Starting from any note set as the tonic of an octave of eight notes, the seven notes above it can be generated by ascending and descending intervals of perfect fifths & fourths. There are two ways of creating the octave of notes without repeating a note:

C→F→C′→G→D→A→E→B

and

C→G→C′→F→D→A→E→B.

The diagram illustrates the first alternative. Alternating jumps of a perfect fifth and a perfect fourth generate the second alternative.

9/8 and the "leimma" of 256/243 (so-called because the left-over (Greek: leimma) interval between the penultimate note with tone ratio 128/243 and the octave with tone ratio 2 is 256/243. The leimma is the equivalent of the semi-tone in the equal-tempered, musical scale through which most Western music is played today.

 

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