367edo - 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"

2026-03-13T13:32:45Z

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 13:32, 13 March 2026
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	\| [[Hanson]]		\| [[Hanson]]
	\|}		\|}
	<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

	== Music ==		== Music ==

ArrowHead294 at 12:49, 21 February 2025

2025-02-21T12:49:02Z

← Older revision		Revision as of 12:49, 21 February 2025
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	\| {{monzo\| 582 -367 }}		\| {{monzo\| 582 -367 }}
	\| {{mapping\| 367 582 }}		\| {{mapping\| 367 582 }}
	\| -0.3288		\| −0.3288
	\| 0.3287		\| 0.3287
	\| 10.05		\| 10.05
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	\| 15625/15552, {{monzo\| 102 -57 -5 }}		\| 15625/15552, {{monzo\| 102 -57 -5 }}
	\| {{mapping\| 367 582 852 }}		\| {{mapping\| 367 582 852 }}
	\| -0.1500		\| −0.1500
	\| 0.3688		\| 0.3688
	\| 11.28		\| 11.28
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	\| [[Hanson]]		\| [[Hanson]]
	\|}		\|}
	~~{{subst:orf~~]}		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

	== Music ==		== Music ==

Francium: changed EDO intro to ED intro

2025-02-21T06:00:52Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:00, 21 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|367~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294: Partial undo

2024-11-16T13:10:32Z

Partial undo

← Older revision		Revision as of 13:10, 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
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	\| 0.3688		\| 0.3688
	\| 11.28		\| 11.28
	~~{{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
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	\| 6/5		\| 6/5
	\| [[Hanson]]		\| [[Hanson]]
	~~{{rank-2 end}~~}		\|}
	{{orf]}		{{subst:orf]}

	== Music ==		== Music ==

ArrowHead294 at 02:07, 16 November 2024

2024-11-16T02:07:05Z

← Older revision		Revision as of 02:07, 16 November 2024
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	== 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
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	\| 0.3688		\| 0.3688
	\| 11.28		\| 11.28
	\|}		{{comma basis end}}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center-all left-5"~~		{{rank-2 begin}}
	~~\|+Table of~~ rank-2 ~~temperaments by generator~~
	~~! Periods<br>per 8ve~~
	! Generator*
	! Cents*
	! Associated<br>Ratio*
	~~! Temperaments~~
	\|-		\|-
	\| 1		\| 1
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	\| 6/5		\| 6/5
	\| [[Hanson]]		\| [[Hanson]]
	\|}		{{rank-2 end}}
	~~<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]}

	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "Loss" from ''End Of Sartorius Membranes'' (2024) – [https://open.spotify.com/track/0fZfyXdtSonjGHoTSQu5O5 Spotify] \| [https://francium223.bandcamp.com/track/loss Bandcamp] \| [https://www.youtube.com/watch?v=5UmRUMSzoHM YouTube]		* "Loss" from ''End Of Sartorius Membranes'' (2024) – [https://open.spotify.com/track/0fZfyXdtSonjGHoTSQu5O5 Spotify] \| [https://francium223.bandcamp.com/track/loss Bandcamp] \| [https://www.youtube.com/watch?v=5UmRUMSzoHM YouTube]

	[[Category:Listen]]		[[Category:Listen]]

Francium: +music

2024-02-20T11:51:35Z

+music

← Older revision		Revision as of 11:51, 20 February 2024
Line 68:		Line 68:
	\|}		\|}
	<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

			== Music ==
			; [[Francium]]
			* "Loss" from ''End Of Sartorius Membranes'' (2024) – [https://open.spotify.com/track/0fZfyXdtSonjGHoTSQu5O5 Spotify] \| [https://francium223.bandcamp.com/track/loss Bandcamp] \| [https://www.youtube.com/watch?v=5UmRUMSzoHM YouTube]

			[[Category:Listen]]

FloraC: Review

2024-01-12T14:09:12Z

Review

← Older revision		Revision as of 14:09, 12 January 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	367et is only consistent to the [[5-odd-limit]], with three mappings possible for the 7-limit:		367et is only [[consistent]] to the [[5-odd-limit]], with three mappings possible for the 7-limit:
	* {{val\|367 582 852 1030}} (patent val)		* {{val\| 367 582 852 1030 }} (patent val)
	* {{val\|367 582 852 '''1031'''}} (367d val)		* {{val\| 367 582 852 '''1031''' }} (367d val)
	* {{val\|367 582 '''853''' '''1031'''}} (367cd val)		* {{val\| 367 582 '''853''' '''1031''' }} (367cd val)

	Using the patent val, it tempers out [[15625/15552]] and {{monzo\|102 -57 -5}} in the 5-limit; [[5120/5103]]~~, 15625/15552~~ and 40353607/39858075 in the 7-limit~~, supporting [[protolangwidge]]~~.		Using the patent val, it tempers out [[15625/15552]] and {{monzo\| 102 -57 -5 }} in the 5-limit; [[5120/5103]] and 40353607/39858075 in the 7-limit.

	Using the 367d val, it tempers out 15625/15552 and {{monzo\|102 -57 -5}} in the 5-limit; ~~15625/15552,~~ 2460375/2458624 and [[2097152/2083725]] in the 7-limit.		Using the 367d val, it tempers out 15625/15552 and {{monzo\| 102 -57 -5 }} in the 5-limit; 2460375/2458624 and [[2097152/2083725]] in the 7-limit.

	Using the 367cd val, it tempers out 268435456/263671875 and {{monzo\|33 -34 9}} in the 5-limit; 5120/5103, 7558272/7503125 and 235298/234375 in the 7-limit.		Using the 367cd val, it tempers out 268435456/263671875 and {{monzo\| 33 -34 9 }} in the 5-limit; 5120/5103, 7558272/7503125 and 235298/234375 in the 7-limit.

	=== Odd harmonics ===		=== Odd harmonics ===
Line 18:		Line 18:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	367edo is the 73rd [[prime ~~EDO~~]]. [[1101edo]], which triples it, gives a good correction to the harmonic 7.		367edo is the 73rd [[prime edo]]. [[1101edo]], which triples 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\|582 -367}}		\| {{monzo\| 582 -367 }}
	\|{{mapping\|367 582}}		\| {{mapping\| 367 582 }}
	\| -0.3288		\| -0.3288
	\| 0.3287		\| 0.3287
	\| 10.05		\| 10.05
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|15625/15552, {{monzo\|102 -57 -5}}		\| 15625/15552, {{monzo\| 102 -57 -5 }}
	\|{{mapping\|367 582 852}}		\| {{mapping\| 367 582 852 }}
	\| -0.1500		\| -0.1500
	\| 0.3688		\| 0.3688
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	! Temperaments		! Temperaments
	\|-		\|-
	\|1		\| 1
	\|28\367		\| 28\367
	\|91.55		\| 91.55
	\|{{monzo\|46 -7 -15}}		\| {{monzo\| 46 -7 -15 }}
	\|[[Gross]]		\| [[Gross]]
	\|-		\|-
	\|1		\| 1
	\|97\367		\| 97\367
	\|317.17		\| 317.17
	\|6/5		\| 6/5
	\|[[Hanson]]		\| [[Hanson]]
	\|}		\|}

	<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|367}} == Theory == 367et is only consistent to the 5-odd-limit, with three mappings possible for the 7-limit: * {{val|367 582 852 1030}} (paten..."

2024-01-04T20:01:48Z

Created page with "{{Infobox ET}} {{EDO intro|367}} == Theory == 367et is only consistent to the 5-odd-limit, with three mappings possible for the 7-limit: * {{val|367 582 852 1030}} (paten..."

New page

{{Infobox ET}}
{{EDO intro|367}}

== Theory ==
367et is only consistent to the [[5-odd-limit]], with three mappings possible for the 7-limit:
* {{val|367 582 852 1030}} (patent val)
* {{val|367 582 852 '''1031'''}} (367d val)
* {{val|367 582 '''853''' '''1031'''}} (367cd val)

Using the patent val, it tempers out [[15625/15552]] and {{monzo|102 -57 -5}} in the 5-limit; [[5120/5103]], 15625/15552 and 40353607/39858075 in the 7-limit, supporting [[protolangwidge]].

Using the 367d val, it tempers out 15625/15552 and {{monzo|102 -57 -5}} in the 5-limit; 15625/15552, 2460375/2458624 and [[2097152/2083725]] in the 7-limit.

Using the 367cd val, it tempers out 268435456/263671875 and {{monzo|33 -34 9}} in the 5-limit; 5120/5103, 7558272/7503125 and 235298/234375 in the 7-limit.

=== Odd harmonics ===
{{Harmonics in equal|367}}

=== Subsets and supersets ===
367edo is the 73rd [[prime EDO]]. [[1101edo]], which triples 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<br>8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|2.3
|{{monzo|582 -367}}
|{{mapping|367 582}}
| -0.3288
| 0.3287
| 10.05
|-
|2.3.5
|15625/15552, {{monzo|102 -57 -5}}
|{{mapping|367 582 852}}
| -0.1500
| 0.3688
| 11.28
|}

=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>Ratio*
! Temperaments
|-
|1
|28\367
|91.55
|{{monzo|46 -7 -15}}
|[[Gross]]
|-
|1
|97\367
|317.17
|6/5
|[[Hanson]]
|}

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