Skip fretting system 34 2 9: Difference between revisions
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One way to play 34-edo on a 17-edo guitar is to tune each pair of adjacent strings 9\34 apart. That's 317.6 cents, just 2 cents sharp of a just 6:5. | One way to play 34-edo on a 17-edo guitar is to tune each pair of adjacent strings 9\34 apart. That's 317.6 cents, just 2 cents sharp of a just 6:5. | ||
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.) | 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.) Since it makes playing music composed using [[keemun]] temperament particularly easy, it could also be called a Keemun or Kleismic guitar. | ||
== Where the first primes intervals lie == | == Where the first primes intervals 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. | ||
headstock on this side | |||
- 15 9 - 13 - | |||
13 - 19 - - - | |||
- - - - - 17 | |||
- 17 - - - - | |||
- - - - - - | |||
bass - - 11 - 1 - treble | |||
side 1 - 23 7 - 5 side | |||
- 5 3 - - 21 | |||
- 21 - 15 9 - | |||
9 - 13 - 19 - | |||
19 - - - - - | |||
bridge on this side | |||
=== As a table === | === As a table === | ||
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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. | 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]] | [[Category:Skip fretting]] [[Category:34edo]] [[Category:Kleismic_family]] | ||