Skip fretting system 53 3 17 - Revision history

TallKite: TallKite moved page 17\53 x 3\53 isomorphic layout to Skip fretting system 53 3 17

2024-03-22T20:16:42Z

TallKite moved page 17\53 x 3\53 isomorphic layout to Skip fretting system 53 3 17

← Older revision	Revision as of 20:16, 22 March 2024
(No difference)

TallKite: category

2024-03-22T20:15:05Z

Jeff Brown: /* The (few?) difficult ratios have easy octave counterparts */

2023-08-24T02:36:00Z

The (few?) difficult ratios have easy octave counterparts

← Older revision		Revision as of 02:36, 24 August 2023
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	== The (few?) difficult ratios have easy octave counterparts ==		== The (few?) harmonically difficult ratios have easy octave counterparts ==
	One notable drawback to this tuning that, because harmonics 3 and 7 lie on the same string, a harmonic 7:6 is difficult to play. (Doing so requires reaching back 13 frets, or 883 cents, and across three strings.) However, the ratio 7:3 (an octave wider than 7:6) is unusually easy to play, being 3 string crossings and 1 fret wide. Following the same logic, for every difficult interval R less than an octave, it can be shown that R plus an octave is easy to play.		One notable drawback to this tuning that, because harmonics 3 and 7 lie on the same string, a harmonic 7:6 is difficult to play. (Doing so requires reaching back 13 frets, or 883 cents, and across three strings.) However, the ratio 7:3 (an octave wider than 7:6) is unusually easy to play, being 3 string crossings and 1 fret wide. Following the same logic, for every difficult interval R less than an octave, it can be shown that R plus an octave is easy to play.

Jeff Brown: /* The few difficult ratios have easy octave counterparts */

2023-08-24T02:35:34Z

The few difficult ratios have easy octave counterparts

← Older revision		Revision as of 02:35, 24 August 2023
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	== The few difficult ratios have easy octave counterparts ==		== The (few?) difficult ratios have easy octave counterparts ==
	One notable drawback to this tuning that, because harmonics 3 and 7 lie on the same string, a harmonic 7:6 is difficult to play. (Doing so requires reaching back 13 frets, or 883 cents, and across three strings.) However, the ratio 7:3 (an octave wider than 7:6) is unusually easy to play, being 3 string crossings and 1 fret wide. Following the same logic, for every difficult interval R less than an octave, it can be shown that R plus an octave is easy to play. There seem to be very few such difficult ratios in the 15-limit. I (Jeff Brown) only see five: 7:6, 13:12, 14:13, 9:8, and 11:9.		One notable drawback to this tuning that, because harmonics 3 and 7 lie on the same string, a harmonic 7:6 is difficult to play. (Doing so requires reaching back 13 frets, or 883 cents, and across three strings.) However, the ratio 7:3 (an octave wider than 7:6) is unusually easy to play, being 3 string crossings and 1 fret wide. Following the same logic, for every difficult interval R less than an octave, it can be shown that R plus an octave is easy to play.

			There seem to be very few such difficult ratios in the 15-limit. I (Jeff Brown) only see five: 7:6, 13:12, 14:13, 9:8, and 11:9.

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

Jeff Brown at 02:26, 24 August 2023

2023-08-24T02:26:27Z

← Older revision		Revision as of 02:26, 24 August 2023
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	This layout allows someone to play in 53-edo on a 17.666-edo guitar, by tuning the guitar in major thirds -- that is, with 17\53 between each pair of adjacent strings. It offers a big range -- very slightly wider than the [[Kite Guitar]]'s -- and a playable layout, with strikingly easy 5-limit chords.		This layout allows someone to play in 53-edo on a 17.666-edo guitar, by tuning the guitar in major thirds -- that is, with 17\53 between each pair of adjacent strings. It offers a big range -- very slightly wider than the [[Kite Guitar]]'s -- and a playable layout, with strikingly easy 5-limit chords.

	The diagram below, which could be interpreted 20 frets of a 12-string guitar, shows where each of the 15-limit harmonics lies. Since 53-edo is mostly (see below) for the exception ~~consistent in the 15-limit~~, these harmonics' positions imply where every interval in that group lies. (For instance, to play 7/6 ~~you move~~ up one string and down one fret~~, because that takes you from harmonic 3 to harmonic 7.) Octaves are indicated as powers of 2 (specifically 1, 2, 4 and 8)~~.		The diagram below, which could be interpreted 20 frets of a 12-string guitar, shows where each of the 15-limit harmonics lies. Since 53-edo is mostly consistent in the 15-limit (see below for the exception), these harmonics' positions imply where every interval in that group lies. For instance, to play 6:5 requires moving up (toward the treble side) one string and down (toward the nut) one fret.

