Skip fretting: Difference between revisions

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For instance, for the standard Kite guitar tuning, `(edo, div, gap)` = `(41,2,13)`. Since `14 = (41 - 1*13)/2` is a whole number, there is an octave 1 string and 14 frets away. And since `1 = (41 - 3*13)/2` is another whole number, there is another octave 3 strings and 1 fret away.

However, if the divisor of the system is coprime with the edo, alternating strings have no unisons or octaves. For example, 41edo has no divisors other than itself, so octaves can be found regardless of what interval the strings are tuned to or how many frets are skipped each time as long as the fretboard is wide enough. 46edo can be divided by two, so alternating strings on a 23edo guitar never have unisons or octaves, making systems like that harder to tune by ear or normal guitar tuners and use in live performance unless tuning to notes that they have in common with 12edo.

== Some skip-fretting systems ==

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In addition to the layouts listed below, every [[:Category:Lumatone mappings|Lumatone mapping]] can also be interpreted as a skip fretting. As three distinct ones, in fact, depending on which of the three hexagonal axes is mapped to the two rectangular axes on the fretboard. (Nothing guarantees that it will be a *good* layout on a guitar, but it will at least often be feasible.)

* [[Skip fretting system 27 2 9]]: 27-edo on a 13.5-edo guitar.

* [[Skip fretting system 31 2 9]]: Make the higher register of a 31-edo guitar easier to play by omitting every other fret, while keeping all the frets in the lower register.

* [[Skip fretting system 31 3 7]]: 31-edo on a 10.33-edo guitar.

* [[Skip fretting system 34 2 9]]: 34-edo on a 17-edo guitar.

* [[Skip fretting system 34 2 11]]: 34-edo on a 17-edo guitar, very much like the [[Kite guitar]].

* [[Skip fretting system 38 2 11]]: 38-edo on a 19-edo guitar.

* [[Skip fretting system 41 2 11]]: Same fret layout as the Kite guitar, with narrower string gaps and easier-to-reach higher-limit intervals.

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* [[Skip fretting system 43 2 9]]: 43-edo on a 21.5-edo guitar.

* [[Skip fretting system 44 2 11]]: 44-edo on a 22-edo guitar.

* [[~~Isomorphic layout 11\46 x 2\46|~~Skip fretting system 46 2 11]]: 46-edo on a 23-edo guitar.

* [[Skip fretting system 46 2 11]]: 46-edo on a 23-edo guitar.

* [[Skip fretting system 48 2 13]]: 48-edo on a 24-edo guitar.

* [[Skip fretting system 53 3 14]]: 53-edo on a 17.66-edo or [[28edt]] guitar.

* [[Skip fretting system 53 3 17]]: 53-edo on a 17.66-edo guitar, with an unusually wide range.

* [[Skip fretting system 58 2 15]]: 58-edo on a 29-edo guitar.

* [[~~4\58 x 15\48 isomorphic layout & skip-fretting system|~~Skip fretting system 58 4 15]]: 58-edo on a 14.5-edo guitar.

* [[Skip fretting system 58 4 15]]: 58-edo on a 14.5-edo guitar.

* [[Skip fretting system 58 2 17]]: 58-edo on a 29-edo guitar.

* [[Skip fretting system 60 2 29]]: 60-edo on a 30-edo guitar.

* [[Skip fretting system 60 3 19]]: 60-edo on a 20-edo guitar.

* [[Skip fretting system 60 4 17]]: 60-edo on a 15-edo guitar.

* [[Skip fretting system 63 3 17]]: 63-edo on a 21-edo guitar.

* [[Skip fretting system 72 2 27~~, a.k.a. Isomorphic grid layout 27\72 x 2\72~~]]: 72-edo on a 36-edo guitar.

* [[Skip fretting system 72 2 27]]: 72-edo on a 36-edo guitar.

* [[Skip fretting system 87 2 17]]: 87-edo on a 43.5-edo guitar.

* [[Skip fretting system 90 5 17]]: 90-edo on an 18-edo guitar.

* [[~~Isomorphic grid layout~~ 7~~\94 x~~ 16~~\94~~]]: 94-edo on a 13.429-edo guitar.

* [[Skip fretting system 94 7 16]]: 94-edo on a 13.429-edo guitar.

* [[Skip fretting system 140 8 37]]: 140edo on a 17.5-edo guitar.

