450edo - Revision history

FloraC: /* Regular temperament properties */ quintile isn't defined beyond the 5-limit

2026-09-04T06:16:56Z

Regular temperament properties: quintile isn't defined beyond the 5-limit

← Older revision		Revision as of 06:16, 4 September 2026
Line 65:		Line 65:
	\| 18.67		\| 18.67
	\| 81/80		\| 81/80
	\| [[Quintile]] ~~(5-limit)~~		\| [[Quintile]]
	\|-		\|-
	\| 10		\| 10

FloraC: More rework. + decile

2026-09-04T06:01:14Z

More rework. + decile

← Older revision		Revision as of 06:01, 4 September 2026
Line 3:		Line 3:

	== Theory ==		== Theory ==
	450edo is [[consistent]] to the [[7-odd-limit]]. It can be considered for the 2.3.5.7.13.17.29.31.37 [[subgroup]], where it [[tempering out\|tempers out]] 651/650, 1666/1665, 1887/1885, 2016/2015, 2295/2294, 5916/5915, 4901/4900 and 14229/14210~~. It [[support]]s [[decal]] and [[varuna]]~~.		450edo is [[consistent]] to the [[7-odd-limit]]. It tempers out the [[triwellisma]] and the [[varunisma]] in the [[7-limit]], [[support]]ing and providing the [[optimal patent val]] for 7-limit [[decile]]. It can be considered for the 2.3.5.7.13.17.29.31.37 [[subgroup]], where it [[tempering out\|tempers out]] 651/650, 1666/1665, 1887/1885, 2016/2015, 2295/2294, 5916/5915, 4901/4900 and 14229/14210.

	=== Odd harmonics ===		=== Odd harmonics ===
Line 9:		Line 9:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	450 factors into 2 × 3<sup>2</sup> × 5<sup>2</sup>, ~~with~~ subset edos {{EDOs\|2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, and 225}}.		Since 450 factors into {{nowrap\| 2 × 3<sup>2</sup> × 5<sup>2</sup> }}, 450edo has subset edos {{EDOs\| 2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, and 225 }}.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 66:		Line 66:
	\| 81/80		\| 81/80
	\| [[Quintile]] (5-limit)		\| [[Quintile]] (5-limit)
			\|-
			\| 10
			\| 7\450
			\| 18.67
			\| 81/80
			\| [[Decile]]
	\|}		\|}
	<nowiki/>* In [[normal forms #Minimal-generator form\|minimal-generator form]]		<nowiki/>* In [[normal forms #Minimal-generator form\|minimal-generator form]]

			[[Category:Decile]]