	The exception to the above ~~consistency rule of thumb~~ is the ratios 11/7 (and its octave-complement 14/11). Since 11:8 is 7.9 cents flat and 7:4 is 4.8 cents sharp in 53-edo, the distance between them is 7.9 + 4.8 = 12.7 cents too wide. 12.7 cents is more than half of 53-edo's step size of 22.6 cents. Thus whereas the diagram below ~~suggests~~ that 11:7 is 34 steps wide, in fact 53-edo's best approximation to 11:7 is 35 steps wide. But ~~that best approximation is still 10 cents sharp, so~~ both approximations are ~~roughly~~ equally wrong, just in opposite directions.		The only exception to the above procedure is the ratios 11/7 (and its octave-complement 14/11). Since 11:8 is 7.9 cents flat and 7:4 is 4.8 cents sharp in 53-edo, the distance between them is 7.9 + 4.8 = 12.7 cents too wide. 12.7 cents is more than half of 53-edo's step size of 22.6 cents. Thus whereas the best approximations to 11:8 and 7:4 (and hence the diagram below) suggest that 11:7 is 34 steps wide, in fact 53-edo's best approximation to 11:7 is 35 steps wide. But both approximations are almost equally wrong, just in opposite directions.

	20 frets of a hypothetical 12-string guitar tuned this way:		20 frets of a hypothetical 12-string guitar tuned this way:

Jeff Brown: elaborate on the silver lining

2023-08-24T02:22:01Z

elaborate on the silver lining

← Older revision		Revision as of 02:22, 24 August 2023
Line 1:		Line 1:
	This layout allows someone to play in 53-edo on a 17.666-edo guitar, by tuning the guitar in major thirds -- that is, with 17\53 between each pair of adjacent strings. It offers a big range -- very slightly wider than the [[Kite Guitar]]'s -- and a playable layout, with strikingly easy 5-limit chords.		This layout allows someone to play in 53-edo on a 17.666-edo guitar, by tuning the guitar in major thirds -- that is, with 17\53 between each pair of adjacent strings. It offers a big range -- very slightly wider than the [[Kite Guitar]]'s -- and a playable layout, with strikingly easy 5-limit chords.

	One notable drawback is that, because harmonics 3 and 7 lie on the same string, a harmonic 7:6 is difficult to play. (Doing so requires reaching back 13 frets, or 883 cents, as well as across three strings.) Perhaps counter-intuitively, 12:7, the octave-complement of 7:6, is much easier to play, requiring a stretch of only 9 frets or 611 cents. However, for exactly the same reason, the ratio 7:3 (an octave wider than 7:6) is extremely easy to play, being 3 string crossings and 1 fret wide.

	The diagram below, which could be interpreted 20 frets of a 12-string guitar, shows where each of the 15-limit harmonics lies. Since 53-edo is mostly (see below) for the exception consistent in the 15-limit, these harmonics' positions imply where every interval in that group lies. (For instance, to play 7/6 you move up one string and down one fret, because that takes you from harmonic 3 to harmonic 7.) Octaves are indicated as powers of 2 (specifically 1, 2, 4 and 8).		The diagram below, which could be interpreted 20 frets of a 12-string guitar, shows where each of the 15-limit harmonics lies. Since 53-edo is mostly (see below) for the exception consistent in the 15-limit, these harmonics' positions imply where every interval in that group lies. (For instance, to play 7/6 you move up one string and down one fret, because that takes you from harmonic 3 to harmonic 7.) Octaves are indicated as powers of 2 (specifically 1, 2, 4 and 8).
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			== The few difficult ratios have easy octave counterparts ==
			One notable drawback to this tuning that, because harmonics 3 and 7 lie on the same string, a harmonic 7:6 is difficult to play. (Doing so requires reaching back 13 frets, or 883 cents, and across three strings.) However, the ratio 7:3 (an octave wider than 7:6) is unusually easy to play, being 3 string crossings and 1 fret wide. Following the same logic, for every difficult interval R less than an octave, it can be shown that R plus an octave is easy to play. There seem to be very few such difficult ratios in the 15-limit. I (Jeff Brown) only see five: 7:6, 13:12, 14:13, 9:8, and 11:9.

