114edo - Revision history

ArrowHead294 at 16:51, 18 February 2025

2025-02-18T16:51:42Z

← Older revision		Revision as of 16:51, 18 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|114~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: +subsets and supersets

2024-06-04T06:29:06Z

+subsets and supersets

← Older revision		Revision as of 06:29, 4 June 2024
Line 7:		Line 7:
	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|114}}		{{Harmonics in equal\|114}}

			=== Subsets and supersets ===
			Since 114 factors into {{factorization\|114}}, 114 edo has subset edos {{EDOs\| 2, 3, 6, 19, 38, and 57 }}.

	== Intervals ==		== Intervals ==

FloraC: Cleanup

2024-06-04T06:27:50Z

Cleanup

← Older revision		Revision as of 06:27, 4 June 2024
Line 2:		Line 2:
	{{EDO intro\|114}}		{{EDO intro\|114}}

	In the [[~~5-limit\|~~5-limit]] it [[~~tempering_out~~\|tempers out]] 2048/2025, in the [[~~7-limit\|~~7-limit]] 245/243, in the [[~~11-limit\|~~11-limit]] 121/120, 176/175 and [[~~Quartisma\|117440512/117406179~~]], in the [[~~13-limit\|~~13-limit]] 196/195 and 325/324, in the [[~~17-limit\|~~17-limit]] 136/135 and 154/153, in the [[~~19-limit\|~~19-limit]] 286/285 and 343/342. These commas make for 114edo being an excellent tuning for [[~~Diaschismic_family\|~~shrutar ~~temperament~~]]; it is in fact the [[~~Optimal_patent_val\|~~optimal patent val]] for ~~[[Shrutar\|~~shrutar]] in the 11- 13- 17- and 19-limit, as well as the rank ~~three~~ bisector temperament.		== Theory ==
			In the [[5-limit]] the equal temperament [[tempering out\|tempers out]] 2048/2025 ([[diaschisma]]), in the [[7-limit]] [[245/243]], in the [[11-limit]] [[121/120]], [[176/175]] and notably the [[quartisma]], in the [[13-limit]] [[196/195]] and [[325/324]], in the [[17-limit]] [[136/135]] and [[154/153]], in the [[19-limit]] [[286/285]] and [[343/342]]. These commas make for 114edo being an excellent tuning for the [[shrutar]] temperament; it is in fact the [[optimal patent val]] for shrutar in the 11-, 13-, 17-, and 19-limit, as well as the rank-3 [[bisector]] temperament.

	== ~~Harmonics~~ ==		=== Odd harmonics ===
	{{Harmonics in equal\|114}}		{{Harmonics in equal\|114}}

Line 11:		Line 12:

	[[Category:Shrutar]]		[[Category:Shrutar]]
			[[Category:Bisector]]

FloraC: -unparsable shit

2024-06-04T06:23:19Z

-unparsable shit

← Older revision		Revision as of 06:23, 4 June 2024
Line 10:		Line 10:
	{{Interval table}}		{{Interval table}}

