Skip fretting system 48 2 13 - Revision history

Yourmusic Productions: formatting

2023-11-07T11:22:37Z

formatting

← Older revision		Revision as of 11:22, 7 November 2023
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	One way to play [[48-edo]] on a [[24-edo ~~guitar~~]] is to tune each pair of adjacent strings 13\48 apart. (That's 325 cents, a bit sharp of 6:5.)		One way to play [[48-edo]] on a [[24-edo]] guitar is to tune each pair of adjacent strings 13\48 apart. (That's 325 cents, a bit sharp of 6:5.)

	48-edo improves on 24-edo's 5:4 a little, its 7:4 a lot, and its 23:16 and 29:16 enormously. Among the possible [[skip fretting]] systems for 48-edo, the (48,2,13) system is especially convenient in that every 11-limit ratio spans at most 3 frets. In fact, so does every ratio in the 2.3.5.7.11.29 group. Since it makes it particularly easy to play music composed in [[doublewide]] temperament, it could also be called a doublewide guitar.		48-edo improves on 24-edo's 5:4 a little, its 7:4 a lot, and its 23:16 and 29:16 enormously. Among the possible [[skip fretting]] systems for 48-edo, the (48,2,13) system is especially convenient in that every 11-limit ratio spans at most 3 frets. In fact, so does every ratio in the 2.3.5.7.11.29 group. Since it makes it particularly easy to play music composed in [[doublewide]] temperament, it could also be called a doublewide guitar.

Yourmusic Productions: Categories, list temperament that makes this layout work well.

2023-11-07T11:22:06Z

Categories, list temperament that makes this layout work well.

← Older revision		Revision as of 11:22, 7 November 2023
Line 1:		Line 1:
	One way to play 48-edo on a 24-edo guitar is to tune each pair of adjacent strings 13\48 apart. (That's 325 cents, a bit sharp of 6:5.)		One way to play [[48-edo]] on a [[24-edo guitar]] is to tune each pair of adjacent strings 13\48 apart. (That's 325 cents, a bit sharp of 6:5.)

	48-edo improves on 24-edo's 5:4 a little, its 7:4 a lot, and its 23:16 and 29:16 enormously. Among the possible [[skip fretting]] systems for 48-edo, the (48,2,13) system is especially convenient in that every 11-limit ratio spans at most 3 frets. In fact, so does every ratio in the 2.3.5.7.11.29 group.		48-edo improves on 24-edo's 5:4 a little, its 7:4 a lot, and its 23:16 and 29:16 enormously. Among the possible [[skip fretting]] systems for 48-edo, the (48,2,13) system is especially convenient in that every 11-limit ratio spans at most 3 frets. In fact, so does every ratio in the 2.3.5.7.11.29 group. Since it makes it particularly easy to play music composed in [[doublewide]] temperament, it could also be called a doublewide guitar.

	Here is where all the primes intervals lie.		Here is where all the primes intervals lie.
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	From these, the location of a compound intervals N can be added by vector-summing the string-fret positions of N's factors. For instance, since 3%2 lies at (string 2, fret 1) and 5%4 lies at (string 1, fret 1), their product 15%8 lies at (string 3, fret 2).		From these, the location of a compound intervals N can be added by vector-summing the string-fret positions of N's factors. For instance, since 3%2 lies at (string 2, fret 1) and 5%4 lies at (string 1, fret 1), their product 15%8 lies at (string 3, fret 2).

	[[Category:Skip fretting]]		[[Category:Skip fretting]] [[Category:48edo]]

Xenwolf: recategorized

2021-05-02T16:55:46Z

recategorized

← Older revision		Revision as of 16:55, 2 May 2021
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	From these, the location of a compound intervals N can be added by vector-summing the string-fret positions of N's factors. For instance, since 3%2 lies at (string 2, fret 1) and 5%4 lies at (string 1, fret 1), their product 15%8 lies at (string 3, fret 2).		From these, the location of a compound intervals N can be added by vector-summing the string-fret positions of N's factors. For instance, since 3%2 lies at (string 2, fret 1) and 5%4 lies at (string 1, fret 1), their product 15%8 lies at (string 3, fret 2).

	[[Category:~~Guitar]]~~		[[Category:Skip fretting]]
	~~[[Category:Howto~~]]

Xenwolf: added categories

2021-05-02T09:33:32Z

added categories

← Older revision		Revision as of 09:33, 2 May 2021
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	From these, the location of a compound intervals N can be added by vector-summing the string-fret positions of N's factors. For instance, since 3%2 lies at (string 2, fret 1) and 5%4 lies at (string 1, fret 1), their product 15%8 lies at (string 3, fret 2).		From these, the location of a compound intervals N can be added by vector-summing the string-fret positions of N's factors. For instance, since 3%2 lies at (string 2, fret 1) and 5%4 lies at (string 1, fret 1), their product 15%8 lies at (string 3, fret 2).

			[[Category:Guitar]]
			[[Category:Howto]]

Jeff Brown: reorder, minor clarifications

2021-05-02T00:44:10Z

reorder, minor clarifications

← Older revision		Revision as of 00:44, 2 May 2021
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	One way to play 48-edo on a 24-edo guitar is to tune each pair of adjacent strings 13\48 apart. (That's 325 cents, a bit sharp of 6:5.)		One way to play 48-edo on a 24-edo guitar is to tune each pair of adjacent strings 13\48 apart. (That's 325 cents, a bit sharp of 6:5.)

