250edo - Revision history

Neutraldown at 02:14, 28 November 2025

2025-11-28T02:14:07Z

← Older revision		Revision as of 02:14, 28 November 2025
Line 7:		Line 7:
	The patent val tempers out [[243/242]], [[3025/3024]], 4375/4356, [[9801/9800]], 14700/14641 in the 11-limit and [[1716/1715]], [[2080/2079]], and [[2200/2197]] in the 13-limit. It [[support]]s the [[Minortonic family #Seminar\|seminar]] temperament.		The patent val tempers out [[243/242]], [[3025/3024]], 4375/4356, [[9801/9800]], 14700/14641 in the 11-limit and [[1716/1715]], [[2080/2079]], and [[2200/2197]] in the 13-limit. It [[support]]s the [[Minortonic family #Seminar\|seminar]] temperament.

	The 250deff… val tempers out [[441/440]], 4125/4096, [[8019/8000]], 9801/9800, 12005/11979, [[14641/14580]] in the 11-limit and [[325/324]], [[676/675]], and 1287/1280 in the 13-limit.		The 250deff… val tempers out [[441/440]], [[4125/4096]], [[8019/8000]], 9801/9800, 12005/11979, [[14641/14580]] in the 11-limit and [[325/324]], [[676/675]], and 1287/1280 in the 13-limit.

	=== Odd harmonics ===		=== Odd harmonics ===

ArrowHead294 at 23:18, 20 February 2025

2025-02-20T23:18:25Z

← Older revision		Revision as of 23:18, 20 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|250~~}}		{{ED intro}}

	== Theory ==		== Theory ==
Line 19:		Line 19:
	== 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]] (%)

FloraC: Review

2024-03-22T15:08:22Z

Review

← Older revision		Revision as of 15:08, 22 March 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|250}}		{{EDO intro\|250}}
	==Theory==
			== Theory ==
	250edo is [[enfactoring\|enfactored]] in the 7-limit, with the same tuning as 125edo, but provides a closer approximation to the harmonics 11 and 13, where the 13/8 derives from [[10edo]] (7\10). Even so, there are a number of mappings to be considered, in particular, a less flat-tending [[patent val]] {{val\| 250 396 580 '''702''' '''865''' '''925''' … }} and a more flat-tending 250deff… val {{val\| 250 396 580 '''701''' '''864''' '''924''' … }}.		250edo is [[enfactoring\|enfactored]] in the 7-limit, with the same tuning as 125edo, but provides a closer approximation to the harmonics 11 and 13, where the 13/8 derives from [[10edo]] (7\10). Even so, there are a number of mappings to be considered, in particular, a less flat-tending [[patent val]] {{val\| 250 396 580 '''702''' '''865''' '''925''' … }} and a more flat-tending 250deff… val {{val\| 250 396 580 '''701''' '''864''' '''924''' … }}.

	The patent val tempers out [[243/242]], [[3025/3024]], 4375/4356, [[9801/9800]], 14700/14641 in the 11-limit and [[1716/1715]], [[2080/2079]], and [[2200/2197]] in the 13-limit. It ~~supports~~ the [[Minortonic family #Seminar\|seminar]] temperament.		The patent val tempers out [[243/242]], [[3025/3024]], 4375/4356, [[9801/9800]], 14700/14641 in the 11-limit and [[1716/1715]], [[2080/2079]], and [[2200/2197]] in the 13-limit. It [[support]]s the [[Minortonic family #Seminar\|seminar]] temperament.

	The 250deff… val tempers out [[441/440]], 4125/4096, [[8019/8000]], 9801/9800, 12005/11979, [[14641/14580]] in the 11-limit and [[325/324]], [[676/675]], and 1287/1280 in the 13-limit.		The 250deff… val tempers out [[441/440]], 4125/4096, [[8019/8000]], 9801/9800, 12005/11979, [[14641/14580]] in the 11-limit and [[325/324]], [[676/675]], and 1287/1280 in the 13-limit.
Line 16:		Line 17:
	Since the 2.3.5.7 subgroup in the patent val comes from 125et, and the 2.11.13 subgroup in the patent val comes from 50et, this system is worthy of being considered as a superset of these two temperaments.		Since the 2.3.5.7 subgroup in the patent val comes from 125et, and the 2.11.13 subgroup in the patent val comes from 50et, this system is worthy of being considered as a superset of these two temperaments.

