Skip fretting system 48 2 13: Difference between revisions

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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, ~~this one~~ 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.

Here is where all the primes intervals lie. From these, the location of any other interval can be added by summing the string-fret positions of its factors as vectors. So, 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).

Here is where all the primes intervals lie.

{| class="wikitable"

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| string 4 fret -3

|}

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).

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 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, this one 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.
-Here is where all the primes intervals lie. From these, the location of any other interval can be added by summing the string-fret positions of its factors as vectors. So, 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).
+Here is where all the primes intervals lie.
 {| class="wikitable"
@@ Line 46: / Line 45: @@
 | string 4 fret -3
 |}
+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).