450edo - Revision history

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

FloraC: Review

2024-01-21T10:22:50Z

Review

← Older revision		Revision as of 10:22, 21 January 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	~~450et~~ is consistent to the [[7-odd-limit]]. It can be considered for the 2.3.5.7.13.17.29.31.37 [[subgroup]], tempering 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 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]].

	=== Odd harmonics ===		=== Odd harmonics ===
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
	\|-		\|-
	![[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
	![[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\|2.3		\| 2.3
	\|{{monzo\|-713 450}}		\| {{monzo\| -713 450 }}
	\|{{mapping\|450 713}}		\| {{mapping\| 450 713 }}
	\| 0.1961		\| +0.1961
	\| 0.1961		\| 0.1961
	\| 7.35		\| 7.35
	\|-		\|-
	\|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
	\| 8.60		\| 8.60
	\|-		\|-
	\|2.3.5.7		\| 2.3.5.7
	\|321489/320000~~, 235298/234375~~, 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
	\| 8.22		\| 8.22
Line 53:		Line 53:
	! Temperaments		! Temperaments
	\|-		\|-
	\|2		\| 2
	\|61\450		\| 61\450
	\|162.67		\| 162.67
	\|1125/1024		\| 1125/1024
	\|[[Kwazy]]		\| [[Kwazy]]
	\|-		\|-
	\|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]]		\| [[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

Francium: Created page with "{{Infobox ET}} {{EDO intro|450}} == Theory == 450et is consistent to the 7-odd-limit. It can be considered for the 2.3.5.7.13.17.29.31.37 subgroup, tempering out 651/..."

2024-01-18T11:18:17Z

Created page with "{{Infobox ET}} {{EDO intro|450}} == Theory == 450et is consistent to the 7-odd-limit. It can be considered for the 2.3.5.7.13.17.29.31.37 subgroup, tempering out 651/..."

New page

{{Infobox ET}}
{{EDO intro|450}}

== Theory ==
450et is consistent to the [[7-odd-limit]]. It can be considered for the 2.3.5.7.13.17.29.31.37 [[subgroup]], tempering out 651/650, 1666/1665, 1887/1885, 2016/2015, 2295/2294, 5916/5915, 4901/4900 and 14229/14210. It [[support]]s [[decal]] and [[varuna]].

=== Odd harmonics ===
{{Harmonics in equal|450}}

=== Subsets and supersets ===
450 factors into 2 × 32 × 52, with subset edos {{EDOs|2, 3, 5, 6, 9, 10, 15, 18, 25, 30, 45, 50, 75, 90, 150, and 225}}.

== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" |[[Subgroup]]
! rowspan="2" |[[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" |Optimal 8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|2.3
|{{monzo|-713 450}}
|{{mapping|450 713}}
| 0.1961
| 0.1961
| 7.35
|-
|2.3.5
|{{monzo|-28 25 -5}}, {{monzo|25 15 -21}}
|{{mapping|450 713 1045}}
| 0.0800
| 0.2293
| 8.60
|-
|2.3.5.7
|321489/320000, 235298/234375, 26873856/26796875
|{{mapping|450 713 1045 1263}}
| 0.1336
| 0.2192
| 8.22
|}

=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
! Periods per 8ve
! Generator*
! Cents*
! Associated Ratio*
! Temperaments
|-
|2
|61\450
|162.67
|1125/1024
|[[Kwazy]]
|-
|5
|187\450 (7\450)
|498.67 (18.67)
|4/3 (81/80)
|[[Pental]]
|}

<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct