677edo - 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"

2026-03-13T13:31:49Z

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 13:31, 13 March 2026
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	\| [[Counterschismic]]		\| [[Counterschismic]]
	\|}		\|}
	<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

2025-04-28T11:54:37Z

Music: +music

← Older revision		Revision as of 11:54, 28 April 2025
Line 94:		Line 94:
	; [[Francium]]		; [[Francium]]
	* "From the Ears of the Eel" from ''Scoop'' (2024) – [https://open.spotify.com/track/163kPfkX9BJ6l7jXbJDVOG Spotify] \| [https://francium223.bandcamp.com/track/from-the-ears-of-the-eel Bandcamp] \| [https://www.youtube.com/watch?v=WHY3EKLi7Zk YouTube]		* "From the Ears of the Eel" from ''Scoop'' (2024) – [https://open.spotify.com/track/163kPfkX9BJ6l7jXbJDVOG Spotify] \| [https://francium223.bandcamp.com/track/from-the-ears-of-the-eel Bandcamp] \| [https://www.youtube.com/watch?v=WHY3EKLi7Zk YouTube]
	* "The Scallop Disco Accident" from ''The Scallop Disco Accident'' (2025) – [https://open.spotify.com/track/3C4sVxcVJWIZqgbpgxoQo1 Spotify] \| [https://francium223.bandcamp.com/track/the-scallop-disco-accident Bandcamp] \| [https://www.youtube.com/watch?v=V12N5jC_UfM YouTube] ~~– in Scarlattic, 677edo tuning~~		* "The Scallop Disco Accident" from ''The Scallop Disco Accident'' (2025) – [https://open.spotify.com/track/3C4sVxcVJWIZqgbpgxoQo1 Spotify] \| [https://francium223.bandcamp.com/track/the-scallop-disco-accident Bandcamp] \| [https://www.youtube.com/watch?v=V12N5jC_UfM YouTube]
	* "Make Gecko Expansion" from ''I Want To'' (2025) – [https://open.spotify.com/track/5dbEP5zQQrrO00f3XZiELV Spotify] \| [https://francium223.bandcamp.com/track/make-gecko-expansion Bandcamp] \| [https://www.youtube.com/watch?v=D55Y0-p_mWU YouTube] – ~~in Genzelic, 677edo tuning~~		* "Make Gecko Expansion" from ''I Want To'' (2025) – [https://open.spotify.com/track/5dbEP5zQQrrO00f3XZiELV Spotify] \| [https://francium223.bandcamp.com/track/make-gecko-expansion Bandcamp] \| [https://www.youtube.com/watch?v=D55Y0-p_mWU YouTube]
			* "Eggs Of An Oven" from ''Eggs'' (2025) – [https://open.spotify.com/track/0pe7FES4PhYa58UBaQScAS Spotify] \| [https://francium223.bandcamp.com/track/eggs-of-an-oven Bandcamp] \| [https://www.youtube.com/watch?v=sejOxKdHd8E YouTube]

ArrowHead294 at 18:19, 20 February 2025

2025-02-20T18:19:35Z

← Older revision		Revision as of 18:19, 20 February 2025
Line 22:		Line 22:
	== 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" \|[[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		! rowspan="2" \| [[Subgroup]]
	\|{{monzo\|-1073 677}}		! rowspan="2" \| [[Comma list]]
	\|{{mapping\|677 1073}}		! rowspan="2" \| [[Mapping]]
			! rowspan="2" \| Optimal<br />8ve stretch (¢)
			! colspan="2" \| Tuning error
			\|-
			! [[TE error\|Absolute]] (¢)
			! [[TE simple badness\|Relative]] (%)
			\|-
			\| 2.3
			\| {{monzo\|-1073 677}}
			\| {{mapping\|677 1073}}
	\| +0.0110		\| +0.0110
	\| 0.0110		\| 0.0110
	\| 0.62		\| 0.62
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|{{monzo\|38 -2 -15}}, {{monzo\|-31 43 -16}}		\| {{monzo\|38 -2 -15}}, {{monzo\|-31 43 -16}}
	\|{{mapping\|677 1073 1572}}		\| {{mapping\|677 1073 1572}}
	\| -0.0066		\| −0.0066
	\| 0.0264		\| 0.0264
	\| 1.49		\| 1.49
	\|-		\|-
	\|2.3.5.7		\| 2.3.5.7
	\|703125/702464, 589824/588245, 14348907/14336000		\| 703125/702464, 589824/588245, 14348907/14336000
	\|{{mapping\|677 1073 1572 1901}}		\| {{mapping\|677 1073 1572 1901}}
	\| -0.0714		\| −0.0714
	\| 0.1145		\| 0.1145
	\| 6.46		\| 6.46
	\|-		\|-
	\|2.3.5.7.11		\| 2.3.5.7.11
	\|3025/3024, 24057/24010, 131072/130977, 759375/758912		\| 3025/3024, 24057/24010, 131072/130977, 759375/758912
	\|{{mapping\|677 1073 1572 1901 2342}}		\| {{mapping\|677 1073 1572 1901 2342}}
	\| -0.0535		\| −0.0535
	\| 0.1084		\| 0.1084
	\| 6.12		\| 6.12
Line 62:		Line 63:
	=== 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		\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
	! Periods<br>per 8ve		\|-
	! Generator~~<br>(reduced)~~*		! Periods<br />per 8ve
	! Cents~~<br>(reduced)~~*		! Generator*
	! Associated<br>~~Ratio~~*		! Cents*
			! Associated<br />ratio*
	! Temperaments		! Temperaments
	\|-		\|-
	\|1		\| 1
	\|109\677		\| 109\677
	\|193.21		\| 193.21
	\|262144/234375		\| 262144/234375
	\|[[Luna]]		\| [[Luna]]
	\|-		\|-
	\|1		\| 1
	\|125\677		\| 125\677
	\|221.57		\| 221.57
	\|8388608/7381125		\| 8388608/7381125
	\|[[Fortune]]		\| [[Fortune]]
	\|-		\|-
	\|1		\| 1
	\|281\677		\| 281\677
	\|498.08		\| 498.08
	\|4/3		\| 4/3
	\|[[Counterschismic]]		\| [[Counterschismic]]
	\|}		\|}
			<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

2025-02-19T18:15:56Z

changed EDO intro to ED intro

← Older revision		Revision as of 18:15, 19 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|677~~}}		{{ED intro}}

	== Theory ==		== Theory ==
	While it does well as a 2.3.5.11 tuning system, it's notable for its high accuracy among EDOs of about its size and lower with the first several [[wikipedia:Metallic_mean\|metallic ratios]]. Among those, it tunes [[acoustic phi]] (the golden ratio) and the acoustic copper ratio each with less than 1% relative error. The first nine metallic ratios are all tuned within 20% of an edostep.		While it does well as a 2.3.5.11 tuning system, it's notable for its high accuracy among EDOs of about its size and lower with the first several [[wikipedia:Metallic_mean\|metallic ratios]]. Among those, it tunes [[acoustic phi]] (the golden ratio) and the acoustic copper ratio each with less than 1% relative error. The first nine metallic ratios are all tuned within 20% of an edostep.

