Skip fretting system 31 3 7: Difference between revisions

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~~The~~ fret spacing is even wider than ~~12-edo~~, at 3\31 = 116.13¢. While there are other skip frettings for 31edo (see [[Skip fretting system 31 2 9|31 2 9]]), this one is of particular interest. ~~It's~~ fret spacing just happens to be extremely close to every other fret of the 41 2 9 skip fretting (117.07¢). As a result, any [[Kite guitar]] can be retuned to within a few cents of 62edo. See [[Tuning A Kite Guitar To 31edo or 62edo]].

This fretting system follows both Orwell temperament with the interval between each string, 7\31, and Miracle temperament with the fret spacing, which is even wider than 12edo, at 3\31 = 116.13¢. While there are other skip frettings for 31edo (see [[Skip fretting system 31 2 9|31 2 9]]), this one is of particular interest. Its fret spacing just happens to be extremely close to every other fret of the 41 2 9 skip fretting (117.07¢). As a result, any [[Kite guitar]] can be retuned to within a few cents of 62edo. See [[Tuning A Kite Guitar To 31edo or 62edo]].

==Where the notes lie==

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===As a diagram===

In the ~~folowing~~ the strings are vertical and the frets are horizontal. 1 represents octave equivalents of the root, 3 represents octave equivalents of the 3rd harmonic (3:2, 3:1, 3:4, etc.), etc.

In the following the strings are vertical and the frets are horizontal. 1 represents octave equivalents of the root, 3 represents octave equivalents of the 3rd harmonic (3:2, 3:1, 3:4, etc.), etc.

nut

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-The fret spacing is even wider than 12-edo, at 3\31 = 116.13¢. While there are other skip frettings for 31edo (see [[Skip fretting system 31 2 9|31 2 9]]), this one is of particular interest. It's fret spacing just happens to be extremely close to every other fret of the 41 2 9 skip fretting (117.07¢). As a result, any [[Kite guitar]] can be retuned to within a few cents of 62edo. See [[Tuning A Kite Guitar To 31edo or 62edo]].
+This fretting system follows both Orwell temperament with the interval between each string, 7\31, and Miracle temperament with the fret spacing, which is even wider than 12edo, at 3\31 = 116.13¢. While there are other skip frettings for 31edo (see [[Skip fretting system 31 2 9|31 2 9]]), this one is of particular interest. Its fret spacing just happens to be extremely close to every other fret of the 41 2 9 skip fretting (117.07¢). As a result, any [[Kite guitar]] can be retuned to within a few cents of 62edo. See [[Tuning A Kite Guitar To 31edo or 62edo]].
 ==Where the notes lie==
@@ Line 5: / Line 5: @@
 ===As a diagram===
-In the folowing the strings are vertical and the frets are horizontal. 1 represents octave equivalents of the root, 3 represents octave equivalents of the 3rd harmonic (3:2, 3:1, 3:4, etc.), etc.
+In the following the strings are vertical and the frets are horizontal. 1 represents octave equivalents of the root, 3 represents octave equivalents of the 3rd harmonic (3:2, 3:1, 3:4, etc.), etc.
                        nut