Chain of fifths: Difference between revisions
Alternatively named "circle of fourths" (esp. in guitar music) |
-"circle of fourths" (I don't think it's much attested); rework; style |
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{{Wikipedia|Circle of fifths}} | {{Wikipedia|Circle of fifths}} | ||
The '''circle of fifths''' | 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 temperament]]s and [[12edo]] to help analysing chord progressions and modultions. 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 == | == See also == | ||
Revision as of 08:24, 17 September 2023
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 modultions. 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.