring into serious doubt the cherished theory of virtual pitch, a theory which took focus away from waves and merely relegated musical harmony to everything we *don't* understand about the brain, a theory which merely expressed the views of the the experimenters themselves, that it is 'subjective'. But to me this is just another excuse for *not practising one's scales*.
> > >
> > > Argh.
> > >
> > > -Mike
> > >
> > Argh! I said that VP could possibly be explained by the fact that the GCD's of JI intervals remain after the wave has been significantly detuned. This has now been proved, will be published, and your and Carl's opinion is now just that, an opinion.
>
> LOL. I wasn't aware that when something is published, it becomes an
> undeniable fact.
>
> We've been over this about a thousand times, and every time it
> resolves the same way: I explain that the term "virtual pitch" is just
> a terminology that for some reason offends you, and you say "ok, I
> understand that." Then, a few weeks later, you start up again with the
> "I have singlehandedly disproven virtual pitch by finding a
> mathematical way to generate the virtual pitch." And then we do it all
> again.
>
> At this point I'm convinced that you simply have some weird kind of
> fetish for finding "glory," or however you view these things.
>
> -Mike
>
Not at all Mike. It's just that sometimes I have to use the term for the entire theory of VP. When I spoke to Bill he said "If you can A) prove this for Fourier series in general and B) show how it relates to harmonic entropy, then I think that you'll have a legitimate alternative to virtual pitch". I mentioned nothing of VP. I then showed him how both of these could be done and he agreed. He also immediately recognised the difference between his own harmonic stretching and this. Whereas his changes the condition of the waves, mine takes them as is and pulls them apart. They are not mutually exclusive.

Also, you shouldn't put words in my mouth. I did not say "I have singlehandedly disproven virtual pitch" at all. What I said was "bring into serious doubt the cherished theory of virtual pitch". What I have in mind is the fact that a scientific theory is never proved 'true' (Hume, Popper). It only ever remains unfalsified up to a given point in time. And according to Popper, highly falsifiable/testible theories are usually those ones that seem the most 'bold and unbelievable'. For eg, if we say "It's going to rain sometime in the future" this is untestable because it gives no time or space limit. Everyone will believe it. Yet if we say "It's going to rain at such and such a time and exactly at this place" then it becomes both highly testable and more unbelievable. So if it does happen to rain then people take notice. Unfortunately, this 'boldness' is too often taken for arrogance or even madness and is why good theories are often ignored for many years (Evolution and Fourier series are two that comes to mind). Really, I'm just finishing up an idea that started in the late 90's and I haven't been able to formulize until now.

Therefore when you say "LOL I wasn't aware that when something is published, it becomes an undeniable fact" you're right because there is no such thing. And I don't have to point out that this runs both ways to Fourier transforms, VP, wavelets, convolution etc...I'll also say again that what worried me about VP theory is that I couldn't think of how it could possibly be falsified, hence my statement "relegated musical harmony to everything we *don't* understand about the brain". "Why do we hear this note? Oh its just the VP". They thought they had applied Occam's razor and eliminated all possible wave theoretical explanations for this phenomena. But they hadn't.

It's much harder finding something new than learning what's already been done because we have to go through all the complicated maths with no guarantee at the end.

-Rick

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> Also, if I remember correctly, didn't your model basically crap out
> for 10 steps out of 12? It kept alternating between 7/4, 16/9, and
> 9/5, or something like that?
>
> -Mike

No, you simply didn't understand what was going on. It gave perfect predictions for the first wave convergents of all the near-epimoric intervals and higher convergents for their inversions. More exactly, he k'th convergent p/q corresponds to (p - q). For eg, 2^(1/3) has 1st WC p/q = 5/4 and 1 = (5 - 4). The major 6th 2^(3/4) has 8/5 as its third WC and (8 - 5) = 3.

Now, each one of these WC don't enter into the wave on an equal footing. The 5/4 for eg will occur much more often than the 19/15's (of which there are more than one, all with different ~ GCD's). This is because it's p/q is small and its ~ GCD is significantly *larger* in comparison to the component frequencies. It will therefore have a higher frequency of occurrence (We can see this quickly by just dividing the component freq's by p and q which puts us in the general area. 81/64 for eg, 81/5 ~ 64/4 ~ 16. 81/19 ~ 64/15 ~ 4 and already we're a long way below).