	==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]] (%)
	\|-		\|-
	\|2.3		\| 2.3.5.7.11
	\|~~{{monzo\|-198 125}}~~		\| 441/440, 4125/4096, 14641/14580, 15625/15552
	\|{{~~val~~\|250 396}}		\| {{mapping\| 250 396 580 701 864 }} (250de)
	\| 0.~~3644~~		\| +0.8703
	\| 0.~~3645~~		\| 0.4930
	\| 7.59		\| 10.3
	\|-		\|-
	\|2.3.5		\| 2.3.5.7.11
	\|~~15625~~/~~15552~~, ~~{{monzo\|-34 20 1}}~~		\| 225/224, 243/242, 4375/4356, 589824/588245
	\|{{~~val~~\|250 396 580}}		\| {{mapping\| 250 396 580 701 864 }} (250)
	\| 0.~~5752~~		\| +0.2503
	\| 0.~~4213~~		\| 0.5149
	\| 8.78		\| 10.7
	\|}		\|}

Francium at 19:34, 30 October 2023

2023-10-30T19:34:02Z

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
 {{EDO intro|250}}
+==Theory==
 edo is [[enfactoring|enfactored]] in the 7-limit, with the same tuning as 125edo, but provides a closer approximation to the harmonics 11 and 13, where the 13/8 derives from [[10edo]] (7\10). Even so, there are a number of mappings to be considered, in particular, a less flat-tending [[patent val]] {{val| 250 396 580 '''702''' '''865''' '''925''' … }} and a more flat-tending 250deff… val {{val| 250 396 580 '''701''' '''864''' '''924''' … }}.
@@ Line 11: / Line 11: @@
 {{Harmonics in equal|250}}
-=== Divisors ===
+=== Subsets and supersets ===
 edo has subset edos {{EDOs| 2, 5, 10, 25, 50, 125 }}.
 Since the 2.3.5.7 subgroup in the patent val comes from 125et, and the 2.11.13 subgroup in the patent val comes from 50et, this system is worthy of being considered as a superset of these two temperaments.

FloraC: +commas

2023-01-24T10:42:25Z

+commas

← Older revision		Revision as of 10:42, 24 January 2023
Line 4:		Line 4:
	250edo is [[enfactoring\|enfactored]] in the 7-limit, with the same tuning as 125edo, but provides a closer approximation to the harmonics 11 and 13, where the 13/8 derives from [[10edo]] (7\10). Even so, there are a number of mappings to be considered, in particular, a less flat-tending [[patent val]] {{val\| 250 396 580 '''702''' '''865''' '''925''' … }} and a more flat-tending 250deff… val {{val\| 250 396 580 '''701''' '''864''' '''924''' … }}.		250edo is [[enfactoring\|enfactored]] in the 7-limit, with the same tuning as 125edo, but provides a closer approximation to the harmonics 11 and 13, where the 13/8 derives from [[10edo]] (7\10). Even so, there are a number of mappings to be considered, in particular, a less flat-tending [[patent val]] {{val\| 250 396 580 '''702''' '''865''' '''925''' … }} and a more flat-tending 250deff… val {{val\| 250 396 580 '''701''' '''864''' '''924''' … }}.

	~~In addition, in the~~ patent val in the 11-limit, ~~it is a tuning for~~ the [[Minortonic family#Seminar\|seminar]] temperament.		The patent val tempers out [[243/242]], [[3025/3024]], 4375/4356, [[9801/9800]], 14700/14641 in the 11-limit and [[1716/1715]], [[2080/2079]], and [[2200/2197]] in the 13-limit. It supports the [[Minortonic family #Seminar\|seminar]] temperament.

			The 250deff… val tempers out [[441/440]], 4125/4096, [[8019/8000]], 9801/9800, 12005/11979, [[14641/14580]] in the 11-limit and [[325/324]], [[676/675]], and 1287/1280 in the 13-limit.

	=== Odd harmonics ===		=== Odd harmonics ===

FloraC: "7\10" is clearer than "0.7 octaves". Harmonics -> subgroup. Add the missing 2 in 2.11.13. Resolve edo vs et

2023-01-24T10:30:28Z

"7\10" is clearer than "0.7 octaves". Harmonics -> subgroup. Add the missing 2 in 2.11.13. Resolve edo vs et

← Older revision		Revision as of 10:30, 24 January 2023
Line 2:		Line 2:
	{{EDO intro\|250}}		{{EDO intro\|250}}

	250edo is [[enfactoring\|enfactored]] in the 7-limit, with the same tuning as 125edo, but provides a closer approximation to the harmonics 11 and 13~~. Being a small multiple of~~ [[10edo]]~~, it equates 13/8 with 0.~~7 ~~octaves~~. Even so, there are a number of mappings to be considered, in particular, a less flat-tending [[patent val]] {{val\| 250 396 580 '''702''' '''865''' '''925''' … }} and a more flat-tending 250deff… val {{val\| 250 396 580 '''701''' '''864''' '''924''' … }}.		250edo is [[enfactoring\|enfactored]] in the 7-limit, with the same tuning as 125edo, but provides a closer approximation to the harmonics 11 and 13, where the 13/8 derives from [[10edo]] (7\10). Even so, there are a number of mappings to be considered, in particular, a less flat-tending [[patent val]] {{val\| 250 396 580 '''702''' '''865''' '''925''' … }} and a more flat-tending 250deff… val {{val\| 250 396 580 '''701''' '''864''' '''924''' … }}.

	In addition, in the patent val in the 11-limit, it is a tuning for the [[Minortonic family#Seminar\|seminar]] temperament.		In addition, in the patent val in the 11-limit, it is a tuning for the [[Minortonic family#Seminar\|seminar]] temperament.

