53edo - Revision history

Hotcrystal0 at 14:47, 27 April 2026

2026-04-27T14:47:15Z

← Older revision		Revision as of 14:47, 27 April 2026
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	''Main article: [[159edo]]''		''Main article: [[159edo]]''

	159edo corrects 53edo's approximate 11th and 17th harmonics to near-just qualities, and also improves the 7th harmonic to a lesser extent, resulting in it being consistent to the 17-odd-limit. If you go further than that, you're forced to choose between the ~~17the~~ harmonic on one hand and both the 19th and 29th harmonics on the other, but you do get a good 23rd harmonic regardless. In addition, you also gain access to a set of intervals that approximates those of simpler systems such as [[10edo]], [[12edo]], [[13edo]], [[14edo]], [[17edo]], [[19edo]], [[22edo]], [[24edo]] and [[31edo]] among others, opening up additional compositional techniques.		159edo corrects 53edo's approximate 11th and 17th harmonics to near-just qualities, and also improves the 7th harmonic to a lesser extent, resulting in it being consistent to the 17-odd-limit. If you go further than that, you're forced to choose between the 17th harmonic on one hand and both the 19th and 29th harmonics on the other, but you do get a good 23rd harmonic regardless. In addition, you also gain access to a set of intervals that approximates those of simpler systems such as [[10edo]], [[12edo]], [[13edo]], [[14edo]], [[17edo]], [[19edo]], [[22edo]], [[24edo]] and [[31edo]] among others, opening up additional compositional techniques.

	159edo may be derived by setting the rastma to 1/3 of a 53edo step - this is the "rastmic" part of SRS, where a rasharp or raflat is 1\159. This is in 159edo also the same as a lift or drop in ups-and-downs notation (assuming the up and down accidentals are used for a 53edo step), and it is notated in text the same way.		159edo may be derived by setting the rastma to 1/3 of a 53edo step - this is the "rastmic" part of SRS, where a rasharp or raflat is 1\159. This is in 159edo also the same as a lift or drop in ups-and-downs notation (assuming the up and down accidentals are used for a 53edo step), and it is notated in text the same way.

Vector at 05:19, 7 April 2026

2026-04-07T05:19:21Z

← Older revision		Revision as of 05:19, 7 April 2026
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	159edo corrects 53edo's approximate 11th and 17th harmonics to near-just qualities, and also improves the 7th harmonic to a lesser extent, resulting in it being consistent to the 17-odd-limit. If you go further than that, you're forced to choose between the 17the harmonic on one hand and both the 19th and 29th harmonics on the other, but you do get a good 23rd harmonic regardless. In addition, you also gain access to a set of intervals that approximates those of simpler systems such as [[10edo]], [[12edo]], [[13edo]], [[14edo]], [[17edo]], [[19edo]], [[22edo]], [[24edo]] and [[31edo]] among others, opening up additional compositional techniques.		159edo corrects 53edo's approximate 11th and 17th harmonics to near-just qualities, and also improves the 7th harmonic to a lesser extent, resulting in it being consistent to the 17-odd-limit. If you go further than that, you're forced to choose between the 17the harmonic on one hand and both the 19th and 29th harmonics on the other, but you do get a good 23rd harmonic regardless. In addition, you also gain access to a set of intervals that approximates those of simpler systems such as [[10edo]], [[12edo]], [[13edo]], [[14edo]], [[17edo]], [[19edo]], [[22edo]], [[24edo]] and [[31edo]] among others, opening up additional compositional techniques.

			159edo may be derived by setting the rastma to 1/3 of a 53edo step - this is the "rastmic" part of SRS, where a rasharp or raflat is 1\159. This is in 159edo also the same as a lift or drop in ups-and-downs notation (assuming the up and down accidentals are used for a 53edo step), and it is notated in text the same way.

	{{Harmonics in ED\|159\|31\|0}}		{{Harmonics in ED\|159\|31\|0}}
	{{Navbox EDO}}		{{Navbox EDO}}
	{{Cat\|Edos}}		{{Cat\|Edos}}

Vector at 02:42, 7 April 2026

2026-04-07T02:42:40Z

← Older revision		Revision as of 02:42, 7 April 2026
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	\|}		\|}

	==== Ups and ~~Downs~~ ====		==== Ups and downs ====
	Ups and downs naturally reflect 53edo's structure, as 5/4 is downmajor, 81/64 is major, and 9/7 is upmajor.		Ups and downs naturally reflect 53edo's structure, as 5/4 is downmajor, 81/64 is major, and 9/7 is upmajor.

