Skip fretting system 53 3 14 - Revision history

Yourmusic Productions: Fix math error, remove depreciated temperament name.

2025-10-07T11:30:07Z

Fix math error, remove depreciated temperament name.

← Older revision		Revision as of 11:30, 7 October 2025
Line 1:		Line 1:
	A good way to play 53-edo on a 17.66-edo guitar (effectively 28edt, or an 18edo guitar with the intonation on the [[Moving_the_bridge_hack\|bridge shifted forwards]] so the third harmonic and the 28th fret sound the same note.) is to tune each pair of adjacent strings 14\43 apart. (That's 317 cents, a bit sharp of [[6/5]].) This is probably best accomplished by ear via fretting a string at the 13th fret and then tuning it to an octave above the one below.		A good way to play 53-edo on a 17.66-edo guitar (effectively [[28edt]], or an [[18edo]] guitar with the intonation on the [[Moving_the_bridge_hack\|bridge shifted forwards]] so the third harmonic and the 28th fret sound the same note.) is to tune each pair of adjacent strings 14\53 apart. (That's 317 cents, a bit sharp of [[6/5]].) This is probably best accomplished by ear via fretting a string at the 13th fret and then tuning it to an octave above the one below.

	Among the possible [[skip fretting]] systems for 53-edo, the (53,3,14) system is especially effective because every ratio in the 2.3.5.13 subgroup can be reached with a stretch of 4 frets or less. Conveniently, this is also the subgroup 53edo is best tuned in, with less than 3 cents error, audibly indistinguishable from just intonation, making the most in tune harmonies also the easiest to play. For this reason, it could also be called a [[Kleismic_family#Catakleismic\|catakleismic~~]] or [[The_Archipelago#Trinidad_aka_cata\|Trinidad~~]] guitar, as it's optimised for playing music in ~~those temperaments~~.		Among the possible [[skip fretting]] systems for 53-edo, the (53,3,14) system is especially effective because every ratio in the 2.3.5.13 subgroup can be reached with a stretch of 4 frets or less. Conveniently, this is also the subgroup 53edo is best tuned in, with less than 3 cents error, audibly indistinguishable from just intonation, making the most in tune harmonies also the easiest to play. For this reason, it could also be called a [[Kleismic_family#Catakleismic\|catakleismic]] guitar, as it's optimised for playing music in that temperament.

Dave Keenan: Corrected spelling from "cataklesmic" to "catakleismic".

2023-04-09T22:59:39Z

Corrected spelling from "cataklesmic" to "catakleismic".

← Older revision		Revision as of 22:59, 9 April 2023
Line 1:		Line 1:
	A good way to play 53-edo on a 17.66-edo guitar (effectively 28edt, or an 18edo guitar with the intonation on the [[Moving_the_bridge_hack\|bridge shifted forwards]] so the third harmonic and the 28th fret sound the same note.) is to tune each pair of adjacent strings 14\43 apart. (That's 317 cents, a bit sharp of [[6/5]].) This is probably best accomplished by ear via fretting a string at the 13th fret and then tuning it to an octave above the one below.		A good way to play 53-edo on a 17.66-edo guitar (effectively 28edt, or an 18edo guitar with the intonation on the [[Moving_the_bridge_hack\|bridge shifted forwards]] so the third harmonic and the 28th fret sound the same note.) is to tune each pair of adjacent strings 14\43 apart. (That's 317 cents, a bit sharp of [[6/5]].) This is probably best accomplished by ear via fretting a string at the 13th fret and then tuning it to an octave above the one below.

	Among the possible [[skip fretting]] systems for 53-edo, the (53,3,14) system is especially effective because every ratio in the 2.3.5.13 subgroup can be reached with a stretch of 4 frets or less. Conveniently, this is also the subgroup 53edo is best tuned in, with less than 3 cents error, audibly indistinguishable from just intonation, making the most in tune harmonies also the easiest to play. For this reason, it could also be called a [[Kleismic_family#Catakleismic\|~~cataklesmic~~]] or [[The_Archipelago#Trinidad_aka_cata\|Trinidad]] guitar, as it's optimised for playing music in those temperaments.		Among the possible [[skip fretting]] systems for 53-edo, the (53,3,14) system is especially effective because every ratio in the 2.3.5.13 subgroup can be reached with a stretch of 4 frets or less. Conveniently, this is also the subgroup 53edo is best tuned in, with less than 3 cents error, audibly indistinguishable from just intonation, making the most in tune harmonies also the easiest to play. For this reason, it could also be called a [[Kleismic_family#Catakleismic\|catakleismic]] or [[The_Archipelago#Trinidad_aka_cata\|Trinidad]] guitar, as it's optimised for playing music in those temperaments.

Yourmusic Productions: Formatting

2021-10-24T11:49:47Z

Formatting

← Older revision		Revision as of 11:49, 24 October 2021
Line 49:		Line 49:
	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:53edo]		[[Category:Skip fretting]] [[Category:53edo]] [[Category:Guitar]]

Yourmusic Productions: Create page.

2021-10-24T07:46:36Z

Create page.

New page

A good way to play 53-edo on a 17.66-edo guitar (effectively 28edt, or an 18edo guitar with the intonation on the [[Moving_the_bridge_hack|bridge shifted forwards]] so the third harmonic and the 28th fret sound the same note.) is to tune each pair of adjacent strings 14\43 apart. (That's 317 cents, a bit sharp of [[6/5]].) This is probably best accomplished by ear via fretting a string at the 13th fret and then tuning it to an octave above the one below.

Among the possible [[skip fretting]] systems for 53-edo, the (53,3,14) system is especially effective because every ratio in the 2.3.5.13 subgroup can be reached with a stretch of 4 frets or less. Conveniently, this is also the subgroup 53edo is best tuned in, with less than 3 cents error, audibly indistinguishable from just intonation, making the most in tune harmonies also the easiest to play. For this reason, it could also be called a [[Kleismic_family#Catakleismic|cataklesmic]] or [[The_Archipelago#Trinidad_aka_cata|Trinidad]] guitar, as it's optimised for playing music in those temperaments.

Here is where all the prime intervals lie.

{| class="wikitable"
! note
! fretboard position
|-
| 0 steps = 1 % 1
| string 0 fret 0
|-
| 53 steps = 2 % 1
| string 4 fret -1
|-
| 31 steps = 3 % 2
| string 2 fret 1
|-
| 17 steps = 5 % 4
| string 1 fret 1
|-
| 43 steps = 7 % 4
| string 2 fret 5
|-
| 24 steps = 11 % 8
| string 3 fret -7
|-
| 37 steps = 13 % 8
| string 2 fret 3
|-
| 5 steps = 17 % 16
| string 1 fret -3
|-
| 13 steps = 19 % 16
| string 2 fret -5
|-
| 28 steps = 23 % 16
| string 2 fret 0
|-
| 45 steps = 29 % 16
| string 3 fret 1
|-
| 51 steps = 31 % 16
| string 3 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).

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