Yahoo Tuning Groups Ultimate Backup tuning new member question from a theory class

Hello Tuning Group. I'm a music theory student at UC Berkeley, but
am interested in acoustics, and the lay-, but often-asked question,
"is music mathematical." I've discussed some of your postings with
the professor and other students, and we came up with the following
questions:

Not to disrespect tuning issues and microtonal music...however, for
starters, we were more intested in some basic acoustics as they
apply to standard practice harmony (say Bach to 12-tone music),
before getting into tuning math issues. Espesially in a functional
harmony context, where the progression and chord context matters as
much as the indidual chord timbers. (Yes...this is but another
shortcoming of that type of music!)

1) Is there any consensus in psychoacoustical research on whether
listeners basically hear, for example, a major third, in an
archetypcal sense, regardless of whether it is pythagorean, just, or
12-ET?. Again, not to smooth over fascinating new, other world, and
ancient tunings, but we're focused on the common practice functional
harmony context.

2) Likewise, is there a consensus on how high-up in harmonic series
that acutally matters to the ear, in the functional harmony common
chord practice, or interms of actual hearing, and not tuning math?.
We had a long discussion about this. Is this related simply to the
low amplitude of the higher harmonics, or to the fact that they are
multiples of lower numbers? We were puzzled by the high harmonic
numbers used to spell chords which we saw in your postings. Our
main concern was that some of these intervals reduce down to a small
number ratio (eg, 10-8, vs. 5-4), and it also seems to work against
the much talked about idea that the ear 'hears the small number
ratios much more strongly. Again, we are sticking to the moment to
functional harmony, which, in its limited way, does not adress
timbre and interesting acoustical phenomonon. (Hope were not being
irrelavant to your expertise.)

Thanks group for any elucidation, and I will pass it on to the class.

John Thompson

Currently, I'm still a bit more into

🔗Carl Lumma <ekin@lumma.org>

Hi John,

Greetings from a fellow Berkeley-dweller.

>Not to disrespect tuning issues and microtonal music...however, for
>starters, we were more intested in some basic acoustics as they
>apply to standard practice harmony (say Bach to 12-tone music),
>before getting into tuning math issues.

Actually, there's been much discussion here on explaining common
practice music in a more generalized language than traditional
theory, with some neat results.

>Espesially in a functional harmony context, where the progression
>and chord context matters as much as the indidual chord timbers.
>(Yes...this is but another shortcoming of that type of music!)

Functional harmony has also been discussed. Unfortunately, Yahoo's
archives are something of a black hole for past dialog.

>1) Is there any consensus in psychoacoustical research on whether
>listeners basically hear, for example, a major third, in an
>archetypcal sense, regardless of whether it is pythagorean, just, or
>12-ET?. Again, not to smooth over fascinating new, other world, and
>ancient tunings, but we're focused on the common practice functional
>harmony context.

What is this "major third" of which you speak? Do you define it
as any interval in a certain range (say, 380-420 cents)? Or do
you define it as something which somehow satisfies a functional
role in diatonic music? Or...?

Even if we pin that down, there are many ways to answer your
question. I believe, and according to Paul Erlich there is now
some evidence, that all healthy humans share a basic experience
of the quality of sounds on some level. But there is also what
cognitive psychologists refer to as "priming" -- what you've
heard immediately prior to the stimulus -- which is just a hair
important if we're talking about music. Then there's cultural
bias -- what you've heard long before the stimulus. Timbre is
also significant. . . an answer to your question must take all
this into account.

At least one form of your question has significance in a
discussion of temperaments -- if temperaments approximate just
intonation, there must be some mental archtype that does too.

>2) Likewise, is there a consensus on how high-up in harmonic
>series that acutally matters to the ear, in the functional
>harmony common chord practice,

There isn't much consensus. Common practice music is generally
explained in terms of the 5-limit, to loosely quote Paul Erlich.
(You may enjoy reading his articles at...

http://lumma.org/tuning/erlich

...). Are you familiar with the term "5-limit"?

>or interms of actual hearing, and not tuning math?.

I'm not aware of any convincing experimental evidence, if that's
what you mean.

>We had a long discussion about this. Is this related simply to the
>low amplitude of the higher harmonics, or to the fact that they are
>multiples of lower numbers?

It is more related to the former than the latter. It appears
that the former fact resulted in the human hearing apparatus
evolving in a certain way...

>We were puzzled by the high harmonic numbers used to spell chords
>which we saw in your postings. Our main concern was that some of
>these intervals reduce down to a small number ratio (eg, 10-8, vs.
>5-4), and it also seems to work against the much talked about idea
>that the ear 'hears the small number ratios much more strongly.

Can you cite any examples here?

-Carl

🔗edfg555 <edfg555@yahoo.com>

hi Carl!

> Actually, there's been much discussion here on explaining common
> practice music in a more generalized language than traditional
> theory, with some neat results.

Can you recommend a particular thread?

> Functional harmony has also been discussed. Unfortunately, Yahoo's
> archives are something of a black hole for past dialog.
>

Ahh! Do you recall a thread, or time frame for me to search, which
might address how we ended up with the major and minor 'modes'
(aeolian and ...)

> What is this "major third" of which you speak? Do you define it
> as any interval in a certain range (say, 380-420 cents)?

Or do
> you define it as something which somehow satisfies a functional
> role in diatonic music?

Yes! this one, above!

> Even if we pin that down, there are many ways to answer your
> question....
Hmm, I see...

> At least one form of your question has significance in a
> discussion of temperaments -- if temperaments approximate just
> intonation, there must be some mental archtype that does too.

That's an interesting idea. If numbers are archetypes, as Jung
supposed, then maybee intervals are too, with culturally specific
varieties, perhaps.

> >2) Likewise, is there a consensus on how high-up in harmonic
> >series that acutally matters to the ear, in the functional
> >harmony common chord practice,

> Are you familiar with the term "5-limit"?

I have it on my list, to read Partch. But Erlich's article looks
good too. (Thanks.) I'll see how it works in with my study of
harmony. I'm still under the impression that 12-ET is necessary
for functional harmony, or at least, that the fine distinctions in
cent values of differently tuned intervals takes a 'back seat' if
the harmony is 'functional' (ie, with progressions, etc, which I
realize comprises sonice and timbre interest...)

> >We were puzzled by the high harmonic numbers used to spell chords
> >which we saw in your postings.
>
> Can you cite any examples here?

Arg... can't find the exact post now, but I recall that in referring
to a 'major sixth chord' (eg, c-e-g), a higher number version was
used (9-11-15...or was it 8-10-13), on the grounds of considering
each chord "As It Appears In The Series". I just wonder if the ear,
or brain processing or whatever, actually relates to the chord
as 'high numbers in the series' when it could just as well (?) hear
(again, archetypically) a major third and a perfect 4th.

Thanks again for sharing your knowledge!

John

🔗Carl Lumma <ekin@lumma.org>

>> Actually, there's been much discussion here on explaining common
>> practice music in a more generalized language than traditional
>> theory, with some neat results.
>
>Can you recommend a particular thread?

I'd start with Paul's stuff (link in my previous message).

>> Functional harmony has also been discussed. Unfortunately, Yahoo's
>> archives are something of a black hole for past dialog.
>
>Ahh! Do you recall a thread, or time frame for me to search, which
>might address how we ended up with the major and minor 'modes'
>(aeolian and ...)

Paul's "Tuning Tonality and Twenty-Two Tone Temperament" paper
suggests why only those two modes are privileged in tonal music.

This also comes to mind...

/tuning-math/message/5945

>> What is this "major third" of which you speak? Do you define it
>> as any interval in a certain range (say, 380-420 cents)?
>
>> Or do
>> you define it as something which somehow satisfies a functional
>> role in diatonic music?
>
>Yes! this one, above!

Which one?

>> >2) Likewise, is there a consensus on how high-up in harmonic
>> >series that acutally matters to the ear, in the functional
>> >harmony common chord practice,
>
>> Are you familiar with the term "5-limit"?
>
>I have it on my list, to read Partch. But Erlich's article looks
>good too. (Thanks.) I'll see how it works in with my study of
>harmony. I'm still under the impression that 12-ET is necessary
>for functional harmony,

Really? What gives you that impression?

>or at least, that the fine distinctions in cent values of
>differently tuned intervals takes a 'back seat' if the harmony is
>'functional' (ie, with progressions, etc, which I realize
>comprises sonice and timbre interest...)

One might say that. But one probably isn't aware that not
only are tunings available that give traditional progressions
a different sound, tunings are available that render traditional
progressions impossible, while making previously-impossible ones
possible!

You may also have luck with...

http://lumma.org/music/theory/tctmo/

That's a major 6th?

>a higher number version was used (9-11-15...or was it 8-10-13), on
>the grounds of considering each chord "As It Appears In The Series".
>I just wonder if the ear, or brain processing or whatever, actually
>relates to the chord as 'high numbers in the series'

Depends on the timbre, musical context, listener. In isolation,
the former chord certainly sounds less like a major triad than the
latter.

>when it could just as well (?) hear (again, archetypically) a major
>third and a perfect 4th.

Eh?

