500edo - Revision history

ArrowHead294 at 12:15, 21 February 2025

2025-02-21T12:15:18Z

← Older revision		Revision as of 12:15, 21 February 2025
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\|Comma List]]
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	\| {{monzo\| 317 -100 }}		\| {{monzo\| 317 -100 }}
	\| {{mapping\| 500 1585 }}		\| {{mapping\| 500 1585 }}
	\| -0.0142		\| −0.0142
	\| 0.0142		\| 0.0142
	\| 0.59		\| 0.59
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	\| {{monzo\| 38 -1 -15 }}, {{monzo\| 55 -32 20 }}		\| {{monzo\| 38 -1 -15 }}, {{monzo\| 55 -32 20 }}
	\| {{mapping\| 500 1585 1161 }}		\| {{mapping\| 500 1585 1161 }}
	\| -0.0219		\| −0.0219
	\| 0.0159		\| 0.0159
	\| 0.66		\| 0.66
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	\| 589824/588245, 703125/702464, 31381059609/31360000000		\| 589824/588245, 703125/702464, 31381059609/31360000000
	\| {{mapping\| 500 1585 1161 1404 }}		\| {{mapping\| 500 1585 1161 1404 }}
	\| -0.0853		\| −0.0853
	\| 0.1108		\| 0.1108
	\| 4.62		\| 4.62
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	\| 9801/9800, 46656/46585, 2252800/2250423, 703125/702464		\| 9801/9800, 46656/46585, 2252800/2250423, 703125/702464
	\| {{mapping\| 500 1585 1161 1404 1730 }}		\| {{mapping\| 500 1585 1161 1404 1730 }}
	\| -0.1077		\| −0.1077
	\| 0.1087		\| 0.1087
	\| 4.53		\| 4.53
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	\| 4096/4095, 9801/9800, 35750/35721, 41600/41503, 91125/91091		\| 4096/4095, 9801/9800, 35750/35721, 41600/41503, 91125/91091
	\| {{mapping\| 500 1585 1161 1404 1730 1850 }}		\| {{mapping\| 500 1585 1161 1404 1730 1850 }}
	\| -0.0660		\| −0.0660
	\| 0.1362		\| 0.1362
	\| 5.68		\| 5.68
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	\| 936/935, 4096/4095, 12376/12375, 9801/9800, 35750/35721, 11016/11011		\| 936/935, 4096/4095, 12376/12375, 9801/9800, 35750/35721, 11016/11011
	\| {{mapping\| 500 1585 1161 1404 1730 1850 2044 }}		\| {{mapping\| 500 1585 1161 1404 1730 1850 2044 }}
	\| -0.0791		\| −0.0791
	\| 0.1301		\| 0.1301
	\| 5.42		\| 5.42

Francium: changed EDO intro to ED intro

2025-02-21T06:23:33Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:23, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|500~~}}		{{ED intro}}

	== Theory ==		== Theory ==

Francium: /* Music */ +links

2024-06-07T15:03:27Z

Music: +links

← Older revision		Revision as of 15:03, 7 June 2024
Line 67:		Line 67:
	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "loveyouforever" from ''albumwithoutspaces'' (2024) – [https://francium223.bandcamp.com/track/loveyouforever Bandcamp] \| [https://www.youtube.com/watch?v=CKXtJSihX-A YouTube]		* "loveyouforever" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/63WBz0dSUO6Q58WMZmckJ2 Spotify] \| [https://francium223.bandcamp.com/track/loveyouforever Bandcamp] \| [https://www.youtube.com/watch?v=CKXtJSihX-A YouTube]

Francium: /* Music */ +links

2024-06-04T12:21:07Z

Music: +links

← Older revision		Revision as of 12:21, 4 June 2024
Line 67:		Line 67:
	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* [https://www.youtube.com/watch?v=CKXtJSihX-A ~~''loveyouforever''~~] ~~(2024)~~		* "loveyouforever" from ''albumwithoutspaces'' (2024) – [https://francium223.bandcamp.com/track/loveyouforever Bandcamp] \| [https://www.youtube.com/watch?v=CKXtJSihX-A YouTube]

FloraC: Review

2024-05-15T12:27:44Z

Review

← Older revision		Revision as of 12:27, 15 May 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	~~500et~~ is ~~only~~ consistent to the [[3-odd-limit]] and the error of the [[harmonic]] [[3/1\|3]] is very large. It can be used in the 2.9.5.7.11.13.17.19.23.29.31.37.41.43 [[subgroup]], [[tempering out]] [[936/935]], [[4096/4095]], [[12376/12375]], [[2025/2024]], 3328/3325, [[9801/9800]], 35750/35721, 46592/46575, 5104/5103, 12555/12544, 1296/1295, 1376/1375 and 6273/6272.		500edo is in[[consistent]] to the [[5-odd-limit]] and the error of the [[harmonic]] [[3/1\|3]] is very large. It can be used in the 2.9.5.7.11.13.17.19.23.29.31.37.41.43 [[subgroup]], [[tempering out]] [[936/935]], [[4096/4095]], [[12376/12375]], [[2025/2024]], 3328/3325, [[9801/9800]], 35750/35721, 46592/46575, 5104/5103, 12555/12544, 1296/1295, 1376/1375 and 6273/6272.

