317edo - Revision history

ArrowHead294 at 12:37, 21 February 2025

2025-02-21T12:37:05Z

← Older revision		Revision as of 12:37, 21 February 2025
Line 15:		Line 15:
	== 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]] (%)
Line 27:		Line 28:
	\| {{monzo\| 1005 -317 }}		\| {{monzo\| 1005 -317 }}
	\| {{mapping\| 317 1005 }}		\| {{mapping\| 317 1005 }}
	\| -0.0799		\| −0.0799
	\| 0.0799		\| 0.0799
	\| 2.11		\| 2.11
Line 34:		Line 35:
	\| {{monzo\| -53 5 16 }}, {{monzo\| 33 -17 9 }}		\| {{monzo\| -53 5 16 }}, {{monzo\| 33 -17 9 }}
	\| {{mapping\| 317 1005 736 }}		\| {{mapping\| 317 1005 736 }}
	\| -0.0254		\| −0.0254
	\| 0.1009		\| 0.1009
	\| 2.67		\| 2.67
Line 41:		Line 42:
	\| 420175/419904, 703125/702464, 33554432/33480783		\| 420175/419904, 703125/702464, 33554432/33480783
	\| {{mapping\| 317 1005 736 890 }}		\| {{mapping\| 317 1005 736 890 }}
	\| -0.0422		\| −0.0422
	\| 0.0921		\| 0.0921
	\| 2.43		\| 2.43
Line 48:		Line 49:
	\| 6250/6237, 12005/11979, 46656/46585, 151263/151250		\| 6250/6237, 12005/11979, 46656/46585, 151263/151250
	\| {{mapping\| 317 1005 736 890 1097 }}		\| {{mapping\| 317 1005 736 890 1097 }}
	\| -0.1126		\| −0.1126
	\| 0.1631		\| 0.1631
	\| 4.31		\| 4.31
Line 55:		Line 56:
	\| 1575/1573, 4459/4455, 6250/6237, 67392/67375, 190125/189728		\| 1575/1573, 4459/4455, 6250/6237, 67392/67375, 190125/189728
	\| {{mapping\| 317 1005 736 890 1097 1173 }}		\| {{mapping\| 317 1005 736 890 1097 1173 }}
	\| -0.0871		\| −0.0871
	\| 0.1594		\| 0.1594
	\| 4.21		\| 4.21
Line 62:		Line 63:
	\| 936/935, 1225/1224, 1575/1573, 12376/12375, 17920/17901, 34000/33957		\| 936/935, 1225/1224, 1575/1573, 12376/12375, 17920/17901, 34000/33957
	\| {{mapping\| 317 1005 736 890 1097 1173 1296 }}		\| {{mapping\| 317 1005 736 890 1097 1173 1296 }}
	\| -0.1109		\| −0.1109
	\| 0.1587		\| 0.1587
	\| 4.19		\| 4.19

Francium: changed EDO intro to ED intro

2025-02-21T06:07:30Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:07, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|317~~}}		{{ED intro}}

	== Theory ==		== Theory ==

Francium: /* Music */ +music

2024-07-17T13:01:11Z

Music: +music

← Older revision		Revision as of 13:01, 17 July 2024
Line 70:		Line 70:
	; [[Francium]]		; [[Francium]]
	* "Narrator Of Myths" from ''Mysteries'' (2023) – [https://open.spotify.com/track/6AYSSw1kVKDDzWVYMyxafv Spotify] \| [https://francium223.bandcamp.com/track/narrator-of-myths Bandcamp] \| [https://www.youtube.com/watch?v=fNmEjgVonHk YouTube]		* "Narrator Of Myths" from ''Mysteries'' (2023) – [https://open.spotify.com/track/6AYSSw1kVKDDzWVYMyxafv Spotify] \| [https://francium223.bandcamp.com/track/narrator-of-myths Bandcamp] \| [https://www.youtube.com/watch?v=fNmEjgVonHk YouTube]
			* "Strange Shade Of Red" from ''You Are A...'' (2024) – [https://open.spotify.com/track/23kTYEBoGRKNLhVSaIxBpC Spotify] \| [https://francium223.bandcamp.com/track/strange-shade-of-red Bandcamp] \| [https://www.youtube.com/watch?v=G6h1qN__F6I YouTube]

	[[Category:Listen]]		[[Category:Listen]]