-Carl

🔗monz <monz@tonalsoft.com>

hi John and Carl,

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> > Not to disrespect tuning issues and microtonal music...
> > however, for starters, we were more intested in some basic
> > acoustics as they apply to standard practice harmony (say
> > Bach to 12-tone music), before getting into tuning math
> > issues.
>
> Actually, there's been much discussion here on explaining
> common practice music in a more generalized language than
> traditional theory, with some neat results.
>
> > Espesially in a functional harmony context, where the
> > progression and chord context matters as much as the
> > indi[vi]dual chord timbers. (Yes...this is but another
> > shortcoming of that type of music!)
>
> Functional harmony has also been discussed. Unfortunately,
> Yahoo's archives are something of a black hole for past dialog.

i know for certain that i discussed functional harmony on
this list, back around 1999, because i remember Joe Pehrson's
amazed response that his musical schooling never gave him such
a clear picture of such a simple concept ... OK, after
writing that i put Yahoo's lousy archive-search feature to
use, and came up with these -- the discussion about
functional harmony was actually in February 2000:

and here are posts by me on the subject:

/tuning/topicId_8358.html#8358
/tuning/topicId_8412.html#8422
/tuning/topicId_8471.html#8471
/tuning/topicId_8471.html#8501
/tuning/topicId_8524.html#8562
/tuning/topicId_8583.html#8606
/tuning/topicId_8583.html#8627

and in the midst of that there was this good message
(among others) by Daniel Wolf:

/tuning/topicId_8440.html#8440

> <snip>
>
> > 2) Likewise, is there a consensus on how high-up in
> > harmonic series that acutally matters to the ear, in the
> > functional harmony common chord practice,
>
> There isn't much consensus. Common practice music is
> generally explained in terms of the 5-limit, to loosely
> quote Paul Erlich.
> (You may enjoy reading his articles at...
>
> http://lumma.org/tuning/erlich
>
> ...). Are you familiar with the term "5-limit"?
>
> >or interms of actual hearing, and not tuning math?.
>
> I'm not aware of any convincing experimental evidence,
> if that's what you mean.

here's something i wrote in 1999 about high prime factors
seen in the theoretical literature:

/tuning/topicId_944.html#1408

Brian McLaren has made a point of composing in very high
prime JI, but aside from his work, the highest prime i've
ever seen in the literature is 499, used by Boethius in
his enharmonic genus.

i have noticed the following in my own listening experiments:

. in a context where precisely-tuned ratios are sustained
by harmonic timbres over a long period of time (as, for
example, in pieces by LaMonte Young), i believe that i
have noticed differences in sound or affect (or both)
with primes going into the high 200's

. in a more "typical" type of Western "common-practice"
context, 11 seems to me to be the highest prime that is
necessary to produce perceptually unique sounds/affects.

unless the musical context specifically emphasizes a certain
prime (as, for example, 19 in the 4:10:14:19 chord in
my piece _Hendrix Chord_), i find that ratios of 13 or
higher primes are often superfluous, tending more or less
to resemble the ratios available within the 11-limit.

-monz

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

--- In tuning@yahoogroups.com, "edfg555" <edfg555@y...> wrote:
>
>
> Hello Tuning Group. I'm a music theory student at UC Berkeley, but
> am interested in acoustics, and the lay-, but often-asked question,
> "is music mathematical." I've discussed some of your postings
with
> the professor and other students, and we came up with the following
> questions:
>
> Not to disrespect tuning issues and microtonal music...however, for
> starters, we were more intested in some basic acoustics as they
> apply to standard practice harmony (say Bach to 12-tone music),
> before getting into tuning math issues. Espesially in a functional
> harmony context, where the progression and chord context matters as
> much as the indidual chord timbers. (Yes...this is but another
> shortcoming of that type of music!)
>
> 1) Is there any consensus in psychoacoustical research on whether
> listeners basically hear, for example, a major third, in an
> archetypcal sense, regardless of whether it is pythagorean, just,
or
> 12-ET?.

In the West, trained musicians typically do. Untrained listeners'
responses follow the assumed patterns less closely, and non-western
listeners will often use different categorizations entirely. A
listener from a region in Africa using equipentatonic scales (or
thereabouts) might place a Pythagorean major third into a different
cognitive category than a just one.

> 2) Likewise, is there a consensus on how high-up in harmonic series
> that acutally matters to the ear, in the functional harmony common
> chord practice, or interms of actual hearing, and not tuning
math?.

It depends on which of the psychoacoustical phenomena that favor
integer ratios your music is relying on. For music which moves along
at a pretty decent clip, uses softer timbres, and is not too loud,
the most important phenomenon is the virtual pitch phenomenon. Unless
you have a lot of notes in your chords, this phenomenon makes chords
sound very stable and unified only if you're using the lower numbers
in the harmonic series. But there are kinds of music where higher
numbers are used and it most definitely matters to the ear. Such
music tends to use very long, sustained sonorities. The relevant
phenomena are beating (which allows you to tune ratios as complex as
17:13 by ear) and combinational tones (which get you even higher up
the harmonic series).

> We had a long discussion about this. Is this related simply to the
> low amplitude of the higher harmonics, or to the fact that they are
> multiples of lower numbers? We were puzzled by the high harmonic
> numbers used to spell chords which we saw in your postings.

Do you consider the numbers in 6:7:9:11 to be high harmonic numbers?

> Our
> main concern was that some of these intervals reduce down to a
small
> number ratio (eg, 10-8, vs. 5-4),

Hmm . . . which postings are you speaking of? I never saw any mention
of a 10:8 interval, unless there was some other context that would
make it necessary not to express it as 5:4 . . . (?)

> and it also seems to work against
> the much talked about idea that the ear 'hears the small number
> ratios much more strongly. Again, we are sticking to the moment to
> functional harmony, which, in its limited way, does not adress
> timbre and interesting acoustical phenomonon. (Hope were not being
> irrelavant to your expertise.)

Western functional harmony arose in the tuning system called meantone
temperament, not in equal temperament. I believe that harmonic series
ratios from the first 6-8 harmonics are relevant here, with a few
additional harmonics perhaps relevant in jazz harmony. There's also a
possibility that the 19th harmonic has a role in explaining certain
features in the evolution away from Picardy thirds.

I'd love to discuss all this in much more detail. But what's more
interesting to me personally is finding new analogues to the
functional harmonic system, based often on non-diatonic scales, which
may be based on these same harmonic series relationships or ones a
little higher in the series too.

Best,
Paul

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

--- In tuning@yahoogroups.com, "edfg555" <edfg555@y...> wrote:

> Ahh! Do you recall a thread, or time frame for me to search,
which
> might address how we ended up with the major and minor 'modes'
> (aeolian and ...)

My explanation of this can be found in my paper _Tuning, Tonality,
and Twenty-Two-Tone Temperament_, which is on Carl's website that he
told you about. The explanation of traditional tonality there can be
read apart from the discussion of new scales or 22-tone tunings.

> > >2) Likewise, is there a consensus on how high-up in harmonic
> > >series that acutally matters to the ear, in the functional
> > >harmony common chord practice,
>
> > Are you familiar with the term "5-limit"?
>
> I have it on my list, to read Partch. But Erlich's article looks
> good too. (Thanks.)

Besides the article I mentioned above, be sure to read my other
articles there too! I believe they will be relevant to you.

> I'll see how it works in with my study of
> harmony. I'm still under the impression that 12-ET is necessary
> for functional harmony,

You can do functional harmony in 19-equal, or in 7/26-comma meantone
tuning, just to name two other examples. I recommend Easley
Blackwood's book _The Structure Of Recognizable Diatonic Tunings_ if
you can get a hold of it.

> or at least, that the fine distinctions in
> cent values of differently tuned intervals takes a 'back seat' if
> the harmony is 'functional' (ie, with progressions, etc, which I
> realize comprises sonice and timbre interest...)

Until about 1800, there was a strong distinction between the tuning
of "enharmonically-equivalent" notes such as G# and Ab. Only with
Beethoven did composers begin to strongly rely on an assumption of a
closed 12-tone tuning system in their music. Functional harmony was
well-established since about 1670, and augmented or diminished
intervals were tuned very differently in 1670 than they are today.
While 12-equal may well preserve the 'functions' of late 17th century
music, the reverse is clearly not the case -- you couldn't perform
Beethoven's Appassionata sonata in a 1670 tuning. And aesthetically,
I feel that 1670 music sounds much more beautiful, and aesthetically
balanced, in a 1670 tuning than in 12-note equal temperament.
Surely 'function' shouldn't blind us to these aesthetic issues.

> > >We were puzzled by the high harmonic numbers used to spell chords
> > >which we saw in your postings.
> >
> > Can you cite any examples here?
>
> Arg... can't find the exact post now, but I recall that in
referring
> to a 'major sixth chord' (eg, c-e-g), a higher number version was
> used (9-11-15...or was it 8-10-13), on the grounds of considering
> each chord "As It Appears In The Series".

I don't think that represented a consensus opinion here by any means -
- did you read the follow-ups? In fact, I think the person who wrote
that has never even once mentioned a single specific tuning system
they were using, be it 12-equal or anything else. So what was behind
those posts remains a mystery to me.

> I just wonder if the ear,
> or brain processing or whatever, actually relates to the chord
> as 'high numbers in the series' when it could just as well (?) hear
> (again, archetypically) a major third and a perfect 4th.

I think it's both and neither :) Seriously, the issue is complicated,
and I believe thinking about it has to start with the psychoacoustic
phenomena which make small-integer ratios relevant in the first
place. It's what happens between the production of the sounds and
their appreciation in our minds -- what happens in the ear and brain -
- that must be invoked here. Unless you want to go down the mystical
path and assume that the numbers themselves directly affect our
souls, or whatnot . . . but I prefer the skeptical approach myself.

-Paul

🔗George D. Secor <gdsecor@yahoo.com>

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
> ...
> i have noticed the following in my own listening experiments:
> ...
> . in a more "typical" type of Western "common-practice"
> context, 11 seems to me to be the highest prime that is
> necessary to produce perceptually unique sounds/affects.

I'm inclined to agree with this.

> unless the musical context specifically emphasizes a certain
> prime (as, for example, 19 in the 4:10:14:19 chord in
> my piece _Hendrix Chord_), i find that ratios of 13 or
> higher primes are often superfluous, tending more or less
> to resemble the ratios available within the 11-limit.

My work with Dave Keenan devising symbols for ratios above the 11-
limit in the Sagittal notation project also tends to confirm this
observation. Once we had created microtonal accidentals to notate
the 11-limit consonances and ratios containing 5^2 (25) and 5*7 (35)
as factors, we found that no additional symbols were required for any
of the 13-limit consonances, inasmuch as we could approximate all of
them with existing symbols without incurring an error greater than
~0.833 cents (2079:2080).

--George

🔗edfg555 <edfg555@yahoo.com>

...Carl, Monz, Paul, George...thanks for the great responses, which
my discussion group and I will be mulling over. I can see how
oversimplifying things can lead one down a mystical or dogmatic
route. You are good teachers!

SIncerly, John

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...>
wrote:
>
> --- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
> > ...
> > i have noticed the following in my own listening experiments:
> > ...
> > . in a more "typical" type of Western "common-practice"
> > context, 11 seems to me to be the highest prime that is
> > necessary to produce perceptually unique sounds/affects.
>
> I'm inclined to agree with this.
>
> > unless the musical context specifically emphasizes a certain
> > prime (as, for example, 19 in the 4:10:14:19 chord in
> > my piece _Hendrix Chord_), i find that ratios of 13 or
> > higher primes are often superfluous, tending more or less
> > to resemble the ratios available within the 11-limit.
>
> My work with Dave Keenan devising symbols for ratios above the 11-
> limit in the Sagittal notation project also tends to confirm this
> observation. Once we had created microtonal accidentals to notate
> the 11-limit consonances and ratios containing 5^2 (25) and 5*7
(35)
> as factors, we found that no additional symbols were required for
any
> of the 13-limit consonances, inasmuch as we could approximate all
of
> them with existing symbols without incurring an error greater than
> ~0.833 cents (2079:2080).
>
> --George

🔗Pete McRae <ambassadorbob@yahoo.com>

wallyesterpaulrus <wallyesterpaulrus@yahoo.com> wrote:

Unless you want to go down the mystical
path and assume that the numbers themselves directly affect our
souls, or whatnot . . . but I prefer the skeptical approach myself.

