Harmonic&subharmonic Scales

Hello, from Denny Genovese

The scale I have primarily used since 1978 is the natural harmonic series from 1 to 32:
>
> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 24 26 27 28 30 32
> - - - - - - - - - -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
> 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
>
>
>
> 1/1 is a low C at 64Hz. All the other pitches are exact multiples of 64Hz.
>
> All even top numbers are doublings of odd numbers that appeared
> previously in the series. It amounts to five octaves. The first octave
> has one pitch: 1/1. Each successive octave has twice as many pitches as
> the one below it.
> This scale can be used both melodically (almost diatonic but a
> little stranger) and harmonically (all pitches blend well with each other
> because they are all harmonics of 1/1).
> I first discovered it in 1974, while sweeping a resonant filter
> over a sawtooth wave. I discovered it again in 1978 while trying to make
> a flute and accidentally inventing the Fipple Pipe.
> Since then I have learned of a few others that also use it including Jules
> Seigle, Robert Dick and Johnny Reinhart. Lou harrison uses the same basic
> scale exept that he uses subsets of the duple between 12 and 24 in an
> octave repeating scale (at least that is what he once told me).
> This scale is a rich resource for discovering new melodies and
> harmonies that are resonant and powerful as well as restfull and peace
> producing. It all depends on how they are used.
> My New College thesis was devoted to an exposition of the
> resources and uses of this scale (THE NATURAL HARMONIC SERIES AS A
> PRACTICAL APPROACH TO JUST INTONATION, Denny Genovese 1991. Available
> from the Southeast Just Intonation Center for $20)
>
> In more recent times, I have been experimenting (and composing!) with
> the inverse of this scale, the Subharmonic Series. This series begins
> with a very high pitch (2048Hz.) and proceeds DOWNWARD by subdivisions:
>
> 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
> - - - - - - - - - -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
> 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28
>
> etc.
>
> This scale is very different in sound from the first one. All the
> individual intervals of the harmonic series are there, but in reverse
> order. This makes chord construction more tricky because of the high
> possibility of dissonance. Again, though it is rich for both new melodies
> and harmonies. You just have to be more careful with it. Also, in the
> subharmonic series it is
> helpfull to think of the octaves being between multiples of 3, rather
> than 2 (other modes are possible in both scales, and these greatly modify
> the character of the scales).
>
> I have found it practical to work gradually from the basic
> materials of the harmonic series and the subharmonic series in order
> to thoroughly learn their characteristics. Now that this has been
> accomplished, my current work is concerned with a matrix-like web of both
> types of scales in which each member of the subharmonic series serves as
> a fundamental for a new harmonic series. At the same time, each member of
> the harmonic series serves as a fundamental for a new subharmonic series.
> This is similar to Harry Partch's tonality diamond, and is equivalent to
> his Primary Tonalities, exept that I am using the series themselves (and
> subsets in various modes) as scales, rather than as resources for a
> composite linear scale. Also I am using much higher primes than the 11
> limit that Partch was satisfied with. My reasons for all this are
> outlined in my thesis.
>

Best wishes,


Denny Genovese

sejic@freenet.ufl.edu

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On Fri, 10 Nov 1995 13:35:59 -0800 John H. Chalmers said:

> (Allen, do you still have your notes from his UCSD
>class?).

Ha! John- that was 28 years ago- I don't even have my hair from that time!
I do remember however Harry telling us the reason he chose the pitch class
G was because it was the lowest note he could sing at the time. Not the 392,
of course, but a 1/2 lower-

>Partch and resolution

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Two days ago, J. Reinhard wrote:
> One should read Chapter 11, "The Question of Resolution,"
>in HP's _Genesis of a Music_, 2nd edition, pp 181-194. While HP
>wrote everything in the key of G (392 hz), in part because of
>material and technical limitations, in part for theoretical reasons
>(monophony is the harmonic expansion of a single tone, the 1/1, see
>the definition on page 71), he was very aware of resolution and
>chordal motion and wrote some extremely dissonant, yet powerful
>progressions.

Don't get me wrong--I love Partch's music. In this chapter, however, (if
I understand it correctly) he is a little shaky on tonal drive.
Partch begins with a disclaimer that these are simply observations
from his own ear. I quote from the Book (Genesis XI):

"The extent and intensity of the influence that a magnet exerts is in
inverse proportion to its ratio to 1... This means simply that the extent
and intensity of the influence of 7, for example, are just a seventh of
those of 1."

His two following observations seem quite in order to me, but this one
reminds me of the scene in "Dead Poet's Society", where poetry is ranked
on a Cartesian Plane. How could HP aurally determine if a tone's pull is
1/7 of another? Often Partch presents strong arguments without strong
facts.

Yes, this is a pedantic observation. I agree that the lower identities
have a stronger pull towards each other. The reason that I grumble at
this is that it only brings the polemic closer to what may be the
inevitable conclusion: that JI tonalities should be treated the same as
12TET ones, but with more care to use microtonality to its fullest
potential, and to intensify consonance and dissonance as needed.

Adam B. Silverman

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