Skip fretting system 27 2 9: Difference between revisions
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# | A good way to play [[27-edo]] on a 13.5-edo guitar is to tune each pair of adjacent strings 9/27 apart, or the familiar 400 cent major third shared with 12edo. | ||
Among the possible [[skip fretting]] systems for 27-edo, the (27, 2, 9) system is especially effective because it makes [[5-limit]] chords easy to play, every interval can be reached with a stretch of 4 frets or less (equivalent to 3.55 on a 12edo guitar) and it can be quickly & easily tuned using an ordinary 12edo guitar tuner, making it well suited to live performance. Since it makes it particularly easy to play music composed using [[Augmented_family#Augmented|augmented]] temperament, it could also be called an augmented or [https://en.wikipedia.org/wiki/Major_thirds_tuning major thirds] guitar. | |||
It does limit your ability to play more complex septimal and higher-limit chords compared to a full 27edo guitar though, so you might want to use a partial system with the full set of frets in the lower octave and skip-fretting higher up, or have multiple instruments adding the more complex upper range harmonies. | |||
Here is where all the prime intervals lie. | |||
{| class="wikitable" | |||
! note | |||
! fretboard position | |||
|- | |||
| 0 steps = 1 % 1 | |||
| string 0 fret 0 | |||
|- | |||
| 27 steps = 2 % 1 | |||
| string 3 fret 0 | |||
|- | |||
| 16 steps = 3 % 2 | |||
| string 2 fret -1 | |||
|- | |||
| 9 steps = 5 % 4 | |||
| string 1 fret 0 | |||
|- | |||
| 22 steps = 7 % 4 | |||
| string 2 fret 2 | |||
|- | |||
| 12 steps = 11 % 8 | |||
| string 2 fret -3 | |||
|- | |||
| 19 steps = 13 % 8 | |||
| string 3 fret -4 | |||
|- | |||
| 2 steps = 17 % 16 | |||
| string 0 fret 1 | |||
|- | |||
| 7 steps = 19 % 16 | |||
| string 1 fret -1 | |||
|- | |||
| 14 steps = 23 % 16 | |||
| string 2 fret -1 | |||
|- | |||
| 23 steps = 29 % 16 | |||
| string 3 fret -2 | |||
|- | |||
| 26 steps = 31 % 16 | |||
| string 2 fret 4 | |||
|} | |||
From these, the location of a compound intervals N can be added by vector-summing the string-fret positions of N's factors. For instance, since 3%2 lies at (string 2, fret 1) and 5%4 lies at (string 1, fret 1), their product 15%8 lies at (string 3, fret 2). | |||
[[Category:Skip fretting]] [[Category:27edo]] [[Category:Guitar]] | |||