1794edo - Revision history

ArrowHead294 at 22:54, 20 February 2025

2025-02-20T22:54:53Z

← Older revision		Revision as of 22:54, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|1794~~}}		{{ED intro}}

	== Theory ==		== Theory ==
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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\|Comma List]]
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	\| {{monzo\| -2843 1794 }}		\| {{monzo\| -2843 1794 }}
	\| {{mapping\| 1794 2843 }}		\| {{mapping\| 1794 2843 }}
	\| 0.0892		\| +0.0892
	\| 0.0892		\| 0.0892
	\| 5.97		\| 5.97
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	\| 9251/9248, 347072/346921, 492043/492032, 128116736/128086823, 151329376/151270111, 378544627/378535936		\| 9251/9248, 347072/346921, 492043/492032, 128116736/128086823, 151329376/151270111, 378544627/378535936
	\| {{mapping\| 1794 6206 7333 7621 8715 8888 9965 }}		\| {{mapping\| 1794 6206 7333 7621 8715 8888 9965 }}
	\| -0.0012		\| −0.0012
	\| 0.0259		\| 0.0259
	\| 1.74		\| 1.74

FloraC: Expand on theory and misc. cleanup

2023-10-30T12:50:35Z

Expand on theory and misc. cleanup

← Older revision		Revision as of 12:50, 30 October 2023
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	== Theory ==		== Theory ==
	~~The~~ best subgroup for 1794 is 2.11.17.19.29.31.47. Notably, it offers a 1794 & [[2016edo\|2016]] temperament, and the years 1794 and 2016 are known for having rather grotesque historical events in proportion to their era (see below).		1794edo is in[[consistent]] to the [[5-odd-limit]] and [[harmonic]]s [[3/1\|3]], [[5/1\|5]], and [[7/1\|7]] are all about halfway between its steps. Otherwise it has decent approximations to [[9/1\|9]], [[15/1\|15]], [[17/1\|17]], and [[21/1\|21]], making it suitable for a 2.9.15.21.17 [[subgroup]] interpretation with an optional addition of either [[11/1\|11]] or [[13/1\|13]].

			For higher harmonics, the best subgroup for 1794 is 2.11.17.19.29.31.47. Notably, it offers a 1794 & [[2016edo\|2016]] temperament, and the years 1794 and 2016 are known for having rather grotesque historical events in proportion to their era (see below).

	It is possible to interpret 1794edo as an intersection of 26edo and 69edo. Using the {{val\| 1794 2834 4160 5037 }} val in the 7-limit, which takes 5-limit from 69edo and 7/4 from 26edo, produces a comma basis 81/80, {{monzo\| -41 1 17 0 }}, {{monzo\| 20 13 14 -26 }}.		It is possible to interpret 1794edo as an intersection of 26edo and 69edo. Using the {{val\| 1794 2834 4160 5037 }} val in the 7-limit, which takes 5-limit from 69edo and 7/4 from 26edo, produces a comma basis 81/80, {{monzo\| -41 1 17 0 }}, {{monzo\| 20 13 14 -26 }}.
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	1794edo has subset edos {{EDOs\| 2, 3, 6, 13, 23, 26, 39, 46, 69, 78, 138, 299, 598, and 897 }}.		Since 1794 factors into {{factorization\|1794}}, 1794edo has subset edos {{EDOs\| 2, 3, 6, 13, 23, 26, 39, 46, 69, 78, 138, 299, 598, and 897 }}.

	== Regular temperament properties ==		== Regular temperament properties ==
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	! 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
	\|-		\|-
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	! [[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\| 2.3		\| 2.3
	\| {{monzo\| -2843 1794 }}		\| {{monzo\| -2843 1794 }}
	\| {{mapping\| 1794 2843 }}		\| {{mapping\| 1794 2843 }}

FloraC: Cleanup (this isn't a number wiki); mark todo

2023-10-15T14:28:07Z

Cleanup (this isn't a number wiki); mark todo

← Older revision		Revision as of 14:28, 15 October 2023
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	The best subgroup for 1794 is 2.11.17.19.29.31.47. Notably, it offers a 1794 & [[2016edo\|2016]] temperament, and the years 1794 and 2016 are known for having rather grotesque historical events in proportion to their era (see below).		The best subgroup for 1794 is 2.11.17.19.29.31.47. Notably, it offers a 1794 & [[2016edo\|2016]] temperament, and the years 1794 and 2016 are known for having rather grotesque historical events in proportion to their era (see below).

	It's possible to interpret 1794edo as an intersection of 26edo and 69edo. Using the {{val\|1794 2834 4160 5037}} val in the 7-limit, which takes 5-limit from 69edo and 7/4 from 26edo, produces a comma basis 81/80, {{monzo\|-41, 1, 17, 0}}, {{monzo\|20, 13, 14, -26}}.		It is possible to interpret 1794edo as an intersection of 26edo and 69edo. Using the {{val\| 1794 2834 4160 5037 }} val in the 7-limit, which takes 5-limit from 69edo and 7/4 from 26edo, produces a comma basis 81/80, {{monzo\| -41 1 17 0 }}, {{monzo\| 20 13 14 -26 }}.

	Nonetheless, 1794edo does offer some simpler interpretations.		Nonetheless, 1794edo does offer some simpler interpretations.
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	Remarkably, using the patent val, 1794edo tempers out the [[schisma]].		Remarkably, using the patent val, 1794edo tempers out the [[schisma]].

	=== ~~Harmonics~~ ===		=== Odd harmonics ===
	{{Harmonics in equal\|1794}}		{{Harmonics in equal\|1794}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
			1794edo has subset edos {{EDOs\| 2, 3, 6, 13, 23, 26, 39, 46, 69, 78, 138, 299, 598, and 897 }}.
	1794edo has subset edos {{EDOs\|2, 3, 6, 13, 23, 26, 39, 46, 69, 78, 138, 299, 598, and 897 }}.

	== 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]]		! rowspan="2" \| [[Comma list\|Comma List]]
	! rowspan="2" \|[[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \|Optimal		! rowspan="2" \| Optimal<br>8ve stretch (¢)
	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
	\|{{monzo\|-2843, 1794}}		\| {{monzo\| -2843 1794 }}
	\|{{~~Val~~\|1794 2843}}		\| {{mapping\| 1794 2843 }}
	\|0.0892		\| 0.0892
	\|0.0892		\| 0.0892
	\|5.97		\| 5.97
	\|-		\|-
	\|2.11.17.19.29.31.47		\| 2.11.17.19.29.31.47
	\|9251/9248, 347072/346921, 492043/492032, 128116736/128086823, 151329376/151270111, 378544627/378535936		\| 9251/9248, 347072/346921, 492043/492032, 128116736/128086823, 151329376/151270111, 378544627/378535936
	\|{{~~Val~~\|1794 6206 7333 7621 8715 8888 9965}}		\| {{mapping\| 1794 6206 7333 7621 8715 8888 9965 }}
	\| -0.0012		\| -0.0012
	\|0.0259		\| 0.0259
	\|1.74		\| 1.74
	\|}		\|}
	~~== Trivia ==~~
	~~{{Wikipedia\| 1794 }}~~

	~~The number 1794 is known for being the fatal year of the French Revolution.~~

	~~[[Category:Equal divisions of the octave~~\|~~####]] <!-- 4-digit number -->~~		{{Todo\| review }}

BudjarnLambeth at 06:57, 9 July 2023

2023-07-09T06:57:34Z

← Older revision		Revision as of 06:57, 9 July 2023
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	~~{{novelty}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|1794}}		{{EDO intro\|1794}}

BudjarnLambeth at 04:52, 9 July 2023

2023-07-09T04:52:12Z

← Older revision		Revision as of 04:52, 9 July 2023
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	{{Infobox ET}}		{{novelty}}{{Infobox ET}}
	{{EDO intro\|1794}}		{{EDO intro\|1794}}

Eliora: sectioning

2023-03-29T23:05:17Z

sectioning

← Older revision		Revision as of 23:05, 29 March 2023
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	== Theory ==		== Theory ==
	~~{{Harmonics in equal\|1794}}~~
	~~1794edo's divisors are {{EDOs\|2, 3, 6, 13, 23, 26, 39, 46, 69, 78, 138, 299, 598, and 897 }}.~~

	The best subgroup for 1794 is 2.11.17.19.29.31.47. Notably, it offers a 1794 & [[2016edo\|2016]] temperament, and the years 1794 and 2016 are known for having rather grotesque historical events in proportion to their era (see below).		The best subgroup for 1794 is 2.11.17.19.29.31.47. Notably, it offers a 1794 & [[2016edo\|2016]] temperament, and the years 1794 and 2016 are known for having rather grotesque historical events in proportion to their era (see below).

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	In the 7-limit in the 1794c val, {{val\| 1794 2843 '''4165''' 5036 }}, it tempers out the [[horwell comma]] and the [[landscape comma]], supporting [[mutt]]. However, it is ''not'' better tuned than [[171edo]]. Using the 1794bd val, {{val\| 1794 '''2844''' 4166 '''5037''' }}, it tempers out {{monzo\| 21 -8 -6 2 }}, {{monzo\| -7 -15 6 6 }}, {{monzo\| -2 -3 15 -10 }}. This mapping of harmonic 7 is the same as [[26edo]]'s. In the 2.11.17 realm, 1794edo supports the 148 & 83 temperament, defined by tempering out the 2.11.17 {{monzo\| -67 43 -20 }} comma. 1794edo tempers out the 2.17.19 {{monzo\| 277 -21 -45 }} and the corresponding temperament is 12 & 891.		In the 7-limit in the 1794c val, {{val\| 1794 2843 '''4165''' 5036 }}, it tempers out the [[horwell comma]] and the [[landscape comma]], supporting [[mutt]]. However, it is ''not'' better tuned than [[171edo]]. Using the 1794bd val, {{val\| 1794 '''2844''' 4166 '''5037''' }}, it tempers out {{monzo\| 21 -8 -6 2 }}, {{monzo\| -7 -15 6 6 }}, {{monzo\| -2 -3 15 -10 }}. This mapping of harmonic 7 is the same as [[26edo]]'s. In the 2.11.17 realm, 1794edo supports the 148 & 83 temperament, defined by tempering out the 2.11.17 {{monzo\| -67 43 -20 }} comma. 1794edo tempers out the 2.17.19 {{monzo\| 277 -21 -45 }} and the corresponding temperament is 12 & 891.

	Remarkably, using the patent val, 1794edo tempers out the schisma.		Remarkably, using the patent val, 1794edo tempers out the [[schisma]].

			=== Harmonics ===
			{{Harmonics in equal\|1794}}
			=== Subsets and supersets ===

			1794edo has subset edos {{EDOs\|2, 3, 6, 13, 23, 26, 39, 46, 69, 78, 138, 299, 598, and 897 }}.

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

Eliora: /* Theory */ clarified now what this means

2022-12-03T14:53:19Z

Theory: clarified now what this means

← Older revision		Revision as of 14:53, 3 December 2022
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	Nonetheless, 1794edo does offer some simpler interpretations.		Nonetheless, 1794edo does offer some simpler interpretations.

	In the 7-limit in the 1794c val, {{val\| 1794 2843 '''4165''' 5036 }}, it tempers out the [[horwell comma]] and the [[landscape comma]], supporting [[mutt]]. However, it is ''not'' better tuned than [[171edo]]. Using the 1794bd val, {{val\| 1794 '''2844''' 4166 '''5037''' }}, it tempers out {{monzo\| 21 -8 -6 2 }}, {{monzo\| -7 -15 6 6 }}, {{monzo\| -2 -3 15 -10 }}. This mapping of harmonic 7 is the same as [[26edo]]'s.		In the 7-limit in the 1794c val, {{val\| 1794 2843 '''4165''' 5036 }}, it tempers out the [[horwell comma]] and the [[landscape comma]], supporting [[mutt]]. However, it is ''not'' better tuned than [[171edo]]. Using the 1794bd val, {{val\| 1794 '''2844''' 4166 '''5037''' }}, it tempers out {{monzo\| 21 -8 -6 2 }}, {{monzo\| -7 -15 6 6 }}, {{monzo\| -2 -3 15 -10 }}. This mapping of harmonic 7 is the same as [[26edo]]'s. In the 2.11.17 realm, 1794edo supports the 148 & 83 temperament, defined by tempering out the 2.11.17 {{monzo\| -67 43 -20 }} comma. 1794edo tempers out the 2.17.19 {{monzo\| 277 -21 -45 }} and the corresponding temperament is 12 & 891.