FloraC: Review

2024-02-21T10:28:27Z

Review

← Older revision		Revision as of 10:28, 21 February 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	~~317et~~ is only consistent to the [[5-odd-limit]] and ~~the~~ [[harmonic]] 3 is about halfway its steps. ~~Using~~ the ~~patent val~~, it ~~tempers out 589824/588245~~, [[~~16875/16807~~]], [[~~65625~~/~~65536~~]] ~~and 49009212/48828125 in the 7-limit; 1835008/1830125, 14700/14641, 2097152/2096325~~, [[~~4000~~/~~3993~~]], ~~2734375/2725888, 1953125/1951488, 172032/171875,~~ [[~~441~~/~~440~~]]~~, 5767168/5764801, 825000/823543, 537109375/536870912, 134775333/134217728, 160083/160000, 16808715/16777216, 539055/537824 and 3294225/3294172 in the 11-limit~~.		317edo is only [[consistent]] to the [[5-odd-limit]] and [[harmonic]] [[3/1\|3]] is about halfway its steps. To start with, it can be considered in the 2.9.5.7 [[subgroup]], in which it is strong, [[tempering out]] [[420175/419904]], [[703125/702464]], and [[33554432/33480783]].

	===Odd harmonics===		Using the [[patent val]] nonetheless, the equal temperament tempers out 78732/78125 ([[sensipent comma]] in the 5-limit; [[16875/16807]], [[65625/65536]], 589824/588245, and 49009212/48828125 in the 7-limit. In the 11-limit, the 317e [[val]] tempers out [[540/539]], 1375/1372, and [[3025/3024]], whereas the patent val tempers out [[441/440]], [[4000/3993]], and 14700/14641.

			=== Odd harmonics ===
	{{Harmonics in equal\|317}}		{{Harmonics in equal\|317}}

	===Subsets and supersets===		=== Subsets and supersets ===
	317edo is the 66th [[prime edo]]. [[634edo]], which doubles it, gives a good correction to the harmonic 3.		317edo is the 66th [[prime edo]]. [[634edo]], which doubles it, gives a good correction to the harmonic 3.

	==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]] (%)
	\|-		\|-
	\|2.9		\| 2.9
	\|{{monzo\|1005 -317}}		\| {{monzo\| 1005 -317 }}
	\|{{mapping\|317 1005}}		\| {{mapping\| 317 1005 }}
	\| -0.0799		\| -0.0799
	\| 0.0799		\| 0.0799
	\| 2.11		\| 2.11
	\|-		\|-
	\|2.9.5		\| 2.9.5
	\|{{monzo\|-53 5 16}}, {{monzo\|33 -17 9}}		\| {{monzo\| -53 5 16 }}, {{monzo\| 33 -17 9 }}
	\|{{mapping\|317 1005 736}}		\| {{mapping\| 317 1005 736 }}
	\| -0.0254		\| -0.0254
	\| 0.1009		\| 0.1009
	\| 2.67		\| 2.67
	\|-		\|-
	\|2.9.5.7		\| 2.9.5.7
	\|420175/419904, 703125/702464, 33554432/33480783		\| 420175/419904, 703125/702464, 33554432/33480783
	\|{{mapping\|317 1005 736 890}}		\| {{mapping\| 317 1005 736 890 }}
	\| -0.0422		\| -0.0422
	\| 0.0921		\| 0.0921
	\| 2.43		\| 2.43
	\|-		\|-
	\|2.9.5.7.11		\| 2.9.5.7.11
	\|6250/6237, 12005/11979, 46656/46585, 151263/151250		\| 6250/6237, 12005/11979, 46656/46585, 151263/151250
	\|{{mapping\|317 1005 736 890 1097}}		\| {{mapping\| 317 1005 736 890 1097 }}
	\| -0.1126		\| -0.1126
	\| 0.1631		\| 0.1631
	\| 4.31		\| 4.31
	\|-		\|-
	\|2.9.5.7.11.13		\| 2.9.5.7.11.13
	\|1575/1573, 4459/4455, 6250/6237, 67392/67375, 190125/189728		\| 1575/1573, 4459/4455, 6250/6237, 67392/67375, 190125/189728
	\|{{mapping\|317 1005 736 890 1097 1173}}		\| {{mapping\| 317 1005 736 890 1097 1173 }}
	\| -0.0871		\| -0.0871
	\| 0.1594		\| 0.1594
	\| 4.21		\| 4.21
	\|-		\|-
	\|2.9.5.7.11.13.17		\| 2.9.5.7.11.13.17
	\|936/935, 1225/1224, 1575/1573, 12376/12375, 17920/17901, 34000/33957		\| 936/935, 1225/1224, 1575/1573, 12376/12375, 17920/17901, 34000/33957
	\|{{mapping\|317 1005 736 890 1097 1173 1296}}		\| {{mapping\| 317 1005 736 890 1097 1173 1296 }}
	\| -0.1109		\| -0.1109
	\| 0.1587		\| 0.1587
Line 67:		Line 69:
	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "Narrator Of Myths" from ''Mysteries'' (2023) [https://open.spotify.com/track/6AYSSw1kVKDDzWVYMyxafv Spotify] \| [https://francium223.bandcamp.com/track/narrator-of-myths Bandcamp] \| [https://www.youtube.com/watch?v=fNmEjgVonHk YouTube]		* "Narrator Of Myths" from ''Mysteries'' (2023) – [https://open.spotify.com/track/6AYSSw1kVKDDzWVYMyxafv Spotify] \| [https://francium223.bandcamp.com/track/narrator-of-myths Bandcamp] \| [https://www.youtube.com/watch?v=fNmEjgVonHk YouTube]

