Skip fretting system 58 2 15 - Revision history

Jeff Brown: /* Where the lowest harmonics lie */

2023-05-10T16:52:09Z

Where the lowest harmonics lie

← Older revision		Revision as of 16:52, 10 May 2023
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	== Where the lowest harmonics lie ==		== Where the lowest harmonics lie ==

	~~In the~~ diagram the ~~strings are vertical and~~ the ~~frets are horizontal~~. 1 represents octave equivalents of the root, 3 represents octave equivalents of the 3rd harmonic (3:2, 3:1, 3:4, etc.), etc.		The diagram below (or at right, or somewhere) is of a hypothetical 12-string guitar in this tuning. It shows where each of the odd harmonics through the 29th lies. 1 represents octave equivalents of the root, 3 represents octave equivalents of the 3rd harmonic (3:2, 3:1, 3:4, etc.), etc.
	[[File:58-edo 15x2.png\|thumb\|Where the harmonics lie in the 15\58 x 2\58 isomorphic layout]]		[[File:58-edo 15x2.png\|thumb\|Where the harmonics lie in the 15\58 x 2\58 isomorphic layout]]

Jeff Brown: /* Where the lowest harmonics lie */

2023-05-10T16:33:19Z

Where the lowest harmonics lie

← Older revision		Revision as of 16:33, 10 May 2023
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	== Where the lowest harmonics lie ==		== Where the lowest harmonics lie ==

	In the ~~folowing~~ the strings are vertical and the frets are horizontal. 1 represents octave equivalents of the root, 3 represents octave equivalents of the 3rd harmonic (3:2, 3:1, 3:4, etc.), etc.		In the diagram the strings are vertical and the frets are horizontal. 1 represents octave equivalents of the root, 3 represents octave equivalents of the 3rd harmonic (3:2, 3:1, 3:4, etc.), etc.
	[[File:58-edo 15x2.png\|thumb\|Where the harmonics lie in the 15\58 x 2\58 isomorphic layout]]		[[File:58-edo 15x2.png\|thumb\|Where the harmonics lie in the 15\58 x 2\58 isomorphic layout]]

Jeff Brown: Replace some text with a picture that makes it clearer, and adjust the remaining text a little.

2023-05-10T16:32:32Z

Replace some text with a picture that makes it clearer, and adjust the remaining text a little.

@@ Line 4: / Line 4: @@
-== Where the first primes intervals lie ==
+== Where the lowest harmonics lie ==
 In the folowing the strings are vertical and the frets are horizontal. 1 represents octave equivalents of the root, 3 represents octave equivalents of the 3rd harmonic (3:2, 3:1, 3:4, etc.), etc.
-                  headstock on this side
+Since 58-edo is consistent in the 17-limit + 29 group, the location of any interval in that group can be determined from the corresponding harmonics. (For instance, to rise by 7:5, go up two strings and down one fret, because that takes you from harmonic 5 to harmonic 7.)
 == Adaptation to Mystery Temperament ==

Jeff Brown at 21:03, 23 April 2023

2023-04-23T21:03:40Z

@@ Line 3: / Line 3: @@
 Among the possible [[skip fretting]] systems for 58-edo, the (58,2,15) system is especially convenient in that every 7-limit interval spans at most 3 frets, and every interval in the 2.3.5.7.13.23 subgroupspans at most 4 frets. As it makes it particularly easy to play music composed using [[myna]] temperament, it could also be called a myna guitar.
-Here is where all the primes intervals in the (58,2,15) system lie:
 {| class="wikitable"

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

2023-04-22T08:48:13Z

Categories, list temperament that makes this layout work well.

← Older revision		Revision as of 08:48, 22 April 2023
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	One way to play 58-edo on a 29-edo guitar is to tune each pair of adjacent strings 15\58 apart. That's about 310.3 cents, or 5.3 cents flat of 6:5.		One way to play 58-edo on a 29-edo guitar is to tune each pair of adjacent strings 15\58 apart. That's about 310.3 cents, or 5.3 cents flat of 6:5.