	Remarkably, using the patent val, 1794edo tempers out the schisma.		Remarkably, using the patent val, 1794edo tempers out the schisma.

	In the 2.11.17 realm, 1794edo shares the {{monzo\| -67 43 -20 }} comma with EDOs like {{EDOs\| 148, 231, and 296 }}. In the 2.17.19 subgroup, 1794edo tempers out the {{monzo\| 277 -21 -45 }}. Most notably, shares this property with {{EDOs\| 12, 24, 36, 48 }}, as well as {{EDOs\| 855, 867, 879 and 891 }}, with 855 being a multiple of 171. This is distantly reminiscent of the technique when 12edo's 1 and 3-step intervals, for example C# and D# counting from C, are assumed to be 17/16 and 19/16.

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

Plumtree: Infobox ET added

2022-10-04T22:11:52Z

Infobox ET added

← Older revision		Revision as of 22:11, 4 October 2022
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			{{Infobox ET}}
	{{EDO intro\|1794}}		{{EDO intro\|1794}}

Eliora at 10:47, 17 September 2022

2022-09-17T10:47:24Z

← Older revision		Revision as of 10:47, 17 September 2022
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	The best subgroup for 1794 is 2.11.17.19.29.31.47. Notably, it offers a 1794 & [[2016edo\|2016]] temperament, and the years 1794 and 2016 are known for having rather grotesque historical events in proportion to their era (see below).		The best subgroup for 1794 is 2.11.17.19.29.31.47. Notably, it offers a 1794 & [[2016edo\|2016]] temperament, and the years 1794 and 2016 are known for having rather grotesque historical events in proportion to their era (see below).

	It's possible to interpret 1794edo as an intersection of 26edo and 69edo. Using the 1794 2834 4160 5037 val in the 7-limit, which takes 5-limit from 69edo and 7/4 from 26edo, produces a comma basis 81/80, [-41, 1, 17, 0⟩, [20, 13, 14, -~~26⟩~~.		It's possible to interpret 1794edo as an intersection of 26edo and 69edo. Using the {{val\|1794 2834 4160 5037}} val in the 7-limit, which takes 5-limit from 69edo and 7/4 from 26edo, produces a comma basis 81/80, {{monzo\|-41, 1, 17, 0}}, {{monzo\|20, 13, 14, -26}}.

	Nonetheless, 1794edo does offer some simpler interpretations.		Nonetheless, 1794edo does offer some simpler interpretations.

Eliora: /* Theory */

2022-09-17T10:46:22Z

Theory

← Older revision		Revision as of 10:46, 17 September 2022
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	== Theory ==		== Theory ==
	{{~~Primes~~ in ~~edo~~\|1794~~\|columns=15~~}}		{{Harmonics in equal\|1794}}

	1794edo's divisors are {{EDOs\|2, 3, 6, 13, 23, 26, 39, 46, 69, 78, 138, 299, 598, and 897 }}.		1794edo's divisors are {{EDOs\|2, 3, 6, 13, 23, 26, 39, 46, 69, 78, 138, 299, 598, and 897 }}.

	The best subgroup for 1794 is 2.11.17.19.29.31.47. Notably, it offers a 1794 & [[2016edo\|2016]] temperament, and the years 1794 and 2016 are known for having rather grotesque historical events in proportion to their era (see below).		The best subgroup for 1794 is 2.11.17.19.29.31.47. Notably, it offers a 1794 & [[2016edo\|2016]] temperament, and the years 1794 and 2016 are known for having rather grotesque historical events in proportion to their era (see below).

			It's possible to interpret 1794edo as an intersection of 26edo and 69edo. Using the 1794 2834 4160 5037 val in the 7-limit, which takes 5-limit from 69edo and 7/4 from 26edo, produces a comma basis 81/80, [-41, 1, 17, 0⟩, [20, 13, 14, -26⟩.

	Nonetheless, 1794edo does offer some simpler interpretations.		Nonetheless, 1794edo does offer some simpler interpretations.