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 [[46edo|46-edo]] on a stringed instrument is with a [[23edo|23-edo]] fretboard and strings tuned 11\46 apart, a [[Gentle_region_(extended_version)|neo-gothic]] approximation of [[13/11]].

=== Layout: Harmonics on the fretboard ===

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=== 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, having one of the lowest [[Relative_errors_of_small_EDOs|high prime limit errors]] of any edo under 100, although it is only consistent up to the 13. 41-edo is consistent up to 15.

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.) But the 5th is less accurate, and sharp as opposed to 12-edo's familiar flatness. (12edo is 2c flat, 41edo is 0.5c sharp, and 46edo is 2.4c sharp.)

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 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). Without being able to play 10ths, 11ths or 12ths, chord voicings are considerably limited.

The Kite tuning is extremely efficient in that every single 9-odd-limit ratio spans at most 4 frets, and almost every ratio within that 4-fret span is in fact a 9-odd-limit ratio. The exceptions are 11/8 and 16/11. Also all minor or neutral 2nds and their octave inverses, which mathematically <u>must</u> be a higher odd limit. Whereas in this system, there are many remote low-odd-limit ratios and many nearby high-odd-limit ratios. For example, 6/5 is 5 frets away, but 11/9 is only 1 fret away. Likewise 7/6 is 5 frets away but 13/11 is 0 frets away. And the highly dissonant wolf 5th 678c is only 2 frets away.

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.

[[Category:Skip fretting]] [[Category:46edo]]

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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 [[46edo|46-edo]] on a stringed instrument is with a [[23edo|23-edo]] fretboard and strings tuned 11\46 apart, a [[Gentle_region_(extended_version)|neo-gothic]] approximation of [[13/11]].
 === Layout: Harmonics on the fretboard ===
@@ Line 21: / Line 21: @@
 === Pros, cons, and comparison to the Kite guitar ===
--edo is harmonically exceptional. Among other virtues, it is the first edo consistent in the 13-limit. See [[46edo]].
+-edo is harmonically exceptional, having one of the lowest [[Relative_errors_of_small_EDOs|high prime limit errors]] of any edo under 100, although it is only consistent up to the 13. 41-edo is consistent up to 15.
-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.) But the 5th is less accurate, and sharp as opposed to 12-edo's familiar flatness. (12edo is 2c flat, 41edo is 0.5c sharp, and 46edo is 2.4c sharp.)
-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 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). Without being able to play 10ths, 11ths or 12ths, chord voicings are considerably limited.
+The Kite tuning is extremely efficient in that every single 9-odd-limit ratio spans at most 4 frets, and almost every ratio within that 4-fret span is in fact a 9-odd-limit ratio. The exceptions are 11/8 and 16/11. Also all minor or neutral 2nds and their octave inverses, which mathematically <u>must</u> be a higher odd limit. Whereas in this system, there are many remote low-odd-limit ratios and many nearby high-odd-limit ratios. For example, 6/5 is 5 frets away, but 11/9 is only 1 fret away. Likewise 7/6 is 5 frets away but 13/11 is 0 frets away. And the highly dissonant wolf 5th 678c is only 2 frets away.
 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.
+[[Category:Skip fretting]] [[Category:46edo]]