	48-edo improves on 24-edo's 5:4 a little, its 7:4 a lot, and its 23:16 and 29:16 enormously. Among the possible [[skip fretting]] systems for 48-edo, ~~this one~~ is especially convenient in that every 11-limit ratio spans at most 3 frets. In fact, so does every ratio in the 2.3.5.7.11.29 group.		48-edo improves on 24-edo's 5:4 a little, its 7:4 a lot, and its 23:16 and 29:16 enormously. Among the possible [[skip fretting]] systems for 48-edo, the (48,2,13) system is especially convenient in that every 11-limit ratio spans at most 3 frets. In fact, so does every ratio in the 2.3.5.7.11.29 group.

	Here is where all the primes intervals lie. From these, the location of any other interval can be added by summing the string-fret positions of its factors as vectors. So, for instance, since 3%2 lies at (string 2, fret 1) and 5%4 lies at (string 1, fret 1), their product 15%8 lies at (string 3, fret 2).

			Here is where all the primes intervals lie.

	{\| class="wikitable"		{\| class="wikitable"
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	\| string 4 fret -3		\| string 4 fret -3
	\|}		\|}

			From these, the location of a compound intervals N can be added by vector-summing the string-fret positions of N's factors. For instance, since 3%2 lies at (string 2, fret 1) and 5%4 lies at (string 1, fret 1), their product 15%8 lies at (string 3, fret 2).

Jeff Brown: format table

2021-05-02T00:41:55Z

format table

← Older revision		Revision as of 00:41, 2 May 2021
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	Here is where all the primes intervals lie. From these, the location of any other interval can be added by summing the string-fret positions of its factors as vectors. So, for instance, since 3%2 lies at (string 2, fret 1) and 5%4 lies at (string 1, fret 1), their product 15%8 lies at (string 3, fret 2).		Here is where all the primes intervals lie. From these, the location of any other interval can be added by summing the string-fret positions of its factors as vectors. So, for instance, since 3%2 lies at (string 2, fret 1) and 5%4 lies at (string 1, fret 1), their product 15%8 lies at (string 3, fret 2).

	0 steps = 1 % 1 : string 0 fret 0
	48 steps = 2 % 1 : string 4 fret -2		{\| class="wikitable"
	28 steps = 3 % 2 : string 2 fret 1		! note
	15 steps = 5 % 4 : string 1 fret 1		! fretboard position
	39 steps = 7 % 4 : string 3 fret 0		\|-
	22 steps = 11 % 8 : string 2 fret -2		\| 0 steps = 1 % 1
	34 steps = 13 % 8 : string 2 fret 4		\| string 0 fret 0
	4 steps = 17 % 16 : string 0 fret 2		\|-
	12 steps = 19 % 16 : string 0 fret 6		\| 48 steps = 2 % 1
	25 steps = 23 % 16 : string 1 fret 6		\| string 4 fret -2
	41 steps = 29 % 16 : string 3 fret 1		\|-
	46 steps = 31 % 16 : string 4 fret -3		\| 28 steps = 3 % 2
			\| string 2 fret 1
			\|-
			\| 15 steps = 5 % 4
			\| string 1 fret 1
			\|-
			\| 39 steps = 7 % 4
			\| string 3 fret 0
			\|-
			\| 22 steps = 11 % 8
			\| string 2 fret -2
			\|-
			\| 34 steps = 13 % 8
			\| string 2 fret 4
			\|-
			\| 4 steps = 17 % 16
			\| string 0 fret 2
			\|-
			\| 12 steps = 19 % 16
			\| string 0 fret 6
			\|-
			\| 25 steps = 23 % 16
			\| string 1 fret 6
			\|-
			\| 41 steps = 29 % 16
			\| string 3 fret 1
			\|-
			\| 46 steps = 31 % 16
			\| string 4 fret -3
			\|}

Jeff Brown: start page

2021-05-02T00:37:49Z

start page

New page

One way to play 48-edo on a 24-edo guitar is to tune each pair of adjacent strings 13\48 apart. (That's 325 cents, a bit sharp of 6:5.)

48-edo improves on 24-edo's 5:4 a little, its 7:4 a lot, and its 23:16 and 29:16 enormously. Among the possible [[skip fretting]] systems for 48-edo, this one is especially convenient in that every 11-limit ratio spans at most 3 frets. In fact, so does every ratio in the 2.3.5.7.11.29 group.

Here is where all the primes intervals lie. From these, the location of any other interval can be added by summing the string-fret positions of its factors as vectors. So, for instance, since 3%2 lies at (string 2, fret 1) and 5%4 lies at (string 1, fret 1), their product 15%8 lies at (string 3, fret 2).

0 steps = 1 % 1 : string 0 fret 0
48 steps = 2 % 1 : string 4 fret -2
28 steps = 3 % 2 : string 2 fret 1
15 steps = 5 % 4 : string 1 fret 1
39 steps = 7 % 4 : string 3 fret 0
22 steps = 11 % 8 : string 2 fret -2
34 steps = 13 % 8 : string 2 fret 4
4 steps = 17 % 16 : string 0 fret 2
12 steps = 19 % 16 : string 0 fret 6
25 steps = 23 % 16 : string 1 fret 6
41 steps = 29 % 16 : string 3 fret 1
46 steps = 31 % 16 : string 4 fret -3