397edo - 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"

2026-03-13T13:33:17Z

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 87:		Line 87:
	\| [[Cotritone]] (397cd)		\| [[Cotritone]] (397cd)
	\|}		\|}
	<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 12:37, 21 February 2025

2025-02-21T12:37:54Z

← Older revision		Revision as of 12:37, 21 February 2025
Line 35:		Line 35:
	\| {{monzo\| -629 397 }}		\| {{monzo\| -629 397 }}
	\| {{mapping\| 397 629 }}		\| {{mapping\| 397 629 }}
	\| 0.2194		\| +0.2194
	\| 0.2195		\| 0.2195
	\| 7.26		\| 7.26
Line 42:		Line 42:
	\| 129140163/128000000, {{monzo\| 55 -1 -23 }}		\| 129140163/128000000, {{monzo\| 55 -1 -23 }}
	\| {{mapping\| 397 629 922 }}		\| {{mapping\| 397 629 922 }}
	\| 0.0618		\| +0.0618
	\| 0.2859		\| 0.2859
	\| 9.46		\| 9.46

Francium: changed EDO intro to ED intro

2025-02-21T06:07:08Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:07, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|397~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 17:05, 15 January 2025

2025-01-15T17:05:26Z

← Older revision		Revision as of 17:05, 15 January 2025
Line 87:		Line 87:
	\| [[Cotritone]] (397cd)		\| [[Cotritone]] (397cd)
	\|}		\|}
	<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

	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "Mysteries Within Us" from ''End Of Sartorius Membranes'' (2024) ~~–~~ [https://open.spotify.com/track/4fbOQF5p1YITudOw866GvH Spotify] \| [https://francium223.bandcamp.com/track/mysteries-within-us Bandcamp] \| [https://www.youtube.com/watch?v=kDdh9XZ4UNE YouTube]		* "Mysteries Within Us" from ''End Of Sartorius Membranes'' (2024) – [https://open.spotify.com/track/4fbOQF5p1YITudOw866GvH Spotify] \| [https://francium223.bandcamp.com/track/mysteries-within-us Bandcamp] \| [https://www.youtube.com/watch?v=kDdh9XZ4UNE YouTube]

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

ArrowHead294: Partial undo

2024-11-16T13:02:21Z

Partial undo

← Older revision		Revision as of 13:02, 16 November 2024
Line 21:		Line 21:

	== 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 36:		Line 45:
	\| 0.2859		\| 0.2859
	\| 9.46		\| 9.46
	~~{{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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	\| 7/5		\| 7/5
	\| [[Cotritone]] (397cd)		\| [[Cotritone]] (397cd)
	~~{{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

	== Music ==		== Music ==

ArrowHead294 at 02:48, 16 November 2024

2024-11-16T02:48:08Z

← Older revision		Revision as of 02:48, 16 November 2024
Line 21:		Line 21:

	== 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 44:		Line 36:
	\| 0.2859		\| 0.2859
	\| 9.46		\| 9.46
	\|}		{{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
Line 84:		Line 70:
	\| 7/5		\| 7/5
	\| [[Cotritone]] (397cd)		\| [[Cotritone]] (397cd)
	\|}		{{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]]
	* "Mysteries Within Us" from ''End Of Sartorius Membranes'' (2024) – [https://open.spotify.com/track/4fbOQF5p1YITudOw866GvH Spotify] \| [https://francium223.bandcamp.com/track/mysteries-within-us Bandcamp] \| [https://www.youtube.com/watch?v=kDdh9XZ4UNE YouTube]		* "Mysteries Within Us" from ''End Of Sartorius Membranes'' (2024) – [https://open.spotify.com/track/4fbOQF5p1YITudOw866GvH Spotify] \| [https://francium223.bandcamp.com/track/mysteries-within-us Bandcamp] \| [https://www.youtube.com/watch?v=kDdh9XZ4UNE YouTube]

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

Francium: +music

2024-02-20T11:57:59Z

+music

← Older revision		Revision as of 11:57, 20 February 2024
Line 86:		Line 86:
	\|}		\|}
	<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]]
			* "Mysteries Within Us" from ''End Of Sartorius Membranes'' (2024) – [https://open.spotify.com/track/4fbOQF5p1YITudOw866GvH Spotify] \| [https://francium223.bandcamp.com/track/mysteries-within-us Bandcamp] \| [https://www.youtube.com/watch?v=kDdh9XZ4UNE YouTube]

			[[Category:Listen]]

FloraC: Review

2024-01-16T14:46:44Z

Review

← Older revision		Revision as of 14:46, 16 January 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	~~397et~~ is only consistent to the [[5-odd-limit]], with three mappings possible for the 7-limit:		397edo is only [[consistent]] to the [[5-odd-limit]], with three mappings possible for the 7-limit:
	* {{val\|397 629 922 1115}} (patent val)		* {{val\| 397 629 922 1115 }} ([[patent val]])
	* {{val\|397 629 922 '''1114'''}} (397d val)		* {{val\| 397 629 922 '''1114''' }} (397d val)
	* {{val\|397 629 '''921''' '''1114'''}} (397cd val)		* {{val\| 397 629 '''921''' '''1114''' }} (397cd val)

	Using the patent val, it tempers out [[129140163/128000000]] and {{monzo\|55 -1 -23}} in the 5-limit; [[6144/6125]], 16875/16807 and 129140163/128000000 in the 7-limit; [[support]]ing [[grendel~~]], [[porwell]] and [[mirkwai~~]].		Using the patent val, it tempers out [[129140163/128000000]] and {{monzo\| 55 -1 -23 }} in the 5-limit; [[6144/6125]], [[16875/16807]] and 129140163/128000000 in the 7-limit; [[support]]ing [[grendel]].

	Using the 397d val, it tempers out 129140163/128000000 and {{monzo\|55 -1 -23}} in the 5-limit; [[3136/3125]], [[420175/419904]] and 33756345/33554432 in the 7-limit; supporting [[sengagen~~]] and [[parahemwuer~~]].		Using the 397d val, it tempers out 129140163/128000000 and {{monzo\| 55 -1 -23 }} in the 5-limit; [[3136/3125]], [[420175/419904]] and 33756345/33554432 in the 7-limit; supporting [[sengagen]].

	Using the 397cd val, it tempers out 390625000/387420489 and {{monzo\|-55 23 8}} in the 5-limit; [[2401/2400]], 390625/387072 and [[14348907/14336000]] in the 7-limit; supporting [[cotritone~~]] and [[breed~~]].		Using the 397cd val, it tempers out 390625000/387420489 and {{monzo\| -55 23 8 }} in the 5-limit; [[2401/2400]], 390625/387072 and [[14348907/14336000]] in the 7-limit; supporting [[cotritone]].

	=== Prime harmonics ===		=== Prime harmonics ===
Line 18:		Line 18:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	397edo is the 78th [[prime ~~EDO~~]]. [[1588edo]], which quadruples it, gives a good correction to the harmonic 7.		397edo is the 78th [[prime edo]]. [[1588edo]], which quadruples 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\|-629 397}}		\| {{monzo\| -629 397 }}
	\|{{mapping\|397 629}}		\| {{mapping\| 397 629 }}
	\| 0.2194		\| 0.2194
	\| 0.2195		\| 0.2195
	\| 7.26		\| 7.26
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|129140163/128000000, {{monzo\|55 -1 -23}}		\| 129140163/128000000, {{monzo\| 55 -1 -23 }}
	\|{{mapping\|397 629 922}}		\| {{mapping\| 397 629 922 }}
	\| 0.0618		\| 0.0618
	\| 0.2859		\| 0.2859
Line 55:		Line 55:
	! Temperaments		! Temperaments
	\|-		\|-
	\|1		\| 1
	\|8\397		\| 8\397
	\|24.18		\| 24.18
	\|686/675		\| 686/675
	\|[[Sengagen]] (397d)		\| [[Sengagen]] (397d)
	\|-		\|-
	\|1		\| 1
	\|37\397		\| 37\397
	\|111.84		\| 111.84
	\|16/15		\| 16/15
	\|[[Vavoom]]		\| [[Vavoom]]
	\|-		\|-
	\|1		\| 1
	\|128\397		\| 128\397
	\|386.90		\| 386.90
	\|5/4		\| 5/4
	\|[[Grendel]] (397)		\| [[Grendel]] (397)
	\|-		\|-
	\|1		\| 1
	\|171\397		\| 171\397
	\|516.88		\| 516.88
	\|27/20		\| 27/20
	\|[[Gravity]]		\| [[Gravity]]
	\|-		\|-
	\|1		\| 1
	\|193\397		\| 193\397
	\|583.38		\| 583.38
	\|7/5		\| 7/5
	\|[[Cotritone]] (397cd)		\| [[Cotritone]] (397cd)
	\|}		\|}

	<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: typo

2024-01-11T09:20:07Z

typo

← Older revision		Revision as of 09:20, 11 January 2024
Line 14:		Line 14:
	Using the 397cd val, it tempers out 390625000/387420489 and {{monzo\|-55 23 8}} in the 5-limit; [[2401/2400]], 390625/387072 and [[14348907/14336000]] in the 7-limit; supporting [[cotritone]] and [[breed]].		Using the 397cd val, it tempers out 390625000/387420489 and {{monzo\|-55 23 8}} in the 5-limit; [[2401/2400]], 390625/387072 and [[14348907/14336000]] in the 7-limit; supporting [[cotritone]] and [[breed]].

	=== Prime harmonics ==		=== Prime harmonics ===
	{{Harmonics in equal\|397}}		{{Harmonics in equal\|397}}

Francium: typo

2024-01-11T09:15:55Z

typo

← Older revision		Revision as of 09:15, 11 January 2024
Line 4:		Line 4:
	== Theory ==		== Theory ==
	397et is only consistent to the [[5-odd-limit]], with three mappings possible for the 7-limit:		397et is only consistent to the [[5-odd-limit]], with three mappings possible for the 7-limit:
	(*) {{val\|397 629 922 1115}} (patent val)		* {{val\|397 629 922 1115}} (patent val)
	(*) {{val\|397 629 922 '''1114'''}} (397d val)		* {{val\|397 629 922 '''1114'''}} (397d val)
	(*) {{val\|397 629 '''921''' '''1114'''}} (397cd val)		* {{val\|397 629 '''921''' '''1114'''}} (397cd val)

	Using the patent val, it tempers out [[129140163/128000000]] and {{monzo\|55 -1 -23}} in the 5-limit; [[6144/6125]], 16875/16807 and 129140163/128000000 in the 7-limit; [[support]]ing [[grendel]], [[porwell]] and [[mirkwai]].		Using the patent val, it tempers out [[129140163/128000000]] and {{monzo\|55 -1 -23}} in the 5-limit; [[6144/6125]], 16875/16807 and 129140163/128000000 in the 7-limit; [[support]]ing [[grendel]], [[porwell]] and [[mirkwai]].