	=== Odd harmonics ===		=== Odd harmonics ===
Line 9:		Line 9:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	500 factors into ~~2<sup>2</sup> * 5<sup>3</sup>~~, ~~with~~ subset edos {{EDOs\|2, 4, 5, 10, 20, 25, 50, 100, 125, and 250}}. [[1000edo]], which doubles it, gives a good correction to the harmonic 3.		Since 500 factors into {{factorization\|500}}, 500edo has subset edos {{EDOs\| 2, 4, 5, 10, 20, 25, 50, 100, 125, and 250 }}. [[1000edo]], 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\|317 -100}}		\| {{monzo\| 317 -100 }}
	\|{{mapping\|500 1585}}		\| {{mapping\| 500 1585 }}
	\| -0.0142		\| -0.0142
	\| 0.0142		\| 0.0142
	\| 0.59		\| 0.59
	\|-		\|-
	\|2.9.5		\| 2.9.5
	\|{{monzo\|38 -1 -15}}, {{monzo\|55 -32 20}}		\| {{monzo\| 38 -1 -15 }}, {{monzo\| 55 -32 20 }}
	\|{{mapping\|500 1585 1161}}		\| {{mapping\| 500 1585 1161 }}
	\| -0.0219		\| -0.0219
	\| 0.0159		\| 0.0159
	\| 0.66		\| 0.66
	\|-		\|-
	\|2.9.5.7		\| 2.9.5.7
	\|703125/702464~~, 589824/588245~~, 31381059609/31360000000		\| 589824/588245, 703125/702464, 31381059609/31360000000
	\|{{mapping\|500 1585 1161 1404}}		\| {{mapping\| 500 1585 1161 1404 }}
	\| -0.0853		\| -0.0853
	\| 0.1108		\| 0.1108
	\| 4.62		\| 4.62
	\|-		\|-
	\|2.9.5.7.11		\| 2.9.5.7.11
	\|9801/9800, 46656/46585, 2252800/2250423, 703125/702464		\| 9801/9800, 46656/46585, 2252800/2250423, 703125/702464
	\|{{mapping\|500 1585 1161 1404 1730}}		\| {{mapping\| 500 1585 1161 1404 1730 }}
	\| -0.1077		\| -0.1077
	\| 0.1087		\| 0.1087
	\| 4.53		\| 4.53
	\|-		\|-
	\|2.9.5.7.11.13		\| 2.9.5.7.11.13
	\|4096/4095, 9801/9800, 35750/35721, 41600/41503, 91125/91091		\| 4096/4095, 9801/9800, 35750/35721, 41600/41503, 91125/91091
	\|{{mapping\|500 1585 1161 1404 1730 1850}}		\| {{mapping\| 500 1585 1161 1404 1730 1850 }}
	\| -0.0660		\| -0.0660
	\| 0.1362		\| 0.1362
	\| 5.68		\| 5.68
	\|-		\|-
	\|2.9.5.7.11.13.17		\| 2.9.5.7.11.13.17
	\|936/935, 4096/4095, 12376/12375, 9801/9800, 35750/35721, 11016/11011		\| 936/935, 4096/4095, 12376/12375, 9801/9800, 35750/35721, 11016/11011
	\|{{mapping\|500 1585 1161 1404 1730 1850 2044}}		\| {{mapping\| 500 1585 1161 1404 1730 1850 2044 }}
	\| -0.0791		\| -0.0791
	\| 0.1301		\| 0.1301

Francium: Created page with "{{Infobox ET}} {{EDO intro|500}} == Theory == 500et is only consistent to the 3-odd-limit and the error of the harmonic 3 is very large. It can be used in the..."

2024-05-14T13:11:35Z

Created page with "{{Infobox ET}} {{EDO intro|500}} == Theory == 500et is only consistent to the 3-odd-limit and the error of the harmonic 3 is very large. It can be used in the..."

New page

{{Infobox ET}}
{{EDO intro|500}}

== Theory ==
500et is only consistent to the [[3-odd-limit]] and the error of the [[harmonic]] [[3/1|3]] is very large. It can be used in the 2.9.5.7.11.13.17.19.23.29.31.37.41.43 [[subgroup]], [[tempering out]] [[936/935]], [[4096/4095]], [[12376/12375]], [[2025/2024]], 3328/3325, [[9801/9800]], 35750/35721, 46592/46575, 5104/5103, 12555/12544, 1296/1295, 1376/1375 and 6273/6272.

=== Odd harmonics ===
{{Harmonics in equal|500}}

=== Subsets and supersets ===
500 factors into 22 * 53, with subset edos {{EDOs|2, 4, 5, 10, 20, 25, 50, 100, 125, and 250}}. [[1000edo]], 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 8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|2.9
|{{monzo|317 -100}}
|{{mapping|500 1585}}
| -0.0142
| 0.0142
| 0.59
|-
|2.9.5
|{{monzo|38 -1 -15}}, {{monzo|55 -32 20}}
|{{mapping|500 1585 1161}}
| -0.0219
| 0.0159
| 0.66
|-
|2.9.5.7
|703125/702464, 589824/588245, 31381059609/31360000000
|{{mapping|500 1585 1161 1404}}
| -0.0853
| 0.1108
| 4.62
|-
|2.9.5.7.11
|9801/9800, 46656/46585, 2252800/2250423, 703125/702464
|{{mapping|500 1585 1161 1404 1730}}
| -0.1077
| 0.1087
| 4.53
|-
|2.9.5.7.11.13
|4096/4095, 9801/9800, 35750/35721, 41600/41503, 91125/91091
|{{mapping|500 1585 1161 1404 1730 1850}}
| -0.0660
| 0.1362
| 5.68
|-
|2.9.5.7.11.13.17
|936/935, 4096/4095, 12376/12375, 9801/9800, 35750/35721, 11016/11011
|{{mapping|500 1585 1161 1404 1730 1850 2044}}
| -0.0791
| 0.1301
| 5.42
|}

== Music ==
; [[Francium]]
* [https://www.youtube.com/watch?v=CKXtJSihX-A ''loveyouforever''] (2024)