There is a local minima at 12 and 53 tones.ītw, people have made use of the 53-tone scale: Taking Flight ģ1-tones is also fairly popular: QUANTUM 7 (Transcendent Tonality) 31 tone guitar. Interestingly, for 53 and 12, our tones get spaced pretty uniformly, as can be seen by plotting the normalized standard deviation of the distance between the tones. The 17 tone scale is used in Arabic and Persian music. In this way, perfect fifth chords will always sound good, and for 12 we also, it turns out, get a good approximation of the overtone series. Is there a point when we get back to the octave at 2? No, that would be impossible since 3 and 2 are both prime so that 3^x/2^y can never be 2 for any x,y. To see this, we will follow an idea by Pythagoras and extend our scale by perfect fifths, we get 1, 3/2, 9/8, 27/32…. But now we have new notes that need even more notes to pair up with, does it ever end? The overtone series is a great scale to use, but it has its limitations.
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