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. | 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. | ||
An important drawback is that harmonics 3 and 7 lie on the same string, | An important 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. | ||
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). | 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). | ||
The exception to the above consistency rule of thumb is the ratios 11/7 (and its octave-complement 14/11). Since 11:8 is 7.9 cents flat and 7:4 is 4.8 cents sharp in 53-edo, the distance between them is 7.9 + 4.8 = 12.7 cents too wide. 12.7 cents is more than half of 53-edo's step size of 22.6 cents. Thus whereas the diagram below suggests that 11:7 is 34 steps wide, in fact 53-edo's best approximation to 11:7 is 35 steps wide. But that best approximation is still 10 cents sharp, so both approximations are roughly equally wrong, just in opposite directions. | The exception to the above consistency rule of thumb is the ratios 11/7 (and its octave-complement 14/11). Since 11:8 is 7.9 cents flat and 7:4 is 4.8 cents sharp in 53-edo, the distance between them is 7.9 + 4.8 = 12.7 cents too wide. 12.7 cents is more than half of 53-edo's step size of 22.6 cents. Thus whereas the diagram below suggests that 11:7 is 34 steps wide, in fact 53-edo's best approximation to 11:7 is 35 steps wide. But that best approximation is still 10 cents sharp, so both approximations are roughly equally wrong, just in opposite directions. | ||
20 frets of a hypothetical 12-string guitar tuned this way: | 20 frets of a hypothetical 12-string guitar tuned this way: | ||