Author Topic: 12 is just a number  (Read 507 times)


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12 is just a number
« on: March 09, 2016, 03:56:41 PM »
The whole tone scale is an 6-tone based on the projection of the major second. The scale's interval content is M2s, M3s, and tritones. It repeats symmetrically; no matter which note you begin on, the resulting intervals are the same. It divides evenly at the tritone.

 Tonality uses the 7-note diatonic scale, and its "dividing point" is the fifth.

 That's because the 12-note chromatic scale was derived from the projection of the fifth; thus the circle of fifths. This is an acoustically-based method.

 But actually, the 12-note scale is an anomaly, an approximation, based on the attempt to close the octave after 212 cycles of 3:2 fifths.

 Thus, "12" is the resulting mathematical result of this error or approximation; there is no acoustic ("tonal") reason for its existence, other than that it approximates fifths. In ET, all these fifths are 2 cents flat, to compensate for this error, and to close the octave, which would otherwise spiral onward into irrational values. No ratio, such as the 3:2 fifth, can be divided into "1" (the octave) as a whole number (such as 12).

 Thus, all the resulting symmetries created by "12" are mathematical in nature, and thus have a way of degrading tonality's supposed "acoustic" nature of ratios, and turning it into a mathematically/geometrically based system. Thus, the "undoing" of tonality was always inherent in the "12" based scale of Pythagoras.
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