I posted some graphic examples which explains it better.
>
>
> On Mon, Jul 19, 2010 at 11:49 AM, Mike Battaglia <battaglia01@...> wrote:
> > On Mon, Jul 19, 2010 at 6:38 AM, rick <rick_ballan@...> wrote:
> >>
> >> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@> wrote:
> >> >
> >> > On Sat, Jul 17, 2010 at 11:34 AM, rick <rick_ballan@> wrote:
> >> > >
> >> > > Do you think that conducting experiments in a laboratory is how one learns or understands music, by collecting data? And yet it took me only 6 months to bring into serious doubt the cherished theory of virtual pitch, a theory which took focus away from waves and merely relegated musical harmony to everything we *don't* understand about the brain, a theory which merely expressed the views of the the experimenters themselves, that it is 'subjective'. But to me this is just another excuse for *not practising one's scales*.
> >> >
> >> > Argh.
> >> >
> >> > -Mike
> >> >
> >> Argh! I said that VP could possibly be explained by the fact that the GCD's of JI intervals remain after the wave has been significantly detuned. This has now been proved, will be published, and your and Carl's opinion is now just that, an opinion.
> >
> > LOL. I wasn't aware that when something is published, it becomes an
> > undeniable fact.
> >
> > We've been over this about a thousand times, and every time it
> > resolves the same way: I explain that the term "virtual pitch" is just
> > a terminology that for some reason offends you, and you say "ok, I
> > understand that." Then, a few weeks later, you start up again with the
> > "I have singlehandedly disproven virtual pitch by finding a
> > mathematical way to generate the virtual pitch." And then we do it all
> > again.
> >
> > At this point I'm convinced that you simply have some weird kind of
> > fetish for finding "glory," or however you view these things.
> >
> > -Mike
> >
>

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Mon, Jul 19, 2010 at 4:03 PM, Chris Vaisvil <chrisvaisvil@...> wrote:
> >
> > Can you give me (us?) the brief version of this finding?
>
> Rick has come up with an algorithm to estimate the fundamental
> frequency for a complex waveform. It works entirely in the time domain
> and doesn't involve an autocorrelation or anything like that. The end.
>
> -Mike
>
You see Chris, it's not about how accurate a theory is or whether it happens to be true or anything as useless as that. It's about how many times one uses words like 'convolution' and 'autocorrelation' in a sentence.

I've NOT only come up an algorithm to estimate the fundamental frequency for a complex waveform. I've shown that these near-fundamentals are *already in the complex waveform*. Theorists have overlooked it because 1. it is not revealed by Fourier analysis, 2. it was tacitly assumed that FA had everything covered. Mike's annoyed that the answer is quite simple and didn't require the use of more 'complicated' maths like autocorrelations. Of course he didn't actually invent autocorrelations. "What was it you did again Mike? I'm sorry, can you speak up a bit please!"

-Rick

On Tue, Jul 20, 2010 at 12:33 AM, rick <rick_ballan@...> wrote:
> >
> Not at all Mike. It's just that sometimes I have to use the term for the entire theory of VP. When I spoke to Bill he said "If you can A) prove this for Fourier series in general and B) show how it relates to harmonic entropy, then I think that you'll have a legitimate alternative to virtual pitch". I mentioned nothing of VP. I then showed him how both of these could be done and he agreed. He also immediately recognised the difference between his own harmonic stretching and this. Whereas his changes the condition of the waves, mine takes them as is and pulls them apart. They are not mutually exclusive.

There is no "theory of VP." We've been over this before. And let's see
this email from Bill Sethares, who I would doubt very much thinks in
primitivisms such as this.

> Also, you shouldn't put words in my mouth. I did not say "I have singlehandedly disproven virtual pitch" at all. What I said was "bring into serious doubt the cherished theory of virtual pitch". What I have in mind is the fact that a scientific theory is never proved 'true' (Hume, Popper). It only ever remains unfalsified up to a given point in time. And according to Popper, highly falsifiable/testible theories are usually those ones that seem the most 'bold and unbelievable'. For eg, if we say "It's going to rain sometime in the future" this is untestable because it gives no time or space limit. Everyone will believe it. Yet if we say "It's going to rain at such and such a time and exactly at this place" then it becomes both highly testable and more unbelievable. So if it does happen to rain then people take notice. Unfortunately, this 'boldness' is too often taken for arrogance or even madness and is why good theories are often ignored for many years (Evolution and Fourier series are two that comes to mind). Really, I'm just finishing up an idea that started in the late 90's and I haven't been able to formulize until now.

There is no "theory of VP." The concept of generating a Fourier series
from a periodic waveform is not a "theory" either. There is nothing to
disprove here.

