59th-octave temperaments - Revision history

Eliora: /* 59-5-commatic */

2026-08-08T16:44:15Z

59-5-commatic

← Older revision		Revision as of 16:44, 8 August 2026
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	== 59-5-commatic ==		== 59-5-commatic ==

	59-5-commatic tempers out the comma which equates , and leaves the harmonic 3 as an independent generator.		59-5-commatic tempers out the comma which equates [[5/4]] with 19 steps of 59edo, and leaves the harmonic 3 as an independent generator.

	Subgroup: 2.3.5		Subgroup: 2.3.5

Eliora: added intro and explained relevance of 59edo

2026-08-08T16:43:47Z

added intro and explained relevance of 59edo

← Older revision		Revision as of 16:43, 8 August 2026
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	{{Infobox fractional-octave\|59}}		{{Infobox fractional-octave\|59}}
	{{~~todo~~\|~~intro~~}}		[[59edo]] features a [[5/4]] is nearly pure (stretched only 0.127{{c}}), as the denominator of a convergent to log<sub>2</sub>5. Hence is natural to consider temperaments that temper out the 59-5-comma, {{monzo\|137 0 -59}}. Additionally, any edo join between equal temperaments whose greatest common divisor is 59 can be used to produce a 59th-octave temperament.

			Additionally, 59edo tunes some harmonics well and others poorly, being an excellent tuning for the 2.9.5.21.11 subgroup but representing harmonics like 3, 7, and 15 poorly, thus there is room for improvement on these harmonics through 59th-octave temperaments.

	== 59-5-commatic ==		== 59-5-commatic ==
	~~[[59edo]] is a denominator to convergent of log<sub>2</sub>~~5.
			59-5-commatic tempers out the comma which equates , and leaves the harmonic 3 as an independent generator.

	Subgroup: 2.3.5		Subgroup: 2.3.5

ArrowHead294 at 03:58, 14 February 2025

2025-02-14T03:58:43Z

← Older revision		Revision as of 03:58, 14 February 2025
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	{{~~Fractional~~-octave ~~navigation~~\|59}}		{{Infobox fractional-octave\|59}}
	{{todo\|intro}}		{{todo\|intro}}

	== 59-5-commatic ==		== 59-5-commatic ==
	[[59edo]] is a denominator to convergent of log<sub>2</sub>5.		[[59edo]] is a denominator to convergent of log<sub>2</sub>5.

BudjarnLambeth: navbox, todo, stub

2024-12-05T07:38:08Z

navbox, todo, stub

← Older revision		Revision as of 07:38, 5 December 2024
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	{{Fractional-octave navigation\|59}}		{{Fractional-octave navigation\|59}}
			{{todo\|intro}}
	== 59-5-commatic ==		== 59-5-commatic ==
	[[59edo]] is a denominator to convergent of log<sub>2</sub>5.		[[59edo]] is a denominator to convergent of log<sub>2</sub>5.
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	[[Support]]ing [[ET]]s: 59N, N = 1 to 80, largest patent val: [[4720edo\|4720]]		[[Support]]ing [[ET]]s: 59N, N = 1 to 80, largest patent val: [[4720edo\|4720]]

			{{Navbox fractional-octave}}
			{{stub}}

Eliora: Created page with "{{Fractional-octave navigation|59}} == 59-5-commatic == 59edo is a denominator to convergent of log₂5. Subgroup: 2.3.5 Comma list: {{monzo|137 0 -59}} {{Mapp..."

2023-09-21T12:33:43Z

Created page with "{{Fractional-octave navigation|59}} == 59-5-commatic == 59edo is a denominator to convergent of log<sub>2</sub>5. Subgroup: 2.3.5 Comma list: {{monzo|137 0 -59}} {{Mapp..."

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