Catch All

Working two full-time jobs and trying to find rent in the landlord's market
that is the Bay Area of California, while living in a friend's house and
contributing to the tuning list (especially when it's been so active --
good to see) is not always easy. So we have the catch all message....

*******************************************************
With Paul Erlich
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>No, 0.6% means a frequency change of 0.6%. Basically Goldstein dealt
>with the way complex tone pitch (virtual pitch) was inferred from sets
>of pure tones which departed by various amounts from an exact harmonic
>series. His experimental results were very well fit by a model with only
>one parameter, sigma, which could vary from listener to listener.
>Essentially the model states that the listener will interpret the set of
>pure tones as a certain virtual pitch if the pure tones have an rms
>deviation less than sigma from a harmonic series above that virtual
>pitch. As the deviations are increased further, the ear shifts to a
>different, lower virtual pitch, whose harmonics better fit the pure
>>tones (this is a very rough description).

Okay. The idea seems to make sense. We're talking about 15 cents, on
average?

What isn't clear is just what the claim is as to what mistuning like this
does to interval perception. Whatever it is, you seem to feel it's big
enough to cause problems in ET's over 35/oct. And then there's the matter
of the thing being based on pure tones. What about tones with partials?

>Here's what I've always said: "a" is preferable for describing the
>resources of a given system of Just Intonations, and "b" is preferable
>for describing the maximum interval complexity in simultaneities
>considered consonant in a given style. The latter is very tied up with
>an acoustical theory of interval perception.

Sorry if I mis-understod your standpoint. Maybe we're closer to agreeing
on this than I thought. I did not mean to mis-represent your ideas.

>>>"An arbitrary power of two produces an effect of equivalence." This must
>>>of course include the case where the power is zero, and the equivalence
>>>is greatest. The equivalence evidently falls off as the power increases.
>>>
>>>But what about steely coldness? Is it there when the power is zero? Does
>>>a unison contain all potential interval qualities, to a greater degree
>>>than the intervals themselves? It would seem hard to argue that way.
>>
>>If he's means what he says ("powers"), then his first paragraph is correct,
>>but his second is not, as "steely coldness" is an attribute of the factor
>>3, not the power 3.
>>
>>If he means factors instead of "powers", then I suppose his whole thing is
>>correct. Although I do not see why he insists on making the unison into
>>some kind of "white light", I am willing to oblige. As far as factor
>>determines which partials line up, and all of the partials in a unison line
>>up, the analogy holds...
>
>I'm not sure what it is in my wording that was problematic. Perhaps you
>could suggest an alternative wording for each of the interpretations you
>mention, and I could endorse one, allowing us to proceed?

Okay. Gary, representing the prime-number advocates (of which, I will be
sure to add, he is not necessarily one), said that steely coldness was
often considered to be related to the FACTOR of 3. You start out by saying
"an arbitrary power of 2 produces an effect of equivalence", and then
finish up asking if a power of 3 can produce steely coldness. But it is a
factor of three that is supposed to produce steely coldness.

Any change in power (stacking the interval two, or however many times) is
supposed to produce equivalence, falling off as stacking brings the
compound interval close in size to an interval with different prime factors
(like you point out with the 81/64 vs. 5/4 example -- although, as I said,
I don't think the the 81/64 is close enough to the 5/4 to mask its 3-ness).

I hope this helps.

>>music has evolved by prime limit. Pull out a CD of English tudor music, as
>>sung by the King's Singers, for example, and try to add the 7's. You
>>won't. They didn't, not for hundreds of years. They've got ratios of 25
>>and everything else needed to modulate around the 5-limit, throwing commas
>>around like frisbees, but no 7's. Barbershop's got 7's and 28's, and 63's
>>a-plenty. And 9's, and 18's, and 27's. But no 11's. Never will you hear
>>an 11 used harmonically in Barbershop music. And the first time you do,
>>you'll be hearing them again soon and often :~)
>
>Again, the odd-limit definition applies not when considering all
>intervals present, but when considering which intervals can be
>considered consonant. In all your examples, the higher composites are
>dissonant.

This is a very good point, provided you allow a movable 1/1.

However, I will note that, in my experience, I have often need caution when
considering attempts of music theory to say, "and in this period,
such-and-such was considered dissonant, etc..." I gather that Mr. Erlich
is quite a fan of such approaches; he insists in his 22TET paper on
nitpicking that "a better definition would be that 5-limit intervals are
considered consonances in this music, and therefore need to be tuned with
some degree of accuracy" [quoting from memory].