> Therefore when you say "LOL I wasn't aware that when something is published, it becomes an undeniable fact" you're right because there is no such thing. And I don't have to point out that this runs both ways to Fourier transforms, VP, wavelets, convolution etc...I'll also say again that what worried me about VP theory is that I couldn't think of how it could possibly be falsified, hence my statement "relegated musical harmony to everything we *don't* understand about the brain". "Why do we hear this note? Oh its just the VP". They thought they had applied Occam's razor and eliminated all possible wave theoretical explanations for this phenomena. But they hadn't.

The Fourier transform, wavelet analysis, and convolution are just
mathematical operators that can be applied to anything. There is no
"theory" or "opinion" or anything to it. The fact that your algorithm
can estimate the period of a waveform is also an undeniable fact. The
notion that the brain is actually performing your specific algorithm
vs another one that does the same thing is for now just a hypothesis
and I don't care if you get it published in AES or ASA or wherever you
want, that's all it is. Come up with a prediction and test it and see.

You know what's another possible way that the brain could come up with
an estimate for the fundamental of a waveform? Performing some kind of
autocorrelation, or a square difference function, as an algorithm I've
been studying lately uses. And then you have that filterbank algorithm
I laid out on tuning-math. Again, explain to me why this random
algorithm you've developed somehow is better than all of those? What
predictions does it make that are accurate when those fail?

-Mike

On Tue, Jul 20, 2010 at 12:54 AM, rick <rick_ballan@...> wrote:
>
> Yet when I speak to the professionals in the field like Sethares and Erlich, they seem to be happy that someone in the world is so interested in music, maths and science that they can have the balls to come up with something that is actually new and challenging.

LOL, I'm really calling bullshit on this one. Let's see some exchange
with Paul where he admits that you have "defeated the cherished theory
of VP." I'd love to see it.

-Mike

On Tue, Jul 20, 2010 at 2:23 AM, rick <rick_ballan@...> wrote:
>
> --- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
> >
> > On Mon, Jul 19, 2010 at 4:03 PM, Chris Vaisvil <chrisvaisvil@...> wrote:
> > >
> > > Can you give me (us?) the brief version of this finding?
> >
> > Rick has come up with an algorithm to estimate the fundamental
> > frequency for a complex waveform. It works entirely in the time domain
> > and doesn't involve an autocorrelation or anything like that. The end.
> >
> > -Mike
> >
> You see Chris, it's not about how accurate a theory is or whether it happens to be true or anything as useless as that. It's about how many times one uses words like 'convolution' and 'autocorrelation' in a sentence.

LOL, you're right. That's the problem with mathematics; it attempts to
obfuscate meaning by employing a vocabulary of multisyllabic words.
These words, such as "convolution," carry no meaning at all except to
make the person saying them look smarter. Now that you've identified
this conspiracy, which goes all the way back to the very beginning of
mathematics, your theories will surely become dominant within the
scientific community.

> I've NOT only come up an algorithm to estimate the fundamental frequency for a complex waveform. I've shown that these near-fundamentals are *already in the complex waveform*.

What in the hell does this even mean? Are the convergents of a number
"in" that number? Is the number 2 "in" the number 5 because 2+3=5?

> Theorists have overlooked it because 1. it is not revealed by Fourier analysis, 2. it was tacitly assumed that FA had everything covered.

We've been over this before, haven't we? Here's an experiment for you
to try, again:

- Go grab a beer bottle and figure out what frequency it resonates at.
- Then, go play a sine wave at that frequency out of your speakers.
Make sure it doesn't distort.
- You will notice the bottle resonates.
- Now, go play a sawtooth wave at that frequency out of your speakers.
Make sure it doesn't distort.
- You will notice the bottle resonates.
- Finally, go play a sawtooth wave with the fundamental removed, at
the same frequency, out of your speakers. Make sure it doesn't
distort.
- You will notice the bottle doesn't resonate, except perhaps very
slightly due to some nonlinear effects.

It's up to you, now, to figure out what this means and why this is
important and how the "virtual fundamental" moniker came to be. Enjoy.

> Mike's annoyed that the answer is quite simple and didn't require the use of more 'complicated' maths like autocorrelations.

Conceptually speaking, the use of an autocorrelation would be much
simpler than what you're doing.

> Of course he didn't actually invent autocorrelations. "What was it you did again Mike? I'm sorry, can you speak up a bit please!"

I feel like I'm talking to a child with his fingers in his ears going
"LA LA LA LA LA LA I CAN'T HEAR YOU LALA LA LA".

-Mike

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

> There is no "theory of VP." The concept of generating a Fourier series
> from a periodic waveform is not a "theory" either. There is nothing to
> disprove here.

For what it's worth, neither Fourier nor Darwin were ignored, though both generated controversy. Fourier's work was controversial partly because the idea of summing analytic functions and getting all sorts of things went against many people's intuitions at the time, and partly because some of what he claimed was just plain wrong.

