source file: mills2.txt Date: Fri, 10 Nov 1995 08:52:32 -0800 Subject: Re: Harmonic&subharmonic Scales From: World Harmony Project 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 Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Fri, 10 Nov 1995 20:57 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id KAA08782; Fri, 10 Nov 1995 10:56:58 -0800 Date: Fri, 10 Nov 1995 10:56:58 -0800 Message-Id: <9511101055.aa05266@cyber.cyber.net> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu