810edo - Revision history

ArrowHead294 at 12:36, 21 February 2025

2025-02-21T12:36:26Z

← Older revision		Revision as of 12:36, 21 February 2025
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	== 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]] (¢)
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	\| 676/675, 1001/1000, 1716/1715, 3025/3024, 4096/4095, 4914/4913		\| 676/675, 1001/1000, 1716/1715, 3025/3024, 4096/4095, 4914/4913
	\| {{mapping\| 810 1284 1881 2274 2802 2997 3311 }}		\| {{mapping\| 810 1284 1881 2274 2802 2997 3311 }}
	\| -0.0281		\| −0.0281
	\| 0.1025		\| 0.1025
	\| 6.92		\| 6.92
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	\| 676/675, 1001/1000, 1216/1215, 1331/1330, 1540/1539, 1729/1728, 4914/4913		\| 676/675, 1001/1000, 1216/1215, 1331/1330, 1540/1539, 1729/1728, 4914/4913
	\| {{mapping\| 810 1284 1881 2274 2802 2997 3311 3441 }}		\| {{mapping\| 810 1284 1881 2274 2802 2997 3311 3441 }}
	\| -0.0324		\| −0.0324
	\| 0.0966		\| 0.0966
	\| 6.52		\| 6.52
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	\| 676/675, 1001/1000, 1216/1215, 1331/1330, 1540/1539, 1729/1728, 2024/2023, 2737/2736		\| 676/675, 1001/1000, 1216/1215, 1331/1330, 1540/1539, 1729/1728, 2024/2023, 2737/2736
	\| {{mapping\| 810 1284 1881 2274 2802 2997 3311 3441 3664 }}		\| {{mapping\| 810 1284 1881 2274 2802 2997 3311 3441 3664 }}
	\| -0.0257		\| −0.0257
	\| 0.0930		\| 0.0930
	\| 6.28		\| 6.28
	\|}		\|}

Francium: changed EDO intro to ED intro

2025-02-21T06:07:46Z

changed EDO intro to ED intro

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

	== Theory ==		== Theory ==

FloraC: /* Theory */

2024-10-12T13:38:48Z

Theory

← Older revision		Revision as of 13:38, 12 October 2024
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	810 = 270 × 3, and 810edo has three copies of [[270edo]] in the 13-limit (and the 2.3.5.7.11.13.19 [[subgroup]]). It makes for a reasonable 17-, 19- and 23-limit system, and perhaps beyond. It is, however, only [[consistent]] to the [[9-odd-limit]]. [[11/9]], [[13/12]], [[13/9]], [[13/10]], and their [[octave complement]]s are all mapped inconsistently in this edo.		810 = 270 × 3, and 810edo has three copies of [[270edo]] in the 13-limit (and the 2.3.5.7.11.13.19 [[subgroup]]). It makes for a reasonable 17-, 19- and 23-limit system, and perhaps beyond. It is, however, only [[consistent]] to the [[9-odd-limit]]. [[11/9]], [[13/12]], [[13/9]], [[13/10]], and their [[octave complement]]s are all mapped inconsistently in this edo.

	As an equal temperament, it [[tempering out\|tempers out]] [[4914/4913]] in the 17-limit; and [[2024/2023]], [[2737/2736]], and [[3520/3519]] in the 23-limit. Although it does quite well in these limits, it is way less efficient as [[270edo]]'s or [[540edo]]'s mappings, as it has greater relative errors (→ [[#Regular temperament properties]]). It is therefore a question of whether one thinks these tuning improvements and differently supplied essentially tempered chords are worth the load of all the extra notes.		As an equal temperament, it [[tempering out\|tempers out]] [[4914/4913]] in the 17-limit; and [[2024/2023]], [[2737/2736]], and [[3520/3519]] in the 23-limit. Although it does quite well in these limits, it is way less efficient than [[270edo]]'s or [[540edo]]'s mappings, as it has greater relative errors (→ [[#Regular temperament properties]]). It is therefore a question of whether one thinks these tuning improvements and differently supplied essentially tempered chords are worth the load of all the extra notes.

	=== Prime harmonics ===		=== Prime harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 810 factors into {{factorization\|810}}, 810edo has subset edos {{EDOs\| 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405 }}.		Since 810 factors into {{factorization\|810}}, 810edo has subset edos {{EDOs\| 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405 }}.

	== Regular temperament properties ==		== Regular temperament properties ==

FloraC: Expand and unstub

2024-10-12T09:57:07Z

Expand and unstub

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
 {{EDO intro}}
 === Prime harmonics ===
@@ Line 8: / Line 13: @@
 Since 810 factors into {{factorization|810}}, 810edo has subset edos {{EDOs| 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405 }}.
+== Regular temperament properties ==
-{{Stub}}
+{| class="wikitable center-4 center-5 center-6"

FloraC: +subsets and supersets

2024-09-01T10:19:05Z

+subsets and supersets

← Older revision		Revision as of 10:19, 1 September 2024
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	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro~~\|810~~}}		{{EDO intro}}

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|810\|prec=3\|columns=15}}		{{Harmonics in equal\|810\|prec=3\|columns=15}}

			=== Subsets and supersets ===
			Since 810 factors into {{factorization\|810}}, 810edo has subset edos {{EDOs\| 2, 3, 5, 6, 9, 10, 15, 18, 27, 30, 45, 54, 81, 90, 135, 162, 270, 405 }}.


	{{Stub}}		{{Stub}}

Lériendil at 21:43, 31 August 2024

2024-08-31T21:43:07Z

← Older revision		Revision as of 21:43, 31 August 2024
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	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|~~870~~}}		{{EDO intro\|810}}

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

Lériendil: Created page with "{{Infobox ET}} {{EDO intro|870}} === Prime harmonics === {{Harmonics in equal|810|prec=3|columns=15}} {{Stub}}"

2024-08-31T21:42:34Z

Created page with "{{Infobox ET}} {{EDO intro|870}} === Prime harmonics === {{Harmonics in equal|810|prec=3|columns=15}} {{Stub}}"

New page

{{Infobox ET}}
{{EDO intro|870}}

=== Prime harmonics ===
{{Harmonics in equal|810|prec=3|columns=15}}

{{Stub}}