--- In tuning@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> On Tue, Jul 20, 2010 at 12:33 AM, rick <rick_ballan@...> wrote:
> > >
> > Not at all Mike. It's just that sometimes I have to use the term for the entire theory of VP. When I spoke to Bill he said "If you can A) prove this for Fourier series in general and B) show how it relates to harmonic entropy, then I think that you'll have a legitimate alternative to virtual pitch". I mentioned nothing of VP. I then showed him how both of these could be done and he agreed. He also immediately recognised the difference between his own harmonic stretching and this. Whereas his changes the condition of the waves, mine takes them as is and pulls them apart. They are not mutually exclusive.
>
> There is no "theory of VP." We've been over this before. And let's see
> this email from Bill Sethares, who I would doubt very much thinks in
> primitivisms such as this.

Mike, you really must begin to understand once and for all that there is a *vast difference* between simplistic and primitive. The theory is not 'simplistic' but is actually quite complicated. It is primitive in the sense that it applies to any combination of sine waves whatsoever. There is no reason why it wouldn't apply to stretched octaves for example. Unlike you, Bill made this calculation straight away. IOW it establishes a first principle. Therefore nothing in the actual application of waves is changed, only how we might think of them. And accusing me of making up emails from Bill, or childishly altering the meaning of what he says because I don't understand them, just goes to show the extent to which you *don't* understand the subtleties of what's involved.
>
> > Also, you shouldn't put words in my mouth. I did not say "I have singlehandedly disproven virtual pitch" at all. What I said was "bring into serious doubt the cherished theory of virtual pitch". What I have in mind is the fact that a scientific theory is never proved 'true' (Hume, Popper). It only ever remains unfalsified up to a given point in time. And according to Popper, highly falsifiable/testible theories are usually those ones that seem the most 'bold and unbelievable'. For eg, if we say "It's going to rain sometime in the future" this is untestable because it gives no time or space limit. Everyone will believe it. Yet if we say "It's going to rain at such and such a time and exactly at this place" then it becomes both highly testable and more unbelievable. So if it does happen to rain then people take notice. Unfortunately, this 'boldness' is too often taken for arrogance or even madness and is why good theories are often ignored for many years (Evolution and Fourier series are two that comes to mind). Really, I'm just finishing up an idea that started in the late 90's and I haven't been able to formulize until now.
>
> There is no "theory of VP." The concept of generating a Fourier series from a periodic waveform is not a "theory" either. There is nothing to disprove here.

Nonsense. Everything is a theory whether it calls itself one or not. The very act of writing a number on a page and saying it represents something is a theory. There have been hundreds upon hundreds of books written, dating way back to ancient Greece, which take to task this false idea that there can be any such thing as 'pure mathematics'. It originated with Plato's 'Theory of Forms' (notice the word 'Theory). And although Aristotle later tore this to pieces quite decisively, Plato's ideas are, unfortunately, still prevalent among average mathematicians. Don't become one of them.

"Any intelligent fool can make things bigger and more complex... It takes a touch of genius - and a lot of courage to move in the opposite direction" Einstein
>
> > Therefore when you say "LOL I wasn't aware that when something is published, it becomes an undeniable fact" you're right because there is no such thing. And I don't have to point out that this runs both ways to Fourier transforms, VP, wavelets, convolution etc...I'll also say again that what worried me about VP theory is that I couldn't think of how it could possibly be falsified, hence my statement "relegated musical harmony to everything we *don't* understand about the brain". "Why do we hear this note? Oh its just the VP". They thought they had applied Occam's razor and eliminated all possible wave theoretical explanations for this phenomena. But they hadn't.
>
> The Fourier transform, wavelet analysis, and convolution are just mathematical operators that can be applied to anything. There is no "theory" or "opinion" or anything to it. The fact that your algorithm can estimate the period of a waveform is also an undeniable fact. The notion that the brain is actually performing your specific algorithm vs another one that does the same thing is for now just a hypothesis and I don't care if you get it published in AES or ASA or wherever you want, that's all it is. Come up with a prediction and test it and see. You know what's another possible way that the brain could come up with an estimate for the fundamental of a waveform? Performing some kind of autocorrelation, or a square difference function, as an algorithm I've been studying lately uses. And then you have that filterbank algorithm I laid out on tuning-math. Again, explain to me why this random algorithm you've developed somehow is better than all of those? What predictions does it make that are accurate when those fail?

