source file: mills2.txt Date: Thu, 27 Jun 1996 15:23:41 -0700 Subject: Reply to Doren Garcia From: PAULE >I am unfamiliar with the aesthetic of the school of 'New Complexity'. Can >someone offer a synopsis of their ideas? I don't know much about this, but I don't think it is so much a "school" as a style defined from without. Perhaps the music journalists concieved of it a a dialectical antithesis to minimalism, i.e., the "new simplicity." Nor is it all that new, as a Frank Zappa book from the early 80's said that Steve Vai's painstaking transcriptions of Zappa's improvisations "look like something out of the new complexity." One defining feature is a metric and rhythmic complexity that would scare away most MIDI programmers, let alone live performers. Some writers have claimed complexity as a coherent movement in recent thought, lumping the musical style in with choas theory in physics, etc. Sounds like hogwash to me. >Can anyone recommend >a book that will explain concepts such as, Wilson CPS scales, subharmonics >and the associated mathematical principles involved? Subharmonics are just upside-down harmonics. The literature on subharmonics is vast; the opinions on their applicability to music theory range from not at all to "a useful construct" to an equivalent status with harmonics. I take the middle view -- the only two ways to arrange consonant intervals into chords are according to the harmonic or subharmonic series, but the consonance of the intervals in both cases is due only to harmonics. The harmonics coincide more often in subharmonic chords, so there is not really an equivalence here. As soon as roots and combination tones enter the picture, harmonic configurations become acoustically simpler than subharmonic ones. As for Wilson CPS scales, Brian McLaren has recently explained them adequately, although he confuses the issue by sometimes adding an extraneous 1/1 and calculating ratios from there. In their simplest and (I believe) originally intended form, an m)n CPS scale takes all possible products of m out of n specified factors, and interprets the products as frequencies. (Transposing by octaves is done freely.) The resulting frequency ratios can often be simplified considerably by renaming one of the notes as 1/1, which Brian does not do. The concept is more powerful than appears at first glance. For example, a 1)3 [1,3,5] scale is a just major triad, and a 2)3 [1,3,5] is a just minor triad. Represented as triangles in (3,5) space, these two triads tile the plane. I recently discovered, in communication with John Chalmers, that this concept extends to n dimensions, where n different CPS scales (represented as hyperpolyhedra with triangular faces) join together to tile n-space. I don't think there's a book on CPS scales, though I believe Erv Wilson has written articles on them for Xenharmonikon. Received: from eartha.mills.edu [144.91.3.20] by vbv40.ezh.nl with SMTP-OpenVMS via TCP/IP; Fri, 28 Jun 1996 02:33 +0100 Received: from by eartha.mills.edu via SMTP (940816.SGI.8.6.9/930416.SGI) for id RAA15153; Thu, 27 Jun 1996 17:32:57 -0700 Date: Thu, 27 Jun 1996 17:32:57 -0700 Message-Id: Errors-To: madole@ella.mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu