1178edo - 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"

2026-03-13T13:32:43Z

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
Line 113:		Line 113:
	\| [[Hemienneadecal]]		\| [[Hemienneadecal]]
	\|}		\|}
	<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 16:53, 18 February 2025

2025-02-18T16:53:05Z

← Older revision		Revision as of 16:53, 18 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|1178~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 19:43, 15 January 2025

2025-01-15T19:43:13Z

← Older revision		Revision as of 19:43, 15 January 2025
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 1178 = {{factorization\|1178}}, 1178edo is notable for containing both 19 and 31. Its subset edos are {{EDOs\| 2, 19, 31, 38, 62, and 589 }}.		Since 1178 factors into {{factorization\|1178}}, 1178edo is notable for containing both 19 and 31. Its subset edos are {{EDOs\| 2, 19, 31, 38, 62, and 589 }}.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 61:		Line 61:
	\| 2500/2499, 3025/3024, 4225/4224, 4375/4374, 4914/4913, 14875/14872		\| 2500/2499, 3025/3024, 4225/4224, 4375/4374, 4914/4913, 14875/14872
	\| {{mapping\| 1178 1867 2735 3307 4075 4359 4815 }}		\| {{mapping\| 1178 1867 2735 3307 4075 4359 4815 }}
	\| 0.0403		\| +0.0403
	\| 0.0327		\| 0.0327
	\| 3.21		\| 3.21
Line 68:		Line 68:
	\| 2500/2499, 3025/3024, 3250/3249, 4200/4199, 4225/4224, 4375/4374, 4914/4913		\| 2500/2499, 3025/3024, 3250/3249, 4200/4199, 4225/4224, 4375/4374, 4914/4913
	\| {{mapping\| 1178 1867 2735 3307 4075 4359 4815 5004 }}		\| {{mapping\| 1178 1867 2735 3307 4075 4359 4815 5004 }}
	\| 0.0370		\| +0.0370
	\| 0.0318		\| 0.0318
	\| 3.12		\| 3.12
Line 113:		Line 113:
	\| [[Hemienneadecal]]		\| [[Hemienneadecal]]
	\|}		\|}
	<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 ==
	; [[Eliora]]		; [[Eliora]]
	* [https://www.youtube.com/watch?v=c9e7MTsIDc4 ''Listening''] (2023) &~~ndash~~; ~~217 &~~ 1178 and enneadecal in 1178edo tuning		* [https://www.youtube.com/watch?v=c9e7MTsIDc4 ''Listening''] (2023) – {{nowrap\|217 & 1178}} and enneadecal in 1178edo tuning

	[[Category:Enneadecal]]		[[Category:Enneadecal]]

ArrowHead294: Partial undo

2024-11-16T12:35:28Z

Partial undo

← Older revision		Revision as of 12:35, 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 62:		Line 71:
	\| 0.0318		\| 0.0318
	\| 3.12		\| 3.12
	~~{{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 96:		Line 112:
	\| 4/3<br />(225/224)		\| 4/3<br />(225/224)
	\| [[Hemienneadecal]]		\| [[Hemienneadecal]]
	~~{{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 04:21, 16 November 2024

2024-11-16T04:21:04Z

← Older revision		Revision as of 04:21, 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 70:		Line 62:
	\| 0.0318		\| 0.0318
	\| 3.12		\| 3.12
	\|}		{{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 88:		Line 74:
	\|-		\|-
	\| 19		\| 19
	\| 489\1178<br>(7\1178)		\| 489\1178<br />(7\1178)
	\| 498.13<br>(7.13)		\| 498.13<br />(7.13)
	\| 4/3<br>(225/224)		\| 4/3<br />(225/224)
	\| [[Enneadecal]]		\| [[Enneadecal]]
	\|-		\|-
	\| 31		\| 31
	\| 581\1178<br>(11\1178)		\| 581\1178<br />(11\1178)
	\| 591.851<br>(11.205)		\| 591.851<br />(11.205)
	\| 936/665<br>(?)		\| 936/665<br />(?)
	\| [[31st-octave temperaments#217 & 1178\|217 & 1178]]		\| [[31st-octave temperaments#217 & 1178\|217 & 1178]]
	\|-		\|-
	\| 38		\| 38
	\| 260\1178<br>(12\1178)		\| 260\1178<br />(12\1178)
	\| 264.86<br>(12.22)		\| 264.86<br />(12.22)
	\| 500/429<br>(144/143)		\| 500/429<br />(144/143)
	\| [[Semihemienneadecal]]		\| [[Semihemienneadecal]]
	\|-		\|-
	\| 38		\| 38
	\| 489\1178<br>(7\1178)		\| 489\1178<br />(7\1178)
	\| 498.13<br>(7.13)		\| 498.13<br />(7.13)
	\| 4/3<br>(225/224)		\| 4/3<br />(225/224)
	\| [[Hemienneadecal]]		\| [[Hemienneadecal]]
	\|}		{{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 ==
	; [[Eliora]]		; [[Eliora]]
	* [https://www.youtube.com/watch?v=c9e7MTsIDc4 ''Listening''] (2023) – 217 & 1178 and enneadecal in 1178edo tuning		* [https://www.youtube.com/watch?v=c9e7MTsIDc4 ''Listening''] (2023) – 217 & 1178 and enneadecal in 1178edo tuning

	[[Category:Enneadecal]]		[[Category:Enneadecal]]
	[[Category:Hemienneadecal]]		[[Category:Hemienneadecal]]
			[[Category:Listen]]
	[[Category:Semihemienneadecal]]		[[Category:Semihemienneadecal]]
	~~[[Category:Listen]]~~

Eliora: /* Rank-2 temperaments */ style

2023-11-06T22:08:29Z

Rank-2 temperaments: style

← Older revision		Revision as of 22:08, 6 November 2023
Line 93:		Line 93:
	\| [[Enneadecal]]		\| [[Enneadecal]]
	\|-		\|-
	\|31		\| 31
	\|581\1178		\| 581\1178<br>(11\1178)
	(11\1178)		\| 591.851<br>(11.205)
	\|591.851		\| 936/665<br>(?)
	(11.205)		\| [[31st-octave temperaments#217 & 1178\|217 & 1178]]
	\|936/665

	(?)
	\|[[217 & 1178]]
	\|-		\|-
	\| 38		\| 38

Eliora: /* Rank-2 temperaments */ + 217 & 1178 as music is composed in it

2023-11-06T22:07:50Z

Rank-2 temperaments: + 217 & 1178 as music is composed in it

@@ Line 92: / Line 92: @@
 | 4/3<br>(225/224)
 | [[Enneadecal]]
 |-
 | 38

FloraC: /* Regular temperament properties */ +semihemienneadecal

2023-11-05T13:50:12Z

Regular temperament properties: +semihemienneadecal

← Older revision		Revision as of 13:50, 5 November 2023
Line 92:		Line 92:
	\| 4/3<br>(225/224)		\| 4/3<br>(225/224)
	\| [[Enneadecal]]		\| [[Enneadecal]]
			\|-
			\| 38
			\| 260\1178<br>(12\1178)
			\| 264.86<br>(12.22)
			\| 500/429<br>(144/143)
			\| [[Semihemienneadecal]]
	\|-		\|-
	\| 38		\| 38

FloraC: Review

2023-11-05T13:38:46Z

Review

← Older revision		Revision as of 13:38, 5 November 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	1178edo is a very strong 19-limit system, and is a [[zeta edo\|zeta peak, integral and gap edo]]. It is also [[consistency\|distinctly consistent]] through to the [[21-odd-limit]], and is the first edo past [[742edo\|742]] with a lower 19-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]]. A basis for its 19-limit [[comma]]s is [[2500/2499]], [[3025/3024]], 3250/3249, 4200/4199, [[4375/4374]], [[4914/4913]] ~~and 5985/5984~~. It [[support]]s and provides a great tuning for [[semihemienneadecal]].		1178edo is a very strong 19-limit system, and is a [[zeta edo\|zeta peak, integral and gap edo]]. It is also [[consistency\|distinctly consistent]] through to the [[21-odd-limit]], and is the first edo past [[742edo\|742]] with a lower 19-limit [[Tenney-Euclidean temperament measures #TE simple badness\|relative error]]. A [[comma basis\|basis]] for its 19-limit [[comma]]s consists of [[2500/2499]], [[3025/3024]], 3250/3249, 4200/4199, [[4225/4224]], [[4375/4374]], and [[4914/4913]]. It [[support]]s and provides a great tuning for [[semihemienneadecal]].

	=== Prime harmonics ===		=== Prime 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\|-1867 1178}}		\| {{monzo\| -1867 1178 }}
	\|{{~~val~~\|1178 1867}}		\| {{mapping\| 1178 1867 }}
	\| 0.0276		\| +0.0276
	\| 0.0276		\| 0.0276
	\| 2.71		\| 2.71
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|{{monzo\|-14 -19-19}}, {{monzo\|-99 61 1}}		\| {{monzo\| -14 -19-19 }}, {{monzo\| -99 61 1 }}
	\|{{~~val~~\|1178 1867 2735}}		\| {{mapping\| 1178 1867 2735 }}
	\| 0.0522		\| +0.0522
	\| 0.0415		\| 0.0415
	\| 4.07		\| 4.07
	\|-		\|-
	\|2.3.5.7		\| 2.3.5.7
	\|4375/4374, 703125/702464, ~~2460375/2458624~~		\| 4375/4374, 703125/702464, {{monzo\| -52 -5 -2 23 }}
	\|{{~~val~~\|1178 1867 2735 3307}}		\| {{mapping\| 1178 1867 2735 3307 }}
	\| 0.0450		\| +0.0450
	\| 0.0380		\| 0.0380
	\| 3.73		\| 3.73
	\|-		\|-
	\|2.3.5.7.11		\| 2.3.5.7.11
	\|3025/3024, 4375/4374, ~~9801~~/~~9800~~, ~~43923/43904~~		\| 3025/3024, 4375/4374, 234375/234256, {{monzo\| -27 3 -4 10 1 }}
	\|{{~~val~~\|1178 1867 2735 3307 4075}}		\| {{mapping\| 1178 1867 2735 3307 4075 }}
	\| 0.0484		\| +0.0484
	\| 0.0347		\| 0.0347
	\| 3.41		\| 3.41
	\|-		\|-
	\|2.3.5.7.11.13		\| 2.3.5.7.11.13
	\|3025/3024, 4225/4224, ~~9801~~/~~9800~~, ~~91125~~/~~91091~~, 1664000/1663893		\| 3025/3024, 4225/4224, 4375/4374, 78125/78078, 1664000/1663893
	\|{{~~val~~\|1178 1867 2735 3307 4075 4359}}		\| {{mapping\| 1178 1867 2735 3307 4075 4359 }}
	\| 0.0457		\| +0.0457
	\| 0.0322		\| 0.0322
	\| 3.16		\| 3.16
	\|-		\|-
	\|2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	\|3025/3024, 4225/4224, ~~5832~~/~~5831~~, ~~9801~~/~~9800~~, 14875/14872~~, 31213/31212~~		\| 2500/2499, 3025/3024, 4225/4224, 4375/4374, 4914/4913, 14875/14872
	\|{{~~val~~\|1178 1867 2735 3307 4075 4359 4815}}		\| {{mapping\| 1178 1867 2735 3307 4075 4359 4815 }}
	\| 0.0403		\| 0.0403
	\| 0.0327		\| 0.0327
	\| 3.21		\| 3.21
	\|-		\|-
	\|2.3.5.7.11.13.17.19		\| 2.3.5.7.11.13.17.19
	\|~~4200~~/~~4199~~, ~~5985~~/~~5984~~, ~~9801~~/~~9800~~, ~~10830~~/~~10829~~, ~~12636~~/~~12635~~, ~~14365~~/~~14364~~, ~~23409~~/~~23408~~		\| 2500/2499, 3025/3024, 3250/3249, 4200/4199, 4225/4224, 4375/4374, 4914/4913
	\|{{~~val~~\|1178 1867 2735 3307 4075 4359 4815 5004}}		\| {{mapping\| 1178 1867 2735 3307 4075 4359 4815 5004 }}
	\| 0.0370		\| 0.0370
	\| 0.0318		\| 0.0318
	\| 3.12		\| 3.12
	\|}		\|}

	=== 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		\|+Table of rank-2 temperaments by generator
	! Periods<br>per 8ve		! Periods<br>per 8ve
	! Generator~~<br>(reduced)~~		! Generator*
	! Cents~~<br>(reduced)~~		! Cents*
	! Associated<br>~~ratio~~		! Associated<br>Ratio*
	! Temperaments		! Temperaments
	\|-		\|-
	\|1		\| 1
	\|337\1178		\| 337\1178
	\|343.29		\| 343.29
	\|8000/6561		\| 8000/6561
	\|[[Raider]]		\| [[Raider]]
	\|-		\|-
	\|19		\| 19
	\|489\1178<br>(7\1178)		\| 489\1178<br>(7\1178)
	\|498.13<br>(7.13)		\| 498.13<br>(7.13)
	\|4/3<br>(225/224)		\| 4/3<br>(225/224)
	\|[[Enneadecal]]		\| [[Enneadecal]]
	\|-		\|-
	\|38		\| 38
	\|489\1178<br>(7\1178)		\| 489\1178<br>(7\1178)
	\|498.13<br>(7.13)		\| 498.13<br>(7.13)
	\|4/3<br>(225/224)		\| 4/3<br>(225/224)
	\|[[Hemienneadecal]]		\| [[Hemienneadecal]]
	\|}		\|}
			<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 ==		== Music ==
	; ~~'''~~[[Eliora]]~~'''~~		; [[Eliora]]
	* [https://www.youtube.com/watch?v=c9e7MTsIDc4 Listening] (2023) - 217 & 1178 and enneadecal in 1178edo tuning		* [https://www.youtube.com/watch?v=c9e7MTsIDc4 ''Listening''] (2023) – 217 & 1178 and enneadecal in 1178edo tuning

	[[Category:Enneadecal]]		[[Category:Enneadecal]]
	[[Category:Hemienneadecal]]		[[Category:Hemienneadecal]]
	[[Category:Semihemienneadecal]]		[[Category:Semihemienneadecal]]
	[[Category:Listen]]		[[Category:Listen]]

Eliora: if there is a music plz add to listen

2023-11-04T19:51:33Z

if there is a music plz add to listen

← Older revision		Revision as of 19:51, 4 November 2023
Line 105:		Line 105:
	[[Category:Hemienneadecal]]		[[Category:Hemienneadecal]]
	[[Category:Semihemienneadecal]]		[[Category:Semihemienneadecal]]
			[[Category:Listen]]