	~~== Period of 19-limit Shrutar ==~~

	~~{\| class="wikitable"~~
	\|-
	~~! \|Degree~~
	~~! \|Cents~~
	~~!Difference from 68edo~~
	\|-
	~~\| \|2~~
	~~\| \|21.05263~~
	~~\|3.40557¢~~
	\|-
	~~\| \|3~~
	~~\| \|31.57895~~
	~~\| -3.71517¢~~
	\|-
	~~\| \| 5~~
	~~\| \| 52.63158~~
	~~\| -0.3096¢~~
	\|-
	~~\| \|7~~
	~~\| \|73.68421~~
	~~\|3.096¢~~
	\|-
	~~\| \|8~~
	~~\| \|84.21053~~
	~~\| -4.02477¢~~
	\|-
	~~\| \|10~~
	~~\| \|105.26316~~
	~~\| -0.619195¢~~
	\|-
	~~\| \|12~~
	~~\| \| 126.31579~~
	~~\|2.78638¢~~
	\|-
	~~\| \|13~~
	~~\| \|136.842105~~
	~~\| -4.334365¢~~
	\|-
	~~\| \|15~~
	~~\| \|157.89474~~
	~~\| -0.9288¢~~
	\|-
	~~\| \| 17~~
	~~\| \|178.94737~~
	~~\|2.47678¢~~
	\|-
	~~\| \|18~~
	~~\| \| 189.47369~~
	~~\| -4.644¢~~
	\|-
	~~\| \|20~~
	~~\| \|210.52632~~
	~~\| -1.23839¢~~
	\|-
	~~\| \|22~~
	~~\| \|231.57895~~
	~~\|2.16718¢~~
	\|-
	~~\| \|23~~
	~~\| \|242.10526~~
	~~\| -4.953560372~~
	\|-
	~~\| \|25~~
	~~\| \|263.157895~~
	~~\| -1.548¢~~
	\|-
	~~\| \|27~~
	~~\| \|284.21053~~
	~~\|1.857585¢~~
	\|-
	~~\| \|29~~
	~~\| \|305.26316~~
	~~\|5.26316¢~~
	\|-
	~~\| \|30~~
	~~\| \|315.78947~~
	~~\| -1.857585¢~~
	\|-
	~~\| \|32~~
	~~\| \|336.842105~~
	~~\|1.548¢~~
	\|-
	~~\| \|34~~
	~~\| \|357.89474~~
	~~\|4.95356¢~~
	\|-
	~~\| \|35~~
	~~\| \| 368.42105~~
	~~\| -2.16718¢~~
	\|-
	~~\| \|37~~
	~~\| \|389.47368~~
	~~\|1.23839¢~~
	\|-
	~~\| \|39~~
	~~\| \|410.52632~~
	~~\|4.64396¢~~
	\|-
	~~\| \|40~~
	~~\| \|421.05263~~
	~~\| -2.47678¢~~
	\|-
	~~\| \|42~~
	~~\| \|442.10526~~
	~~\|0.92879¢~~
	\|-
	~~\| \|44~~
	~~\| \|463.157895~~
	~~\|4.334365¢~~
	\|-
	~~\| \|45~~
	~~\| \|473.68421~~
	~~\| -2.78638¢~~
	\|-
	~~\| \|47~~
	~~\| \|494.73684~~
	~~\|0.619195¢~~
	\|-
	~~\| \|49~~
	~~\| \|515.78947~~
	~~\|4.02477¢~~
	\|-
	~~\| \|50~~
	~~\| \|526.31579~~
	~~\| -3.095975¢~~
	\|-
	~~\| \|52~~
	~~\| \|547.36842~~
	~~\|0.3096¢~~
	\|-
	~~\| \|54~~
	~~\| \|568.42105~~
	~~\|3.71517¢~~
	\|-
	~~\| \|55~~
	~~\| \|578.94737~~
	~~\| -3.40557¢~~
	\|}

	~~[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->~~
	[[Category:Shrutar]]		[[Category:Shrutar]]

BudjarnLambeth: Edo intro

2024-01-25T09:45:01Z

Edo intro

← Older revision		Revision as of 09:45, 25 January 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	~~'''114edo''' is the [[Equal_division_of_the_octave~~\|~~equal division of the octave]] into~~ 114 ~~parts, each of 10.52632 [[cent]]s.~~ In the [[5-limit\|5-limit]] it [[tempering_out\|tempers out]] 2048/2025, in the [[7-limit\|7-limit]] 245/243, in the [[11-limit\|11-limit]] 121/120, 176/175 and [[Quartisma\|117440512/117406179]], in the [[13-limit\|13-limit]] 196/195 and 325/324, in the [[17-limit\|17-limit]] 136/135 and 154/153, in the [[19-limit\|19-limit]] 286/285 and 343/342. These commas make for 114edo being an excellent tuning for [[Diaschismic_family\|shrutar temperament]]; it is in fact the [[Optimal_patent_val\|optimal patent val]] for [[Shrutar\|shrutar]] in the 11- 13- 17- and 19-limit, as well as the rank three bisector temperament.		{{EDO intro\|114}}

			In the [[5-limit\|5-limit]] it [[tempering_out\|tempers out]] 2048/2025, in the [[7-limit\|7-limit]] 245/243, in the [[11-limit\|11-limit]] 121/120, 176/175 and [[Quartisma\|117440512/117406179]], in the [[13-limit\|13-limit]] 196/195 and 325/324, in the [[17-limit\|17-limit]] 136/135 and 154/153, in the [[19-limit\|19-limit]] 286/285 and 343/342. These commas make for 114edo being an excellent tuning for [[Diaschismic_family\|shrutar temperament]]; it is in fact the [[Optimal_patent_val\|optimal patent val]] for [[Shrutar\|shrutar]] in the 11- 13- 17- and 19-limit, as well as the rank three bisector temperament.

