Skip fretting: Difference between revisions
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Jeff Brown (talk | contribs) Elaborate on relevance to keyboard players |
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(Note: Despite it's name, skip-fretting is relevant not only to fretted stringed instruments, but to the layout of | (Note: Despite it's name, skip-fretting is relevant not only to fretted stringed instruments, but to the layout of other two-dimensional grid instruments like the Lumatone and the monome.) | ||
== Introduction == | == Introduction == | ||
Skip fretting (a.k.a. Thanos tuning) allows a player of a fretted stringed instrument to play in a higher EDO than would otherwise be possible or convenient. In most skip-fretting systems, the guitar skips every other fret, so each string has only half of the notes. | Skip fretting (a.k.a. Thanos tuning) allows a player of a fretted stringed instrument to play in a higher EDO than would otherwise be possible or convenient. In most skip-fretting systems, the guitar skips every other fret, so each string has only half of the notes. | ||
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[In retrospect, I wish I had used notation like "2,13\41" instead of "(41,2,13)". Both of those represent the [[Kite guitar]] tuning equally unambiguously, but I think the first is clearer.] | [In retrospect, I wish I had used notation like "2,13\41" instead of "(41,2,13)". Both of those represent the [[Kite guitar]] tuning equally unambiguously, but I think the first is clearer.] | ||
== The relevance to keyboard players of skip-fretting == | |||
Any skip-fretting system can be used on any two-dimensional grid instrument, such as the Lumatone or the monome. Whereas for a string player the numbers `div` and `gap` in an `(edo, div, gap)` system have different meanings, for a keyboardist they don't: Both `div` and `gap` describe the amount by which the pitch changes between two keys adjacent on a particular axis. | |||
For example, the Kite skip-fretting system (41,2,13) involves keeping only every 2nd fret from 41-edo and putting 13\41 between the strings. The reverse, keeping every 13th fret and putting 2\41 between every pair of strings, would be ridiculous on a guitar, but makes just as much sense on a keyboard, and in fact results in the same system, just swapping the two axes. | |||
== 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 === | === 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. | ||
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=== Ease of reach vs. harmonic accuracy === | === 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 == | ||
In skip-fretting system `(edo, div, gap)`, the unison to any note lies `div` strings and `gap` frets away. | In skip-fretting system `(edo, div, gap)`, the unison to any note lies `div` strings and `gap` frets away. | ||
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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. | 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 == | ||