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How to get Equally Spaced Semitones in scales when using spirals of fifths for scale generation

🔗Michael <djtrancendance@...>

2/28/2011 9:02:25 AM

I made the following scale by

A) Taking (roughly) 3/2 * 3/2 * 3/2 * 22/15 * 3/2 * 3/2 * 22/15
B) Adding in two notes, one (roughly) at 3/2 * 3/2 * 14/9....
...and another at 3/2 * 3/2 * 3/2 * 22/15 * 3/2 *14/9
C) Reducing everything to the octave

1/1
9/8
7/6
11/9
15/11
10/7
3/2
5/3
11/6

   This is what gets me: the way the different types of fifths are distributed seems to be maximally distant apart....

  However the spacing of semi-tones seems to be crowded near 9/8 to 7/6 to 11/9 (semitone-ish gaps) and again between 15/11 to 10/7 to 3/2...while all the larger gaps become clustered between 3/2 and 9/8 on the next octave...not evenly distributed at all. 

   Why is this?...and how can I guard against that when designing any scale using a "spiral of fifths"?   Ideally it would be nice if I could get both the odd (non-3/2) fifths and the closer semitones ALL evenly distributed...