	==== ~~Syntonic-Rastmic Subchroma~~ notation ====		==== Just notation systems ====
	~~Syntonic~~-~~Rastmic Subchroma notation~~, or ~~SRS~~ notation ~~for short, uses '~~''synsharp''' and '''synflat''~~' as accidentals~~ to ~~cover the syntonic comma. However, while SRS notation is~~ a 2.3.5.11 ~~notation, only the 2.3.5 portion of the notation for 53edo is shared with multiples like 159edo.~~		Ups and downs in 53edo are synonymous with an alteration by 81/80 or 64/63, which may be written equivalently as FJS ^5/_5, ^7/_7, BJ -/+, color yo/gu, zo/ru, or the syntonic comma accidentals in sagittal, HEJI, or syntonic-rastmic subchroma notation (which calls them ''synsharp'' and ''synflat'' and generalizes to 159edo with a 2.3.5.11 extension).

	~~==== Accidentals ====~~
	~~53edo's accidentals, as mentioned and demonstrated previously, consist of sharps and flats, as well as either up and down accidentals, or, alternatively, synsharps and synflats and their derivatives~~.

	== Multiples ==		== Multiples ==

Vector: remove the anti-106edo propaganda

2026-04-06T19:59:23Z

remove the anti-106edo propaganda

← Older revision		Revision as of 19:59, 6 April 2026
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	===106edo===		===106edo===
	106edo has ~~inconsistent~~ 11th and 17th harmonics, ~~and~~ also loses some ability to be consistent that 53edo has due to inconsistencies in the 7-odd-limit.		106edo has better mappings for the 11th and 17th harmonics in both relative and absolute error, but also loses some ability to be consistent that 53edo has due to inconsistencies in the 7-odd-limit. However, it is a hemipythagorean edo, with a perfect tritone and perfect neutral third (mapped to 17/12 and 11/9 respectively).

	{{Harmonics in ED\|106\|31\|0}}		{{Harmonics in ED\|106\|31\|0}}

Aura: Moved the Navbox and category tag

2026-04-06T09:53:37Z

Moved the Navbox and category tag

← Older revision		Revision as of 09:53, 6 April 2026
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	==== Accidentals ====		==== Accidentals ====
	53edo's accidentals, as mentioned and demonstrated previously, consist of sharps and flats, as well as either up and down accidentals, or, alternatively, synsharps and synflats and their derivatives.		53edo's accidentals, as mentioned and demonstrated previously, consist of sharps and flats, as well as either up and down accidentals, or, alternatively, synsharps and synflats and their derivatives.
	~~{{Navbox EDO}}~~
	~~{{Cat\|Edos}}~~

	== Multiples ==		== Multiples ==
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	{{Harmonics in ED\|159\|31\|0}}		{{Harmonics in ED\|159\|31\|0}}
			{{Navbox EDO}}
			{{Cat\|Edos}}

Aura: /* 159edo */

2026-03-29T03:05:46Z

159edo

← Older revision		Revision as of 03:05, 29 March 2026
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	''Main article: [[159edo]]''		''Main article: [[159edo]]''

	159edo corrects 53edo's approximate 11th and 17th harmonics to near-just qualities, and also improves the 7th harmonic to a lesser extent, resulting in it being consistent to the 17-odd-limit. If you go further than that, you're forced to choose between the 17the harmonic on one hand and both the 19th and 29th harmonics on the other, but you do get a good 23rd harmonic regardless. In addition, you also gain access to a set of ~~pitches~~ that approximates those of simpler systems such as [[10edo]], [[12edo]], [[13edo]], [[14edo]], [[17edo]], [[19edo]], [[22edo]], [[24edo]] and [[31edo]] among others, opening up additional compositional techniques.		159edo corrects 53edo's approximate 11th and 17th harmonics to near-just qualities, and also improves the 7th harmonic to a lesser extent, resulting in it being consistent to the 17-odd-limit. If you go further than that, you're forced to choose between the 17the harmonic on one hand and both the 19th and 29th harmonics on the other, but you do get a good 23rd harmonic regardless. In addition, you also gain access to a set of intervals that approximates those of simpler systems such as [[10edo]], [[12edo]], [[13edo]], [[14edo]], [[17edo]], [[19edo]], [[22edo]], [[24edo]] and [[31edo]] among others, opening up additional compositional techniques.