Francium: /* Music */ +music

2025-02-05T12:42:51Z

Music: +music

← Older revision		Revision as of 12:42, 5 February 2025
Line 91:		Line 91:
	* "From the Ears of the Eel" from ''Scoop'' (2024) – [https://open.spotify.com/track/163kPfkX9BJ6l7jXbJDVOG Spotify] \| [https://francium223.bandcamp.com/track/from-the-ears-of-the-eel Bandcamp] \| [https://www.youtube.com/watch?v=WHY3EKLi7Zk YouTube]		* "From the Ears of the Eel" from ''Scoop'' (2024) – [https://open.spotify.com/track/163kPfkX9BJ6l7jXbJDVOG Spotify] \| [https://francium223.bandcamp.com/track/from-the-ears-of-the-eel Bandcamp] \| [https://www.youtube.com/watch?v=WHY3EKLi7Zk YouTube]
	* "The Scallop Disco Accident" from ''The Scallop Disco Accident'' (2025) – [https://open.spotify.com/track/3C4sVxcVJWIZqgbpgxoQo1 Spotify] \| [https://francium223.bandcamp.com/track/the-scallop-disco-accident Bandcamp] \| [https://www.youtube.com/watch?v=V12N5jC_UfM YouTube] – in Scarlattic, 677edo tuning		* "The Scallop Disco Accident" from ''The Scallop Disco Accident'' (2025) – [https://open.spotify.com/track/3C4sVxcVJWIZqgbpgxoQo1 Spotify] \| [https://francium223.bandcamp.com/track/the-scallop-disco-accident Bandcamp] \| [https://www.youtube.com/watch?v=V12N5jC_UfM YouTube] – in Scarlattic, 677edo tuning
			* "Make Gecko Expansion" from ''I Want To'' (2025) – [https://open.spotify.com/track/5dbEP5zQQrrO00f3XZiELV Spotify] \| [https://francium223.bandcamp.com/track/make-gecko-expansion Bandcamp] \| [https://www.youtube.com/watch?v=D55Y0-p_mWU YouTube] – in Genzelic, 677edo tuning

Francium: /* Music */ +music

2025-01-13T13:24:54Z

Music: +music

← Older revision		Revision as of 13:24, 13 January 2025
Line 90:		Line 90:
	; [[Francium]]		; [[Francium]]
	* "From the Ears of the Eel" from ''Scoop'' (2024) – [https://open.spotify.com/track/163kPfkX9BJ6l7jXbJDVOG Spotify] \| [https://francium223.bandcamp.com/track/from-the-ears-of-the-eel Bandcamp] \| [https://www.youtube.com/watch?v=WHY3EKLi7Zk YouTube]		* "From the Ears of the Eel" from ''Scoop'' (2024) – [https://open.spotify.com/track/163kPfkX9BJ6l7jXbJDVOG Spotify] \| [https://francium223.bandcamp.com/track/from-the-ears-of-the-eel Bandcamp] \| [https://www.youtube.com/watch?v=WHY3EKLi7Zk YouTube]
			* "The Scallop Disco Accident" from ''The Scallop Disco Accident'' (2025) – [https://open.spotify.com/track/3C4sVxcVJWIZqgbpgxoQo1 Spotify] \| [https://francium223.bandcamp.com/track/the-scallop-disco-accident Bandcamp] \| [https://www.youtube.com/watch?v=V12N5jC_UfM YouTube] – in Scarlattic, 677edo tuning

Francium: +music

2024-11-13T13:18:48Z

+music

← Older revision		Revision as of 13:18, 13 November 2024
Line 86:		Line 86:
	\|[[Counterschismic]]		\|[[Counterschismic]]
	\|}		\|}

			== Music ==
			; [[Francium]]
			* "From the Ears of the Eel" from ''Scoop'' (2024) – [https://open.spotify.com/track/163kPfkX9BJ6l7jXbJDVOG Spotify] \| [https://francium223.bandcamp.com/track/from-the-ears-of-the-eel Bandcamp] \| [https://www.youtube.com/watch?v=WHY3EKLi7Zk YouTube]

Francium: /* Theory */

2023-11-22T18:35:25Z

Theory

← Older revision		Revision as of 18:35, 22 November 2023
Line 2:		Line 2:
	{{EDO intro\|677}}		{{EDO intro\|677}}
	== Theory ==		== Theory ==
	~~'''677 equal divisions of the octave''' (677edo) is a tuning system with notes that are about 1.77¢ apart.~~ While it does well as a 2.3.5.11 tuning system, it's notable for its high accuracy among EDOs of about its size and lower with the first several [[wikipedia:Metallic_mean\|metallic ratios]]. Among those, it tunes [[acoustic phi]] (the golden ratio) and the acoustic copper ratio each with less than 1% relative error. The first nine metallic ratios are all tuned within 20% of an edostep.		While it does well as a 2.3.5.11 tuning system, it's notable for its high accuracy among EDOs of about its size and lower with the first several [[wikipedia:Metallic_mean\|metallic ratios]]. Among those, it tunes [[acoustic phi]] (the golden ratio) and the acoustic copper ratio each with less than 1% relative error. The first nine metallic ratios are all tuned within 20% of an edostep.

	=== Prime harmonics ===		=== Prime harmonics ===

Francium at 18:34, 22 November 2023

2023-11-22T18:34:48Z

@@ Line 1: / Line 1: @@
-{{Infobox ET|677edo}}
+{{Infobox ET}}
+{{EDO intro|677}}
 '''677 equal divisions of the octave''' (677edo) is a tuning system with notes that are about 1.77¢ apart. While it does well as a 2.3.5.11 tuning system, it's notable for its high accuracy among EDOs of about its size and lower with the first several [[wikipedia:Metallic_mean|metallic ratios]]. Among those, it tunes [[acoustic phi]] (the golden ratio) and the acoustic copper ratio each with less than 1% relative error. The first nine metallic ratios are all tuned within 20% of an edostep.
 {{Harmonics in equal
 | steps = 677
@@ Line 13: / Line 15: @@
 | intervals = prime
 }}

Tristanbay: Added infoboxes

2023-11-15T09:36:22Z

Added infoboxes

← Older revision		Revision as of 09:36, 15 November 2023
Line 1:		Line 1:
			{{Infobox ET\|677edo}}

	'''677 equal divisions of the octave''' (677edo) is a tuning system with notes that are about 1.77¢ apart. While it does well as a 2.3.5.11 tuning system, it's notable for its high accuracy among EDOs of about its size and lower with the first several [[wikipedia:Metallic_mean\|metallic ratios]]. Among those, it tunes [[acoustic phi]] (the golden ratio) and the acoustic copper ratio each with less than 1% relative error. The first nine metallic ratios are all tuned within 20% of an edostep.		'''677 equal divisions of the octave''' (677edo) is a tuning system with notes that are about 1.77¢ apart. While it does well as a 2.3.5.11 tuning system, it's notable for its high accuracy among EDOs of about its size and lower with the first several [[wikipedia:Metallic_mean\|metallic ratios]]. Among those, it tunes [[acoustic phi]] (the golden ratio) and the acoustic copper ratio each with less than 1% relative error. The first nine metallic ratios are all tuned within 20% of an edostep.

			{{Harmonics in equal
			\| steps = 677
			\| num = 2
			\| denom = 1
			\| columns = 9
			\| start = 1
			\| prec = 2
			\| title = Approximation of prime harmonics in 677edo
			\| intervals = prime
			}}