	[[Category:Listen]]		[[Category:Listen]]

Francium: +categories

2024-02-13T17:59:17Z

+categories

← Older revision		Revision as of 17:59, 13 February 2024
Line 68:		Line 68:
	; [[Francium]]		; [[Francium]]
	* "Narrator Of Myths" from ''Mysteries'' (2023) [https://open.spotify.com/track/6AYSSw1kVKDDzWVYMyxafv Spotify] \| [https://francium223.bandcamp.com/track/narrator-of-myths Bandcamp] \| [https://www.youtube.com/watch?v=fNmEjgVonHk YouTube]		* "Narrator Of Myths" from ''Mysteries'' (2023) [https://open.spotify.com/track/6AYSSw1kVKDDzWVYMyxafv Spotify] \| [https://francium223.bandcamp.com/track/narrator-of-myths Bandcamp] \| [https://www.youtube.com/watch?v=fNmEjgVonHk YouTube]

			[[Category:Listen]]

Francium: misc.

2023-12-31T10:08:37Z

misc.

← Older revision		Revision as of 10:08, 31 December 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|317}}		{{EDO intro\|317}}

	== Theory ==		== Theory ==
	317et tempers out 589824/588245, [[16875/16807]], [[65625/65536]] and 49009212/48828125 in the 7-limit; 1835008/1830125, 14700/14641, 2097152/2096325, [[4000/3993]], 2734375/2725888, 1953125/1951488, 172032/171875, [[441/440]], 5767168/5764801, 825000/823543, 537109375/536870912, 134775333/134217728, 160083/160000, 16808715/16777216, 539055/537824 and 3294225/3294172 in the 11-limit.		317et is only consistent to the [[5-odd-limit]] and the [[harmonic]] 3 is about halfway its steps. Using the patent val, it tempers out 589824/588245, [[16875/16807]], [[65625/65536]] and 49009212/48828125 in the 7-limit; 1835008/1830125, 14700/14641, 2097152/2096325, [[4000/3993]], 2734375/2725888, 1953125/1951488, 172032/171875, [[441/440]], 5767168/5764801, 825000/823543, 537109375/536870912, 134775333/134217728, 160083/160000, 16808715/16777216, 539055/537824 and 3294225/3294172 in the 11-limit.

	===Odd harmonics===		===Odd harmonics===
	{{Harmonics in equal\|317}}		{{Harmonics in equal\|317}}

	===Subsets and supersets===		===Subsets and supersets===
	317edo is the 66th [[prime edo]]. [[634edo]], which doubles it, gives a good correction to the harmonic 3.		317edo is the 66th [[prime edo]]. [[634edo]], which doubles it, gives a good correction to the harmonic 3.

	==Regular temperament properties==		==Regular temperament properties==
	{\| class="wikitable center-4 center-5 center-6"		{\| class="wikitable center-4 center-5 center-6"

