Skip fretting system 72 2 27 - Revision history

BudjarnLambeth at 04:52, 27 April 2025

2025-04-27T04:52:53Z

← Older revision		Revision as of 04:52, 27 April 2025
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	The same advantage holds for the 29\72 x 2\72 skip-fretting system, but fourths on adjacent strings are hard to play in that system, because the player must bend one note while playing an adjacent string at the same fret.		The same advantage holds for the 29\72 x 2\72 skip-fretting system, but fourths on adjacent strings are hard to play in that system, because the player must bend one note while playing an adjacent string at the same fret.

	Here is where all the ~~primes~~ intervals through 31 lie:		Here is where all the [[prime]] intervals through 31 lie:

	{\| class="wikitable"		{\| class="wikitable"

BudjarnLambeth at 04:52, 27 April 2025

2025-04-27T04:52:33Z

← Older revision		Revision as of 04:52, 27 April 2025
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	72-edo approximates the 11-limit astoundingly well, and is quite good in higher limits too. 36-edo, by contrast, has a 5:4 that's 14 cents sharp (identical to 12-edo's), and an 11:8 that's 15 cents sharp.		72-edo approximates the 11-limit astoundingly well, and is quite good in higher limits too. 36-edo, by contrast, has a 5:4 that's 14 cents sharp (identical to 12-edo's), and an 11:8 that's 15 cents sharp.

	But whereas a 72-edo guitar would not be, a 36-edo guitar is playable. Neil Haverstick does it.		But whereas a 72-edo guitar would not be, a 36-edo guitar is playable. [[Neil Haverstick]] does it.

	Among the possible [[skip fretting]] systems for 72-edo, the 27\72 x 2\72 (or equivalently, 4.5\12 x 1\36) system is especially convenient because every ratio in the 31-limit group sans 21 can be played within a block 4 strings wide by 17 frets long. (17 frets of 36-edo is shorter than 6 frets of 12-edo.)		Among the possible [[skip fretting]] systems for 72-edo, the 27\72 x 2\72 (or equivalently, 4.5\12 x 1\36) system is especially convenient because every ratio in the 31-limit group sans 21 can be played within a block 4 strings wide by 17 frets long. (17 frets of 36-edo is shorter than 6 frets of 12-edo.)

BudjarnLambeth: Add links

2025-04-27T04:51:47Z

Add links

← Older revision		Revision as of 04:51, 27 April 2025
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	One way to play ~~72-edo~~ on a ~~36-edo~~ guitar is to tune each pair of adjacent strings 450 cents apart. The equivalent tuning on a grid controller would be for notes to rise by 2\72 (33.3 cents) along each column and by 27\72 (450 cents) along each row.		One way to play [[72edo]] on a [[36edo]] [[guitar]] is to tune each pair of adjacent strings 450 [[cents]] apart. The equivalent tuning on a grid controller would be for notes to rise by 2\72 (33.3 cents) along each column and by 27\72 (450 cents) along each row.

	The resulting range across six strings is 2250 cents -- close to the 2-octave spread on a ~~12-edo~~ guitar in standard tuning.		The resulting range across six strings is 2250 cents -- close to the 2-octave spread on a [[12edo]] guitar in standard tuning.

	72-edo approximates the 11-limit astoundingly well, and is quite good in higher limits too. 36-edo, by contrast, has a 5:4 that's 14 cents sharp (identical to 12-edo's), and an 11:8 that's 15 cents sharp.		72-edo approximates the 11-limit astoundingly well, and is quite good in higher limits too. 36-edo, by contrast, has a 5:4 that's 14 cents sharp (identical to 12-edo's), and an 11:8 that's 15 cents sharp.

TallKite: TallKite moved page Skip fretting system 72 2 27, a.k.a. Isomorphic grid layout 27\72 x 2\72 to Skip fretting system 72 2 27

2024-03-22T20:38:17Z

TallKite moved page Skip fretting system 72 2 27, a.k.a. Isomorphic grid layout 27\72 x 2\72 to Skip fretting system 72 2 27

← Older revision	Revision as of 20:38, 22 March 2024
(No difference)

Jeff Brown: Correct an errant plural.

2021-07-11T14:20:06Z

Correct an errant plural.

← Older revision		Revision as of 14:20, 11 July 2021
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	\|}		\|}

	From these, the location of any compound ~~intervals~~ N can be added by vector-summing the string-fret positions of N's factors. See [[Skip fretting system 48 2 13]] for details on how that's done.		From these, the location of any compound interval N can be added by vector-summing the string-fret positions of N's factors. See [[Skip fretting system 48 2 13]] for details on how that's done.

