877edo - 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"

2026-03-13T13:32:11Z

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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	\| [[Sesesix]]		\| [[Sesesix]]
	\|}		\|}
	<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 ==

Francium: /* Music */ +music

2025-05-21T11:03:59Z

Music: +music

← Older revision		Revision as of 11:03, 21 May 2025
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	* "Stay In the Eyes of the House." from ''Random Sentences'' (2025) – [https://open.spotify.com/track/1fi1zIHjccUpBin6WacaoA Spotify] \| [https://francium223.bandcamp.com/track/stay-in-the-eyes-of-the-house Bandcamp] \| [https://www.youtube.com/watch?v=P0nCXyQdYCg YouTube]		* "Stay In the Eyes of the House." from ''Random Sentences'' (2025) – [https://open.spotify.com/track/1fi1zIHjccUpBin6WacaoA Spotify] \| [https://francium223.bandcamp.com/track/stay-in-the-eyes-of-the-house Bandcamp] \| [https://www.youtube.com/watch?v=P0nCXyQdYCg YouTube]
	* "My Throat Is Not An Egg" from ''Eggs'' (2025) – [https://open.spotify.com/track/4LEaU8QXI2BUv1gMcNIl5S Spotify] \| [https://francium223.bandcamp.com/track/my-throat-is-not-an-egg Bandcamp] \| [https://www.youtube.com/watch?v=G-HZx5Rv7QE YouTube]		* "My Throat Is Not An Egg" from ''Eggs'' (2025) – [https://open.spotify.com/track/4LEaU8QXI2BUv1gMcNIl5S Spotify] \| [https://francium223.bandcamp.com/track/my-throat-is-not-an-egg Bandcamp] \| [https://www.youtube.com/watch?v=G-HZx5Rv7QE YouTube]
			* "Ghost In the Attic" from ''Void'' (2025) – [https://open.spotify.com/track/1hecNwT1QIrlUZqzTsx2i7 Spotify] \| [https://francium223.bandcamp.com/track/ghost-in-the-attic Bandcamp] \| [https://www.youtube.com/watch?v=VJO_Ysm50AY YouTube]

Francium: /* Music */ +music

2025-04-29T11:04:30Z

Music: +music

← Older revision		Revision as of 11:04, 29 April 2025
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	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "Stay In the Eyes of the House." from ''Random Sentences'' (2025) – [https://open.spotify.com/track/1fi1zIHjccUpBin6WacaoA Spotify] \| [https://francium223.bandcamp.com/track/stay-in-the-eyes-of-the-house Bandcamp] \| [https://www.youtube.com/watch?v=P0nCXyQdYCg YouTube] – ~~in Pedersenic, 877edo tuning~~		* "Stay In the Eyes of the House." from ''Random Sentences'' (2025) – [https://open.spotify.com/track/1fi1zIHjccUpBin6WacaoA Spotify] \| [https://francium223.bandcamp.com/track/stay-in-the-eyes-of-the-house Bandcamp] \| [https://www.youtube.com/watch?v=P0nCXyQdYCg YouTube]
			* "My Throat Is Not An Egg" from ''Eggs'' (2025) – [https://open.spotify.com/track/4LEaU8QXI2BUv1gMcNIl5S Spotify] \| [https://francium223.bandcamp.com/track/my-throat-is-not-an-egg Bandcamp] \| [https://www.youtube.com/watch?v=G-HZx5Rv7QE YouTube]

Francium: +music

2025-02-20T12:04:32Z

+music

← Older revision		Revision as of 12:04, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|877~~}}		{{ED intro}}

	== Theory ==		== Theory ==
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	\|}		\|}
	<nowiki/>* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct		<nowiki/>* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

			== Music ==
			; [[Francium]]
			* "Stay In the Eyes of the House." from ''Random Sentences'' (2025) – [https://open.spotify.com/track/1fi1zIHjccUpBin6WacaoA Spotify] \| [https://francium223.bandcamp.com/track/stay-in-the-eyes-of-the-house Bandcamp] \| [https://www.youtube.com/watch?v=P0nCXyQdYCg YouTube] – in Pedersenic, 877edo tuning

FloraC: Cleanup. It's best to present nullity-1 temps in terms of commas

2025-01-10T17:16:11Z

Cleanup. It's best to present nullity-1 temps in terms of commas

← Older revision		Revision as of 17:16, 10 January 2025
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	== Theory ==		== Theory ==
	877edo is [[consistent]] to the [[15-odd-limit]]. It [[tempers out]] [[3025/3024]], 496125/495616, [[420175/419904]] ~~and~~ 40960000/40920957 in the 11-limit; [[2080/2079]]~~, 3025/3024~~, [[123201/123200]], 91125/91091 and [[65625/65536]] in the 13-limit. Using the 2.3.7.11.23.43 [[subgroup]], it tempers out [[3312/3311]]. ~~The equal temperament~~ [[support]]s ~~[[quartic]],~~ [[quarterframe]] ~~and pulsar temperaments~~.		877edo is [[consistent]] to the [[15-odd-limit]]. As an equal temperament, it [[tempering out\|tempers out]] [[3025/3024]], 496125/495616, [[420175/419904]], 40960000/40920957, as well as the [[quartisma]] in the 11-limit; [[2080/2079]], [[123201/123200]], 91125/91091 and [[65625/65536]] in the 13-limit. Using the 2.3.7.11.23.43 [[subgroup]]<!-- explain why this subgroup is good to consider -->, it tempers out [[3312/3311]]. It [[support]]s the [[quarterframe]] temperament.

	=== 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]]
	! 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\|-1390 877}}		\| {{monzo\| -1390 877 }}
	\| {{mapping\|877 1390}}		\| {{mapping\| 877 1390 }}
	\| 0.0052		\| 0.0052
	\| 0.0052		\| 0.0052
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	\|-		\|-
	\| 2.3.5		\| 2.3.5
	\| {{monzo\|-20 -24 25}}, {{monzo\|54 -37 2}}		\| {{monzo\| -20 -24 25 }}, {{monzo\| 54 -37 2 }}
	\| {{mapping\|877 1390 2036}}		\| {{mapping\| 877 1390 2036 }}
	\| 0.0685		\| 0.0685
	\| 0.0896		\| 0.0896
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	\|-		\|-
	\| 2.3.5.7		\| 2.3.5.7
	\| 65625/65536, 420175/419904, {{monzo\|18 -18 13 -7}}		\| 65625/65536, 420175/419904, {{monzo\| 18 -18 13 -7 }}
	\| {{mapping\|877 1390 2036 2462}}		\| {{mapping\| 877 1390 2036 2462 }}
	\| 0.0575		\| 0.0575
	\| 0.0799		\| 0.0799
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	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 3025/3024, 496125/495616, 420175/419904, 40960000/40920957		\| 3025/3024, 496125/495616, 420175/419904, 40960000/40920957
	\| {{mapping\|877 1390 2036 2462 3034}}		\| {{mapping\| 877 1390 2036 2462 3034 }}
	\| 0.0398		\| 0.0398
	\| 0.0797		\| 0.0797
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	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 2080/2079, 3025/3024, 123201/123200, 91125/91091, 65625/65536		\| 2080/2079, 3025/3024, 123201/123200, 91125/91091, 65625/65536
	\| {{mapping\|877 1390 2036 2462 3034 3245}}		\| {{mapping\| 877 1390 2036 2462 3034 3245 }}
	\| 0.0508		\| 0.0508
	\| 0.0768		\| 0.0768
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	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br>~~Ratio~~*		! Associated<br>ratio*
	! Temperaments		! Temperaments
	\|-		\|-
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	\| 182\877		\| 182\877
	\| 249.031		\| 249.031
	\| {{monzo\|-26 18 -1}}		\| {{monzo\| -26 18 -1 }}
	\| [[Monzismic]]		\| [[Monzismic]]
	\|-		\|-
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	\| [[Sesesix]]		\| [[Sesesix]]
	\|}		\|}
			<nowiki/>* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct
	<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|877}} == Theory == 877edo is consistent to the 15-odd-limit. It tempers out 3025/3024, 496125/495616, 420175/419904 and 4096000..."

2025-01-07T12:26:50Z

Created page with "{{Infobox ET}} {{EDO intro|877}} == Theory == 877edo is consistent to the 15-odd-limit. It tempers out 3025/3024, 496125/495616, 420175/419904 and 4096000..."

New page

{{Infobox ET}}
{{EDO intro|877}}

== Theory ==
877edo is [[consistent]] to the [[15-odd-limit]]. It [[tempers out]] [[3025/3024]], 496125/495616, [[420175/419904]] and 40960000/40920957 in the 11-limit; [[2080/2079]], 3025/3024, [[123201/123200]], 91125/91091 and [[65625/65536]] in the 13-limit. Using the 2.3.7.11.23.43 [[subgroup]], it tempers out [[3312/3311]]. The equal temperament [[support]]s [[quartic]], [[quarterframe]] and pulsar temperaments.

=== Prime harmonics ===
{{Harmonics in equal|877}}

=== Subsets and supersets ===
877edo is the 151st [[prime edo]].

== 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|-1390 877}}
| {{mapping|877 1390}}
| 0.0052
| 0.0052
| 0.38
|-
| 2.3.5
| {{monzo|-20 -24 25}}, {{monzo|54 -37 2}}
| {{mapping|877 1390 2036}}
| 0.0685
| 0.0896
| 6.55
|-
| 2.3.5.7
| 65625/65536, 420175/419904, {{monzo|18 -18 13 -7}}
| {{mapping|877 1390 2036 2462}}
| 0.0575
| 0.0799
| 5.84
|-
| 2.3.5.7.11
| 3025/3024, 496125/495616, 420175/419904, 40960000/40920957
| {{mapping|877 1390 2036 2462 3034}}
| 0.0398
| 0.0797
| 5.82
|-
| 2.3.5.7.11.13
| 2080/2079, 3025/3024, 123201/123200, 91125/91091, 65625/65536
| {{mapping|877 1390 2036 2462 3034 3245}}
| 0.0508
| 0.0768
| 5.61
|}

=== 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
| 182\877
| 249.031
| {{monzo|-26 18 -1}}
| [[Monzismic]]
|-
| 1
| 231\877
| 316.078
| 6/5
| [[Counterhanson]]
|-
| 1
| 359\877
| 491.220
| 8388608/6328125
| [[Sesesix]]
|}

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

← Older revision		Revision as of 11:03, 21 May 2025
Line 91:		Line 91:
	* "Stay In the Eyes of the House." from ''Random Sentences'' (2025) – [https://open.spotify.com/track/1fi1zIHjccUpBin6WacaoA Spotify] \| [https://francium223.bandcamp.com/track/stay-in-the-eyes-of-the-house Bandcamp] \| [https://www.youtube.com/watch?v=P0nCXyQdYCg YouTube]		* "Stay In the Eyes of the House." from ''Random Sentences'' (2025) – [https://open.spotify.com/track/1fi1zIHjccUpBin6WacaoA Spotify] \| [https://francium223.bandcamp.com/track/stay-in-the-eyes-of-the-house Bandcamp] \| [https://www.youtube.com/watch?v=P0nCXyQdYCg YouTube]
	* "My Throat Is Not An Egg" from ''Eggs'' (2025) – [https://open.spotify.com/track/4LEaU8QXI2BUv1gMcNIl5S Spotify] \| [https://francium223.bandcamp.com/track/my-throat-is-not-an-egg Bandcamp] \| [https://www.youtube.com/watch?v=G-HZx5Rv7QE YouTube]		* "My Throat Is Not An Egg" from ''Eggs'' (2025) – [https://open.spotify.com/track/4LEaU8QXI2BUv1gMcNIl5S Spotify] \| [https://francium223.bandcamp.com/track/my-throat-is-not-an-egg Bandcamp] \| [https://www.youtube.com/watch?v=G-HZx5Rv7QE YouTube]
			* "Ghost In the Attic" from ''Void'' (2025) – [https://open.spotify.com/track/1hecNwT1QIrlUZqzTsx2i7 Spotify] \| [https://francium223.bandcamp.com/track/ghost-in-the-attic Bandcamp] \| [https://www.youtube.com/watch?v=VJO_Ysm50AY YouTube]