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

I hope you'll forgive any impertinence on my part for feeling the need to chime in here, again.

Once again, a statement like that does a tremendous disservice to intellectuals who are quite capable (to say the least) of discerning the difference between "objective" quantification, and experiential "knowing", but who may be skeptical towards the "science".

I know from the flurry of nonsense that came from the very mention of ___, that "real" intellectuals are just as prey to their affections and affectations as anyone else. And, I just met a physics professor who insists on calling 12Tet a "well-temperament", presumably to obfuscate the nature of his real agenda, which is preserving the institution as it serves himself.

For my money, Western "functional" harmony is merely a function of Western "teleological" or "pragmatic" considerations, NOT of any particular physical reality, ie the overtone series.

If one considers a harmonic progression (eg V-I) in the Music Theory class sense "profound", or insipid and sentimental (as I do), what does that mean with respect to someone who considers an interval, or scale, or Rag, or whatever, "devotional"?

The former probably does not believe that he or she is merely buffeted by their own emotions, in other words they don't believe it's insipid or sentimental, anymore than the latter believes that their devotion will actually cure disease, or achieve enlighenment, in any time-constrained fashion.

I hope we can keep the "debunking" on topic, and somehow mitigate so much, pardon the expression, musical Eugenics.

Best,

Pete

---------------------------------
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🔗Carl Lumma <ekin@lumma.org>

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

🔗Pete McRae <ambassadorbob@yahoo.com>

>>Unless you want to go down the mystical
>>path and assume that the numbers themselves directly affect our
>>souls, or whatnot . . . but I prefer the skeptical approach myself.
>
>Once again, a statement like that does a tremendous disservice to
>intellectuals who are quite capable (to say the least) of discerning
>the difference between "objective" quantification, and experiential
>"knowing", but who may be skeptical towards the "science".

Carl Lumma <ekin@lumma.org> wrote:

How does it do that?

- - - - - - -

Hi Carl,

You're right to ask, of course. Thanks! If you emphasize the "Unless you want to..." part of the remark, then I'm out of line, because if you want to, then you may, I suppose.

I took it as another example of a tendency toward the derision of certain philosophical/ideological/idealistic (!) motivations that cause people to join the list in the first place. These are motives that are encouraging people to investigate tunings and develop their own ideas as to what is meaningful in music, and in my opinion, are NOT to be discouraged, if at all possible.

The "mystical", the "numerological", the (bonus :-) "astrological", or any other "geometrical" or "religious" implications of what we're discussing are our responsibility to respectfully, and--again, whenever possible--advisedly acknowledge, I feel.

>>I hope we can keep the "debunking" on topic, and somehow mitigate
>>so much, pardon the expression, musical Eugenics.

>I appreciate this point, but I think it may be slightly misplaced
>in this case?

Yeah, probably in this case, but I couldn't resist, today. I'll stand on my worry and alarm, for the time being. Thank you for taking it so well. I'm in the thicket of "academia" myself, and wondering if I can endure the final stretch just to get one damned undergrad degree.

__________________________________________________
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🔗traktus5 <kj4321@hotmail.com>

Though I've presented somewhat irrelavant 'numerological', mystical-
leaning ideas about 'chord energy', I find the tuning group to be
very generous, patient, and courteous, and usually willing to
provide a wealth of information and instruction. Overall, things
balance out (the skeptical vs the mystical), but I don't beieve they
should be expected to on this list.

CHeers,

Kelly

--- In tuning@yahoogroups.com, Pete McRae <ambassadorbob@y...> wrote:
> >>Unless you want to go down the mystical
> >>path and assume that the numbers themselves directly affect our
> >>souls, or whatnot . . . but I prefer the skeptical approach
myself.
> >
> >Once again, a statement like that does a tremendous disservice to
> >intellectuals who are quite capable (to say the least) of
discerning
> >the difference between "objective" quantification, and
experiential
> >"knowing", but who may be skeptical towards the "science".
>
> Carl Lumma <ekin@l...> wrote:
>
> How does it do that?
>
> - - - - - - -
>
> Hi Carl,
>
> You're right to ask, of course. Thanks! If you emphasize
the "Unless you want to..." part of the remark, then I'm out of
line, because if you want to, then you may, I suppose.
>
> I took it as another example of a tendency toward the derision of
certain philosophical/ideological/idealistic (!) motivations that
cause people to join the list in the first place. These are motives
that are encouraging people to investigate tunings and develop their
own ideas as to what is meaningful in music, and in my opinion, are
NOT to be discouraged, if at all possible.
>
> The "mystical", the "numerological", the (bonus :-
) "astrological", or any other "geometrical" or "religious"
implications of what we're discussing are our responsibility to
respectfully, and--again, whenever possible--advisedly acknowledge,
I feel.
>
> >>I hope we can keep the "debunking" on topic, and somehow mitigate
> >>so much, pardon the expression, musical Eugenics.
>
> >I appreciate this point, but I think it may be slightly misplaced
> >in this case?
>
> Yeah, probably in this case, but I couldn't resist, today. I'll
stand on my worry and alarm, for the time being. Thank you for
taking it so well. I'm in the thicket of "academia" myself, and
wondering if I can endure the final stretch just to get one damned
undergrad degree.
>
>
>
>
>
>
> __________________________________________________
> Do You Yahoo!?
> Tired of spam? Yahoo! Mail has the best spam protection around
> http://mail.yahoo.com

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

--- In tuning@yahoogroups.com, Pete McRae <ambassadorbob@y...> wrote:

> wallyesterpaulrus <wallyesterpaulrus@y...> wrote:
>
> Unless you want to go down the mystical
> path and assume that the numbers themselves directly affect our
> souls, or whatnot . . . but I prefer the skeptical approach myself.
>
> ---------------------------------
>
> I hope you'll forgive any impertinence on my part for feeling the
>need to chime in here, again.
>
> Once again, a statement like that does a tremendous disservice to
>intellectuals who are quite capable (to say the least) of
>discerning the difference between "objective" quantification, and
>experiential "knowing", but who may be skeptical towards
>the "science".

Why does the statement to a disservice to them? You must have misread
something if you think the skepticism I referred (and meant to
express only as a personal preference anyway) to meant anything other
than skepticism of "authority" or "received wisdom."

Why does my personal preference to be skeptical of authority or
received wisdom to a disservice to the intellectual of whom you speak?

> I know from the flurry of nonsense that came from the very mention
>of ___, that "real" intellectuals are just as prey to their
>affections and affectations as anyone else. And, I just met a
>physics professor who insists on calling 12Tet a "well-temperament",
>presumably to obfuscate the nature of his real agenda, which is
>preserving the institution as it serves himself.

12-equal is a well-temperament, it's just the most boring one. What
musical institution serves a physics professor???

> For my money, Western "functional" harmony is merely a function of
>Western "teleological" or "pragmatic" considerations, NOT of any
>particular physical reality, ie the overtone series.

Good, then let's keep making music that doesn't obey
western "functional" harmony, shall we?

> If one considers a harmonic progression (eg V-I) in the Music
>Theory class sense "profound", or insipid and sentimental (as I do),
>what does that mean with respect to someone who considers an
>interval, or scale, or Rag, or whatever, "devotional"?

Not much, that I can tell. Can you elaborate on the connection as you
see it?

> The former probably does not believe that he or she is merely
>buffeted by their own emotions, in other words they don't believe
>it's insipid or sentimental, anymore than the latter believes that
>their devotion will actually cure disease, or achieve enlighenment,
>in any time-constrained fashion.

Wow, that's a knotty analogy, and I can't say I understand it.

> I hope we can keep the "debunking" on topic, and somehow mitigate
>so much, pardon the expression, musical Eugenics.

If you read my posts (especially the ones that inflamed Peter Sault),
you'd know that I'm among the first stand up in the defense of the
worth of all musical cultures, particularly those cultures whose
existence is becoming endangered, and to knock down any claims of
superiority for the Western tradition. So equating my statements
with "musical Eugenics" seems . . . ? I just feel . . . .

???????????????????????????????????????????????????????????

(?)

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

--- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:

> >> . in a more "typical" type of Western "common-practice"
> >> context, 11 seems to me to be the highest prime that is
> >> necessary to produce perceptually unique sounds/affects.
> >
> >I'm inclined to agree with this.
>
> I'm inclined to disagree, sort of.
>
> 20th century music is clearly inhabiting 12-tET, and the
> just intonation interpretation of much of it is not clear,
> or at least non-unique.

I agree,.Carl. I didn't raise an objection because I thought Monz
would be willing to substitute "odd" instead of "prime" above. Would
you, Monz?

> The effects of circulating temperaments go back much
> further, and there is even medieval music that treats
> Pythagorean tuning as more circular than it actually
> is, wolves be damned.
>
> Temperament aside, there is also the point of expressive
> vs. structural intonation. In terms of the latter, common
> practice music is clearly 5-limit,

I tend to agree.

> while in terms of the
> former, it is hard to place any absolute upper limit on
> things.

Or, some might argue, Pythagorean or 3-limit JI encapsulates the
tendencies of expressive intonation in Western common practice music.

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

--- In tuning@yahoogroups.com, Pete McRae <ambassadorbob@y...> wrote:

> I took it as another example of a tendency toward the derision of
>certain philosophical/ideological/idealistic (!) motivations that
>cause people to join the list in the first place. These are motives
>that are encouraging people to investigate tunings and develop their
>own ideas as to what is meaningful in music, and in my opinion, are
>NOT to be discouraged, if at all possible.

I think the highest, worthiest goal is for people to investigate
tunings and develop their own ideas as to what is meaningful in
music. And I personally don't think "authority" or "received wisdom"
have much place in my own pursuit of this goal. Thus I practice
skepticism of same. But I won't get in your way if you want to
encourage something else. Really I was only expressing my own
preference.