	{{Harmonics in ED\|159\|31\|0}}		{{Harmonics in ED\|159\|31\|0}}

Vector: i think this is what pitch-hue palette means???

2026-03-29T01:07:36Z

i think this is what pitch-hue palette means???

← Older revision		Revision as of 01:07, 29 March 2026
Line 147:		Line 147:
	''Main article: [[159edo]]''		''Main article: [[159edo]]''

	159edo corrects 53edo's approximate 11th and 17th harmonics to near-just qualities, and also improves the 7th harmonic to a lesser extent, resulting in it being consistent to the 17-odd-limit. If you go further than that, you're forced to choose between the 17the harmonic on one hand and both the 19th and 29th harmonics on the other, but you do get a good 23rd harmonic regardless. In addition, you also gain access to a ~~pitch hue palette~~ that approximates those of simpler systems such as [[10edo]], [[12edo]], [[13edo]], [[14edo]], [[17edo]], [[19edo]], [[22edo]], [[24edo]] and [[31edo]] among others, opening up additional compositional techniques.		159edo corrects 53edo's approximate 11th and 17th harmonics to near-just qualities, and also improves the 7th harmonic to a lesser extent, resulting in it being consistent to the 17-odd-limit. If you go further than that, you're forced to choose between the 17the harmonic on one hand and both the 19th and 29th harmonics on the other, but you do get a good 23rd harmonic regardless. In addition, you also gain access to a set of pitches that approximates those of simpler systems such as [[10edo]], [[12edo]], [[13edo]], [[14edo]], [[17edo]], [[19edo]], [[22edo]], [[24edo]] and [[31edo]] among others, opening up additional compositional techniques.

	{{Harmonics in ED\|159\|31\|0}}		{{Harmonics in ED\|159\|31\|0}}

Aura at 22:48, 28 March 2026

2026-03-28T22:48:35Z

← Older revision		Revision as of 22:48, 28 March 2026
Line 140:		Line 140:

	===106edo===		===106edo===
	106edo has inconsistent 11th and 17th harmonics, and also loses some ability to be consistent due to inconsistencies in the 7-odd-limit.		106edo has inconsistent 11th and 17th harmonics, and also loses some ability to be consistent that 53edo has due to inconsistencies in the 7-odd-limit.

	{{Harmonics in ED\|106\|31\|0}}		{{Harmonics in ED\|106\|31\|0}}

Aura at 22:48, 28 March 2026

2026-03-28T22:48:03Z

← Older revision		Revision as of 22:48, 28 March 2026
Line 140:		Line 140:

	===106edo===		===106edo===
	106edo ~~still~~ has inconsistent 11th and 17th harmonics, and also loses some ability to be consistent due to inconsistencies in the 7-odd-limit.		106edo has inconsistent 11th and 17th harmonics, and also loses some ability to be consistent due to inconsistencies in the 7-odd-limit.

	{{Harmonics in ED\|106\|31\|0}}		{{Harmonics in ED\|106\|31\|0}}

Aura at 11:18, 28 March 2026

2026-03-28T11:18:58Z

← Older revision		Revision as of 11:18, 28 March 2026
Line 136:		Line 136:
	{{Navbox EDO}}		{{Navbox EDO}}
	{{Cat\|Edos}}		{{Cat\|Edos}}

			== Multiples ==

			===106edo===
			106edo still has inconsistent 11th and 17th harmonics, and also loses some ability to be consistent due to inconsistencies in the 7-odd-limit.

			{{Harmonics in ED\|106\|31\|0}}

			===159edo===
			''Main article: [[159edo]]''

			159edo corrects 53edo's approximate 11th and 17th harmonics to near-just qualities, and also improves the 7th harmonic to a lesser extent, resulting in it being consistent to the 17-odd-limit. If you go further than that, you're forced to choose between the 17the harmonic on one hand and both the 19th and 29th harmonics on the other, but you do get a good 23rd harmonic regardless. In addition, you also gain access to a pitch hue palette that approximates those of simpler systems such as [[10edo]], [[12edo]], [[13edo]], [[14edo]], [[17edo]], [[19edo]], [[22edo]], [[24edo]] and [[31edo]] among others, opening up additional compositional techniques.

			{{Harmonics in ED\|159\|31\|0}}