Skip fretting system 34 2 9: Difference between revisions

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Among the possible [[skip fretting]] systems for 34-edo, the (34,2,9) system is especially convenient in that every 11-limit interval spans at most 2 frets, and if you exclude intervals involving the 17th and 19th harmonic, every 31-limit interval spans at most six frets. If you include 17 and 19, the range rises to eight frets. (Note that 8 frets on a 17-edo guitar is a big stretch, equivalent to 5.67 frets on a 12-edo guitar.)

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

== Where the first primes intervals 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 on this side

- 15 9 - 13 -

13 - 19 - - -

- - - - - 17

- 17 - - - -

bass - - - - - - treble

strings - - 11 - 1 - strings

1 - 23 7 - 5

- 5 3 - - 21

- 21 - 15 9 -

9 - 13 - 19 -

19 - - - - -

bridge on this side

=== As a table ===

{| class="wikitable"

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|}

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.

From these, the location of most compound intervals 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.

[[Category:Skip fretting]]

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 Among the possible [[skip fretting]] systems for 34-edo, the (34,2,9) system is especially convenient in that every 11-limit interval spans at most 2 frets, and if you exclude intervals involving the 17th and 19th harmonic, every 31-limit interval spans at most six frets. If you include 17 and 19, the range rises to eight frets. (Note that 8 frets on a 17-edo guitar is a big stretch, equivalent to 5.67 frets on a 12-edo guitar.)
-Here is where all the primes intervals lie:
+== Where the first primes intervals 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 on this side
+         - 15  9  - 13  -
+  - 19  -  -  -
+         -  -  -  -  - 17
+         - 17  -  -  -  -
+bass     -  -  -  -  -  -   treble
+strings  -  - 11  -  1  -   strings
+  - 23  7  -  5
+         -  5  3  -  - 21
+         - 21  - 15  9  -
+  - 13  - 19  -
+  -  -  -  -  -
+       bridge on this side
+=== As a table ===
 {| class="wikitable"
@@ Line 46: / Line 66: @@
 |}
-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.
+From these, the location of most compound intervals 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.
 [[Category:Skip fretting]]