source file: mills2.txt Date: Thu, 3 Oct 1996 02:11:55 -0700 Subject: More response to Paul From: Daniel Wolf <106232.3266@compuserve.com> (1) Please read more carefully, my approach is independent of combination tones, and is not affected one way or another by their presence. This choice of independence - like the choice of just intonation as a mode - was made to streamline matters, including the avoidance of pitch masking by spectra of pitches belonging to a harmonic series. My use of subharmonic characterization is strictly to identify a class of complexes that are more _efficiently_ (I am momentarily at a loss for a more precise word) heard not a part of a harmonic series. I know, for example, that I can hear, identify, and reproduce the sine wave complex 500, 600, 750 Hz. I hear it distinctly as a "minor" triad and neither as a mistuned harmonic series segment where 500Hz = 2^n nor as a harmonic series segment over the fundamental of 50Hz. (2) Phase differences can have dramatic effects on pitch perception. With long duration sound installations, the relative phase positions are apparent in physical space. I recently heard an extraordinary installation by Hauke Harder in Copenhagen, where phase relationships were essentially the only dynamic element in the work. When phases were locked this entire quality disappeared. Young has worked with _drifting_ phases and has made some interesting psychoacoustical conjectures. (I have had similar - but not precisely so - experiences in recording sine wave complexes from my Rayna synthesize onto CD or DAT, where differences in sampling speed all but destroyed entire works). (3) A spacing theory would be a method of analysis and not a theory of composition, although the information obtained might be useful to composers. Last time I checked, composers were free to proceed with or without a theory. (4) I believe your procedure is closely tied to western musical materials (I try to be a bit more global in my approach, but the simple matter is that the number of repertoires with pitch complexes of three or more members is limited; a parallel project of mine involves harmonization procedures for repertoires with melodic properties distinctive from the German folksongs upon which classical chorale harmonization is based); for this reason, a coupling of your algorithm with an approach to chord progression is worthwhile if not necessary, since your procedure demands parameters only close to those offered by traditional western classical and vernacular musics. In this (broadly defined) repertoire, contrast between harmonic structures is a (if not THE) defining feature. (5) For the Boomsliter and Creel example, I should have said harmonic _progressions_, for the choice of 224/128 over 7/4 was aopparently made in reference to position in a larger network of relationships, and not to a stretching preference (although Linus Liu recently sent me an example of a scale for Chinese music - which is primarily melodic - where a sequence of just melodic intervals leads to an octave stretched by 81/80). (6) I would appreciate it if some other readers would let me know if this material is interesting or whether we should take the colloquy private; I do not want this to burden anybody-s email facilities. Daniel Wolf, Frankfurt Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Fri, 4 Oct 1996 13:41 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA00376; Fri, 4 Oct 1996 12:43:08 +0100 Received: from eartha.mills.edu by ns (smtpxd); id XA00374 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id EAA01836; Fri, 4 Oct 1996 04:43:00 -0700 Date: Fri, 4 Oct 1996 04:43:00 -0700 Message-Id: <961004114052_71670.2576_HHB38-3@CompuServe.COM> Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu