Chain of fifths: Difference between revisions

Line 1:

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 at least the 13th century<ref>Schulter, Margo “[https://web.archive.org/web/20120215000445/http://www.medieval.org:80/emfaq/harmony/pyth4.html Pythagorean Tuning and Medieval Polyphony]"</ref>, and was applied in [[meantone]], [[~~well temperament~~]]s, and [[~~12edo~~]] to help analysing chord progressions and modulations.

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 at least the 13th century<ref>Schulter, Margo “[https://web.archive.org/web/20120215000445/http://www.medieval.org:80/emfaq/harmony/pyth4.html Pythagorean Tuning and Medieval Polyphony]"</ref>, and was applied in [[meantone]] (including [[12edo]]), [[3-limit|Pythagorean tuning]], and [[well temperament]]s, 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.

@@ Line 1: / Line 1: @@
 {{Wikipedia|Circle of fifths}}
-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 at least the 13th century<ref>Schulter, Margo “[https://web.archive.org/web/20120215000445/http://www.medieval.org:80/emfaq/harmony/pyth4.html Pythagorean Tuning and Medieval Polyphony]"</ref>, and was applied in [[meantone]], [[well temperament]]s, and [[12edo]] to help analysing chord progressions and modulations.
+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 at least the 13th century<ref>Schulter, Margo “[https://web.archive.org/web/20120215000445/http://www.medieval.org:80/emfaq/harmony/pyth4.html Pythagorean Tuning and Medieval Polyphony]"</ref>, and was applied in [[meantone]] (including [[12edo]]), [[3-limit|Pythagorean tuning]], and [[well temperament]]s, 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.