	Among the possible [[skip fretting]] systems for 58-edo, the (58,2,15) system is especially convenient in that every 7-limit interval spans at most 3 frets, and every interval in the 2.3.5.7.13.23 subgroupspans at most 4 frets.		Among the possible [[skip fretting]] systems for 58-edo, the (58,2,15) system is especially convenient in that every 7-limit interval spans at most 3 frets, and every interval in the 2.3.5.7.13.23 subgroupspans at most 4 frets. As it makes it particularly easy to play music composed using [[myna]] temperament, it could also be called a myna guitar.

	Here is where all the primes intervals in the (58,2,15) system lie:		Here is where all the primes intervals in the (58,2,15) system lie:
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	The [[Kite Guitar]] uses 20.5 frets per octave to make a 41-edo instrument, and its frets are wide enough to be quite playable. If a standard guitar's scale length is 25", then an instrument using the 15\58 x 2\58 tuning described in this article would have a minimum fret width equal to the Kite Guitar's if it had a scale length of 25" * 29 / 20.5 = 35.4 inches. That is, while a 29-edo guitar might be difficult to play, a long-scale tapping instrument in 29-edo would be as playable as a Kite Guitar. (The most well-known tapping instrument, the Chapman Stick, has a scale length of 36".)		The [[Kite Guitar]] uses 20.5 frets per octave to make a 41-edo instrument, and its frets are wide enough to be quite playable. If a standard guitar's scale length is 25", then an instrument using the 15\58 x 2\58 tuning described in this article would have a minimum fret width equal to the Kite Guitar's if it had a scale length of 25" * 29 / 20.5 = 35.4 inches. That is, while a 29-edo guitar might be difficult to play, a long-scale tapping instrument in 29-edo would be as playable as a Kite Guitar. (The most well-known tapping instrument, the Chapman Stick, has a scale length of 36".)

	[[Category:Skip fretting]]		[[Category:Skip fretting]] [[Category:58edo]] [[Category:Myna]]

Jeff Brown: add a section, comparing to the Kite Guitar

2022-03-06T12:15:06Z

add a section, comparing to the Kite Guitar

← Older revision		Revision as of 12:15, 6 March 2022
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	A 29-edo guitar is not much easier to play than a 31-edo guitar. In particular you'll need to use your fingernail to fret the highest notes. A skip-fretting system is substantially more confusing than one that includes every note. While 58-edo is more faithful to the harmonic series, 31-edo is nonetheless exceptionally good.		A 29-edo guitar is not much easier to play than a 31-edo guitar. In particular you'll need to use your fingernail to fret the highest notes. A skip-fretting system is substantially more confusing than one that includes every note. While 58-edo is more faithful to the harmonic series, 31-edo is nonetheless exceptionally good.

			== Comparison to the Kite tuning ==

			The [[Kite Guitar]] uses 20.5 frets per octave to make a 41-edo instrument, and its frets are wide enough to be quite playable. If a standard guitar's scale length is 25", then an instrument using the 15\58 x 2\58 tuning described in this article would have a minimum fret width equal to the Kite Guitar's if it had a scale length of 25" * 29 / 20.5 = 35.4 inches. That is, while a 29-edo guitar might be difficult to play, a long-scale tapping instrument in 29-edo would be as playable as a Kite Guitar. (The most well-known tapping instrument, the Chapman Stick, has a scale length of 36".)

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

X31eq: Added reference to mystery temperament

2021-05-16T07:08:36Z

Added reference to mystery temperament

← Older revision		Revision as of 07:08, 16 May 2021
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	From these, the location of any compound interval can be added by vector-summing the string-fret positions of the interval's factors. See [[Skip fretting system 48 2 13]] for details on how that's done.		From these, the location of any compound interval can be added by vector-summing the string-fret positions of the interval's factors. See [[Skip fretting system 48 2 13]] for details on how that's done.