			=== Odd harmonics ===
			{{Harmonics in equal\|250}}

	=== Divisors ===		=== Divisors ===
	250edo has subset edos {{EDOs\|1, 2, 5, 10, 25, 50, 125}}.		250edo has subset edos {{EDOs\| 2, 5, 10, 25, 50, 125 }}.

	Since 2.3.5.7 harmonics in the patent val 250edo come from 125edo, and 11.13 harmonics in the patent val come from 50edo, this system is worthy of being considered as a superset of these two temperaments.

	~~=== Odd harmonics ===~~		Since the 2.3.5.7 subgroup in the patent val comes from 125et, and the 2.11.13 subgroup in the patent val comes from 50et, this system is worthy of being considered as a superset of these two temperaments.
	~~{{Harmonics~~ in ~~equal\|250}}~~

Eliora: superset of 125 and 50

2023-01-23T23:53:45Z

superset of 125 and 50

← Older revision		Revision as of 23:53, 23 January 2023
Line 8:		Line 8:
	=== Divisors ===		=== Divisors ===
	250edo has subset edos {{EDOs\|1, 2, 5, 10, 25, 50, 125}}.		250edo has subset edos {{EDOs\|1, 2, 5, 10, 25, 50, 125}}.

			Since 2.3.5.7 harmonics in the patent val 250edo come from 125edo, and 11.13 harmonics in the patent val come from 50edo, this system is worthy of being considered as a superset of these two temperaments.

	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|250}}		{{Harmonics in equal\|250}}

Eliora: expanding a bit, divisors

2023-01-23T23:44:35Z

expanding a bit, divisors

← Older revision		Revision as of 23:44, 23 January 2023
Line 2:		Line 2:
	{{EDO intro\|250}}		{{EDO intro\|250}}

	250edo is [[enfactoring\|enfactored]] in the 7-limit, with the same tuning as 125edo, but provides a closer approximation to the harmonics 11 and 13. Even so, there are a number of mappings to be considered, in particular, a less flat-tending [[patent val]] {{val\| 250 396 580 '''702''' '''865''' '''925''' … }} and a more flat-tending 250deff… val {{val\| 250 396 580 '''701''' '''864''' '''924''' … }}.		250edo is [[enfactoring\|enfactored]] in the 7-limit, with the same tuning as 125edo, but provides a closer approximation to the harmonics 11 and 13. Being a small multiple of [[10edo]], it equates 13/8 with 0.7 octaves. Even so, there are a number of mappings to be considered, in particular, a less flat-tending [[patent val]] {{val\| 250 396 580 '''702''' '''865''' '''925''' … }} and a more flat-tending 250deff… val {{val\| 250 396 580 '''701''' '''864''' '''924''' … }}.

			In addition, in the patent val in the 11-limit, it is a tuning for the [[Minortonic family#Seminar\|seminar]] temperament.

			=== Divisors ===
			250edo has subset edos {{EDOs\|1, 2, 5, 10, 25, 50, 125}}.

	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|250}}		{{Harmonics in equal\|250}}

FloraC: Expansion. An edo page should at least include the information about quality of the one or few obvious mappings

2023-01-23T16:47:06Z

Expansion. An edo page should at least include the information about quality of the one or few obvious mappings

← Older revision		Revision as of 16:47, 23 January 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|250}}		{{EDO intro\|250}}
	~~==Theory==~~
	250edo is enfactored in the 7-limit, with the same tuning as 125edo.		250edo is [[enfactoring\|enfactored]] in the 7-limit, with the same tuning as 125edo, but provides a closer approximation to the harmonics 11 and 13. Even so, there are a number of mappings to be considered, in particular, a less flat-tending [[patent val]] {{val\| 250 396 580 '''702''' '''865''' '''925''' … }} and a more flat-tending 250deff… val {{val\| 250 396 580 '''701''' '''864''' '''924''' … }}.

	=== Odd harmonics ===		=== Odd harmonics ===
	{{~~harmonics~~ in equal\|250}}		{{Harmonics in equal\|250}}

Eliora: Created page with "{{Infobox ET}} {{EDO intro|250}} ==Theory== 250edo is enfactored in the 7-limit, with the same tuning as 125edo. === Odd harmonics === {{harmonics in equal|250}}"

2023-01-23T13:40:29Z

Created page with "{{Infobox ET}} {{EDO intro|250}} ==Theory== 250edo is enfactored in the 7-limit, with the same tuning as 125edo. === Odd harmonics === {{harmonics in equal|250}}"

New page

{{Infobox ET}}
{{EDO intro|250}}
==Theory==
250edo is enfactored in the 7-limit, with the same tuning as 125edo.
=== Odd harmonics ===
{{harmonics in equal|250}}

← Older revision		Revision as of 23:18, 20 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|250~~}}		{{ED intro}}

	== Theory ==		== Theory ==
Line 19:		Line 19:
	== 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]] (%)