source file: mills2.txt Date: Wed, 15 Nov 1995 05:12:51 -0800 Subject: Partch progressions From: "John H. Chalmers" Adam et al. in re Partch: I don't think anyone should take his statements on the "magnetic" tendencies of prime identities too literally, but only as a general guide. HP often separated his theory from his practice. One might imagine upon reading about Monophony that it would be applied to sustained tones with harmonic spectra and vocal texts, however, HP used plucked string and inharmonic percussion timbres primarily and except in Oedipus and some other early works, seldom wrote extended lyrical vocal lines, instead preferring short aphoristic phrases, nonsense syllables, interjections, etc. So, I think we can justifiably divorce his chordal progressions from his theoretical 43-tone scale and even add extra tones whenever necessary to make the harmony less static. For the benefit of those without access to a copy of _Genesis of a Music_, I've translated some of HP's progressions into ratios which show the voicing better: (The page #'s are from the first edition of Genesis.) The O's and U's refer to Otonality and Utonality, HP's terms for harmonic and subharmonic as applied to chords. O and U come from Over and Under. p185: 3/1 -> 3/1 21/8 -> 5/2 9/4 -> 2/1 15/8 -> 2/1 3/2 -> 1/1 3/2 O 1/1 O (V7 to I) p.186, Diagram 13: 11/8 -> 11/8 (both voices to 11/8) 27/20 -> 33/32 -> 11/10 -> 11/12 (11/6 in lower octave) 11/8 O? 11/8 U (HP admits that the first chord is not easily analysed and not very tonal.) p. 186: 33/16 -> 2/1 27/16 -> 7/4 21/16 -> 5/4 9/8 -> 9/8 15/16 -> 1/1 3/4 -> 3/4 (3/2 in lowest octave) 3/2 O 1/1 O p. 187: 8/3 -> 8/3 32/15 -> 2/1 16/9 -> 16/9 32/31 -> 8/5 32/27 -> 8/7 32/33 -> 1/1 (64/32 in lowest octave) 4/3 U 1/1 U (plagal cadence) p. 188, Diagram 14: 12/7 -> 7/4 10/7 -> 7/5 8/7 -> 7/6 8/7 O 7/4 U (example of "tonality flux" p. 188, Diagram 15: 11/5 -> 24/11 11/6 -> 20/11 11/8 -> 16/11 11/8 U 16/11 O (the other example) My class notes state that the homework for the Nov 9, 1967 class was to choose any two hexads which resolve by small intervals and to also write 3 lines of counterpoint in any scale that can be played on the Chromelodeon. The progression HP gave us in class was from 11/8 U to 8/5 O in which the 11/6 moved to 8/5 in the bass, 11/9 to 6/5, 11/7 to 9/5, 2/1 and 11/5 were held, and 11/4 resolved to 14/5. Other examples I have in my notes are 5/4 U to 1/1 O, 8/7 O to 4/3 O, and 8/5 O to 4/3 O. I suspect these were my own solutions. What I can't seem to find are any examples of the strongly beating progressions that I recall HP played for us, unless the second one from the top (above) is one of them one. My question to Allen about the class notes was partly rhetorical and partly because mine are very incomplete, especially about the chordal sequences we studied. Most of what HP taught us was in Genesis, save for the beating progressions. I'm sure I've seen a score of them somewhere, but I can't find it now, even though I am back in Texas in my own house at the moment. --John Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Wed, 15 Nov 1995 15:15 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id FAA09311; Wed, 15 Nov 1995 05:15:22 -0800 Date: Wed, 15 Nov 1995 05:15:22 -0800 Message-Id: <9511150512.aa23790@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