[[Category:Guitar]]

[[Category:Skip fretting| ]]

@@ Line 43: / Line 43: @@
 For instance, for the standard Kite guitar tuning, `(edo, div, gap)` = `(41,2,13)`. Since `14 = (41 - 1*13)/2` is a whole number, there is an octave 1 string and 14 frets away. And since `1 = (41 - 3*13)/2` is another whole number, there is another octave 3 strings and 1 fret away.
+However, if the divisor of the system is coprime with the edo, alternating strings have no unisons or octaves. For example, 41edo has no divisors other than itself, so octaves can be found regardless of what interval the strings are tuned to or how many frets are skipped each time as long as the fretboard is wide enough. 46edo can be divided by two, so alternating strings on a 23edo guitar never have unisons or octaves, making systems like that harder to tune by ear or normal guitar tuners and use in live performance unless tuning to notes that they have in common with 12edo.
 == Some skip-fretting systems ==
@@ Line 48: / Line 50: @@
 In addition to the layouts listed below, every [[:Category:Lumatone mappings|Lumatone mapping]] can also be interpreted as a skip fretting. As three distinct ones, in fact, depending on which of the three hexagonal axes is mapped to the two rectangular axes on the fretboard. (Nothing guarantees that it will be a *good* layout on a guitar, but it will at least often be feasible.)
+* [[Skip fretting system 27 2 9]]: 27-edo on a 13.5-edo guitar.
 * [[Skip fretting system 31 2 9]]: Make the higher register of a 31-edo guitar easier to play by omitting every other fret, while keeping all the frets in the lower register.
+* [[Skip fretting system 31 3 7]]: 31-edo on a 10.33-edo guitar.
 * [[Skip fretting system 34 2 9]]: 34-edo on a 17-edo guitar.
+* [[Skip fretting system 34 2 11]]: 34-edo on a 17-edo guitar, very much like the [[Kite guitar]].
 * [[Skip fretting system 38 2 11]]: 38-edo on a 19-edo guitar.
 * [[Skip fretting system 41 2 11]]: Same fret layout as the Kite guitar, with narrower string gaps and easier-to-reach higher-limit intervals.
@@ Line 55: / Line 60: @@
 * [[Skip fretting system 43 2 9]]: 43-edo on a 21.5-edo guitar.
 * [[Skip fretting system 44 2 11]]: 44-edo on a 22-edo guitar.
-* [[Isomorphic layout 11\46 x 2\46|Skip fretting system 46 2 11]]: 46-edo on a 23-edo guitar.
+* [[Skip fretting system 46 2 11]]: 46-edo on a 23-edo guitar.
 * [[Skip fretting system 48 2 13]]: 48-edo on a 24-edo guitar.
 * [[Skip fretting system 53 3 14]]: 53-edo on a 17.66-edo or [[28edt]] guitar.
+* [[Skip fretting system 53 3 17]]: 53-edo on a 17.66-edo guitar, with an unusually wide range.
 * [[Skip fretting system 58 2 15]]: 58-edo on a 29-edo guitar.
-* [[4\58 x 15\48 isomorphic layout & skip-fretting system|Skip fretting system 58 4 15]]: 58-edo on a 14.5-edo guitar.
+* [[Skip fretting system 58 4 15]]: 58-edo on a 14.5-edo guitar.
+* [[Skip fretting system 58 2 17]]: 58-edo on a 29-edo guitar.
+* [[Skip fretting system 60 2 29]]: 60-edo on a 30-edo guitar.
 * [[Skip fretting system 60 3 19]]: 60-edo on a 20-edo guitar.
 * [[Skip fretting system 60 4 17]]: 60-edo on a 15-edo guitar.
 * [[Skip fretting system 63 3 17]]: 63-edo on a 21-edo guitar.
-* [[Skip fretting system 72 2 27, a.k.a. Isomorphic grid layout 27\72 x 2\72]]: 72-edo on a 36-edo guitar.
+* [[Skip fretting system 72 2 27]]: 72-edo on a 36-edo guitar.
 * [[Skip fretting system 87 2 17]]: 87-edo on a 43.5-edo guitar.
 * [[Skip fretting system 90 5 17]]: 90-edo on an 18-edo guitar.
-* [[Isomorphic grid layout 7\94 x 16\94]]: 94-edo on a 13.429-edo guitar.
+* [[Skip fretting system 94 7 16]]: 94-edo on a 13.429-edo guitar.
+* [[Skip fretting system 140 8 37]]: 140edo on a 17.5-edo guitar.
 [[Category:Guitar]]
 [[Category:Skip fretting| ]] <!-- main category -->