894edo - Revision history

FloraC: Add trivish to the theory section

2026-06-20T15:28:14Z

Add trivish to the theory section

← Older revision		Revision as of 15:28, 20 June 2026
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	894edo is [[consistent]] to the [[17-odd-limit]], and except for [[19/13]], [[19/17]], [[25/13]], [[25/17]] and their [[octave complement]]s, it is consistent to the [[31-odd-limit]], thus making it a reasonable [[31-limit]] system. Its [[prime interval\|primes]] [[5/1\|5]], [[17/1\|17]], [[19/1\|19]], and [[23/1\|23]] come from [[149edo]], its [[11/1\|11]] from [[298edo]], and its [[7/1\|7]] and [[13/1\|13]] from [[447edo]].		894edo is [[consistent]] to the [[17-odd-limit]], and except for [[19/13]], [[19/17]], [[25/13]], [[25/17]] and their [[octave complement]]s, it is consistent to the [[31-odd-limit]], thus making it a reasonable [[31-limit]] system. Its [[prime interval\|primes]] [[5/1\|5]], [[17/1\|17]], [[19/1\|19]], and [[23/1\|23]] come from [[149edo]], its [[11/1\|11]] from [[298edo]], and its [[7/1\|7]] and [[13/1\|13]] from [[447edo]].

	As an equal temperament, it [[tempering out\|tempers out]] {{monzo\| 23 6 -14 }} ([[vishnu comma]]) in the [[5-limit]]; 250047/250000 ([[landscape comma]]) in the [[7-limit]]; [[9801/9800]], [[131072/130977]], [[151263/151250]] in the [[11-limit]]; [[1716/1715]], [[2080/2079]], [[4096/4095]], [[4225/4224]], 34398/34375 in the [[13-limit]]; [[1156/1155]], [[2431/2430]], [[2601/2600]], [[11016/11011]] in the [[17-limit]]; [[1521/1520]], [[2376/2375]], [[3250/3249]] in the [[19-limit]]; and [[1863/1862]], [[2300/2299]] among others in the [[23-limit]].		As an equal temperament, it [[tempering out\|tempers out]] {{monzo\| 23 6 -14 }} ([[vishnu comma]]) in the [[5-limit]]; 250047/250000 ([[landscape comma]]) in the [[7-limit]]; [[9801/9800]], [[131072/130977]], [[151263/151250]] in the [[11-limit]]; [[1716/1715]], [[2080/2079]], [[4096/4095]], [[4225/4224]], 34398/34375 in the [[13-limit]]; [[1156/1155]], [[2431/2430]], [[2601/2600]], [[11016/11011]] in the [[17-limit]]; [[1521/1520]], [[2376/2375]], [[3250/3249]] in the [[19-limit]]; and [[1863/1862]], [[2300/2299]] among others in the [[23-limit]]. It provides the [[optimal patent val]] for the 13-limit [[trivish]] temperament.

	=== Prime harmonics ===		=== Prime harmonics ===
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	\|}		\|}
	<nowiki/>* In [[normal forms #Minimal-generator form\|minimal-generator form]]		<nowiki/>* In [[normal forms #Minimal-generator form\|minimal-generator form]]

			[[Category:Trivish]]

FloraC: /* Rank-2 temperaments */ + trivish. Also convert the table to minimal form since we're already reducing it to the first semi-octave

2026-06-20T15:25:12Z

Rank-2 temperaments: + trivish. Also convert the table to minimal form since we're already reducing it to the first semi-octave

← Older revision		Revision as of 15:25, 20 June 2026
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	\| 25/24		\| 25/24
	\| [[Vishnu]] (5-limit)		\| [[Vishnu]] (5-limit)
			\|-
			\| 6
			\| 53\894
			\| 71.14
			\| 25/24
			\| [[Trivish]]
	\|}		\|}
	<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~~		<nowiki/>* In [[normal forms #Minimal-generator form\|minimal-generator form]]

FloraC: /* Theory */ correction

2026-06-18T15:19:12Z

Theory: correction

← Older revision		Revision as of 15:19, 18 June 2026
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	== Theory ==		== Theory ==
	894edo is [[consistent]] to the [[17-odd-limit]], and except for [[19/13]], [[19/17]] and their [[octave complement]]s, it is consistent to the [[31-odd-limit]], thus making it a ~~good~~ [[31-limit]] system. Its [[prime interval\|primes]] [[5/1\|5]], [[17/1\|17]], [[19/1\|19]], and [[23/1\|23]] come from [[149edo]], its [[11/1\|11]] from [[298edo]], and its [[7/1\|7]] and [[13/1\|13]] from [[447edo]].		894edo is [[consistent]] to the [[17-odd-limit]], and except for [[19/13]], [[19/17]], [[25/13]], [[25/17]] and their [[octave complement]]s, it is consistent to the [[31-odd-limit]], thus making it a reasonable [[31-limit]] system. Its [[prime interval\|primes]] [[5/1\|5]], [[17/1\|17]], [[19/1\|19]], and [[23/1\|23]] come from [[149edo]], its [[11/1\|11]] from [[298edo]], and its [[7/1\|7]] and [[13/1\|13]] from [[447edo]].

	As an equal temperament, it [[tempering out\|tempers out]] {{monzo\| 23 6 -14 }} ([[vishnu comma]]) in the [[5-limit]]; 250047/250000 ([[landscape comma]]) in the [[7-limit]]; [[9801/9800]], [[131072/130977]], [[151263/151250]] in the [[11-limit]]; [[1716/1715]], [[2080/2079]], [[4096/4095]], [[4225/4224]], 34398/34375 in the [[13-limit]]; [[1156/1155]], [[2431/2430]], [[2601/2600]], [[11016/11011]] in the [[17-limit]]; [[1521/1520]], [[2376/2375]], [[3250/3249]] in the [[19-limit]]; and [[1863/1862]], [[2300/2299]] among others in the [[23-limit]].		As an equal temperament, it [[tempering out\|tempers out]] {{monzo\| 23 6 -14 }} ([[vishnu comma]]) in the [[5-limit]]; 250047/250000 ([[landscape comma]]) in the [[7-limit]]; [[9801/9800]], [[131072/130977]], [[151263/151250]] in the [[11-limit]]; [[1716/1715]], [[2080/2079]], [[4096/4095]], [[4225/4224]], 34398/34375 in the [[13-limit]]; [[1156/1155]], [[2431/2430]], [[2601/2600]], [[11016/11011]] in the [[17-limit]]; [[1521/1520]], [[2376/2375]], [[3250/3249]] in the [[19-limit]]; and [[1863/1862]], [[2300/2299]] among others in the [[23-limit]].

FloraC: Birth

2026-06-18T06:28:30Z

Birth

New page

{{Infobox ET}}
{{ED intro}}

== Theory ==
894edo is [[consistent]] to the [[17-odd-limit]], and except for [[19/13]], [[19/17]] and their [[octave complement]]s, it is consistent to the [[31-odd-limit]], thus making it a good [[31-limit]] system. Its [[prime interval|primes]] [[5/1|5]], [[17/1|17]], [[19/1|19]], and [[23/1|23]] come from [[149edo]], its [[11/1|11]] from [[298edo]], and its [[7/1|7]] and [[13/1|13]] from [[447edo]].

As an equal temperament, it [[tempering out|tempers out]] {{monzo| 23 6 -14 }} ([[vishnu comma]]) in the [[5-limit]]; 250047/250000 ([[landscape comma]]) in the [[7-limit]]; [[9801/9800]], [[131072/130977]], [[151263/151250]] in the [[11-limit]]; [[1716/1715]], [[2080/2079]], [[4096/4095]], [[4225/4224]], 34398/34375 in the [[13-limit]]; [[1156/1155]], [[2431/2430]], [[2601/2600]], [[11016/11011]] in the [[17-limit]]; [[1521/1520]], [[2376/2375]], [[3250/3249]] in the [[19-limit]]; and [[1863/1862]], [[2300/2299]] among others in the [[23-limit]].

=== Prime harmonics ===
{{Harmonics in equal|894|columns=11}}
{{Harmonics in equal|894|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 894edo (continued)}}

=== Subsets and supersets ===
Since 894 factors into primes as {{nowrap| 2 × 3 × 149 }}, 894edo contains subset edos {{EDOs| 2, 3, 6, 149, 298, and 447 }}.

== Regular temperament properties ==
{| 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
| {{Monzo| 1417 -894 }}
| {{Mapping| 894 1417 }}
| −0.0184
| 0.0184
| 1.37
|-
| 2.3.5
| {{Monzo| 23 6 -14 }}, {{monzo| 93 -66 5 }}
| {{Mapping| 894 1417 2076 }}
| −0.0501
| 0.0473
| 3.52
|-
| 2.3.5.7
| 250047/250000, 43046721/43025920, 134217728/133984375
| {{Mapping| 894 1417 2076 2510 }}
| −0.0644
| 0.0479
| 3.57
|-
| 2.3.5.7.11
| 9801/9800, 131072/130977, 151263/151250, 1771875/1771561
| {{Mapping| 894 1417 2076 2510 3093 }}
| −0.0724
| 0.0456
| 3.40
|-
| 2.3.5.7.11.13
| 1716/1715, 2080/2079, 4096/4095, 34398/34375, 1574640/1574573
| {{Mapping| 894 1417 2076 2510 3093 3308 }}
| −0.0486
| 0.0675
| 5.03
|-
| 2.3.5.7.11.13.17
| 1156/1155, 1716/1715, 2080/2079, 2431/2430, 4096/4095, 34398/34375
| {{Mapping| 894 1417 2076 2510 3093 3308 3654 }}
| −0.0327
| 0.0737
| 5.49
|-
| 2.3.5.7.11.13.17.19
| 1156/1155, 1521/1520, 1716/1715, 2080/2079, 2376/2375, 2431/2430, 3250/3249
| {{Mapping| 894 1417 2076 2510 3093 3308 3654 3798 }}
| −0.0425
| 0.0737
| 5.49
|-
| 2.3.5.7.11.13.17.19.23
| 1156/1155, 1521/1520, 1716/1715, 1863/1862, 2080/2079, 2376/2375, 2431/2430, 3250/3249
| {{Mapping| 894 1417 2076 2510 3093 3308 3654 3798 4044 }}
| −0.0357
| 0.0721
| 5.37
|}

=== Rank-2 temperaments ===
{| 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
| 53\894
| 71.14
| 25/24
| [[Vishnu]] (5-limit)
|}
<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