Skip fretting system 31 2 9: Difference between revisions

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The system involves including only every other fret of 31-edo, with each pair of adjacent strings tuned 9\31 apart. That's 348.4 cents, a very neutral third. Among the other possible [[skip fretting]] systems for 31-edo, the (31,2,9) system is especially convenient in that every interval in the 3.7.11.13.23.29 group spans at most 4 frets. Intervals involving the fifth harmonic are not extremely convenient, because the major third spans four frets and lies on the same string as the perfect fifth. This layout restricts certain harmonic possibilities -- but if frets were only skipped in the higher registers, those harmonic possibilities would remain in the lower registers, which is arguably the only place they can be played anyway.

~~Here is where all~~ the ~~primes intervals~~ lie:

== Where the notes lie ==

=== 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.

headstock this side

- - 5 - - - -

7 - - - - - -

- 9 11 - - 5 -

- - - 7 - - -

bass 1 - 3 - 9 11 - treble

strings - - - - - - 7 strings

- - 13 1 - 3 -

- - - - - - -

- - - - - 13 1

5 - - - - - -

- - - - - - -

bridge this side

=== As a table ===

{| class="wikitable"

!note

@@ Line 3: / Line 3: @@
 The system involves including only every other fret of 31-edo, with each pair of adjacent strings tuned 9\31 apart. That's 348.4 cents, a very neutral third. Among the other possible [[skip fretting]] systems for 31-edo, the (31,2,9) system is especially convenient in that every interval in the 3.7.11.13.23.29 group spans at most 4 frets. Intervals involving the fifth harmonic are not extremely convenient, because the major third spans four frets and lies on the same string as the perfect fifth. This layout restricts certain harmonic possibilities -- but if frets were only skipped in the higher registers, those harmonic possibilities would remain in the lower registers, which is arguably the only place they can be played anyway.
-Here is where all the primes intervals lie:
+== Where the notes lie ==
+=== 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.
+             headstock this side
+             -  -  5  -  -  -  -
+  -  -  -  -  -  -
+             -  9 11  -  -  5  -
+             -  -  -  7  -  -  -
+     bass    1  -  3  -  9 11  -  treble
+    strings  -  -  -  -  -  -  7  strings
+             -  - 13  1  -  3  -
+             -  -  -  -  -  -  -
+             -  -  -  -  - 13  1
+  -  -  -  -  -  -
+             -  -  -  -  -  -  -
+              bridge this side
+=== As a table ===
 {| class="wikitable"
 !note