Skip fretting system 46 2 11: Difference between revisions
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A good way to play in 46-edo on a stringed instrument is with a 23-edo fretboard and strings tuned 11\46 apart. | A good way to play in 46-edo on a stringed instrument is with a 23-edo fretboard and strings tuned 11\46 apart. | ||
=== | === Layout: Harmonics on the fretboard === | ||
Each number in this diagram represents a harmonic modulo octaves -- so 3 represents 3:2, 15 represents 15:8, etc. A trailing _ indicates that the harmonic lies in the octave below 1 (i.e. 15_ represents 15:16 as opposed to 15:8), and a trailing ' indicates the harmonic lies an octave above 2 (so, e.g., 17' represents 17:8 rather than 17:16). | |||
headstock on this side | |||
-- -- -- 3 -- | -- -- -- 3 -- | ||
15_-- -- -- -- | 15_-- -- -- -- | ||
-- -- -- -- 15 | |||
1 -- -- -- | 1 19 -- -- -- | ||
-- -- 23 -- 2 | -- -- 23 -- 2 treble strings | ||
17 5 -- 7 -- | 17 5 -- 7 -- on this side | ||
-- -- -- -- 17' | -- -- -- -- 17' | ||
9 -- -- -- -- | 9 -- -- -- -- | ||
-- 11 13 -- 9' | -- 11 13 -- 9' | ||
bridge on this side | |||
An | An appealing aspect of this layout is that each string carries a substantial number of harmonics. For instance, since 1, 3 and 5 all lie on different strings, close-position major chords are easily playable. If they were all on the same string, that would not be the case. | ||
Since 11\46 is small, some intervals that look unplayable can in fact be played. for instance, 7:6 looks like it can't, because 3 and 7 lie on the same string. However, for each | Since 11\46 is small, some intervals that look unplayable can in fact be played. for instance, 7:6 looks like it can't, because 3 and 7 lie on the same string. However, for each harmonic drawn, the same note can be played two strings up and eleven frets down. Thus 7:6 can be played by reaching across two strings and down 6 frets (which requires a stretch of the hand equivalent to 3.1 frets of 12-edo). | ||
=== | === Pros, cons, and comparison to the Kite guitar === | ||
46-edo is harmonically exceptional. Among other virtues, it is the first edo consistent in the 13-limit. See [[46edo]]. | 46-edo is harmonically exceptional. Among other virtues, it is the first edo consistent in the 13-limit. See [[46edo]]. | ||
The thirds in 46-edo can be easier for a listener used to 12-edo to accept than those in 41-edo. (In 46-edo, thirds are 5c sharp; in 12-edo they are 14c sharp; and in 41-edo they are 6c flat.) | The thirds in 46-edo can be easier for a listener used to 12-edo to accept than those in 41-edo. (In 46-edo, thirds are 5c sharp; in 12-edo they are 14c sharp; and in 41-edo they are 6c flat.) | ||
The Kite tuning is more economical with strings. If the root is at string 0 fret 0, then the octave in the Kite system lies on string 3 fret 1, whereas in this system it lies at string 4 fret 1. | The Kite tuning is more economical with strings. If the root is at string 0 fret 0, then the octave in the Kite system lies on string 3 fret 1, whereas in this system it lies at string 4 fret 1. Whereas 6 open strings in the Kite system spans 1902 cents (a root and a fifth), in this one they span 1435 cents (a root and a septimal second). | ||
The most difficult 15-limit ratios (12:11 and 13:12) to play span 8 frets of 23-edo, which is equivalent to 4.2 frets of 12-edo (since 8*12/23 = 4.2). This | The most difficult 15-limit ratios (12:11 and 13:12) to play span 8 frets of 23-edo, which is equivalent to 4.2 frets of 12-edo (since 8*12/23 = 4.2). This is a little narrower (i.e. easier) than the widest 15-limit stretch in the Kite tuning, which is 4.6 frets of 12 edo. | ||