Text: Subject: [biosonic] possible phi scale Date: Sun, 25 Jun 2000 16:35:44 -0400 From: Char B Reply-To: biosonic@egroups.com To: biosonic@egroups.com Hello list - Well I am really surprised what has turned up here... Started playing with a series using powers of phi (1.618033989). In other words: phi phi squared phi cubed phi to power of 4 phi to power of 5 etc Then I would divide the resulting numbers down by octave dividers, to fall between 1 and 2 as many musical ratios are expressed, to see how they compared with common scale ratios of the western scale, or possibly other important ratios of natural harmonics etc. The pattern that turned up was, a series of these (phi to certain powers), showed a very close link to the western scale ratios using this method. Let me demonstrate - phi to power of 3 = 4.236067979 reduced (divide by 4) = 1.059017 This falls just short of the ratio location for the musical interval minor second (1.059463). the next one: phi to power of 6 = 17.944272 reduced (divide by 16) = 1.121517 This falls just short of the ratio location for the major second (1.1224619) phi to power of 9 = 76.01315572 reduced (divide by 64) = 1.187706 This falls just short of the ratio location for the minor third (1.189207) phi to power of 12 = 321.996895 reduced (divide by 256) = 1.2578 This falls just short of the ratio location for the major third (1.259921) phi to power of 15 = 1364.000736 reduced (divide by 1024) = 1.332 This falls just short of the ratio location for the perfect fourth (1.33484) Perhaps by now some will have noticed, this pattern is related to the following phi powers: 3, 6, 9, 12, 15, etc... Let's jump to where the upper octave would fall. Here we have to use phi to the power of 36 (interesting correlation with 360 degrees !!) phi to power of 36 = 33,385,282.19 reduced by octave dividers = 1.9899 And this is just short of the ratio location for the perfect octave (2.0000) Other points of interest - - the corresponding location near square root of 2 (augmented fourth) falls at 1.4106444. - the corresponding location near the perfect fifth falls at 1.4938. - the corresponding location near minor sixth falls at 1.58206. - the corresponding location near major sixth falls at 1.67543. - the corresponding location near minor seventh falls at 1.77431. - the corresponding location near the major seventh falls at 1.87902. A comment for Dan Winter & Marysol...I'm not sure if this is what you had in mind for a possible phi scale construction, or nested phi waves, but thought I'd pass this rather interesting pattern along to you for your consideration. Many regards, Char

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