# Skip fretting system 31 3 7

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.