> The "mystical", the "numerological", the (bonus :-) "astrological",
>or any other "geometrical" or "religious" implications of what we're
>discussing are our responsibility to respectfully, and--again,
>whenever possible--advisedly acknowledge, I feel.

Unfortunately the arbiters of "mystical" or "religious" truth
sometimes feel they have a right to "authority" on such matters due
to access to "secret texts", "received learning", or merely their own
desire to dictate to and be revered by the masses. Certainly this can
equally be said of many "academics" as well. I happen to believe that
with each individual feel free and able to investigate and judge the
world, phenomena, and art for him or herself, the cultural stew can
cook up its richest flavors, if you know what I mean. Though, as I
said, it's really just a personal choice -- I prefer to take
this "freethinking" approach, while others may rest more comfortably
in the arms of a tradition or dogma. I'm just glad that I live in an
age when I can admit to this without risking the wrath of an
Inquisition!

> I'll stand on my worry and alarm, for the time being.

I personally worry more about people not thinking, and not
experimenting, for themselves. But I won't start a war over it. Only
the other day I was being accused of promoting mysticism here! How
quickly the tide turns. It seems it's awfully perilous to defend free
speech and free thought these days -- there's always going to be
someone who takes offense and wishes to muzzle the ideas they're not
comfortable/happy with.

Really -- what could be so worrisome and alarming about people
discussing and playing with new sounds and coming up with music that
uses them? Even if they're respecting/acknowledging a
certain "religious" or "mystical" set of parameters, won't they
necessarily be failing to respect/acknowledge some
different "religious" or "mystical" outlook from somewhere else on
the globe?

🔗ambassadorbob <ambassadorbob@yahoo.com>

Hi Paul,

--- In tuning@yahoogroups.com, "wallyesterpaulrus"
<wallyesterpaulrus@y...> wrote:> The former probably does not
believe that he or she is merely
>buffeted by their own emotions, in other words they don't believe
>it's insipid or sentimental, anymore than the latter believes that
>their devotion will actually cure disease, or achieve enlighenment,
>in any time-constrained fashion.

>Wow, that's a knotty analogy, and I can't say I understand it.

Yeah, sorry it's knotty, and sorry I didn't say it very well. I'm
working on it...I did my best to clarify in response to Carl.

>
> If you read my posts (especially the ones that inflamed Peter
Sault),
> you'd know that I'm among the first stand up in the defense of the
> worth of all musical cultures, particularly those cultures whose
> existence is becoming endangered, and to knock down any claims of
> superiority for the Western tradition. So equating my statements
> with "musical Eugenics" seems . . . ? I just feel . . . .
>
> ???????????????????????????????????????????????????????????
>
> (?)

As I indicated to Carl, I'm afraid your personal skepticism tends to
become a kind of logical jingoism that any one of us could take as
encouragement to exclude another's ideas as "nonsense"
(or "treason"!?!?!?), which Dan Stearns (may he forgive me) happily
pointed out is a huge danger in our present "conservative" culture.

--Pete

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

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

> As I indicated to Carl, I'm afraid your personal skepticism tends
to
> become a kind of logical jingoism

I must admit ignorance of this concept. All jingoism is illogical to
me, since national borders are so arbitrary (and for lots of other
reasons). And logic itself knows no national boundaries. So . . . I'm
confused.

> that any one of us could take as
> encouragement to exclude another's ideas as "nonsense"
> (or "treason"!?!?!?),

Hmm . . . the last time I saw that word here, it was being leveled
against me for daring to make music with other people in 12-equal.

> which Dan Stearns (may he forgive me) happily
> pointed out is a huge danger in our present "conservative" culture.

Ny personal skepticism would be lucky if it got to be a huge danger
to our conservative culture. Meanwhile, I've stood up in the name of
defending free expression against accusations of "nonsense" or worse,
no matter what the ideological or philosophical bent, and angered
some of my best friends here in doing so, including very recently. So
excuse me if everything you're saying to me seems completely
backwards right now. I'd like to get a better understanding of what
it is you're saying so that I can attempt to take remedial action
right away -- if I can make things better toward the ends we both
value, I'd love to do so right away.

🔗Pete McRae <ambassadorbob@yahoo.com>

Paul,

I guess the only thing I need to emphasize here is what I see NOT as a personal failing--far from it!--but a kind of smugness in the tone of some remarks, which has absolutely nothing to do with you. It just seems to be a condition of the general state of communications these days. Mine may be ass-backwards and self-abnegating in that sense, too! Not to mention grandiose and hypocritical, in some significant ways.

In fact, I've observed you to be extraordinarily generous and patient, at times. I hope I can hope we'll be able to meet up sometime, because the "cyber-space" detachment is really deadly in a lot of ways, too, I think.

In any case, I hope that my remarks can be understood as just words about words, and the tangles that we're trying to untangle (I hope!), all of us, every day.

I've finally gotten around to reading Bob Gilmore's lovely bio of Harry Partch and it's forcing me to come to terms with my own self-defeating moods and rhetoric, because as I said to someone the other day, "I thought [HP] cleared the way for me, in some sense, but in fact, he was just the first one in my time to die trying." That's sort of the drama queen version, but maybe you take my point. The struggle hasn't changed much, and as I indicated by using the word "treason" (which was really just a reference to the news stories about the college professor and The Young Republicans) there's a chilling mentality about that uses "skepticism" AND "faith" to literally vanish people in the Stalinist sense, so I guess that's why I was compelled to speak up.

It's our participation in the general liguistic and cognitive laziness that makes these kind of movements viable. And it's why I think tuning is great place to start to mitigate the complacency we all run up against in trying to do something truly creative.

As I was watching the great songwriter (and terrible musician!) Robyn Hitchcock last night, I couldn't help thinking that this list is categorized under "songwriting", isn't it? That means, to me, that it's about poetry, not science.

wallyesterpaulrus <wallyesterpaulrus@yahoo.com> wrote:

--- In tuning@yahoogroups.com, "ambassadorbob"
wrote:

> As I indicated to Carl, I'm afraid your personal skepticism tends
to
> become a kind of logical jingoism

> that any one of us could take as
> encouragement to exclude another's ideas as "nonsense"
> (or "treason"!?!?!?),

Hmm . . . the last time I saw that word here, it was being leveled
against me for daring to make music with other people in 12-equal.

> which Dan Stearns (may he forgive me) happily
> pointed out is a huge danger in our present "conservative" culture.

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🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

--- In tuning@yahoogroups.com, Pete McRae <ambassadorbob@y...> wrote:

> As I was watching the great songwriter (and terrible musician!)
>Robyn Hitchcock last night, I couldn't help thinking that this list
>is categorized under "songwriting", isn't it? That means, to me,
>that it's about poetry, not science.

Hi Pete,

I know it must seem very small of me right now to bring up this
pedantic point, but: the tuning list didn't start here on Yahoo, or
its predecessor eGroups, or its predecessor Onelist. It started on
the Mills College list server, and flourished there for several
years. When that server had to retire, this list was moved to
Onelist. The only category that Onelist had that seemed to fit
was "songwriting" -- the feeling expressed about putting the tuning
list in that category at the time were, it seemed to me, were "well,
that's not a great category to put the tuning list in, but there
aren't any others that qualify, so here we go." Meanwhile, the
description of this list which is on the home page was copied word-
for-word from the old tuning list. So if there's anything which
carries the "intent" of this list, it's that description, and not
the fact that the list was placed in the "songwriting" category.

Music as poetry and as magic plays a huge role in my life; I won't
go on and on about that.

Anyway, science? I don't think there's much science here at all. But
for as long as this list has been around, questions of
psychoacoustics (not a hard science, but an embryonic field of
phenomenological study) have come up. And often, it's indeed with
some trepidation: "I don't know if this question belongs here,
but . . ." Now, I'd hate for there to be _yet another_ list that
questions here need to be re-directed to if an answer which touches
on psychoacoustics or neurology is to be allowed -- I was not happy
with all the list-splitting that has happened before. But OK, if all
the questions about human hearing need to be answered poetically (?)
here, so be it . . . if and when I have time, I'll start a
psychoacoustics list (since there wasn't one last time I checked),
and (gulp) re-direct people there next time I want to give them
a "scientific" reply.

Did you mean math? Don't you use the Eikosany tuning? Gene
independently discovered this and other CPS scales in the 1960's by
considering the so-called "deep holes" in the lattice. I mean, of
course you aren't going to be thinking about math or science when
you're composing or improvising -- you listen, become one with the
music, and let the magic/poetry/emotion/spirit move you. But to come
up with the tuning in the first place . . . is one of the things
this list is about, and it would be strange for you to deprecate the
kinds of investigations that lead to the very tunings you use, IMHO.

Well, whatever -- I'm sure we'll have a good laugh about this when
we finally get together and jam. I realize that my tone in writing
can seem condescending at times (and that *is* totally my fault) --
I think you're in for a pleasant surprise when we interact in
person. I guess I'm cursed with a piece of brain that wants to find
out the "whethers" and "whys" of things through direct experiential
evidence. Luckily, that piece of brain can do little but sit in
wonder when the musical "magic" starts happening . . . and often
continues well into the morning!

Speaking of jamming, a shameless plug: This Wednesday night is my
night at the Burren (247 Elm St. Davis Square, Somerville, MA, USA --
from Boston or Cambridge, take the Red Line to Davis Sq.), with two
of my rhythm-oriented, improv-oriented musical groups playing in the
back room (the room with the stage), and I'll be having a party
afterwards, so I'd love any local list readers to come down and say
hi -- meeting in person is always so much more rewarding
than "meeting in ASCII" :)

-Paul

🔗monz <monz@tonalsoft.com>

hi George,

--- In tuning@yahoogroups.com, "George D. Secor" <gdsecor@y...> wrote:
>
> --- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
> > ...
> > i have noticed the following in my own listening experiments:
> > ...
> > . in a more "typical" type of Western "common-practice"
> > context, 11 seems to me to be the highest prime that is
> > necessary to produce perceptually unique sounds/affects.
>
> I'm inclined to agree with this.
>
> > unless the musical context specifically emphasizes a certain
> > prime (as, for example, 19 in the 4:10:14:19 chord in
> > my piece _Hendrix Chord_), i find that ratios of 13 or
> > higher primes are often superfluous, tending more or less
> > to resemble the ratios available within the 11-limit.
>
> My work with Dave Keenan devising symbols for ratios above
> the 11-limit in the Sagittal notation project also tends to
> confirm this observation. Once we had created microtonal
> accidentals to notate the 11-limit consonances and ratios
> containing 5^2 (25) and 5*7 (35) as factors, we found that
> no additional symbols were required for any of the 13-limit
> consonances, inasmuch as we could approximate all of
> them with existing symbols without incurring an error
> greater than ~0.833 cents (2079:2080).

wow, that's awesome! i've been quite firmly convinced of
this for about 10 years now, based only on my observations
in listening experiments. it's nice to know that those
more-or-less vague observations have apparently been confirmed
by a methodical and systematic investigation!

