619edo - 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"

2026-03-13T13:32:41Z

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 61:		Line 61:
	\| [[Helmholtz (temperament)\|Helmholtz]]		\| [[Helmholtz (temperament)\|Helmholtz]]
	\|}		\|}
	<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]]		; [[Francium]]
	* "Would You Like An Egg?" from ''Questions'' (2024) – [https://open.spotify.com/track/6Wuq8NVg0gzlPx71BwrWIV Spotify] \| [https://francium223.bandcamp.com/track/would-you-like-an-egg Bandcamp] \| [https://www.youtube.com/watch?v=f5I9VCz1b-o YouTube] – helmholtz in 619edo tuning		* "Would You Like An Egg?" from ''Questions'' (2024) – [https://open.spotify.com/track/6Wuq8NVg0gzlPx71BwrWIV Spotify] \| [https://francium223.bandcamp.com/track/would-you-like-an-egg Bandcamp] \| [https://www.youtube.com/watch?v=f5I9VCz1b-o YouTube] – helmholtz in 619edo tuning

Lériendil: Text replacement - "[[Helmholtz temperament|" to "[[Helmholtz (temperament)|"

2025-04-17T02:29:01Z

Text replacement - "[[Helmholtz temperament|" to "[[Helmholtz (temperament)|"

← Older revision		Revision as of 02:29, 17 April 2025
Line 59:		Line 59:
	\| 498.223		\| 498.223
	\| 4/3		\| 4/3
	\| [[Helmholtz temperament\|Helmholtz]]		\| [[Helmholtz (temperament)\|Helmholtz]]
	\|}		\|}
	<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

Sintel: fix helmholtz link

2025-04-16T15:33:06Z

fix helmholtz link

← Older revision		Revision as of 15:33, 16 April 2025
Line 59:		Line 59:
	\| 498.223		\| 498.223
	\| 4/3		\| 4/3
	\| [[Helmholtz]]		\| [[Helmholtz temperament\|Helmholtz]]
	\|}		\|}
	<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

Francium: changed EDO intro to ED intro

2025-02-21T05:47:52Z

changed EDO intro to ED intro

← Older revision		Revision as of 05:47, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 16:46, 15 January 2025

2025-01-15T16:46:18Z

← Older revision		Revision as of 16:46, 15 January 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro~~\|619~~}}		{{EDO intro}}

	== Theory ==		== Theory ==
Line 27:		Line 27:
	\| {{mapping\|619 981}}		\| {{mapping\|619 981}}
	\| 0.0561		\| 0.0561
	\| 0.0561		\| +0.0561
	\| 2.89		\| 2.89
	\|-		\|-
Line 34:		Line 34:
	\| {{mapping\|619 981 1437}}		\| {{mapping\|619 981 1437}}
	\| 0.1135		\| 0.1135
	\| 0.0932		\| +0.0932
	\| 4.81		\| 4.81
	\|-		\|-
Line 41:		Line 41:
	\| {{mapping\|619 981 1437 2141}}		\| {{mapping\|619 981 1437 2141}}
	\| 0.1395		\| 0.1395
	\| 0.0925		\| +0.0925
	\| 4.77		\| 4.77
	\|}		\|}
Line 61:		Line 61:
	\| [[Helmholtz]]		\| [[Helmholtz]]
	\|}		\|}
	<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]]
	* "Would You Like An Egg?" from ''Questions'' (2024) – [https://open.spotify.com/track/6Wuq8NVg0gzlPx71BwrWIV Spotify] \| [https://francium223.bandcamp.com/track/would-you-like-an-egg Bandcamp] \| [https://www.youtube.com/watch?v=f5I9VCz1b-o YouTube] – helmholtz in 619edo tuning		* "Would You Like An Egg?" from ''Questions'' (2024) – [https://open.spotify.com/track/6Wuq8NVg0gzlPx71BwrWIV Spotify] \| [https://francium223.bandcamp.com/track/would-you-like-an-egg Bandcamp] \| [https://www.youtube.com/watch?v=f5I9VCz1b-o YouTube] – helmholtz in 619edo tuning

ArrowHead294: Partial undo

2024-11-16T13:18:57Z

Partial undo

← Older revision		Revision as of 13:18, 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 34:		Line 43:
	\| 0.0925		\| 0.0925
	\| 4.77		\| 4.77
	~~{{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 44:		Line 60:
	\| 4/3		\| 4/3
	\| [[Helmholtz]]		\| [[Helmholtz]]
	~~{{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 ==
	; [[Francium]]		; [[Francium]]
	* "Would You Like An Egg?" from ''Questions'' (2024) – [https://open.spotify.com/track/6Wuq8NVg0gzlPx71BwrWIV Spotify] \| [https://francium223.bandcamp.com/track/would-you-like-an-egg Bandcamp] \| [https://www.youtube.com/watch?v=f5I9VCz1b-o YouTube] – helmholtz in 619edo tuning		* "Would You Like An Egg?" from ''Questions'' (2024) – [https://open.spotify.com/track/6Wuq8NVg0gzlPx71BwrWIV Spotify] \| [https://francium223.bandcamp.com/track/would-you-like-an-egg Bandcamp] \| [https://www.youtube.com/watch?v=f5I9VCz1b-o YouTube] – helmholtz in 619edo tuning

ArrowHead294 at 01:38, 16 November 2024

2024-11-16T01:38:05Z

← Older revision		Revision as of 01:38, 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 43:		Line 34:
	\| 0.0925		\| 0.0925
	\| 4.77		\| 4.77
	\|}		{{comma basis end}}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center-all left-5"~~		{{rank-2 begin}}
	~~\|+ style="font-size: 105%;" \| Table of~~ rank-2 ~~temperaments by generator~~
	\|-
	~~! Periods<br />per 8ve~~
	! Generator*
	! Cents*
	! Associated<br />Ratio*
	~~! Temperaments~~
	\|-		\|-
	\| 1		\| 1
Line 60:		Line 44:
	\| 4/3		\| 4/3
	\| [[Helmholtz]]		\| [[Helmholtz]]
	\|}		{{rank-2 end}}
	{{orf}}		{{orf}}

ArrowHead294 at 00:56, 16 November 2024

2024-11-16T00:56:42Z

← Older revision		Revision as of 00:56, 16 November 2024
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" \|[[Comma list\|Comma List]]		! rowspan="2" \| [[Subgroup]]
	! rowspan="2" \|[[Mapping]]		! rowspan="2" \| [[Comma list\|Comma List]]
	! rowspan="2" \|Optimal<br>8ve Stretch (¢)		! rowspan="2" \| [[Mapping]]
	! colspan="2" \|Tuning Error		! rowspan="2" \| Optimal<br />8ve Stretch (¢)
	\|-		! colspan="2" \| Tuning Error
	![[TE error\|Absolute]] (¢)		\|-
	![[TE simple badness\|Relative]] (%)		! [[TE error\|Absolute]] (¢)
			! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\| 2.3		\| 2.3
Line 46:		Line 47:
	=== 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		\|-
			! Periods<br />per 8ve
	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br>Ratio*		! Associated<br />Ratio*
	! Temperaments		! Temperaments
	\|-		\|-
Line 59:		Line 61:
	\| [[Helmholtz]]		\| [[Helmholtz]]
	\|}		\|}
	~~<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]]
	* "Would You Like An Egg?" from ''Questions'' (2024) – [https://open.spotify.com/track/6Wuq8NVg0gzlPx71BwrWIV Spotify] \| [https://francium223.bandcamp.com/track/would-you-like-an-egg Bandcamp] \| [https://www.youtube.com/watch?v=f5I9VCz1b-o YouTube] – helmholtz in 619edo tuning		* "Would You Like An Egg?" from ''Questions'' (2024) – [https://open.spotify.com/track/6Wuq8NVg0gzlPx71BwrWIV Spotify] \| [https://francium223.bandcamp.com/track/would-you-like-an-egg Bandcamp] \| [https://www.youtube.com/watch?v=f5I9VCz1b-o YouTube] – helmholtz in 619edo tuning

Francium: +music

2024-07-29T13:01:19Z

+music

← Older revision		Revision as of 13:01, 29 July 2024
Line 60:		Line 60:
	\|}		\|}
	<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]]
			* "Would You Like An Egg?" from ''Questions'' (2024) – [https://open.spotify.com/track/6Wuq8NVg0gzlPx71BwrWIV Spotify] \| [https://francium223.bandcamp.com/track/would-you-like-an-egg Bandcamp] \| [https://www.youtube.com/watch?v=f5I9VCz1b-o YouTube] – helmholtz in 619edo tuning

Francium: Created page with "{{Infobox ET}} {{EDO intro|619}} == Theory == 619edo is consistent to the 5-odd-limit. It can be used in the 2.3.5.11.17.19.23.29.41 subgroup, tempering out 202..."

2024-06-15T14:15:01Z

Created page with "{{Infobox ET}} {{EDO intro|619}} == Theory == 619edo is consistent to the 5-odd-limit. It can be used in the 2.3.5.11.17.19.23.29.41 subgroup, tempering out 202..."

New page

{{Infobox ET}}
{{EDO intro|619}}

== Theory ==
619edo is [[consistent]] to the [[5-odd-limit]]. It can be used in the 2.3.5.11.17.19.23.29.41 [[subgroup]], tempering out [[2025/2024]], [[1089/1088]], 3520/3519, 1045/1044, 2755/2754, 71875/71808, 374000/373977 and [[1025/1024]].

=== Prime harmonics ===
{{Harmonics in equal|619}}

=== Subsets and supersets ===
619edo is the 114th [[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|-981 619}}
| {{mapping|619 981}}
| 0.0561
| 0.0561
| 2.89
|-
| 2.3.5
| 32805/32768, {{monzo|-54 -67 69}}
| {{mapping|619 981 1437}}
| 0.1135
| 0.0932
| 4.81
|-
| 2.3.5.11
| 32805/32768, 234375/234256, 314552734375/313456656384
| {{mapping|619 981 1437 2141}}
| 0.1395
| 0.0925
| 4.77
|}

=== 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
| 257\619
| 498.223
| 4/3
| [[Helmholtz]]
|}
<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct