Skip fretting system 87 2 17: Difference between revisions
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One way to play | One way to play [[87edo]] on a guitar is with frets every 2\87 (43.5edo), tuning each pair of adjacent strings 17\87 apart, or about 234.5 cents, corresponding to the sharp [[~]][[8/7]] generator of [[Rodan|rodan temperament]]. | ||
This tuning | This tuning may work better on instruments like the [[harpejji]] better than on traditional stringed instruments. However, Ron Sword has built a 46edo guitar and claims it is playable. | ||
Among the possible [[skip fretting]] systems for 87-edo, one reason (87,2,17) is special is that every 17-limit interval spans at most 8 frets. | Among the possible [[skip fretting]] systems for 87-edo, one reason (87,2,17) is special is that every 17-limit interval spans at most 8 frets. | ||
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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 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. | ||
[[Category:Skip fretting]] | |||
Latest revision as of 10:07, 20 January 2025
One way to play 87edo on a guitar is with frets every 2\87 (43.5edo), tuning each pair of adjacent strings 17\87 apart, or about 234.5 cents, corresponding to the sharp ~8/7 generator of rodan temperament.
This tuning may work better on instruments like the harpejji better than on traditional stringed instruments. However, Ron Sword has built a 46edo guitar and claims it is playable.
Among the possible skip fretting systems for 87-edo, one reason (87,2,17) is special is that every 17-limit interval spans at most 8 frets.
The following table describes where all the primes intervals lie in the (87,2,17) system:
| note | fretboard position |
|---|---|
| 0 steps = 1 % 1 | string 0 fret 0 |
| 87 steps = 2 % 1 | string 5 fret 1 |
| 51 steps = 3 % 2 | string 3 fret 0 |
| 28 steps = 5 % 4 | string 2 fret - 3 |
| 70 steps = 7 % 4 | string 4 fret 1 |
| 40 steps = 11 % 8 | string 2 fret 3 |
| 61 steps = 13 % 8 | string 3 fret 5 |
| 8 steps = 17 % 16 | string 0 fret 4 |
| 22 steps = 19 % 16 | string 0 fret 11 |
| 46 steps = 23 % 16 | string 2 fret 6 |
| 75 steps = 29 % 16 | string 3 fret 12 |
| 83 steps = 31 % 16 | string 5 fret - 1 |
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.