			== Adaptation to Mystery Temperament ==

			The same guitar with 29-edo frets can be played in an arbitrary [[Mystery\|mystery temperament]] by retuning adjacent strings to alternating tunings. For example, 315 cents as the approximate 6:5 and 306 cents as the residue to make skip strings 15 steps of 29-edo. Such a tuning gives improved approximations to just intonation at the expense of half of all intervals and half of all chords being incorrect and more out of tune then 58-edo.

	== Comparison to 31-edo ==		== Comparison to 31-edo ==

Xenwolf: add category

2021-05-02T16:58:18Z

add category

← Older revision		Revision as of 16:58, 2 May 2021
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	A 29-edo guitar is not much easier to play than a 31-edo guitar. In particular you'll need to use your fingernail to fret the highest notes. A skip-fretting system is substantially more confusing than one that includes every note. While 58-edo is more faithful to the harmonic series, 31-edo is nonetheless exceptionally good.		A 29-edo guitar is not much easier to play than a 31-edo guitar. In particular you'll need to use your fingernail to fret the highest notes. A skip-fretting system is substantially more confusing than one that includes every note. While 58-edo is more faithful to the harmonic series, 31-edo is nonetheless exceptionally good.

			[[Category:Skip fretting]]

Jeff Brown: Compare to 31-edo

2021-05-02T03:29:25Z

Compare to 31-edo

← Older revision		Revision as of 03:29, 2 May 2021
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	Among the possible [[skip fretting]] systems for 58-edo, the (58,2,15) system is especially convenient in that every 7-limit interval spans at most 3 frets, and every interval in the 2.3.5.7.13.23 subgroupspans at most 4 frets.		Among the possible [[skip fretting]] systems for 58-edo, the (58,2,15) system is especially convenient in that every 7-limit interval spans at most 3 frets, and every interval in the 2.3.5.7.13.23 subgroupspans at most 4 frets.

	Here is where all the primes intervals lie:		Here is where all the primes intervals in the (58,2,15) system lie:

	{\| class="wikitable"		{\| class="wikitable"
Line 47:		Line 47:

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

			== Comparison to 31-edo ==

			A 29-edo guitar is not much easier to play than a 31-edo guitar. In particular you'll need to use your fingernail to fret the highest notes. A skip-fretting system is substantially more confusing than one that includes every note. While 58-edo is more faithful to the harmonic series, 31-edo is nonetheless exceptionally good.

Jeff Brown: start page

2021-05-02T03:24:53Z

start page

New page

One way to play 58-edo on a 29-edo guitar is to tune each pair of adjacent strings 15\58 apart. That's about 310.3 cents, or 5.3 cents flat of 6:5.

Among the possible [[skip fretting]] systems for 58-edo, the (58,2,15) system is especially convenient in that every 7-limit interval spans at most 3 frets, and every interval in the 2.3.5.7.13.23 subgroupspans at most 4 frets.

Here is where all the primes intervals lie:

{| class="wikitable"
! note
! fretboard position
|-
| 0 steps = 1 % 1
| string 0 fret 0
|-
| 58 steps = 2 % 1
| string 4 fret - 1
|-
| 34 steps = 3 % 2
| string 2 fret 2
|-
| 19 steps = 5 % 4
| string 1 fret 2
|-
| 47 steps = 7 % 4
| string 3 fret 1
|-
| 27 steps = 11 % 8
| string 1 fret 6
|-
| 41 steps = 13 % 8
| string 3 fret - 2
|-
| 5 steps = 17 % 16
| string - 1 fret 10
|-
| 14 steps = 19 % 16
| string 0 fret 7
|-
| 30 steps = 23 % 16
| string 2 fret 0
|-
| 50 steps = 29 % 16
| string 2 fret 10
|-
| 55 steps = 31 % 16
| string 3 fret 5
|}

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