Re: Young's 9:7:4 and high primes, a proposed experiment

Sorry to take so long to reply.

From: Patrick Pagano <ppagano@bellsouth.net>, Digest Number 47, 11 Feb 1999:
>Dave
>simply put primes are the rungs of the ladder of the Harmonic spiral. The prime opens up an entire new mode revealing new identities a main example being the 7/4 or 7th harmonic. If we had stayed with the 5 limit we would never gotten this new identity. You simply must have prime #s to advance up the spiral. And I do not think anyone at Dreamhouse will be
>tampering with Lamonte's Installation. 11 reveals new tones almost all new except for the 11/11 22/11 0r 11/1 of course and then 13 and 17 are similar in their New Music Resources.
>I hope this helps.

No Patrick, I'm sorry but it doesn't help. You are describing certain properties of the positive integers (which I well understand), but failing to say why you believe that the *musical* (or psycho-acoustic) significance of the primes continues indefinitely, when it's well accepted by others that the significance of primes fizzles out somewhere around 19.

Any assumption that mathematical beauty or utility necessarily implies musical beauty or utility is merely a variety of the numerological fallacy.

I understand that this fizzling out is because, for example, few people can distinguish a frequency ratio involving 23 from nearby ratios having smaller numerator and denominator. Note that for intervals smaller than a twelfth (3/1) there is always such a lower-numbered ratio within 8.4 cents of any ratio of 23. Some are as close as 2.8 cents. Apart from human discrimination, the 23rd partial of many natural timbres, if it has a significant amplitude at all, could easily differ from 23 times the frequency of the fundamental by a similar number of cents.

I concede that using sustained sine tones, and playing them at high amplitudes or passing them thru a non-linear system, will emphasise the difference tone effect (assuming the difference tone is not infrasonic), and play down the coincidence of harmonics. This may allow people to distinguish ratios near 1, such as 23/22 from 22/21. This is because the pitch change in the difference tone is (in this example) about 22 times that of the change in one of the original tones (assuming that only one tone changes). You get a kind of leverage by working near 1/1. (Note that if the tones of a 23/22 are much below A(440Hz) the difference tone will be infrasonic)

However, once we are depending on difference tones rather than coincidence of harmonics for our musical distinctions, primeness, (and beyond 19, even integer-ness), becomes irrelevant. I expect that, to most people, the difference between 23/22 and 22/21 is much the same as the difference between 22/21 and 21/20 or 22/21 and 21.04348/20.04545.

As I understand it, the reason low primes are important in ordinary music with ordinary timbres is that, for example, when the 2nd harmonic of one note coincides with the 3rd harmonic of the other you also get the 4th harmonic coinciding with the 6th, the 6th with the 9th, the 8th with the 12th, the 10th with the 15th. You get all these others for free. This removes *many* pairs of harmonics from contributing to dissonance via critical band roughness.

When the 23rd harmonic of one tone coincides with some other harmonic of the other tone, we also get the 46th harmonic (if it exists) coinciding for free. Big deal! (Note that the 46th harmonic of A(440Hz) is ultrasonic).

From: David Beardsley <xouoxno@virtulink.com>, Digest Number 48, 12 Feb 1999:
>We just turn the sound and lights up. The synth is
>located downstairs in La Monte's apt.

Any chance you can pass my original question and suggested experiment on to La Monte, and report his response? Or does my suggestion amount to blasphemy?

Regards,
-- Dave Keenan
http://dkeenan.com

Dave Keenan <d.keenan@uq.net.au> writes:

> Sorry to take so long to reply.
>
> From: Patrick Pagano <ppagano@bellsouth.net>, Digest Number 47, 11
Feb 1999:
> >Dave
> >simply put primes are the rungs of the ladder of the Harmonic
spiral. The
> prime opens up an entire new mode revealing new identities a main
example
> being the 7/4 or 7th harmonic. If we had stayed with the 5 limit we
would
> never gotten this new identity. You simply must have prime #s to
advance up
> the spiral. And I do not think anyone at Dreamhouse will be
> >tampering with Lamonte's Installation. 11 reveals new tones almost
all new
> except for the 11/11 22/11 0r 11/1 of course and then 13 and 17 are
similar
> in their New Music Resources.
> >I hope this helps.
>
> No Patrick, I'm sorry but it doesn't help. You are describing certain

> properties of the positive integers (which I well understand), but
failing to
> say why you believe that the *musical* (or psycho-acoustic)
significance of
> the primes continues indefinitely, when it's well accepted by others
that the
> significance of primes fizzles out somewhere around 19.
>
> Any assumption that mathematical beauty or utility necessarily
implies
> musical beauty or utility is merely a variety of the numerological
fallacy.

Read Genesis of a Music by Harry Partch. He explores
the difference of primes.

Tune a synthesizer to a five limit tuning.
Tune a synthesizer to a seven limit tuning.
Tune a synthesizer to a eleven limit tuning.
Tune a synthesizer to a thirteen limit tuning.

Now. Can you describe what sounds different about these tunings?

Does eleven sound ugly? Do seven or five sound beautiful?
Describe why five and seven sound different.

So what do you think now?

> I concede that using sustained sine tones, and playing them at high
> amplitudes or passing them thru a non-linear system, will emphasise
the
> difference tone effect (assuming the difference tone is not
infrasonic), and
> play down the coincidence of harmonics.

You better believe it!

> From: David Beardsley <xouoxno@virtulink.com>, Digest Number 48, 12
Feb 1999:
>
> >We just turn the sound and lights up. The synth is
> >located downstairs in La Monte's apt.
>
> Any chance you can pass my original question and suggested experiment
on to
> La Monte, and report his response? Or does my suggestion amount to
blasphemy?

I'm not going to bother him with experiments. I can do 'em on my own.

--
* D a v i d B e a r d s l e y
* xouoxno@virtulink.com
*
* J u x t a p o s i t i o n E z i n e
* M E L A v i r t u a l d r e a m house monitor
*
* http://www.virtulink.com/immp/lookhere.htm