FloraC: /* Regular temperament properties */ update

2026-09-04T05:57:12Z

Regular temperament properties: update

← Older revision		Revision as of 05:57, 4 September 2026
Line 17:		Line 17:
	! rowspan="2" \| [[Comma list]]		! rowspan="2" \| [[Comma list]]
	! rowspan="2" \| [[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \| Optimal<br />8ve stretch (¢)		! rowspan="2" \| Optimal<br>8ve stretch (¢)
	! colspan="2" \| Tuning error		! colspan="2" \| Tuning error
	\|-		\|-
Line 24:		Line 24:
	\|-		\|-
	\| 2.3		\| 2.3
	\| {{~~monzo~~\| -713 450 }}		\| {{Monzo\| -713 450 }}
	\| {{~~mapping~~\| 450 713 }}		\| {{Mapping\| 450 713 }}
	\| +0.1961		\| +0.1961
	\| 0.1961		\| 0.1961
Line 31:		Line 31:
	\|-		\|-
	\| 2.3.5		\| 2.3.5
	\| {{~~monzo~~\| -28 25 -5 }}, {{monzo\| 25 15 -21 }}		\| {{Monzo\| -28 25 -5 }}, {{monzo\| 25 15 -21 }}
	\| {{~~mapping~~\| 450 713 1045 }}		\| {{Mapping\| 450 713 1045 }}
	\| +0.0800		\| +0.0800
	\| 0.2293		\| 0.2293
Line 39:		Line 39:
	\| 2.3.5.7		\| 2.3.5.7
	\| 235298/234375, 321489/320000, 26873856/26796875		\| 235298/234375, 321489/320000, 26873856/26796875
	\| {{~~mapping~~\| 450 713 1045 1263 }}		\| {{Mapping\| 450 713 1045 1263 }}
	\| +0.1336		\| +0.1336
	\| 0.2192		\| 0.2192
Line 49:		Line 49:
	\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator		\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
	\|-		\|-
	! Periods<br />per 8ve		! Periods<br>per 8ve
	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br />ratio*		! Associated<br>ratio*
	! Temperaments		! Temperaments
	\|-		\|-
Line 62:		Line 62:
	\|-		\|-
	\| 5		\| 5
	\| ~~187\450<br />(~~7\450)		\| 7\450
	\| ~~498.67<br />(~~18.67)		\| 18.67
	\| ~~4/3<br />(~~81/80)		\| 81/80
	\| [[~~Pental (temperament)\|Pental~~]] (5-limit)		\| [[Quintile]] (5-limit)
	\|}		\|}
	<nowiki />* ~~[[Normal forms #Equave-reduced-generator form\|Octave-reduced form]], reduced to the first half-octave, and~~ [[normal forms #Minimal-generator form\|minimal form]] ~~in parentheses if distinct~~		<nowiki/>* In [[normal forms #Minimal-generator form\|minimal-generator form]]

FloraC: Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

2026-03-13T13:33:04Z

Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

← Older revision		Revision as of 13:33, 13 March 2026
Line 67:		Line 67:
	\| [[Pental (temperament)\|Pental]] (5-limit)		\| [[Pental (temperament)\|Pental]] (5-limit)
	\|}		\|}
	<nowiki />* [[Normal ~~lists~~\|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~\|minimal form]] in parentheses if distinct		<nowiki />* [[Normal forms #Equave-reduced-generator form\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form\|minimal form]] in parentheses if distinct

Francium: changed EDO intro to ED intro

2025-02-21T06:20:32Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:20, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|450~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 16:19, 15 January 2025

2025-01-15T16:19:16Z

← Older revision		Revision as of 16:19, 15 January 2025
Line 67:		Line 67:
	\| [[Pental (temperament)\|Pental]] (5-limit)		\| [[Pental (temperament)\|Pental]] (5-limit)
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if ~~it is~~ distinct		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

ArrowHead294: Partial undo

2024-11-16T13:15:54Z

Partial undo

← Older revision		Revision as of 13:15, 16 November 2024
Line 12:		Line 12:

	== Regular temperament properties ==		== Regular temperament properties ==
	{~~{comma basis begin}}~~		{\| class="wikitable center-4 center-5 center-6"
			\|-
			! rowspan="2" \| [[Subgroup]]
			! rowspan="2" \| [[Comma list]]
			! rowspan="2" \| [[Mapping]]
			! rowspan="2" \| Optimal<br />8ve stretch (¢)
			! colspan="2" \| Tuning error
			\|-
			! [[TE error\|Absolute]] (¢)
			! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\| 2.3		\| 2.3
Line 34:		Line 43:
	\| 0.2192		\| 0.2192
	\| 8.22		\| 8.22
	~~{{comma basis end}~~}		\|}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{{rank-2 ~~begin}}~~		{\| class="wikitable center-all left-5"
			\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
			\|-
			! Periods<br />per 8ve
			! Generator*
			! Cents*
			! Associated<br />ratio*
			! Temperaments
	\|-		\|-
	\| 2		\| 2
Line 50:		Line 66:
	\| 4/3<br />(81/80)		\| 4/3<br />(81/80)
	\| [[Pental (temperament)\|Pental]] (5-limit)		\| [[Pental (temperament)\|Pental]] (5-limit)
	~~{{rank-2 end}~~}		\|}
	~~{{orf}}~~		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

