Skip fretting: Difference between revisions
Jeff Brown (talk | contribs) Write about tradeoffs, and how to find octaves and unisons |
Jeff Brown (talk | contribs) m Capitalization, grammar |
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== Tradeoffs inherent in skip-fretting systems == | == Tradeoffs inherent in skip-fretting systems == | ||
The ideal skip-fretting system would be one that offers the player a big range without requiring too much movement or stretching, good approximations to the just intervals they want, and convenient unison or octave equivalents to any given note. These qualities are in tension. | The ideal skip-fretting system would be one that offers the player a big range without requiring too much movement or stretching, good approximations to the just intervals they want, and convenient unison or octave equivalents to any given note. These qualities are in tension. | ||
=== | === Ease of reach vs. frequency range === | ||
The smaller the interval between adjacent strings, the easier it becomes to reach all the notes of interest in a given octave, but this reduces the total range of the instrument. | The smaller the interval between adjacent strings, the easier it becomes to reach all the notes of interest in a given octave, but this reduces the total range of the instrument. | ||
The narrow 11\41 and (standard) wide 13\41 Kite guitar tunings illustrate this tradeoff. In the narrow tuning, intervals based on the 7th and 13th harmonic are much easier to play, but the interval from the first string to the sixth is 1609 cents. In the wider tuning, by contrast, it is 1902 cents. | The narrow 11\41 and (standard) wide 13\41 Kite guitar tunings illustrate this tradeoff. In the narrow tuning, intervals based on the 7th and 13th harmonic are much easier to play, but the interval from the first string to the sixth is 1609 cents. In the wider tuning, by contrast, it is 1902 cents. | ||
=== | === Ease of reach vs. harmonic accuracy === | ||
The relationship is not linear, but as a loose rule, higher EDOs provide closer approxiamtions to the harmonic series. However, skip-frettings for higher EDOs provide fewer unisons and octaves. For instance, [[Skip fretting system 63 3 17]] is in general more faithful than 41-edo is to the harmonic series, but unisons lie 17 frets apart on a guitar with 21 frets per octave. That's equivalent to a stretch of 9.7 frets on a standard 12-edo guitar. By contrast, on the Kite guitar, which uses 41-edo, the distance between unisons is only 13 frets on a 20.5-fret guitar, equivalent to about 7.6 frets on a 12-edo guitar. | The relationship is not linear, but as a loose rule, higher EDOs provide closer approxiamtions to the harmonic series. However, skip-frettings for higher EDOs provide fewer unisons and octaves. For instance, [[Skip fretting system 63 3 17]] is in general more faithful than 41-edo is to the harmonic series, but unisons lie 17 frets apart on a guitar with 21 frets per octave. That's equivalent to a stretch of 9.7 frets on a standard 12-edo guitar. By contrast, on the Kite guitar, which uses 41-edo, the distance between unisons is only 13 frets on a 20.5-fret guitar, equivalent to about 7.6 frets on a 12-edo guitar. | ||
== Finding unisons and octaves in a skip-fretting system == | == Finding unisons and octaves in a skip-fretting system == | ||
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This author has yet to find or see a formula for determining the octaves. However, the following procedure does the job: Let `n` be a number of strings. If `f = (edo - n*gap) / div` is a whole number, then an octave can be found `n` strings and `f` frets away. | This author has yet to find or see a formula for determining the octaves. However, the following procedure does the job: Let `n` be a number of strings. If `f = (edo - n*gap) / div` is a whole number, then an octave can be found `n` strings and `f` frets away. | ||
For instance, for the standard Kite tuning, `(edo, div, gap)` = `(41,2,13)`. Since `14 = (41 - 1*13)/2` a whole number, there is an octave 1 string and 14 frets away. And since `1 = (41 - 3*13)/2`, there is another octave 3 strings and 1 fret away. | For instance, for the standard Kite 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. | ||
== Some skip-fretting systems == | == Some skip-fretting systems == | ||