← Older revision		Revision as of 11:54, 28 April 2025
Line 94:		Line 94:
	; [[Francium]]		; [[Francium]]
	* "From the Ears of the Eel" from ''Scoop'' (2024) – [https://open.spotify.com/track/163kPfkX9BJ6l7jXbJDVOG Spotify] \| [https://francium223.bandcamp.com/track/from-the-ears-of-the-eel Bandcamp] \| [https://www.youtube.com/watch?v=WHY3EKLi7Zk YouTube]		* "From the Ears of the Eel" from ''Scoop'' (2024) – [https://open.spotify.com/track/163kPfkX9BJ6l7jXbJDVOG Spotify] \| [https://francium223.bandcamp.com/track/from-the-ears-of-the-eel Bandcamp] \| [https://www.youtube.com/watch?v=WHY3EKLi7Zk YouTube]
	* "The Scallop Disco Accident" from ''The Scallop Disco Accident'' (2025) – [https://open.spotify.com/track/3C4sVxcVJWIZqgbpgxoQo1 Spotify] \| [https://francium223.bandcamp.com/track/the-scallop-disco-accident Bandcamp] \| [https://www.youtube.com/watch?v=V12N5jC_UfM YouTube] ~~– in Scarlattic, 677edo tuning~~		* "The Scallop Disco Accident" from ''The Scallop Disco Accident'' (2025) – [https://open.spotify.com/track/3C4sVxcVJWIZqgbpgxoQo1 Spotify] \| [https://francium223.bandcamp.com/track/the-scallop-disco-accident Bandcamp] \| [https://www.youtube.com/watch?v=V12N5jC_UfM YouTube]
	* "Make Gecko Expansion" from ''I Want To'' (2025) – [https://open.spotify.com/track/5dbEP5zQQrrO00f3XZiELV Spotify] \| [https://francium223.bandcamp.com/track/make-gecko-expansion Bandcamp] \| [https://www.youtube.com/watch?v=D55Y0-p_mWU YouTube] – ~~in Genzelic, 677edo tuning~~		* "Make Gecko Expansion" from ''I Want To'' (2025) – [https://open.spotify.com/track/5dbEP5zQQrrO00f3XZiELV Spotify] \| [https://francium223.bandcamp.com/track/make-gecko-expansion Bandcamp] \| [https://www.youtube.com/watch?v=D55Y0-p_mWU YouTube]
			* "Eggs Of An Oven" from ''Eggs'' (2025) – [https://open.spotify.com/track/0pe7FES4PhYa58UBaQScAS Spotify] \| [https://francium223.bandcamp.com/track/eggs-of-an-oven Bandcamp] \| [https://www.youtube.com/watch?v=sejOxKdHd8E YouTube]

← Older revision		Revision as of 12:42, 5 February 2025
Line 91:		Line 91:
	* "From the Ears of the Eel" from ''Scoop'' (2024) – [https://open.spotify.com/track/163kPfkX9BJ6l7jXbJDVOG Spotify] \| [https://francium223.bandcamp.com/track/from-the-ears-of-the-eel Bandcamp] \| [https://www.youtube.com/watch?v=WHY3EKLi7Zk YouTube]		* "From the Ears of the Eel" from ''Scoop'' (2024) – [https://open.spotify.com/track/163kPfkX9BJ6l7jXbJDVOG Spotify] \| [https://francium223.bandcamp.com/track/from-the-ears-of-the-eel Bandcamp] \| [https://www.youtube.com/watch?v=WHY3EKLi7Zk YouTube]
	* "The Scallop Disco Accident" from ''The Scallop Disco Accident'' (2025) – [https://open.spotify.com/track/3C4sVxcVJWIZqgbpgxoQo1 Spotify] \| [https://francium223.bandcamp.com/track/the-scallop-disco-accident Bandcamp] \| [https://www.youtube.com/watch?v=V12N5jC_UfM YouTube] – in Scarlattic, 677edo tuning		* "The Scallop Disco Accident" from ''The Scallop Disco Accident'' (2025) – [https://open.spotify.com/track/3C4sVxcVJWIZqgbpgxoQo1 Spotify] \| [https://francium223.bandcamp.com/track/the-scallop-disco-accident Bandcamp] \| [https://www.youtube.com/watch?v=V12N5jC_UfM YouTube] – in Scarlattic, 677edo tuning
			* "Make Gecko Expansion" from ''I Want To'' (2025) – [https://open.spotify.com/track/5dbEP5zQQrrO00f3XZiELV Spotify] \| [https://francium223.bandcamp.com/track/make-gecko-expansion Bandcamp] \| [https://www.youtube.com/watch?v=D55Y0-p_mWU YouTube] – in Genzelic, 677edo tuning