# circle-of-5ths

[Joe Monzo]

The circle-of-5ths is a feature of all equal-temperaments which have an interval whose size is in the vicinity of the 3:2 ratio = ~702 cents, give or take about 20 cents.

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###### 12edo:

In 12-edo, if C is the reference pitch at 0 degrees, then following the circle counterclockwise thru the sharp keys and clockwise thru the flat keys, gives us 5 pairs of notes which have the same pitch, and are thus enharmonically equivalent:

• A# = Bb
• C# = Db
• D# = Eb
• F# = Gb
• G# = Ab
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###### 19edo:

In 19edo, the circle shows us that outside of the 7 diatonic notes in C-major, all 12 of the other notes have double names.

(In this diagram the conventions are different than in the one above: C is at the top, clockwise goes thru the sharp keys and counterclockwise thru the flat.)

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###### 31edo:

For the 31-edo circle, the degree numbers of the notes are shown along with the letter notation.

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###### 53edo:

For the 53-edo circle, the degree numbers are shown.

###### REFERENCE

Blackwood, Easley. 1985.

The Structure of Recognizable Diatonic Tunings.
Princeton University Press, Princeton NJ.
ISBN 0-691-09129-3
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