Skip fretting system 48 2 13: Difference between revisions

Line 1:

One way to play 48-edo on a 24-edo guitar is to tune each pair of adjacent strings 13\48 apart. (That's 325 cents, a bit sharp of 6:5.)

One way to play [[48-edo]] on a [[24-edo guitar]] is to tune each pair of adjacent strings 13\48 apart. (That's 325 cents, a bit sharp of 6:5.)

48-edo improves on 24-edo's 5:4 a little, its 7:4 a lot, and its 23:16 and 29:16 enormously. Among the possible [[skip fretting]] systems for 48-edo, the (48,2,13) system is especially convenient in that every 11-limit ratio spans at most 3 frets. In fact, so does every ratio in the 2.3.5.7.11.29 group.

48-edo improves on 24-edo's 5:4 a little, its 7:4 a lot, and its 23:16 and 29:16 enormously. Among the possible [[skip fretting]] systems for 48-edo, the (48,2,13) system is especially convenient in that every 11-limit ratio spans at most 3 frets. In fact, so does every ratio in the 2.3.5.7.11.29 group. Since it makes it particularly easy to play music composed in [[doublewide]] temperament, it could also be called a doublewide guitar.

Here is where all the primes intervals lie.

Line 48:

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:Skip fretting]] [[Category:48edo]]

@@ Line 1: / Line 1: @@
-One way to play 48-edo on a 24-edo guitar is to tune each pair of adjacent strings 13\48 apart. (That's 325 cents, a bit sharp of 6:5.)
+One way to play [[48-edo]] on a [[24-edo guitar]] is to tune each pair of adjacent strings 13\48 apart. (That's 325 cents, a bit sharp of 6:5.)
--edo improves on 24-edo's 5:4 a little, its 7:4 a lot, and its 23:16 and 29:16 enormously. Among the possible [[skip fretting]] systems for 48-edo, the (48,2,13) system is especially convenient in that every 11-limit ratio spans at most 3 frets. In fact, so does every ratio in the 2.3.5.7.11.29 group.
+-edo improves on 24-edo's 5:4 a little, its 7:4 a lot, and its 23:16 and 29:16 enormously. Among the possible [[skip fretting]] systems for 48-edo, the (48,2,13) system is especially convenient in that every 11-limit ratio spans at most 3 frets. In fact, so does every ratio in the 2.3.5.7.11.29 group. Since it makes it particularly easy to play music composed in [[doublewide]] temperament, it could also be called a doublewide guitar.
 Here is where all the primes intervals lie.
@@ Line 48: / Line 48: @@
 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:Skip fretting]] [[Category:48edo]]