Skip fretting system 53 3 17: Difference between revisions

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This layout allows someone to play in 53-edo on a 17.666-edo guitar, by tuning the guitar in major thirds -- that is, with 17\53 between each pair of adjacent strings. It offers a big range -- very slightly wider than the [[Kite Guitar]]'s -- and a playable layout, with strikingly easy 5-limit chords.

One notable drawback is that, because harmonics 3 and 7 lie on the same string, a harmonic 7:6 is difficult to play. (Doing so requires reaching back 13 frets, or 883 cents, as well as across three strings.) Perhaps counter-intuitively, 12:7, the octave-complement of 7:6, is much easier to play, requiring a stretch of only 9 frets or 611 cents. However, for exactly the same reason, the ratio 7:3 (an octave wider than 7:6) is extremely easy to play, being 3 string crossings and 1 fret wide.

The diagram below, which could be interpreted 20 frets of a 12-string guitar, shows where each of the 15-limit harmonics lies. Since 53-edo is mostly (see below) for the exception consistent in the 15-limit, these harmonics' positions imply where every interval in that group lies. (For instance, to play 7/6 you move up one string and down one fret, because that takes you from harmonic 3 to harmonic 7.) Octaves are indicated as powers of 2 (specifically 1, 2, 4 and 8).

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== The few difficult ratios have easy octave counterparts ==

One notable drawback to this tuning that, because harmonics 3 and 7 lie on the same string, a harmonic 7:6 is difficult to play. (Doing so requires reaching back 13 frets, or 883 cents, and across three strings.) However, the ratio 7:3 (an octave wider than 7:6) is unusually easy to play, being 3 string crossings and 1 fret wide. Following the same logic, for every difficult interval R less than an octave, it can be shown that R plus an octave is easy to play. There seem to be very few such difficult ratios in the 15-limit. I (Jeff Brown) only see five: 7:6, 13:12, 14:13, 9:8, and 11:9.

[[Category:Skip fretting]]

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 This layout allows someone to play in 53-edo on a 17.666-edo guitar, by tuning the guitar in major thirds -- that is, with 17\53 between each pair of adjacent strings. It offers a big range -- very slightly wider than the [[Kite Guitar]]'s -- and a playable layout, with strikingly easy 5-limit chords.
-One notable drawback is that, because harmonics 3 and 7 lie on the same string, a harmonic 7:6 is difficult to play. (Doing so requires reaching back 13 frets, or 883 cents, as well as across three strings.) Perhaps counter-intuitively, 12:7, the octave-complement of 7:6, is much easier to play, requiring a stretch of only 9 frets or 611 cents. However, for exactly the same reason, the ratio 7:3 (an octave wider than 7:6) is extremely easy to play, being 3 string crossings and 1 fret wide.
 The diagram below, which could be interpreted 20 frets of a 12-string guitar, shows where each of the 15-limit harmonics lies. Since 53-edo is mostly (see below) for the exception consistent in the 15-limit, these harmonics' positions imply where every interval in that group lies. (For instance, to play 7/6 you move up one string and down one fret, because that takes you from harmonic 3 to harmonic 7.) Octaves are indicated as powers of 2 (specifically 1, 2, 4 and 8).
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+== The few difficult ratios have easy octave counterparts ==
+One notable drawback to this tuning that, because harmonics 3 and 7 lie on the same string, a harmonic 7:6 is difficult to play. (Doing so requires reaching back 13 frets, or 883 cents, and across three strings.) However, the ratio 7:3 (an octave wider than 7:6) is unusually easy to play, being 3 string crossings and 1 fret wide. Following the same logic, for every difficult interval R less than an octave, it can be shown that R plus an octave is easy to play. There seem to be very few such difficult ratios in the 15-limit. I (Jeff Brown) only see five: 7:6, 13:12, 14:13, 9:8, and 11:9.
 [[Category:Skip fretting]]