Re: [tuning] Digest Number 2221

tuning@yahoogroups.com wrote:
Message: 2
Date: Tue, 24 Sep 2002 21:56:15 UT
From: "unstruck"
Subject: Lucy's cave

Was: Re: [tuning] "hear or tune beyond commas." + note on Microtonal
notation.

On Sun, 15 Sep 2002 15:19:49 +0100, "Charles Lucy"
said:

> "hear or tune beyond commas." suggests that those who refuse to
> consider any intervals other that whole number ratios, are artificially
> restricting the possibilities.

Your analogy of the Cave suggests that Just Intonation is an imperfect
distorted one-dimensional shadow cast by the Ideal, and that if our
attention gets drawn towards JI, our attention gets drawn away from the
Truth.

You further suggest that Harrison and yourself are considering this
True Harmony, and you seem to suggest that its vibrations are not
locked rigidly into whole-number ratios, but have a different
"topology".

-Jeremy

>
> This may be a suitable occasion to attempt to explain by an analogy.
>
> This concept comes from Book VII of Plato's Republic, and is my > analogy (not John Harrison's)
>
> Imagine that you are holding a coiled spring between a light source and
> a wall. A shadow is cast on the wall by the spring. There are positions to > which you can move the spring so that it will cast a shadow on the wall, > which resembles a sine wave.
>
> You could measure the shadow, and map the topology of the shadow.
> or you could map the topology of the spring.
>
> I am suggesting that the advocates of whole number ratios, are mapping
> the "shadow"; whereas John 'Longitude' Harrison was mapping the
> "spring".
>
>
> Some people enjoy chasing shadows.
>
> Have fun!

*************************************

Hello Jeremy and Everyone,

Your usage of the term "topology" somehow struck a chord with my gut feeling about "non-deterministic" scales, as I call them, practiced by performers on non-fretted, non-keyboard instruments. To me the term 'topology' accomodates a sophisticated level of fuzziness that appears to have the potential of simulating what goes on in the mind of a legendary performer of, say the violin, in the way of "dynamic" scales being created in real time as the piece is being played.

When I first looked at a book on Western music while I was in Turkey and saw the frequency layout for the piano keyboard given to several decimal place accuracy, my immediate reaction was a "wow !". I said to myself, "musicologists in the West must have nailed down the standard piano scale with such great accuracy".

Then I happened to look at Carl Seashore's book "Psychology of Music" (1938) and read the following observations on page 207:

". . . we note the following course of pitch intonation:

A plays the second note 0.15 of a tone sharp, B plays it true {he is referring to two violin players A and B}; A plays the third note true, B plays it 0.05 sharp; A plays the fourth note true, B plays it 0.2 of a tone sharp; A plays the fifth note true, B plays it 0.1 flat; A plays the sixth note 0.05 sharp, B plays it true; A plays the seventh note true, B plays it 0.05 flat; A plays the eight note 0.1 sharp, B plays it true.

This may suffice as a guide for the reading of phrasing through pitch. The melody is, of course, set by the composer. The player's interpretation consists in the adoption of a scale, for example, the natural scale, and then deviating from this for artistic values."

As you can imagine I was totally confused. I had the piano scale on one hand, accurate to several decimal places in Hz, and then Seasore's measurements on the violin, displaying deviations in the order of 30 cents from the tempered scale. The violin player deviating from an "adopted" scale -- I thought "the scale" was set in stone centuries ago by musical giants -- for artistic reasons was the most intriguing part for me.

However, the performer making up an ever-changing, dynamic scale at the micro level during the course of a performance made a lot of sense to my pedestrian instincts. The practice would allow the musician unfettered freedom of expression, at the micro level within certain norms, to reflect the ever-changing impressions in his/her inner soul. Furhermore, the performer would have the freedom of playing the same piece on "different" dynamic micro scales for each performance, to reflect the mood of his/her spiritual universe at that moment.

When I started making measurements on performances by master musicians of traditional Turkish music, I was swept off my feet to discover exactly the same practice, at a much bolder level.

If what I have said up to this point is sensible and coherent, -- I would not bet on it -- then the mathematical concept of "topological spaces" in some general sense might serve as a potentially useful "setting" for formulating, and hopefully characterizing, such structures found in performances, but not mentioned explicitly in theoretical constructs.

With regard to the "spring" analogy, I am not certain at this point to even speculate on whether the topology of the said "made-up scales" would represent the "spring" itself or its projection onto some subspace of the "musical imagery", as Carl Seashore puts it, embedded in the individual performer's soul.

Can Akkoc

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