Francium: +music

2023-11-20T05:40:30Z

+music

← Older revision		Revision as of 05:40, 20 November 2023
Line 20:		Line 20:
	\|2.9		\|2.9
	\|{{monzo\|1005 -317}}		\|{{monzo\|1005 -317}}
	\|{{~~val~~\|317 1005}}		\|{{mapping\|317 1005}}
	\| -0.0799		\| -0.0799
	\| 0.0799		\| 0.0799
Line 27:		Line 27:
	\|2.9.5		\|2.9.5
	\|{{monzo\|-53 5 16}}, {{monzo\|33 -17 9}}		\|{{monzo\|-53 5 16}}, {{monzo\|33 -17 9}}
	\|{{~~val~~\|317 1005 736}}		\|{{mapping\|317 1005 736}}
	\| -0.0254		\| -0.0254
	\| 0.1009		\| 0.1009
Line 34:		Line 34:
	\|2.9.5.7		\|2.9.5.7
	\|420175/419904, 703125/702464, 33554432/33480783		\|420175/419904, 703125/702464, 33554432/33480783
	\|{{~~val~~\|317 1005 736 890}}		\|{{mapping\|317 1005 736 890}}
	\| -0.0422		\| -0.0422
	\| 0.0921		\| 0.0921
Line 41:		Line 41:
	\|2.9.5.7.11		\|2.9.5.7.11
	\|6250/6237, 12005/11979, 46656/46585, 151263/151250		\|6250/6237, 12005/11979, 46656/46585, 151263/151250
	\|{{~~val~~\|317 1005 736 890 1097}}		\|{{mapping\|317 1005 736 890 1097}}
	\| -0.1126		\| -0.1126
	\| 0.1631		\| 0.1631
Line 48:		Line 48:
	\|2.9.5.7.11.13		\|2.9.5.7.11.13
	\|1575/1573, 4459/4455, 6250/6237, 67392/67375, 190125/189728		\|1575/1573, 4459/4455, 6250/6237, 67392/67375, 190125/189728
	\|{~~val~~\|317 1005 736 890 1097 1173}}		\|{{mapping\|317 1005 736 890 1097 1173}}
	\| -0.0871		\| -0.0871
	\| 0.1594		\| 0.1594
Line 55:		Line 55:
	\|2.9.5.7.11.13.17		\|2.9.5.7.11.13.17
	\|936/935, 1225/1224, 1575/1573, 12376/12375, 17920/17901, 34000/33957		\|936/935, 1225/1224, 1575/1573, 12376/12375, 17920/17901, 34000/33957
	\|{~~val~~\|317 1005 736 890 1097 1173 1296}}		\|{{mapping\|317 1005 736 890 1097 1173 1296}}
	\| -0.1109		\| -0.1109
	\| 0.1587		\| 0.1587
	\| 4.19		\| 4.19
	\|}		\|}

			== Music ==
			; [[Francium]]
			* "Narrator Of Myths" from ''Mysteries'' (2023) [https://open.spotify.com/track/6AYSSw1kVKDDzWVYMyxafv Spotify] \| [https://francium223.bandcamp.com/track/narrator-of-myths Bandcamp] \| [https://www.youtube.com/watch?v=fNmEjgVonHk YouTube]

Francium: Created page with "{{Infobox ET}} {{EDO intro|317}} == Theory == 317et tempers out 589824/588245, 16875/16807, 65625/65536 and 49009212/48828125 in the 7-limit; 1835008/1830125, 14700/14..."

2023-07-20T13:15:12Z

Created page with "{{Infobox ET}} {{EDO intro|317}} == Theory == 317et tempers out 589824/588245, 16875/16807, 65625/65536 and 49009212/48828125 in the 7-limit; 1835008/1830125, 14700/14..."

New page

{{Infobox ET}}
{{EDO intro|317}}
== Theory ==
317et tempers out 589824/588245, [[16875/16807]], [[65625/65536]] and 49009212/48828125 in the 7-limit; 1835008/1830125, 14700/14641, 2097152/2096325, [[4000/3993]], 2734375/2725888, 1953125/1951488, 172032/171875, [[441/440]], 5767168/5764801, 825000/823543, 537109375/536870912, 134775333/134217728, 160083/160000, 16808715/16777216, 539055/537824 and 3294225/3294172 in the 11-limit.
===Odd harmonics===
{{Harmonics in equal|317}}
===Subsets and supersets===
317edo is the 66th [[prime edo]]. [[634edo]], which doubles it, gives a good correction to the harmonic 3.
==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]] (%)
|-
|2.9
|{{monzo|1005 -317}}
|{{val|317 1005}}
| -0.0799
| 0.0799
| 2.11
|-
|2.9.5
|{{monzo|-53 5 16}}, {{monzo|33 -17 9}}
|{{val|317 1005 736}}
| -0.0254
| 0.1009
| 2.67
|-
|2.9.5.7
|420175/419904, 703125/702464, 33554432/33480783
|{{val|317 1005 736 890}}
| -0.0422
| 0.0921
| 2.43
|-
|2.9.5.7.11
|6250/6237, 12005/11979, 46656/46585, 151263/151250
|{{val|317 1005 736 890 1097}}
| -0.1126
| 0.1631
| 4.31
|-
|2.9.5.7.11.13
|1575/1573, 4459/4455, 6250/6237, 67392/67375, 190125/189728
|{val|317 1005 736 890 1097 1173}}
| -0.0871
| 0.1594
| 4.21
|-
|2.9.5.7.11.13.17
|936/935, 1225/1224, 1575/1573, 12376/12375, 17920/17901, 34000/33957
|{val|317 1005 736 890 1097 1173 1296}}
| -0.1109
| 0.1587
| 4.19
|}