Chain of fifths: Difference between revisions

Line 1:

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 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.

The '''chain of fifths''' is a tool to show and measure relationships between chords or key signatures, applicable to all [[tuning system]]s generated by an octave and a fifth. The concept dates back to Baroque era, and was applied in [[meantone]], [[well temperament]]s and [[12edo]] to help analysing chord progressions and modulations.

For [[edo]]s in particular, this becomes a '''circle of fifths'''. If the fifth is a number of steps that is co-prime to the edo number itself, all intervals will be visited when traversing the edo by fifth-steps. 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 ==

* [[~~Circle~~-of-fifths notation]]

* [[Chain-of-fifths notation]]

* [[Fifthspan]]

* [[Ring number]]

* [[Antipodes]]

@@ Line 1: / Line 1: @@
 {{Wikipedia|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 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.
+The '''chain of fifths''' is a tool to show and measure relationships between chords or key signatures, applicable to all [[tuning system]]s generated by an octave and a fifth. The concept dates back to Baroque era, and was applied in [[meantone]], [[well temperament]]s and [[12edo]] to help analysing chord progressions and modulations.
+For [[edo]]s in particular, this becomes a '''circle of fifths'''. If the fifth is a number of steps that is co-prime to the edo number itself, all intervals will be visited when traversing the edo by fifth-steps. 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 ==
-* [[Circle-of-fifths notation]]
+* [[Chain-of-fifths notation]]
 * [[Fifthspan]]
+* [[Ring number]]
 * [[Antipodes]]