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Doug, check out this guys enneagram study of music. Sound familiar? http://www.awakenings.com/properties/ So these and Doug's are examples of geometric mathematical processes. And of course the circle of fourths / fifths. Jim and I are also working on similar processes for transforming from mode to mode (for a given root note) that follows the cycle of fourths or fifths, in a way very similar to the way this cycle relates to key changes For me, the geometry helps me to see relations that I might not hear otherwise. Mike ----- Original Message ----- From: "Douglas Baldwin" <coyotelk@optonline.net> To: "Per Boysen" <per@boysen.se>; <Loopers-Delight@loopers-delight.com> Sent: Tuesday, December 17, 2002 3:16 PM Subject: Re: Elliot sharp's --> mathematic processes cnanging your hearing > Per Boysen wrote: > > One thing he said was very interesting IMO: "It changes the way you >hear > > music when you start working with mathematic processes". Can someone on > > this list tell about similar experiences? > > Briefly: Draw the chromatic scale out like a twelve-pointed circle - a > dodecahedron - and note the locations of various chords and scales on >this > circle. This simple geometric view of intervals will quickly reveal numerous > patterns in the music you care to chart in this way, and in the construction > of music generally. Now I often "hear" these shapes and associate the shapes > with certain sounds. I am amazed that this simple process is not used in > music education. > Douglas Baldwin, coyote-at-large > coyotelk@optonline.net >