Circle of fifths

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The circle of fifths is a tool to show and measure relationships between chords or key signatures. The concept dates back to Baroqe era, and was applied in meantone, well temperaments and 12edo to help analysing chord progressions and modulations. In fact, it is applicable to all tuning systems generated by an octave and a fifth. For edos in particular, this means those which 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