-Mike

You've got what I'm saying all wrong Mike. It is not simply an algorithm nor is there anything random about it. It's more a form of analysis which 'reveals' the harmonic content that is already there. This is distinct from, but not mutually exclusive with, all the waveforms you mention above. The difference between continued fractions and wave convergents is that the former *are* just methods for finding rational approximations, but the latter are physically present in the wave as envelopes. I suspected something was going on with the GCD's but was just as surprised as anyone to find these. They were "hiding in plain sight" as the saying goes. Now there exist a new class of external phenomena that must be factored into any calculation, perception of pitch being just one of them. Even in the simplest case of the dyad there's a whole new world of possibilities. What occurs when we apply these to more complex waveforms like the ones you mention above? I'd be interested to see how it applies to stretched 8ves.
>
"It is the theory that determines what is to be observed" Einstein

The connection between the outside world and sensory experience is far more problematic than you make out here. We often see what we expect (want) to see and go about 'proving' it after the fact. (Hegel says that mathematicians are the worst for doing this). Admit the possibility that you *already* have in mind that the brain is some type of algorithm calculator. And you know many possible examples, mine becoming just one of them. But this very idea itself came from VP (which is a theory despite what you say). It might now be that we just hear the frequency directly, taken in this broader sense of the word. Or it might not. In any case, it has become more problematic.
>
>

(I've been staying out of this, but have finally been tempted in.)
First, can I appeal to all to keep the discussion good tempered, non-personal, and logical. Second, please see a coupla points in line below.

--- In tuning@yahoogroups.com, "rick" <rick_ballan@...> wrote:
> What I said was "bring into serious doubt the cherished theory of virtual pitch".

But what theory is this? I am not aware of any single theory that proposes how to calculate VP (could be my ignorance, of course).

> I'll also say again that what worried me about VP theory is that I couldn't think of how it could possibly be falsified, hence my statement "relegated musical harmony to everything we *don't* understand about the brain". "Why do we hear this note? Oh its just the VP".

Do people really do this? If so, they are hardly invoking a theory.

> They thought they had applied Occam's razor and eliminated all possible wave theoretical explanations for this phenomena. But they hadn't.

I've not heard anyone claim this, either. What theory does this?

Steve M.

On 20 July 2010 15:37, martinsj013 <martinsj@...> wrote:

> But what theory is this?  I am not aware of any single theory that proposes how to calculate VP (could be my ignorance, of course).

There certainly is one, from Terhardt. I have some C code somebody
sent me based on one of his papers. I never looked at it, I'm afraid.
But something to do with subharmonic matching.

There are also algorithms to extract the pitch from audio signals.
They aren't intended to model what the ear does but the closer they
get the better.

Graham

Graham, do you still have this? I would very much like to see it.

Also, what do you mean by "subharmonic matching?"

-Mike

On Tue, Jul 20, 2010 at 11:39 AM, Graham Breed <gbreed@...> wrote:
>
> On 20 July 2010 15:37, martinsj013 <martinsj@...> wrote:
>
> > But what theory is this?  I am not aware of any single theory that proposes how to calculate VP (could be my ignorance, of course).
>
> There certainly is one, from Terhardt. I have some C code somebody
> sent me based on one of his papers. I never looked at it, I'm afraid.
> But something to do with subharmonic matching.
>
> There are also algorithms to extract the pitch from audio signals.
> They aren't intended to model what the ear does but the closer they
> get the better.
>
> Graham

On 20 July 2010 17:07, Mike Battaglia <battaglia01@...> wrote:
> Graham, do you still have this? I would very much like to see it.

I'm sure I have it somewhere but not on this computer. I'll dig it out for you.

> Also, what do you mean by "subharmonic matching?"

You reduce the signal by a subharmonic series. So you transpose it by
1:2, 1:3, 1:4, 1:5, and so on, and add all the results together. The
virtual pitch should then be the strongest sine wave, from Fourier
analysis, or however else you find it.

Graham

--- In tuning@yahoogroups.com, "rick" <rick_ballan@...> wrote:

>There have been hundreds upon hundreds of books written, dating way back to ancient Greece, which take to task this false idea that there can be any such thing as 'pure mathematics'.

No, there haven't been. Your credibility suffers because you continually make claims like this, which seem to be pulled out of your nether regions. If you are so unreliable when talking about the history of music or the philosophy of mathematics or all of the myriad other subjects you know little about but choose to lecture the rest of us on anyway, it casts doubt on everything you say.

> The connection between the outside world and sensory experience is far more problematic than you make out here. We often see what we expect (want) to see and go about 'proving' it after the fact. (Hegel says that mathematicians are the worst for doing this).

Hegel's grotesque and laughably ignorant ideas about both science and mathematics do not make him an ideal choice as a person to cite to support your point. Next you;ll be quoting Hobbes.