ArrowHead294 at 01:46, 16 November 2024

2024-11-16T01:46:20Z

← Older revision		Revision as of 01:46, 16 November 2024
Line 12:		Line 12:

	== Regular temperament properties ==		== Regular temperament properties ==
	{~~\| class="wikitable center-4 center-5 center-6"~~		{{comma basis begin}}
	\|-
	~~! rowspan="2" \| [[Subgroup]]~~
	~~! rowspan="2" \| [[Comma list\|Comma List]]~~
	~~! rowspan="2" \| [[Mapping]]~~
	~~! rowspan="2" \| Optimal<br />8ve Stretch (¢)~~
	~~! colspan="2" \| Tuning Error~~
	\|-
	~~! [[TE error\|Absolute]] (¢)~~
	~~! [[TE simple badness\|Relative]] (%)~~
	\|-		\|-
	\| 2.3		\| 2.3
Line 43:		Line 34:
	\| 0.2192		\| 0.2192
	\| 8.22		\| 8.22
	\|}		{{comma basis end}}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center-all left-5"~~		{{rank-2 begin}}
	~~\|+ style="font-size: 105%;" \| Table of~~ rank-2 ~~temperaments by generator~~
	\|-
	~~! Periods<br />per 8ve~~
	! Generator*
	! Cents*
	! Associated<br />Ratio*
	~~! Temperaments~~
	\|-		\|-
	\| 2		\| 2
Line 66:		Line 50:
	\| 4/3<br />(81/80)		\| 4/3<br />(81/80)
	\| [[Pental (temperament)\|Pental]] (5-limit)		\| [[Pental (temperament)\|Pental]] (5-limit)
	\|}		{{rank-2 end}}
	{{orf}}		{{orf}}

ArrowHead294 at 01:07, 16 November 2024

2024-11-16T01:07:04Z

← Older revision		Revision as of 01:07, 16 November 2024
Line 13:		Line 13:
	== Regular temperament properties ==		== Regular temperament properties ==
	{\| class="wikitable center-4 center-5 center-6"		{\| class="wikitable center-4 center-5 center-6"
			\|-
	! rowspan="2" \| [[Subgroup]]		! rowspan="2" \| [[Subgroup]]
	! rowspan="2" \| [[Comma list\|Comma List]]		! rowspan="2" \| [[Comma list\|Comma List]]
	! rowspan="2" \| [[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \| Optimal<br>8ve Stretch (¢)		! rowspan="2" \| Optimal<br />8ve Stretch (¢)
	! colspan="2" \| Tuning Error		! colspan="2" \| Tuning Error
	\|-		\|-
Line 46:		Line 47:
	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	\|+Table of rank-2 temperaments by generator		\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
	! Periods<br>per 8ve		\|-
			! Periods<br />per 8ve
	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br>Ratio*		! Associated<br />Ratio*
	! Temperaments		! Temperaments
	\|-		\|-
Line 60:		Line 62:
	\|-		\|-
	\| 5		\| 5
	\| 187\450<br>(7\450)		\| 187\450<br />(7\450)
	\| 498.67<br>(18.67)		\| 498.67<br />(18.67)
	\| 4/3<br>(81/80)		\| 4/3<br />(81/80)
	\| [[Pental (temperament)\|Pental]] (5-limit)		\| [[Pental (temperament)\|Pental]] (5-limit)
	\|}		\|}
	~~<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct~~		{{orf}}

Fredg999: Skip disambiguation

2024-09-09T02:00:03Z

Skip disambiguation

← Older revision		Revision as of 02:00, 9 September 2024
Line 63:		Line 63:
	\| 498.67<br>(18.67)		\| 498.67<br>(18.67)
	\| 4/3<br>(81/80)		\| 4/3<br>(81/80)
	\| [[Pental]] (5-limit)		\| [[Pental (temperament)\|Pental]] (5-limit)
	\|}		\|}
	<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct		<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct