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→Inconsistencies between 12 Tones and Pure Intervals
In the idealized world, intervals are very harmonic ratios between pitches. For example, a perfect 5th is a 3:2 ratio. This doesn't exactly match up to how we define the 12-tone chromatic scale, where each 5th is another note inside the chromatic scale, but each octave is 2x the pitch of a note. An A note at 55 HZ should follow the circle of fifths, through 12 movements to arrive back at A. But if we multiply the pitch by 3:2 each time...
{|class="wikitable"
! Movement
| || 1 || 2 || 3 || 4 || 5 || 6 || 7 || 8 || 9 || 10 || 11 || 12