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

Jeff Brown: Note a happy counterweight to the 7:6 flaw

2023-08-24T01:49:56Z

Note a happy counterweight to the 7:6 flaw

← Older revision		Revision as of 01:49, 24 August 2023
Line 1:		Line 1:
	This layout allows someone to play in 53-edo on a 17.666-edo guitar, by tuning the guitar in major thirds -- that is, with 17\53 between each pair of adjacent strings. It offers a big range -- very slightly wider than the [[Kite Guitar]]'s -- and a playable layout, with strikingly easy 5-limit chords.		This layout allows someone to play in 53-edo on a 17.666-edo guitar, by tuning the guitar in major thirds -- that is, with 17\53 between each pair of adjacent strings. It offers a big range -- very slightly wider than the [[Kite Guitar]]'s -- and a playable layout, with strikingly easy 5-limit chords.

	~~An important~~ drawback is that, because harmonics 3 and 7 lie on the same string, a harmonic 7:6 is difficult to play. (Doing so requires reaching back 13 frets, or 883 cents, as well as across three strings.) Perhaps counter-intuitively, 12:7, the octave-complement of 7:6, is much easier to play, requiring a stretch of only 9 frets or 611 cents.		One notable drawback is that, because harmonics 3 and 7 lie on the same string, a harmonic 7:6 is difficult to play. (Doing so requires reaching back 13 frets, or 883 cents, as well as across three strings.) Perhaps counter-intuitively, 12:7, the octave-complement of 7:6, is much easier to play, requiring a stretch of only 9 frets or 611 cents. However, for exactly the same reason, the ratio 7:3 (an octave wider than 7:6) is extremely easy to play, being 3 string crossings and 1 fret wide.

	The diagram below, which could be interpreted 20 frets of a 12-string guitar, shows where each of the 15-limit harmonics lies. Since 53-edo is mostly (see below) for the exception consistent in the 15-limit, these harmonics' positions imply where every interval in that group lies. (For instance, to play 7/6 you move up one string and down one fret, because that takes you from harmonic 3 to harmonic 7.) Octaves are indicated as powers of 2 (specifically 1, 2, 4 and 8).		The diagram below, which could be interpreted 20 frets of a 12-string guitar, shows where each of the 15-limit harmonics lies. Since 53-edo is mostly (see below) for the exception consistent in the 15-limit, these harmonics' positions imply where every interval in that group lies. (For instance, to play 7/6 you move up one string and down one fret, because that takes you from harmonic 3 to harmonic 7.) Octaves are indicated as powers of 2 (specifically 1, 2, 4 and 8).

Jeff Brown at 01:34, 24 August 2023

2023-08-24T01:34:01Z

← Older revision		Revision as of 01:34, 24 August 2023
Line 1:		Line 1:
	This layout allows someone to play in 53-edo on a 17.666-edo guitar, by tuning the guitar in major thirds -- that is, with 17\53 between each pair of adjacent strings. It offers a big range -- very slightly wider than the [[Kite Guitar]]'s -- and a playable layout, with strikingly easy 5-limit chords.		This layout allows someone to play in 53-edo on a 17.666-edo guitar, by tuning the guitar in major thirds -- that is, with 17\53 between each pair of adjacent strings. It offers a big range -- very slightly wider than the [[Kite Guitar]]'s -- and a playable layout, with strikingly easy 5-limit chords.

	An important drawback is that harmonics 3 and 7 lie on the same string, ~~making~~ a harmonic 7:6 difficult to play. (Doing so requires reaching across three strings ~~and down 13 frets~~.) ~~The~~ octave-complement of 7/6, ~~12/7~~, ~~is similarly difficult~~.		An important drawback is that, because harmonics 3 and 7 lie on the same string, a harmonic 7:6 is difficult to play. (Doing so requires reaching back 13 frets, or 883 cents, as well as across three strings.) Perhaps counter-intuitively, 12:7, the octave-complement of 7:6, is much easier to play, requiring a stretch of only 9 frets or 611 cents.

