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Including the octave, the 7 diatonic musical
scales have 13 types of rising intervals.* They have 13 falling counterparts. Therefore, there
are 1. D & E scales → 6 (=V) and A, B, & C
scales → 10 (=Y); The depicted scheme seems the most natural
because it has more letters with number values that denote numbers of Pythagorean notes in
a * The rising interval between two notes with tone ratios m & n (m>n) is m/n. Their falling interval is n/m. The tonic has tone ratio 1, so that a falling interval 1/n can be associated with every note with tone ratio n. ** A "falling Pythagorean interval" is not necessarily an actual note of the next lower octave of the Pythagorean scale (in fact, only the perfect fourth with tone ratio 4/3 and the perfect fifth with tone ratio 3/2 have this property). In the current context this term means simply the reciprocal of the tone ratio of a Pythagorean note. |

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