Circle of fifths

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The circle of fifths is a tool to show and measure relationships between chords or key signatures. It's commonly used (and known) in 12edo but applicable to all EDOs that map the fifth to a number of steps that is co-prime to the EDO number itself; so when traversing these EDOs by fifth-steps, all intervals will be visited. See for example the intervals in 7edo: (0, 4, 1, 5, 2, 6, 3)\7. Other EDOs have more than one circle of fifths, 10edo for example has two of them: (0, 6, 2, 8, 4)\10 and (1, 7, 3, 9, 5)\10. 15edo has three distinct circles of fifths: (0, 9, 3, 12, 6)\15, (1, 10, 4, 13, 7)\15, and (2, 11, 5, 14, 8)\15.

See also