Skip fretting system 31 3 7: Difference between revisions
added link to the 31edo/62edo page |
Tristanbay (talk | contribs) m Added information at the beginning of the article and fixed some conventions issues (misspellings, etc.) |
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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== | ==Where the notes lie== | ||
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===As a diagram=== | ===As a diagram=== | ||
In the | 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 | nut | ||
Latest revision as of 04:55, 19 October 2023
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 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
As a diagram
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
- - - - - - - -
- - - 9 - - - -
- - - - - 13 - 9
- - - - 3 7 - -
bass - 1 - 11 - - - - treble
strings - - 5 - - 1 - 11 strings
- - - - - - 5 -
- - - - - - - -
9 - - - - - - -
- - - - 9 - - -
- - - - - - - -
bridge
9 is shown twice because it's such an outlier. Note the awkwardness of playing do-re-mi (1-9-5).
As a table
| interval | fretboard vector
(strings, frets) |
|---|---|
| unison | +3, -7 |
| 2/1 = 31\31 | +4, +1 |
| 3/2 = 18\31 | +3, -1 |
| 5/4 = 10\31 | +1, +1 |
| 7/4 = 25\31 | +4, -1 |
| 11/8 = 14\31 | +2, 0 |
| 13/8 = 22\31 | +4, -3 |
From these, the location of any compound interval can be added by vector-summing the string-fret positions of the interval's factors. See Skip fretting system 48 2 13 for details on how that's done.