	[[Category:Skip fretting]]		[[Category:Skip fretting]]

Jeff Brown: Fix a typo -- I had misrecorded the size of the string x fret block of 31-limit ratios as 4x15, but that's the size of the 13-limit block The 31-limit block is a little bigger.

2021-07-11T14:19:08Z

Fix a typo -- I had misrecorded the size of the string x fret block of 31-limit ratios as 4x15, but that's the size of the 13-limit block The 31-limit block is a little bigger.

← Older revision		Revision as of 14:19, 11 July 2021
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	But whereas a 72-edo guitar would not be, a 36-edo guitar is playable. Neil Haverstick does it.		But whereas a 72-edo guitar would not be, a 36-edo guitar is playable. Neil Haverstick does it.

	Among the possible [[skip fretting]] systems for 72-edo, the 27\72 x 2\72 (or equivalently, 4.5\12 x 1\36) system is especially convenient because every ratio in the 31-limit group sans 21 can be played within a block 4 strings wide by 15 frets long. (15 frets of 36-edo is ~~as long as 5~~ frets of 12-edo~~, so none of those stretches are unreachable except near the nut~~.)		Among the possible [[skip fretting]] systems for 72-edo, the 27\72 x 2\72 (or equivalently, 4.5\12 x 1\36) system is especially convenient because every ratio in the 31-limit group sans 21 can be played within a block 4 strings wide by 17 frets long. (17 frets of 36-edo is shorter than 6 frets of 12-edo.)

	The same advantage holds for the 29\72 x 2\72 skip-fretting system, but fourths on adjacent strings are hard to play in that system, because the player must bend one note while playing an adjacent string at the same fret.		The same advantage holds for the 29\72 x 2\72 skip-fretting system, but fourths on adjacent strings are hard to play in that system, because the player must bend one note while playing an adjacent string at the same fret.

Jeff Brown: Clarify a sentence

2021-07-11T14:15:40Z

Clarify a sentence

← Older revision		Revision as of 14:15, 11 July 2021
Line 9:		Line 9:
	Among the possible [[skip fretting]] systems for 72-edo, the 27\72 x 2\72 (or equivalently, 4.5\12 x 1\36) system is especially convenient because every ratio in the 31-limit group sans 21 can be played within a block 4 strings wide by 15 frets long. (15 frets of 36-edo is as long as 5 frets of 12-edo, so none of those stretches are unreachable except near the nut.)		Among the possible [[skip fretting]] systems for 72-edo, the 27\72 x 2\72 (or equivalently, 4.5\12 x 1\36) system is especially convenient because every ratio in the 31-limit group sans 21 can be played within a block 4 strings wide by 15 frets long. (15 frets of 36-edo is as long as 5 frets of 12-edo, so none of those stretches are unreachable except near the nut.)

	The same ~~is true~~ for the 29\72 x 2\72 skip-fretting system, but fourths on adjacent strings are hard to play in that system, because the player must bend one note while playing an adjacent string at the same fret.		The same advantage holds for the 29\72 x 2\72 skip-fretting system, but fourths on adjacent strings are hard to play in that system, because the player must bend one note while playing an adjacent string at the same fret.

	Here is where all the primes intervals through 31 lie:		Here is where all the primes intervals through 31 lie:

Jeff Brown: Fix a typo -- 12-edo has a sharp 5:4, not a flat one.

2021-07-11T14:13:41Z

Fix a typo -- 12-edo has a *sharp* 5:4, not a flat one.

← Older revision		Revision as of 14:13, 11 July 2021
Line 3:		Line 3:
	The resulting range across six strings is 2250 cents -- close to the 2-octave spread on a 12-edo guitar in standard tuning.		The resulting range across six strings is 2250 cents -- close to the 2-octave spread on a 12-edo guitar in standard tuning.

	72-edo approximates the 11-limit astoundingly well, and is quite good in higher limits too. 36-edo, by contrast, has a 5:4 that's 14 cents ~~flat~~ (identical to 12-edo's), and an 11:8 that's 15 cents sharp.		72-edo approximates the 11-limit astoundingly well, and is quite good in higher limits too. 36-edo, by contrast, has a 5:4 that's 14 cents sharp (identical to 12-edo's), and an 11:8 that's 15 cents sharp.