-monz

🔗monz <monz@tonalsoft.com>

hi Paul and Carl,

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

>
> --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
>
> > >> . in a more "typical" type of Western "common-practice"
> > >> context, 11 seems to me to be the highest prime that is
> > >> necessary to produce perceptually unique sounds/affects.
> > >
> > > I'm inclined to agree with this.
> >
> > I'm inclined to disagree, sort of.
> >
> > 20th century music is clearly inhabiting 12-tET, and the
> > just intonation interpretation of much of it is not clear,
> > or at least non-unique.
>
> I agree,.Carl. I didn't raise an objection because I
> thought Monz would be willing to substitute "odd" instead
> of "prime" above. Would you, Monz?

oh boy, this again. you guys know that i'm a "prime-dude"
and not an "odd-dude". i don't tend to think in terms of
odd factors giving anything distinctive to a tuning that's
not already there because of a smaller prime factor.

but in any case, yes, i suppose i could agree to change
what i wrote to "odd", because it doesn't affect my point,
which is that when i hear ratios of 13, 17, 19, 23, etc.,
they don't seem to add anything distinctively new to the
harmonic fabric that's not already there if 11 is being used
-- *unless the musical context places some special emphasis
on them* !!

(and i still think that ratios of 9 sound like ratios of 3.)

> > The effects of circulating temperaments go back much
> > further, and there is even medieval music that treats
> > Pythagorean tuning as more circular than it actually
> > is, wolves be damned.
> >
> > Temperament aside, there is also the point of expressive
> > vs. structural intonation. In terms of the latter, common
> > practice music is clearly 5-limit,
>
> I tend to agree.
>
> > while in terms of the
> > former, it is hard to place any absolute upper limit on
> > things.
>
> Or, some might argue, Pythagorean or 3-limit JI encapsulates
> the tendencies of expressive intonation in Western common
> practice music.

in the context of this thread, i think it's also worth pointing
out that 12-tET almost always really does sound a lot like
pythagorean tuning, to me anyway.

-monz

🔗Pete McRae <ambassadorbob@yahoo.com>

-Paul

I hate it when I get plugs for things I can't just jump in the car and go check out! :-) Break a string! :-)

Cheers, mate!

Pete

wallyesterpaulrus <wallyesterpaulrus@yahoo.com> wrote:

--- In tuning@yahoogroups.com, Pete McRae wrote:

Hi Pete,

Music as poetry and as magic plays a huge role in my life; I won't
go on and on about that.

-Paul

Yahoo! Groups Links

---------------------------------
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🔗Gene Ward Smith <genewardsmith@coolgoose.com>

🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗monz <monz@tonalsoft.com>

hi Gene (and George and John),

--- In tuning@yahoogroups.com, "Gene Ward Smith" <genewardsmith@c...>
wrote:

> --- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
>
> > wow, that's awesome! i've been quite firmly convinced of
> > this for about 10 years now, based only on my observations
> > in listening experiments. it's nice to know that those
> > more-or-less vague observations have apparently been confirmed
> > by a methodical and systematic investigation!
>
> What exactly is the question here? Of course we can get as
> close as we like to any limit, and therefore notate any limit,
> simply sticking to the 3-limit.

yes, of course ... if you carry out a block of intervals
in any prime-limit you can come arbitrarily close to ratios
of any other limit, depending on how far out from 1/1
you carry the block.

(the block is simply a chain in 3-limit or any other
single-prime tuning, and a plane in 5-limit or any other
double-prime tuning ... not counting the primes which
constitute the equivalence interval.)

i should have specified the assumption that the blocks
being compared are rather small and compact, close to 1/1.

so restating my observation with that assumption given:
i find that a fairly small 11-limit periodicity-block
contains sounds which audibly approximate ratios of any
higher prime-limit.

(i'm happy to hone this statement to something more precise.)

-monz

🔗Pete McRae <ambassadorbob@yahoo.com>

wallyesterpaulrus <wallyesterpaulrus@yahoo.com> wrote:

<<Did you mean math? Don't you use the Eikosany tuning? Gene
independently discovered this and other CPS scales in the 1960's by
considering the so-called "deep holes" in the lattice.>>

Hmmm. Sounds to me like Lucky Charms claiming to be oatmeal. Not to mention vampirism? ;-)

I got my documentation on the Eikosany and other innovations (including source materials!) in hard copies from Erv Wilson himself 15 years ago, and I've never seen the slightest blip until now that there was any other seminal work along the same lines, especially with the kind of musical insight that Erv brings to bear on many different musics, and the kind of consideration he practices--and expects to be practiced!--in acknowledging previous, parallel, or similar work.

If certain persons on this list wish to write themselves into history, I suppose they are welcome to their megalomania.

Pete

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🔗Carl Lumma <ekin@lumma.org>

🔗Pete McRae <ambassadorbob@yahoo.com>

Left field is an honored position, after you've been in right field, where hardly anyone ever hits the ball.

In the bigger picture, of course, you're right. But in in this tiny little window, when I hear people naming commas and temperaments and such after themselves, and citing their own writings, it comes to seem to me like there may be a lack of humility at work somewhere in the vicinity, and a need to call attention to bigger--or maybe just older--people than ourselves who paid the dues and were there when the real work was being done to produce art that could reach a larger audience, only because we don't have the "luxury" of a less fragmented media, or the pain of more intense public (!) scrutiny. I guess. In that sense, I'm a megalomaniac myself, because I'd like to think I can make a difference, somehow.

But you didn't express any concern about my core statement, so where's the issue?

Carl Lumma <ekin@lumma.org> wrote:

>If certain persons on this list wish to write themselves into
>history, I suppose they are welcome to their megalomania.

Whoa, where's this coming from? You are totally, completely in
left field here, Pete.

-Carl

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🔗Ozan Yarman <ozanyarman@superonline.com>

That would be me with the megalomania in this case. Pete has delivered a most righteous blow against my thoughtless acts of vanity. It was in my excitement for discovery that I was so reckless regarding onomastic conventions. Be assured that I will not be so quick for naming anything after anyone (particularly myself) anymore, even if for quick reference. I retract all personal inferences to my ego.

Cordially,
Ozan

----- Original Message -----
From: Pete McRae
To: tuning@yahoogroups.com
Sent: 07 Mart 2005 Pazartesi 8:12
Subject: Re: [tuning] Count Chocula?

Left field is an honored position, after you've been in right field, where hardly anyone ever hits the ball.

But you didn't express any concern about my core statement, so where's the issue?

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

🔗Carl Lumma <ekin@lumma.org>

🔗Kraig Grady <kraiggrady@anaphoria.com>

The Hexany has nothing to do with cubes, except possibly Eulers. Eulers work and Erv' s are almost a match of which he is the first to point out, but they are not the same. . The stellate hexany is the union of two crossets. In two dimension it is quite easy to by pass the hexany, as well as to miss it significance

What--that someone would independently discover something Erv found?
Erv found lots of things I didn't find, but the converse is true as
well. It's hardly surprising that there was overlap. For the record,
the Eikosany isn't something I independently discovered; I *did* find
the hexany and stellated hexany, and even wrote hexany music back
when. The geometric point of view on the hexany is a natural one, I
think. The chord cubes, crystal balls, dwarf scales and etc. I've talked
about may not have attracted much attention, but I think they might be
of interest to the same people who find the eikosany interesting. The
stellated hexany, in fact, is the first of the chord cubes unless you
count a single tetrad, and the next chord cube of 27 chords I've
written in.

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

Yahoo hasn't put it up yet, so I can't correct with a follow-up. How
it should have read is:

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@a...> wrote:

> The Hexany has nothing to do with cubes, except possibly Eulers.

Here's yet another way to work cubic stuff into this. We can think of
7-limit intervals as represented by a cubic lattice of monzos Z4,
consisting of quadruples of integers |w x y z> with the ordinary
Euclidean metric. Suppose we decide to represent the lattice of octave
equivalence classes by means of a representative interval, with the
property that w+x+y+z=0. We can reduce an interval to its octave-class
representative by

red(q) = 2^(-ordp(q,3)-ordp(q,5)-ordp(q,7)) * 3^ordp(q,3) 5^ordp(q,5)
7^ordp(q,7)

where ordp is the p-adic valuation, meaning the monzo coordinate value
corresponding to the prime p, so that

q = 2^ordp(2,q) 3^ordp(3,q) 5^ordp(5,q) 7^ordp(7,q)

If |w x y z> is a monzo, then red(|w x y z>) = |-x-y-z x y z>.

We now find the symmetrical lattice of octave classes, with its
octahedra and tetrahedra and so forth, is just the sublattice of
reduced representatives, under the Eulicidean metric. For example the
cps {3,5,7,15,21,35} reduces to {3/2,5/2,7/2,15/4,21/4,35/4}, or in
monzo terms {|-1 1 0 0>, |-1 0 1 0>, |-1 0 0 1>, |-2 1 1 0>,
|-2 1 0 1>, |-2 0 1 1>}. It is easy to verify that these are the
verticies of an octahedron in four-dimensional space, so here you have
the hexany sitting inside of a cubic (4D) lattice.

🔗Pete McRae <ambassadorbob@yahoo.com>

Carl Lumma <ekin@lumma.org> wrote:

>>In the bigger picture, of course, you're right. But in in this tiny
>>little window, when I hear people naming commas and temperaments and
>>such after themselves,

>Who does that?

Nevermind. They know who they are.

>>and citing their own writings,

>That's standard practice in scholarly work.

So is megalomania. I thought that was part of why the tuning list was started...to counter some of that, and give credit where it's due.

>>it comes to seem to me like there may be a lack of humility at work
>>somewhere in the vicinity, and a need to call attention to bigger--or
>>maybe just older--people than ourselves who paid the dues and were
>>there when the real work was being done to produce art that could
>>reach ...

>Eh? Gene is no spring chicken, and he's composed considerably
>more music than Erv.

Erv Wilson is not a composer and doesn't claim to be. Gene is NOT a composer and claims to be, if you want to look at it that way. (Sorry, Gene) ;-)

>>But you didn't express any concern about my core statement,

>Sorry, was there a core statement? Maybe you can clarify.

My core statement was clear enough, and I think you know it to be true. It's an awful sad day (in the puny little tuning sense?), if you do, and won't admit it.

-Pete

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--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@a...> wrote:

> The Hexany has nothing to do with cubes, except possibly Eulers.

Sure it does. The hexany is an octahedron, and the dual polytope to
that is a cube. If you stellate the octohedron, the centers of the
tetrahedra, representing 7-limit tetrads, are in a cube. If you take
the lattice of 7-limit intervals in its symmetrical form, you get a
lattice called "A3" or "face-centered cubic". This lattice has two
sizes of hole, the "deep holes" are the octahedrons, and the "shallow
holes" tetrahedrons. If you make lattice points out of the centers of
the tetrahedrons, you are making a lattice of the 7-limit tetrads.
This is simply the cubic lattice, called "Z3". The dual lattice to A3,
A3*, is the "body-centered cubic lattice". This can be defined as the
lattice of all triples of integers (x,y,z) where either x, y and z
are all even, or they are all odd. A3 is also D3, which means it can
be thought of as triples (x,y,z) of integers such that x+y+z is even.
Hence, there are a lot of cube-related features of this.

What's Euler's cube?

Eulers work and Erv' s are almost a match of which he is the first to
point out, but they are not the same. .

What was Erv's work on lattices?

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

🔗David Beardsley <db@biink.com>

🔗Pete McRae <ambassadorbob@yahoo.com>

I gotta give it to you, DB, you've come up with some FUNNY ones, lately!

Salud,

David Beardsley <db@biink.com> wrote:

Pete McRae wrote:

> So is megalomania. I thought that was part of why the tuning list
> was started...to counter some of that, and give credit where it's due.
>

Yooze new 'round here. Ain't you?

--
* David Beardsley
* microtonal guitar
* http://biink.com/db

Yahoo! Groups Links

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🔗David Beardsley <db@biink.com>

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

>So is megalomania. I thought that was part of why the tuning list
>was started...to counter some of that, and give credit where it's
>due.

I like giving credit where it's due whenever I know it's due someone
(see all the personal names in my new paper). But I thought this list
was about discussing tuning and helping people to grasp tuning
concepts for themselves, so that (for example) they can (if they
wish) climb the same mountains and view the same vistas that have
been viewed before, and perhaps also see something that no human has
seen before. To me, the climb relevant in this particular case is a
pretty straightforward one, that anyone with enough interest can
pursue. And many such climbs have been ventured on these lists and in
my private conversations with others. I always mention Erv Wilson and
his work wherever it's relevant.

Suggesting megalomania in this connection seems to imply something
that disturbs me. It suggests that the average reader of this list
can't formulate thoughts with enough depth or clarity to come to the
same concepts themselves. This discourages both independent thought
and thought within a thinking group, and encourages "cultism" where
only an "elite" are entitled to dictate the "sacred cow" concepts,
and anyone outside this elite is an "infidel" who surely can't have
thought of the same concepts themselves.

Pete, the reason this came up is because you brought up "science" on
this list, I didn't know if you meant "math" but certain ways of
applying math to the question of tuning lead directly to constructs
like the CPS scales. I believe that if you, or anyone else on this
list, pursues certain theoretical questions, such as how to display
all the consonances in a tuning system at a glance, perhaps getting
help from others if they need some math they haven't learned,
you/they will naturally see how the CPS scales arise. Perhaps this
kind of theoretical thinking doesn't interest you, and (like many
people) it is painful for you to engage in. I see nothing wrong with
that. But . . . oops I have to run to rehearsal right now, let's
continue this later, OK? Maybe on another list. On this list, maybe
we can instead discuss the relevant tuning concepts and constructs
themselves, as has been done in the past, such as in 2000:

http://sonic-arts.org/td/erlich/paul-cps.htm

where I gave Erv Wilson credit for "best single illustration of the
CPS concept" among other things . . .

P.S. Sorry I remembered wrong. It appears that Erv Wilson is indeed
the earliest we know of to write down any Eikosany scales. But it
would be sad indeed if someone who claimed precedence had to be
accused of "megalomania". Anyway, we'll have to continue this at some
point in the near future . . .

--- In tuning@yahoogroups.com, Pete McRae <ambassadorbob@y...> wrote:
>
>
> Carl Lumma <ekin@l...> wrote:
>
> >>In the bigger picture, of course, you're right. But in in this
tiny
> >>little window, when I hear people naming commas and temperaments
and
> >>such after themselves,
>
> >Who does that?
>
> Nevermind. They know who they are.
>
> >>and citing their own writings,
>
> >That's standard practice in scholarly work.
>
> So is megalomania. I thought that was part of why the tuning list
was started...to counter some of that, and give credit where it's due.
>
> >>it comes to seem to me like there may be a lack of humility at
work
> >>somewhere in the vicinity, and a need to call attention to bigger-
-or
> >>maybe just older--people than ourselves who paid the dues and were
> >>there when the real work was being done to produce art that could
> >>reach ...
>
> >Eh? Gene is no spring chicken, and he's composed considerably
> >more music than Erv.
>
> Erv Wilson is not a composer and doesn't claim to be. Gene is NOT
a composer and claims to be, if you want to look at it that way.
(Sorry, Gene) ;-)
>
> >>But you didn't express any concern about my core statement,
>
> >Sorry, was there a core statement? Maybe you can clarify.
>
> My core statement was clear enough, and I think you know it to be
true. It's an awful sad day (in the puny little tuning sense?), if
you do, and won't admit it.
>
> -Pete
>
>
>
>
> You can configure your subscription by sending an empty email to one
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> tuning-help@yahoogroups.com - receive general help information.
>
> Yahoo! Groups Links
>
>
>
>
>
>
>
>
>
>
>
> ---------------------------------
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🔗David Beardsley <db@biink.com>

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
>
> hi Paul and Carl,
>
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> <wallyesterpaulrus@y...> wrote:
>
> >
> > --- In tuning@yahoogroups.com, Carl Lumma <ekin@l...> wrote:
> >
> > > >> . in a more "typical" type of Western "common-practice"
> > > >> context, 11 seems to me to be the highest prime that is
> > > >> necessary to produce perceptually unique sounds/affects.
> > > >
> > > > I'm inclined to agree with this.
> > >
> > > I'm inclined to disagree, sort of.
> > >
> > > 20th century music is clearly inhabiting 12-tET, and the
> > > just intonation interpretation of much of it is not clear,
> > > or at least non-unique.
> >
> > I agree,.Carl. I didn't raise an objection because I
> > thought Monz would be willing to substitute "odd" instead
> > of "prime" above. Would you, Monz?
>
>
> oh boy, this again. you guys know that i'm a "prime-dude"
> and not an "odd-dude". i don't tend to think in terms of
> odd factors giving anything distinctive to a tuning that's
> not already there because of a smaller prime factor.
>
> but in any case, yes, i suppose i could agree to change
> what i wrote to "odd", because it doesn't affect my point,
> which is that when i hear ratios of 13, 17, 19, 23, etc.,
> they don't seem to add anything distinctively new to the
> harmonic fabric that's not already there if 11 is being used
> -- *unless the musical context places some special emphasis
> on them* !!

Can you hear this distinct 11-ness even if no ratios within the 11-
odd-limit are used? If so, which extended-11-limit ratios evoke it?

🔗David Beardsley <db@biink.com>

🔗Kraig Grady <kraiggrady@anaphoria.com>

🔗David Beardsley <db@biink.com>

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

🔗Carl Lumma <ekin@lumma.org>

🔗monz <monz@tonalsoft.com>

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@a...> wrote:

> it is quite
> easy to overlap this territory, as one could find , say a hexany,
within
> Euler, yet Euler missed it .

Euler's lattices, as implied by the Genus concept, were rectangular.
So the hexany with the symmetries that Erv and Gene consider it to
have would not appear within Euler's work. If you do highlight the
hexany notes within one of Euler's Genera, it appears to be much more
asymmetrical than the Genus. And in fact, there are other non-hexany
sets of 6 notes that have the same geometry/symmetry as the hexany
does when viewed in the rectangular, or Genus-based, arrangement. So
to me, it's not only that Euler missed it, he has the wrong "lens" to
see it as "something special" in the first place, even if someone had
pointed it out to him.

I never liked the rectangular arrangement for octave-equivalent
lattices, as they don't show acoustic affinity as accurately as they
could. If you invent or see the symmetric 5-odd-limit lattice
somewhere (such as Barbour), which is based on equilateral triangles,
and then decide to extend the symmetry to the 7-odd-limit, you
immediately get the tetrahedral-octahedral lattice, in which the
tetrahedra are major and minor tetrads and the octahedra are
hexanies. I did this in 1991 (I have a drawing from then), never
having seen any one else use a tetrahedral-octahedral lattice before,
or having heard of Erv Wilson. I'm sure plenty of other people made
this same discovery independently too.

🔗Gene Ward Smith <genewardsmith@coolgoose.com>

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

> I never liked the rectangular arrangement for octave-equivalent
> lattices, as they don't show acoustic affinity as accurately as they
> could. If you invent or see the symmetric 5-odd-limit lattice
> somewhere (such as Barbour), which is based on equilateral triangles,
> and then decide to extend the symmetry to the 7-odd-limit, you
> immediately get the tetrahedral-octahedral lattice, in which the
> tetrahedra are major and minor tetrads and the octahedra are
> hexanies. I did this in 1991 (I have a drawing from then), never
> having seen any one else use a tetrahedral-octahedral lattice before,
> or having heard of Erv Wilson. I'm sure plenty of other people made
> this same discovery independently too.

Ditto, pretty much, though for me Schoenberg was influential, so that
I also looked at the dual tiling by hexagons, and in the 7-limit, the
cubic lattice of tetrads.

I'm still not clear who was the first to find the symmetrical 5-limit
lattice. Wikipedia seems to think that Riemann did not introduce this
in his lattice diagrams, and if so he didn't really advance
significantly beyond Euler. I also don't know who first considered a
7-limit symmetrical lattice of octave classes, nor who first noticed
the cubic lattice of tetrads. Anyway I think I was doing this in 1968,
but it could have been no later than 1969.

🔗monz <monz@tonalsoft.com>

hi Paul,

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

> --- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
> >
> > <snip>
> >
> > but in any case, yes, i suppose i could agree to change
> > what i wrote to "odd", because it doesn't affect my point,
> > which is that when i hear ratios of 13, 17, 19, 23, etc.,
> > they don't seem to add anything distinctively new to the
> > harmonic fabric that's not already there if 11 is being used
> > -- *unless the musical context places some special emphasis
> > on them* !!
>
> Can you hear this distinct 11-ness even if no ratios
> within the 11-odd-limit are used? If so, which
> extended-11-limit ratios evoke it?

as i just wrote in another post which you quoted:
/tuning/topicId_57195.html#57299

>> " i find that a fairly small 11-limit periodicity-block
>> contains sounds which audibly approximate ratios of any
>> higher prime-limit."

so i'm not really talking about *extended*-11-limit,
and i'm also not really saying that there's a "distinct
11-ness" ... in fact quite the opposite: that the
distinctness of a prime-factor diminishes as the number
becomes larger. thus:

. 2-ness
--------

the affect of 2 is extraordinarily distinct, and produces
the effect of "octave-equivalence" ... it's so distinct
that in traditional music theory, for notes which are
separated by a 2:1 or something audibly close to it, one
aspect of the notation -- the naming of the nominals --
recognizes it, by giving those notes the same name.

(but observe that the standard staff-notation does *not*
recognize it ... however, many new proposals, including
several of my own, do.)

. 3-ness
--------

the affect of 3 at least in terms of "equivalence" is
less distinct than that of 2 ... i.e, it's obvious to
most listeners that two notes which are separated by
a 3:2 or something audibly close to it, are notes which
have a very close relationship, but yet they are still
perceived to be "different pitches" or "different notes",
in the sense that notes separated by a 2:1 are not.

but at the same time, the 3:2 is recognized in traditional
theory as having enough of this "equivalence" effect that
when ratios-of-5 became recognized in theory and common
in practice, parallel motion of 3:2's and 4:3's was
"officially" banned.

. 5-ness
--------

the resemblance between the 5-limit 5:4 major-3rd with
(2,)3,5-monzo [* 0, 1> and the 3-limit pythagorean 81:64
major-3rd with (2,)3,5-monzo [* 4, 0> is close enough
that they are both recognized as "major-3rd's", and
in fact both become synonymous in the meantone family of
tunings upon which standard western music theory is based
... but yet audibly different enough that the comma
difference was recognized as a problem for which the
meantone tuning itself was the solution.

the 5-limit Euler-genus which contains the 5:4 and 81:64
only has 8 notes: 3^(0...4) 5^(0...1) . the fact that
the diatonic scales all have 7 notes played a large role
in the desire to temper out the syntonic comma which
separates these two pitches, which lie at opposite
corners of the lattice of this Euler-genus.

. 7-ness
--------

the resemblance between the 7-limit 7:4 harmonic-7th
with (2,)3,5,7-monzo [* 0, 0 1> , the 5-limit 9:5
"just minor-7th" with (2,)3,5,7-monzo [* 2, -1 0> ,
and the 3-limit pythagorean 16:9 minor-7th with
(2,)3,5,7-monzo [* -2, 0 0> , is close enough that
they are all recognized as some type of 7th, but audibly
different enough that the 7:4 seems for most listeners to
give a clearly more concordant periodicity-buzz than the
other two.

however, one does not have to go to far away from
the origin (1:1) in the 5-limit lattice to find a
pitch with a different nominal and theoretical function
which audibly resembles 7:4 -- namely, the 225:128
augmented-6th with (2,)3,5-monzo [* 2, 2> . thus, already
within the fairly small (18-tone) 7-limit Euler-Fokker-genus
of 3^(0...2) 5^(0...2) 7^(0...1) , we find two pitches
separated by the small interval (~ 7.711522991 cents) of
a 225:224 septimal-kleisma with (2,)3,5,7-monzo [- 2, 2 -1> .

the Euler-Fokker-genus which contains all four of these
ratios has 40 tones: 3^(-2...2) 5^(-1...2) 7^(0...1) ,
which is still fairly small, and in fact some steps in
the monzo exponent series are not required, so that
all four pitches can be contained within the genus
3^(-2,0,2) 5^(-1,0,2) 7^(0,1) .

similarly, the 9:7 "super-major-3rd" is also clearly distinct
from its 5-limit counterparts, however, the just 32:25
diminished-4th with (2,),3,5,7-monzo [* 0, -2 0> is quite
close in size. etc.

thus, we begin to see that as more prime-factors and
allowances for approximation are admitted, we get a
more compact Euler-Fokker-genus. perhaps i really mean
a more compact periodicity-block ... i don't know, and
must leave it to others to discuss.

. 11-ness
---------

for tuning systems which have 11 as a factor, i find (by
my own perceptions ... YMMV) that any of the pitches in a
fairly small 4-dimensional Euler-genus can approximate
tolerably well pitches with any other set of prime-factors.

(please notice that i'm being deliberately vague and
incomplete in my description here.)

-monz

🔗monz <monz@tonalsoft.com>

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

> --- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
>
> > --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> > <wallyesterpaulrus@y...> wrote:
> >
> > > If you invent or see the symmetric 5-odd-limit lattice
> > > somewhere (such as Barbour), which is based on equilateral
> > > triangles, and then decide to extend the symmetry to the
> > > 7-odd-limit, you immediately get the tetrahedral-octahedral
> > > lattice, in which the tetrahedra are major and minor tetrads
> > > and the octahedra are hexanies. I did this in 1991 (I have
> > > a drawing from then), never having seen any one else use a
> > > tetrahedral-octahedral lattice before, or having heard of
> > > Erv Wilson. I'm sure plenty of other people made
> > > this same discovery independently too.
> >
> >
> > yup ... me too, around 1984 or '87 or sometime around then.
>
>
> my efforts stemmed directly from a desire to streamline
> Partch's tonality diamond concept. i hadn't yet seen
> tonal diagrams by anyone else at the time.

oops ... not entirely true. (Gene reminded me)

i *had* seen Schoenberg's diagram of the overtone series,
up to the 12th partials, of 3^(-1...1) , in the old English
translation of his _Harmonielehre_ ("Theory of Harmony",
trans. Robert Adams 1948)

... and in fact that was years before i ever knew anything
about Partch ... around 1976.

-monz

🔗monz <monz@tonalsoft.com>

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

>
> <big snip>
>
> . 11-ness
> ---------
>
> for tuning systems which have 11 as a factor, i find (by
> my own perceptions ... YMMV) that any of the pitches in a
> fairly small 4-dimensional Euler-genus can approximate
> tolerably well pitches with any other set of prime-factors.
>
> (please notice that i'm being deliberately vague and
> incomplete in my description here.)

OK ... since i was so detailed with the other prime-ness
descriptions, i suppose i can flesh this one out a bit.

suppose we have the 12-tone Euler-genus
3^(0...2) 11^(-1...0) 13^(0...1) .

this tuning contains 8 pairs of ratios separated by a 33:32
near-quarter-tone tridecimal-diesis with (2,)3,(5,7,)11,13-monzo
[* 1, 0 0 1, 0> = ~53.27294323 cents. this is not particularly
relevant to the current topic, other than to point out the
non-diatonic character of the scale produced by the complete
genus.

along with the 13:8 ratio [* 0, 0 0 0, 1> = ~840.5276618 cents,
it also contains an approximation to the 13:8 which i find
is pretty much audibly indistinguishable from it: 18:11 ratio
[* 2, 0 0 -1, 0> = ~852.5920594 cents -- these two pitches
are separated by the 144:143 ratio [* 2, 0 0 -1, -1> =
~12.0643976 cents.

this is larger than the 225:224 septimal-kleisma which i
described under "7-ness", but yet i hear a clear difference
in the 7-limit case, but not here ... neither as a bare
dyad interval nor in the context of larger chords.

also interesting, from the point of view of the emphasis
i'm placing on how the unison-vectors cause the Euler-genus
(or periodicity-block?) to become more compact as the
prime limit goes higher (i.e., smaller unison-vectors
appear closer to the 1:1 origin), is this fact: if the
exponents of 3 are extended only one more step in the
negative direction, we get not only the 4:3 perfect-4th
[* -1, 0 0 0, 0> = ~498.0449991 cents, but also the
117:88 ratio [* 2, 0 0 -1, 1> = ~493.1197211 cents,
the two pitches being separated by the 352:351 ratio
[* -3, 0 0 1, -1> = ~4.925277999 cents -- however,
despite the great similarity in pitch, in this case
i do hear an audible difference because the 117:88 has
quite noticeable beating which 4:3 lacks. (the caveat is
that this might be an artifact of the timbres i've used.)

-monz

🔗pgreenhaw@nypl.org

NERDS!!!!!!

(things are getting out of control)

__________________________________________

"monz" <monz@tonalsoft.com>
03/08/2005 04:37 AM
Please respond to tuning

To: tuning@yahoogroups.com
cc:
Subject: [tuning] Re: new member question from a theory class

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

> If you invent or see the symmetric 5-odd-limit lattice
> somewhere (such as Barbour), which is based on equilateral
> triangles, and then decide to extend the symmetry to the
> 7-odd-limit, you immediately get the tetrahedral-octahedral
> lattice, in which the tetrahedra are major and minor tetrads
> and the octahedra are hexanies. I did this in 1991 (I have
> a drawing from then), never having seen any one else use a
> tetrahedral-octahedral lattice before, or having heard of
> Erv Wilson. I'm sure plenty of other people made
> this same discovery independently too.

yup ... me too, around 1984 or '87 or sometime around then.

-monz

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🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
>
> --- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
>
> >
> > <big snip>
> >
> > . 11-ness
> > ---------
> >
> > for tuning systems which have 11 as a factor, i find (by
> > my own perceptions ... YMMV) that any of the pitches in a
> > fairly small 4-dimensional Euler-genus can approximate
> > tolerably well pitches with any other set of prime-factors.
> >
> > (please notice that i'm being deliberately vague and
> > incomplete in my description here.)
>
>
>
> OK ... since i was so detailed with the other prime-ness
> descriptions, i suppose i can flesh this one out a bit.
>
> suppose we have the 12-tone Euler-genus
> 3^(0...2) 11^(-1...0) 13^(0...1) .
>
> this tuning contains 8 pairs of ratios separated by a 33:32
> near-quarter-tone tridecimal-diesis with (2,)3,(5,7,)11,13-monzo
> [* 1, 0 0 1, 0> = ~53.27294323 cents. this is not particularly
> relevant to the current topic, other than to point out the
> non-diatonic character of the scale produced by the complete
> genus.
>
> along with the 13:8 ratio [* 0, 0 0 0, 1> = ~840.5276618 cents,
> it also contains an approximation to the 13:8 which i find
> is pretty much audibly indistinguishable from it: 18:11 ratio
> [* 2, 0 0 -1, 0> = ~852.5920594 cents -- these two pitches
> are separated by the 144:143 ratio [* 2, 0 0 -1, -1> =
> ~12.0643976 cents.
>
> this is larger than the 225:224 septimal-kleisma which i
> described under "7-ness", but yet i hear a clear difference
> in the 7-limit case, but not here ... neither as a bare
> dyad interval nor in the context of larger chords.
>
> also interesting, from the point of view of the emphasis
> i'm placing on how the unison-vectors cause the Euler-genus
> (or periodicity-block?)