	The diagram below, which could be interpreted 20 frets of a 12-string guitar, shows where each of the 15-limit harmonics lies. Since 53-edo is mostly (see below) for the exception consistent in the 15-limit, these harmonics' positions imply where every interval in that group lies. (For instance, to play 7/6 you move up one string and down one fret, because that takes you from harmonic 3 to harmonic 7.) Octaves are indicated as powers of 2 (specifically 1, 2, 4 and 8).		The diagram below, which could be interpreted 20 frets of a 12-string guitar, shows where each of the 15-limit harmonics lies. Since 53-edo is mostly (see below) for the exception consistent in the 15-limit, these harmonics' positions imply where every interval in that group lies. (For instance, to play 7/6 you move up one string and down one fret, because that takes you from harmonic 3 to harmonic 7.) Octaves are indicated as powers of 2 (specifically 1, 2, 4 and 8).

	The exception to the above consistency rule of thumb is the ratios 11/7 (and its octave-complement 14/11). Since 11:8 is 7.9 cents flat and 7:4 is 4.8 cents sharp in 53-edo, the distance between them is 7.9 + 4.8 = 12.7 cents too wide. 12.7 cents is more than half of 53-edo's step size of 22.6 cents. Thus whereas the diagram below suggests that 11:7 is 34 steps wide, in fact 53-edo's best approximation to 11:7 is 35 steps wide. But that best approximation is still 10 cents sharp, so both approximations are roughly equally wrong, just in opposite directions.		The exception to the above consistency rule of thumb is the ratios 11/7 (and its octave-complement 14/11). Since 11:8 is 7.9 cents flat and 7:4 is 4.8 cents sharp in 53-edo, the distance between them is 7.9 + 4.8 = 12.7 cents too wide. 12.7 cents is more than half of 53-edo's step size of 22.6 cents. Thus whereas the diagram below suggests that 11:7 is 34 steps wide, in fact 53-edo's best approximation to 11:7 is 35 steps wide. But that best approximation is still 10 cents sharp, so both approximations are roughly equally wrong, just in opposite directions.

	20 frets of a hypothetical 12-string guitar tuned this way:		20 frets of a hypothetical 12-string guitar tuned this way:

Jeff Brown: Note a drawback.

2023-08-24T01:26:49Z

Note a drawback.

← Older revision		Revision as of 01:26, 24 August 2023
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	This layout allows someone to play in 53-edo on a 17.666-edo guitar, by tuning the guitar in major thirds -- that is, with 17\53 between each pair of adjacent strings.		This layout allows someone to play in 53-edo on a 17.666-edo guitar, by tuning the guitar in major thirds -- that is, with 17\53 between each pair of adjacent strings. It offers a big range -- very slightly wider than the [[Kite Guitar]]'s -- and a playable layout, with strikingly easy 5-limit chords.

			An important drawback is that harmonics 3 and 7 lie on the same string, making a harmonic 7:6 difficult to play. (Doing so requires reaching across three strings and down 13 frets.) The octave-complement of 7/6, 12/7, is similarly difficult.

	The diagram below, which could be interpreted 20 frets of a 12-string guitar, shows where each of the 15-limit harmonics lies. Since 53-edo is mostly (see below) for the exception consistent in the 15-limit, these harmonics' positions imply where every interval in that group lies. (For instance, to play 7/6 you move up one string and down one fret, because that takes you from harmonic 3 to harmonic 7.) Octaves are indicated as powers of 2 (specifically 1, 2, 4 and 8).		The diagram below, which could be interpreted 20 frets of a 12-string guitar, shows where each of the 15-limit harmonics lies. Since 53-edo is mostly (see below) for the exception consistent in the 15-limit, these harmonics' positions imply where every interval in that group lies. (For instance, to play 7/6 you move up one string and down one fret, because that takes you from harmonic 3 to harmonic 7.) Octaves are indicated as powers of 2 (specifically 1, 2, 4 and 8).

Fredg999: Categories

2023-08-24T01:20:37Z

← Older revision		Revision as of 20:15, 22 March 2024
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	There seem to be very few such difficult ratios in the 15-limit. I (Jeff Brown) only see five: 7:6, 13:12, 14:13, 9:8, and 11:9.		There seem to be very few such difficult ratios in the 15-limit. I (Jeff Brown) only see five: 7:6, 13:12, 14:13, 9:8, and 11:9.

	[[Category:Skip fretting]]		[[Category:Skip fretting]] [[Category:53edo]]

← Older revision		Revision as of 01:20, 24 August 2023
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			[[Category:Skip fretting]]