	But whereas a 72-edo guitar would not be, a 36-edo guitar is playable. Neil Haverstick does it.		But whereas a 72-edo guitar would not be, a 36-edo guitar is playable. Neil Haverstick does it.

Jeff Brown: delete a duplicate row

2021-07-11T02:17:04Z

delete a duplicate row

← Older revision		Revision as of 02:17, 11 July 2021
Line 16:		Line 16:
	! note		! note
	! fretboard position		! fretboard position
	\|-
	~~\| 0 steps = 1 % 1~~
	~~\| string 0 fret 0~~
	\|-		\|-
	\| 0 steps = 1 % 1		\| 0 steps = 1 % 1

Jeff Brown: start

2021-07-11T02:16:02Z

start

New page

One way to play 72-edo on a 36-edo guitar is to tune each pair of adjacent strings 450 cents apart. The equivalent tuning on a grid controller would be for notes to rise by 2\72 (33.3 cents) along each column and by 27\72 (450 cents) along each row.

The resulting range across six strings is 2250 cents -- close to the 2-octave spread on a 12-edo guitar in standard tuning.

72-edo approximates the 11-limit astoundingly well, and is quite good in higher limits too. 36-edo, by contrast, has a 5:4 that's 14 cents flat (identical to 12-edo's), and an 11:8 that's 15 cents sharp.

But whereas a 72-edo guitar would not be, a 36-edo guitar is playable. Neil Haverstick does it.

Among the possible [[skip fretting]] systems for 72-edo, the 27\72 x 2\72 (or equivalently, 4.5\12 x 1\36) system is especially convenient because every ratio in the 31-limit group sans 21 can be played within a block 4 strings wide by 15 frets long. (15 frets of 36-edo is as long as 5 frets of 12-edo, so none of those stretches are unreachable except near the nut.)

The same is true for the 29\72 x 2\72 skip-fretting system, but fourths on adjacent strings are hard to play in that system, because the player must bend one note while playing an adjacent string at the same fret.

Here is where all the primes intervals through 31 lie:

{| class="wikitable"
! note
! fretboard position
|-
| 0 steps = 1 % 1
| string 0 fret 0
|-
| 0 steps = 1 % 1
| string 0 fret 0
|-
| 72 steps = 2 % 1
| string 2 fret 9
|-
| 42 steps = 3 % 2
| string 2 fret - 6
|-
| 23 steps = 5 % 4
| string 1 fret - 2
|-
| 58 steps = 7 % 4
| string 2 fret 2
|-
| 12 steps = 9 % 8
| string 0 fret 6
|-
| 33 steps =11 % 8
| string 1 fret 3
|-
| 50 steps =13 % 8
| string 2 fret - 2
|-
| 65 steps =15 % 8
| string 3 fret -8
|-
| 6 steps =17 % 16
| string 0 fret 3
|-
| 18 steps =19 % 16
| string 0 fret 9
|-
| 28 steps =21 % 16
| string 0 fret 14, or string 2 fret -13, or bend up 1\72 from string 1 fret 0.
|-
| 38 steps =23 % 16
| string 2 fret -8
|-
| 46 steps =25 % 16
| string 2 fret -4
|-
| 54 steps =27 % 16
| string 2 fret 0
|-
| 62 steps =29 % 16
| string 2 fret 4
|-
| 69 steps =31 % 16
| string 3 fret -6
|}

From these, the location of any compound intervals N can be added by vector-summing the string-fret positions of N's factors. See [[Skip fretting system 48 2 13]] for details on how that's done.

[[Category:Skip fretting]]

Skip fretting system 72 2 27 - Revision history

BudjarnLambeth at 04:52, 27 April 2025

BudjarnLambeth at 04:52, 27 April 2025

BudjarnLambeth: Add links

TallKite: TallKite moved page Skip fretting system 72 2 27, a.k.a. Isomorphic grid layout 27\72 x 2\72 to Skip fretting system 72 2 27

Jeff Brown: Correct an errant plural.

Jeff Brown: Fix a typo -- I had misrecorded the size of the string x fret block of 31-limit ratios as 4x15, but that's the size of the 13-limit block The 31-limit block is a little bigger.

Jeff Brown: Clarify a sentence

Jeff Brown: Fix a typo -- 12-edo has a *sharp* 5:4, not a flat one.

Jeff Brown: delete a duplicate row

Jeff Brown: start

Jeff Brown: Fix a typo -- 12-edo has a sharp 5:4, not a flat one.