source file: mills2.txt Date: Wed, 9 Jul 1997 21:58:34 +0200 Subject: Modulating dekanies by hexanies (was RE: Meantone, Partch) From: Daniel Wolf Paul Hahn wrote: ''Hmm, sounds more like modulation in the signal-processing sense than inthe musical sense of the word. Also, the result has, potentially, up to sixty pitches! Isn't that rather overwhelming, cognitively speaking?'' In fact, modulation of this sort is a primary resource in 20th century composition. Stravinsky's tonal resources included playing the octotonic collection against each diatonic transposition (and vice versa); Partch and Schoenberg multiplied a set of tone by their inversion (the row box and diamond are remarkably strange bedfellows); Boulez's ''multiplication'' technique is another species of the same. As to the number of pitches, all of the tones of a hexany multiplied by adexany fit onto a stellate eikosany (which adds the pitches needed to fill out all of the hexads of an eikosany). Wilson has done some impressive work with the 70 tone, 4(8 ''Hebdomekontany'', including construction of a metallophone with all pitches; using similar kinds of transposition, I find it easy the tonal relationships easy hear, if difficult to play. Of course, any of these might be mapped onto closed temperaments... As to the cognitive digestibility of such transpositions, it is entirely a compositional problem - to compose in such a way that the tonal relationships are projected audibly. I would venture that it is easier with a dekany and a hexany based on simple harmonic ratios than with any non-trivial 12 tone row. Received: from ns.ezh.nl [137.174.112.59] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Wed, 9 Jul 1997 23:32 +0200 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA07913; Wed, 9 Jul 1997 23:32:49 +0200 Received: from ns.NL.net by ns (smtpxd); id XA07896 Received: from ella.mills.edu by ns.NL.net (5.65b/NLnet1.3) id AA09483; Wed, 9 Jul 1997 23:32:46 +0200 Date: Wed, 9 Jul 1997 23:32:46 +0200 Received: (qmail 4655 invoked from network); 9 Jul 1997 21:19:26 -0000 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 9 Jul 1997 21:19:26 -0000 Message-Id: Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu