465edo - 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"

2026-03-13T13:33:16Z

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
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	\| [[Qintosec]] (465)		\| [[Qintosec]] (465)
	\|}		\|}
	<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

2025-02-21T06:20:00Z

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~~\|465~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 16:19, 15 January 2025

2025-01-15T16:19:01Z

← Older revision		Revision as of 16:19, 15 January 2025
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	\| {{monzo\| 25 15 -21 }}, {{monzo\| -22 30 -11 }}		\| {{monzo\| 25 15 -21 }}, {{monzo\| -22 30 -11 }}
	\| {{mapping\| 465 737 1080 }}		\| {{mapping\| 465 737 1080 }}
	\| -0.1083		\| −0.1083
	\| 0.1619		\| 0.1619
	\| 6.27		\| 6.27
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	\| [[Qintosec]] (465)		\| [[Qintosec]] (465)
	\|}		\|}
	<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

2024-11-16T13:16:27Z

Partial undo

← Older revision		Revision as of 13:16, 16 November 2024
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	== 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 27:		Line 36:
	\| 0.1619		\| 0.1619
	\| 6.27		\| 6.27
	~~{{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
	\|-		\|-
	\| 1		\| 1
Line 43:		Line 59:
	\| 80/49<br />(15/14)		\| 80/49<br />(15/14)
	\| [[Qintosec]] (465)		\| [[Qintosec]] (465)
	~~{{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 01:44, 16 November 2024

2024-11-16T01:44:23Z

← Older revision		Revision as of 01:44, 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 36:		Line 27:
	\| 0.1619		\| 0.1619
	\| 6.27		\| 6.27
	\|}		{{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~~
	\|-		\|-
	\| 1		\| 1
Line 59:		Line 43:
	\| 80/49<br />(15/14)		\| 80/49<br />(15/14)
	\| [[Qintosec]] (465)		\| [[Qintosec]] (465)
	\|}		{{rank-2 end}}
	{{orf}}		{{orf}}

ArrowHead294 at 01:05, 16 November 2024

2024-11-16T01:05:18Z

← Older revision		Revision as of 01:05, 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 39:		Line 40:
	=== 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
	\|-		\|-
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	\|-		\|-
	\| 5		\| 5
	\| 322\465<br>(43\465)		\| 322\465<br />(43\465)
	\| 830.97<br>(110.97)		\| 830.97<br />(110.97)
	\| 80/49<br>(15/14)		\| 80/49<br />(15/14)
	\| [[Qintosec]] (465)		\| [[Qintosec]] (465)
	\|}		\|}
	~~<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}}

FloraC: Review

2024-02-18T13:36:41Z

Review

← Older revision		Revision as of 13:36, 18 February 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	~~465et~~ is consistent to the [[5-odd-limit]]. It can be considered for the 2.3.5.11.13.17 [[subgroup]], tempering out [[936/935]], 1377/1375, 71874/71825, 131648/131625 and 225000/224939. It [[support]]s [[~~birds~~]], [[~~counterschismic~~]] and [[belobog]].		465edo is only [[consistent]] to the [[5-odd-limit]], and the errors of [[harmonic]]s beyond [[3/1\|3]] tend to be quite large. It can be considered for the 2.3.5.11.13.17 [[subgroup]], [[tempering out]] [[936/935]], 1377/1375, 71874/71825, 131648/131625 and 225000/224939. It [[support]]s [[counterschismic]] in the 5-limit, and [[birds]] and [[belobog]] in the 7-limit using the [[patent val]].

	=== Prime harmonics ===		=== Prime harmonics ===
Line 9:		Line 9:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	465 factors into 3 × 5 × 31, ~~with~~ subset edos {{EDOs\|3, 5, 15, 31, 93, and 155}}. [[930edo]], which doubles it, gives a good correction to the harmonic 7.		Since 465 factors into 3 × 5 × 31, 465edo has subset edos {{EDOs\| 3, 5, 15, 31, 93, and 155 }}. [[930edo]], which doubles it, gives a good correction to the harmonic 7.

	== 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\|-737 465}}		\| {{monzo\| -737 465 }}
	\|{{mapping\|465 737}}		\| {{mapping\| 465 737 }}
	\| +0.0062		\| +0.0062
	\| 0.0062		\| 0.0062
	\| 0.24		\| 0.24
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|{{monzo\|25 15 -21}}, {{monzo\|-22 30 -11}}		\| {{monzo\| 25 15 -21 }}, {{monzo\| -22 30 -11 }}
	\|{{mapping\|465 737 1080}}		\| {{mapping\| 465 737 1080 }}
	\| -0.1083		\| -0.1083
	\| 0.1619		\| 0.1619
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	! Temperaments		! Temperaments
	\|-		\|-
	\|1		\| 1
	\|193\465		\| 193\465
	\|498.06		\| 498.06
	\|4/3		\| 4/3
	\|[[Counterschismic]]		\| [[Counterschismic]]
	\|-		\|-
	\|5		\| 5
	\|322\465<br>(43\465)		\| 322\465<br>(43\465)
	\|830.97<br>(110.97)		\| 830.97<br>(110.97)
	\|80/49<br>(15/14)		\| 80/49<br>(15/14)
	\|[[Qintosec]]		\| [[Qintosec]] (465)
	\|}		\|}

	<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|465}} == Theory == 465et is consistent to the 5-odd-limit. It can be considered for the 2.3.5.11.13.17 subgroup, tempering out 936/935,..."

2024-02-18T13:12:39Z

Created page with "{{Infobox ET}} {{EDO intro|465}} == Theory == 465et is consistent to the 5-odd-limit. It can be considered for the 2.3.5.11.13.17 subgroup, tempering out 936/935,..."

New page

{{Infobox ET}}
{{EDO intro|465}}

== Theory ==
465et is consistent to the [[5-odd-limit]]. It can be considered for the 2.3.5.11.13.17 [[subgroup]], tempering out [[936/935]], 1377/1375, 71874/71825, 131648/131625 and 225000/224939. It [[support]]s [[birds]], [[counterschismic]] and [[belobog]].

=== Prime harmonics ===
{{Harmonics in equal|465}}

=== Subsets and supersets ===
465 factors into 3 × 5 × 31, with subset edos {{EDOs|3, 5, 15, 31, 93, and 155}}. [[930edo]], which doubles it, gives a good correction to the harmonic 7.

== 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|-737 465}}
|{{mapping|465 737}}
| +0.0062
| 0.0062
| 0.24
|-
|2.3.5
|{{monzo|25 15 -21}}, {{monzo|-22 30 -11}}
|{{mapping|465 737 1080}}
| -0.1083
| 0.1619
| 6.27
|}

=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
! Periods per 8ve
! Generator*
! Cents*
! Associated Ratio*
! Temperaments
|-
|1
|193\465
|498.06
|4/3
|[[Counterschismic]]
|-
|5
|322\465 (43\465)
|830.97 (110.97)
|80/49 (15/14)
|[[Qintosec]]
|}

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