The two are not the same, of course. Euler genera aren't defined by
unison vectors . . .

> to become more compact as the
> prime limit goes higher (i.e., smaller unison-vectors
> appear closer to the 1:1 origin), is this fact: if the
> exponents of 3 are extended only one more step in the
> negative direction, we get not only the 4:3 perfect-4th
> [* -1, 0 0 0, 0> = ~498.0449991 cents, but also the
> 117:88 ratio [* 2, 0 0 -1, 1> = ~493.1197211 cents,
> the two pitches being separated by the 352:351 ratio
> [* -3, 0 0 1, -1> = ~4.925277999 cents -- however,
> despite the great similarity in pitch, in this case
> i do hear an audible difference because the 117:88 has
> quite noticeable beating which 4:3 lacks. (the caveat is
> that this might be an artifact of the timbres i've used.)
>
>
>
> -monz

Hi Monz,

All this sounds like perfect evidence for the aural importance of
some measure that simply tells you "how small the numbers are" in the
ratio, rather than prime limit (which doesn't). From the above, it
would seem to me that you, like me, can tune ratios such as 4:3 or
7:4 with arbitrary accuracy by ear, just by listening to the beating
and other psychoacoustical phenomena associated with nearby ratios.
But ratios like 13:8 and 18:11 are borderline in that I need either
more notes in the chord, or extremely overtone-rich timbres, in order
to tune them accurately and/or hear whether they're tuned accurately.
More complex ratios still, and there's nothing aurally distinct about
them (compared with nearby ratios) when heard as lone dyads.

(Harmonic entropy accounts for this fairly nicely)

I don't think any of these observations have anything to do with
prime limit. Do you know of any reason I should think otherwise?

🔗Pete McRae <ambassadorbob@yahoo.com>

Carl Lumma <ekin@lumma.org> wrote:

>>>>and citing their own writings,
>>>
>>>That's standard practice in scholarly work.
>>
>>So is megalomania

>How'ya figure?

Ever read any scholarly literature? Dunno.

>>I thought that was part of why the tuning list was
>>started...to counter some of that, and give credit where
>>it's due.

>Does anyone here know why the list was started, and does
>anyone care?

Nope.

>>Erv Wilson is not a composer and doesn't claim to be. Gene
>>is NOT a composer and claims to be, if you want to look at it
>>that way. (Sorry, Gene) ;-)

>Gene's pieces are above average for these lists.

That's pretty bad. (Sorry... ;-)

>>>>But you didn't express any concern about my core statement,
>>>
>>>Sorry, was there a core statement? Maybe you can clarify.
>>
>>My core statement was clear enough, and I think you know it to be
>>true.

>Actually I haven't the slightest clue what you're talking about.

Good. Then I was never here. Send your assassins to another address.

-P

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🔗monz <monz@tonalsoft.com>

hi Paul,

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

> All this sounds like perfect evidence for the aural
> importance of some measure that simply tells you
> "how small the numbers are" in the ratio, rather than
> prime limit (which doesn't). From the above, it would
> seem to me that you, like me, can tune ratios such as
> 4:3 or 7:4 with arbitrary accuracy by ear, just by
> listening to the beating and other psychoacoustical
> phenomena associated with nearby ratios. But ratios
> like 13:8 and 18:11 are borderline in that I need
> either more notes in the chord, or extremely overtone-rich
> timbres, in order to tune them accurately and/or hear
> whether they're tuned accurately. More complex ratios
> still, and there's nothing aurally distinct about
> them (compared with nearby ratios) when heard as
> lone dyads.
>
> (Harmonic entropy accounts for this fairly nicely)
>
> I don't think any of these observations have anything to
> do with prime limit. Do you know of any reason I should
> think otherwise?

i stayed up much later last night than i should have
writing those posts ... so at this point i think i'll
just have to agree with you for now and drop the discussion.

i'm obviously interested in pursuing theoretical questions
like this, but just don't have time to dig into it.
(i'm still only midway thru the "C's" in converting the
Encyclopedia ... and it's supposed to be finished by
the end of March.)

-monz

🔗wallyesterpaulrus <wallyesterpaulrus@yahoo.com>

--- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
>
> hi Paul,
>
>
> --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> <wallyesterpaulrus@y...> wrote:
>
>
> > --- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
> > >
> > > <snip>
> > >
> > > but in any case, yes, i suppose i could agree to change
> > > what i wrote to "odd", because it doesn't affect my point,
> > > which is that when i hear ratios of 13, 17, 19, 23, etc.,
> > > they don't seem to add anything distinctively new to the
> > > harmonic fabric that's not already there if 11 is being used
> > > -- *unless the musical context places some special emphasis
> > > on them* !!
> >
> > Can you hear this distinct 11-ness even if no ratios
> > within the 11-odd-limit are used? If so, which
> > extended-11-limit ratios evoke it?
>
>
> as i just wrote in another post which you quoted:
> /tuning/topicId_57195.html#57299
>
> >> " i find that a fairly small 11-limit periodicity-block
> >> contains sounds which audibly approximate ratios of any
> >> higher prime-limit."
>
>
> so i'm not really talking about *extended*-11-limit,

If you're not talking about 11-odd-limit (that is, the set of ratios
in Partch's diamond), but about any 11-prime-limit ratios outside
that, you're talking about "extended 11-limit", in Partch's
terminology.

> and i'm also not really saying that there's a "distinct
> 11-ness" ... in fact quite the opposite: that the
> distinctness of a prime-factor diminishes as the number
> becomes larger.

You seemed to be saying above that primes 13 and above don't add
anything distinctively new to the harmonic fabric. So I took that to
mean that prime 11 does. This is what I'm asking you about. I won't
be upset if you change your mind -- I'm just asking you what you
hear/feel/find that was behind these statements of yours.

🔗Kraig Grady <kraiggrady@anaphoria.com>

While the possibility of running across a hexany as an octahedron, at this point all limited to the 1-3-5-7, it is a great leap of vision in order to get to the eikosany which really is your first extensive CPS structure one might use in an extended possibility. There are other ways also to map to an octahedron that do not involve the 2 out of 4 set where the products are reduced into a single point in the set. The former was done by Fuller for one who made a big to do over it
I am quite aware of being a lunatic, but all true beginnings always look like madness. Still i await a concrete example of combination product sets as such.
the discovery of this was not some accidental discovery. Erv has stated that the moon flights were instrumental in conceiving of such weightless structures. In retrospect salso he has pointed out to me the diagram on Page 123 of Partch's Genesis of a Music ( a book he did quite a few of the diagrams for) and finds that possibly this chart might have halso had an influence on him if one thinks for these as a product into tones instead of triads. Regardless , it takes something to realize the signigance of this structure and what it can do musically. In order to let those not familiar with the extent and in depth development and understanding of trhe Combination product sets i refer the readers to the section in the Wilson archive
being the fourth section under the header

http://www.anaphoria.com/wilson.html
This still awaits all the papers on the hebdomekontany which have not been put up yet

Also for some applications i have papers of my own
http://anaphoria.com/eikopapers.html
-- Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

🔗monz <monz@tonalsoft.com>

hi Paul,

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

> --- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
> >
> > hi Paul,
> >
> >
> > --- In tuning@yahoogroups.com, "wallyesterpaulrus"
> > <wallyesterpaulrus@y...> wrote:
> >
> >
> > > --- In tuning@yahoogroups.com, "monz" <monz@t...> wrote:
> > > >
> > > > <snip>
> > > >
> > > > but in any case, yes, i suppose i could agree to change
> > > > what i wrote to "odd", because it doesn't affect my point,
> > > > which is that when i hear ratios of 13, 17, 19, 23, etc.,
> > > > they don't seem to add anything distinctively new to the
> > > > harmonic fabric that's not already there if 11 is being used
> > > > -- *unless the musical context places some special emphasis
> > > > on them* !!
> > >
> > > Can you hear this distinct 11-ness even if no ratios
> > > within the 11-odd-limit are used? If so, which
> > > extended-11-limit ratios evoke it?
> >
> >
> > as i just wrote in another post which you quoted:
> > /tuning/topicId_57195.html#57299
> >
> > >> " i find that a fairly small 11-limit periodicity-block
> > >> contains sounds which audibly approximate ratios of any
> > >> higher prime-limit."
> >
> >
> > so i'm not really talking about *extended*-11-limit,
>
> If you're not talking about 11-odd-limit (that is, the set of ratios
> in Partch's diamond), but about any 11-prime-limit ratios outside
> that, you're talking about "extended 11-limit", in Partch's
> terminology.
>
> > and i'm also not really saying that there's a "distinct
> > 11-ness" ... in fact quite the opposite: that the
> > distinctness of a prime-factor diminishes as the number
> > becomes larger.
>
> You seemed to be saying above that primes 13 and above don't
> add anything distinctively new to the harmonic fabric. So I
> took that to mean that prime 11 does. This is what I'm asking
> you about. I won't be upset if you change your mind -- I'm
> just asking you what you hear/feel/find that was behind
> these statements of yours.

i guess my point is not being made clearly ... i'll try again.

what i'm saying is that the prime-factors 2, 3, 5, and 7
(they may be thought of as the octave-normalized pitch-class
ratios 2:1, 3:2, 5:4 and 7:4 otonalities, and their inversions
in utonalities, and also all 8 ratios as dyads) seem to me
to each carry a distinctive affect, something in their sound
that makes them clearly separate entities.

but while 11 also seems distinct if 13 has not been introduced,
when 13 *is* introduced i can't tell much difference between
ratios-of-11 and ratios-of-13 which resemble those ratios-of-11.
so at some point between 11 and 13 the distinctiveness of affect
seems to break down.

(unless, as i've emphasized all along, the musical context
deliberately points out those prime-factors.)

-monz