My objection to this approach is basically that:

1. It seems to be an over-generalization. Different composers use lots of
different things in lots of different ways, even in the same "period".

2. It has never, in my experience, proven useful in the composition of new
music.

Don't I use this idea when talking about music evolving by prime limit?
Not really. Because you will NEVER hear a higher prime being used
harmonically in the earlier style. It's not a question of what they
considered it because they *didn't* consider it.

But I may yet be swayed, if only it can be demonstrated that odd limit is
really needed to describe a real phenomenon in the way intervals are
treated in music.

>>The reason, I suspect, that Paul Erlich fights for odd limits: He is a man
>>of equal temperaments :~)
>
>Equal temperaments or not, that has nothing to do with this issue.

I'm going to catch you yet Erlich, biasing your science to support equal
temperaments!

>>The idea that 9's do not become harmonically significan't until we have
7's >>does not hold in my experience. Try playing just 4-5-6-8-9 chords
and see >>if the 9 doesn't serve the same purpose as it does in a
4-5-6-7-8-9 chord.
>
>That is not at all a valid interpretaion of anything I've tried to say.

Shit.

*************************************************************
With Joseph L. Monzo [ Hello! :~) ]
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>As I stated in a recent posting, La Monte Young's
>"Well-Tuned Piano" is a 5-hour-long JI piece using
>intervals with factors of only 3 and 7 -- no 5's.

An intentional effort by a composer using a fixed-pitch instrument.
Covered in my post.

>When I hear composite odd identites, like 9, 15, 21,
>etc., in quickly-moving real music, I don't get any
>particular sense of their particular odd-integer
>quality, but I _do_ hear the qualities of the prime
>factors. Under different conditions, such as
>listening to experiments at home, the qualities of
>individual odd identities can be isolated.

Sort of like you could tell what prime limit music on a 33 is, playing at
45 rpms, but not what odd limit the same music was without hearing it at
actual speed?

>3-limit music can be written in which 9 and 27, and probably
>even 81, have harmonic significance. 27 and
>especially 81 sound pretty dissonant, but that
>doesn't mean they can't be used as chord
>members. ( Who wants chords that are always
>consonant?)

I agree, and will go one further. I believe the 81/64 can be treated as a
consonance. I believe anything can (and has been) treated as a consonance
(and I am not talking about serialsim, where consonance is not an issue).
The 12-tone 5/4 is treated as a consonance. I wonder what Mr. Erlich
thinks about this, since it very close both in size and derrivation to the
81/64. He doesn't seem to have a problem considering a 7 cent sharp 3/2
consonant!
This 3/2, to my ear, makes the triads of 22 no better than those of 12,
despite the better third.

>This variety is exactly what makes JI so
>compositionally useful. One of the reasons why
>working in JI is so wonderful is because there
>are so many different ways to combine the
>prime qualities and compare identities which are
>very close in frequency but have different prime
>factors (for example, chord tones an 81/80 apart).

I've always viewed these "commas" as making modulation more interesting.
But many disagree. Partch's chapter in Genesis of a Music is really great
about this point (the one with the letter from Fox-Strangeways). Boy that
chapter is really a thrill!

Basically, what I got from this chapter is that modulation is best defined
simply as switching the 1/1, and that common tones, while playing, of all
things, perhaps the most important role in the use of modulation, are not
necessary in its definition or execution. And perhaps, that a theory of
modulation may be constructed where tones separated by a comma can still be
considered "common"!

>As I've stated many times before, I believe we
>_do_ perform prime factorization on music
>_as we listen_. Perhaps this is so because
>it is the fastest way to understand the harmonic
>relationships occuring in the music as it flies
>past our ears in real time. I will argue that
>harmonic relationships are _always_ implied,
>whether implied well or badly.

I agree. And while the scalpal cuts into some dead guy's ear, I will ask:

Even if the "association of certain intervals with the tuning systems in
which they occur" (that is, I asume, some sort of cultural conditioning) is
the only way we can pick prime factors apart from odd ones in music, are we
not still performing a prime factorization on what we hear?

*****************************************************************
With Eduardo Sabat-Garibald
*****************************************************************

>A friend of mine asked for an orchestration book written in the last 20
>years.

I will also recommend Adler's book, which was recommened by Paul Hahn. I
have another book which I also like, which is very new, by Kent Kennan.
These are the two standard texts in orchestration right now. I have them
both, but cannot remember the titles of either of them (they're both back in
Pennsylvania).

Carl