53edo - Revision history

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}}

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}}

2026-03-29T01:07:36Z

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

← Older revision		Revision as of 01:07, 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 ~~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}}

2026-03-28T22:48:35Z

← Older revision		Revision as of 22:48, 28 March 2026
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	===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}}

2026-03-28T22:48:03Z

← Older revision		Revision as of 22:48, 28 March 2026
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	===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}}

2026-03-28T11:18:58Z

← Older revision		Revision as of 11:18, 28 March 2026
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	{{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}}

2026-03-05T01:57:24Z

forgot to bold

2026-03-03T12:29:04Z

adding navbox

← Older revision		Revision as of 12:29, 3 March 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}}		{{Cat\|Edos}}

2026-03-03T00:00:41Z

← Older revision		Revision as of 00:00, 3 March 2026
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	'''53edo''', or 53 equal divisions of the octave, is the equal tuning featuring steps of (1200/53) ~= 22.64 cents, 53 of which stack to the perfect octave [[2/1]]. Theoretical interest in this tuning system goes back to antiquity.		'''53edo''', or 53 equal divisions of the octave, is the equal tuning featuring steps of (1200/53) ~= 22.64 cents, 53 of which stack to the perfect octave [[2/1]]. 53edo is an excellent approximation to Pythagorean tuning (stacking pure 3/2 fifths). Theoretical interest in this tuning system goes back to antiquity.

	== Theory ==		== Theory ==

2026-03-02T23:51:11Z

added steps to the thirds table ! just thought this was useful and was kinda annoyed this wasn't there already

@@ Line 68: / Line 68: @@
 |9/7, 32/25
 |13/10
 |}
 Diatonic thirds are bolded.