	== Harmonics ==		== Harmonics ==

BudjarnLambeth: Changed subheading from prime harmonics to harmonics, added interval table

2024-01-21T07:17:12Z

Changed subheading from prime harmonics to harmonics, added interval table

← Older revision		Revision as of 07:17, 21 January 2024
Line 2:		Line 2:
	'''114edo''' is the [[Equal_division_of_the_octave\|equal division of the octave]] into 114 parts, each of 10.52632 [[cent]]s. In the [[5-limit\|5-limit]] it [[tempering_out\|tempers out]] 2048/2025, in the [[7-limit\|7-limit]] 245/243, in the [[11-limit\|11-limit]] 121/120, 176/175 and [[Quartisma\|117440512/117406179]], in the [[13-limit\|13-limit]] 196/195 and 325/324, in the [[17-limit\|17-limit]] 136/135 and 154/153, in the [[19-limit\|19-limit]] 286/285 and 343/342. These commas make for 114edo being an excellent tuning for [[Diaschismic_family\|shrutar temperament]]; it is in fact the [[Optimal_patent_val\|optimal patent val]] for [[Shrutar\|shrutar]] in the 11- 13- 17- and 19-limit, as well as the rank three bisector temperament.		'''114edo''' is the [[Equal_division_of_the_octave\|equal division of the octave]] into 114 parts, each of 10.52632 [[cent]]s. In the [[5-limit\|5-limit]] it [[tempering_out\|tempers out]] 2048/2025, in the [[7-limit\|7-limit]] 245/243, in the [[11-limit\|11-limit]] 121/120, 176/175 and [[Quartisma\|117440512/117406179]], in the [[13-limit\|13-limit]] 196/195 and 325/324, in the [[17-limit\|17-limit]] 136/135 and 154/153, in the [[19-limit\|19-limit]] 286/285 and 343/342. These commas make for 114edo being an excellent tuning for [[Diaschismic_family\|shrutar temperament]]; it is in fact the [[Optimal_patent_val\|optimal patent val]] for [[Shrutar\|shrutar]] in the 11- 13- 17- and 19-limit, as well as the rank three bisector temperament.

	== ~~Prime harmonics~~ ==		== Harmonics ==
	{{Harmonics in equal\|114}}		{{Harmonics in equal\|114}}

			== Intervals ==
			{{Interval table}}

	== Period of 19-limit Shrutar ==		== Period of 19-limit Shrutar ==

Eliora: /* Circulating temperaments */

2023-05-30T21:17:34Z

Circulating temperaments

Show changes

BudjarnLambeth: /* Circulating temperaments */

2023-05-02T11:11:37Z

Circulating temperaments

← Older revision		Revision as of 11:11, 2 May 2023
Line 148:		Line 148:
	== Circulating temperaments ==		== Circulating temperaments ==

	Since 114edo has a step of 10.52632 cents, it also allows one to use its MOS scales as circulating ~~temperaments~~.		Since 114edo has a step of 10.52632 cents, it also allows one to use its MOS scales as [[circulating temperament]]s.
	{\| class="wikitable"		{\| class="wikitable"
	\|+Circulating temperaments in 114edo		\|+Circulating temperaments in 114edo

BudjarnLambeth: Cleaned up subheadings and added harmonics table

2023-05-02T11:11:22Z

Cleaned up subheadings and added harmonics table

← Older revision		Revision as of 11:11, 2 May 2023
Line 2:		Line 2:
	'''114edo''' is the [[Equal_division_of_the_octave\|equal division of the octave]] into 114 parts, each of 10.52632 [[cent]]s. In the [[5-limit\|5-limit]] it [[tempering_out\|tempers out]] 2048/2025, in the [[7-limit\|7-limit]] 245/243, in the [[11-limit\|11-limit]] 121/120, 176/175 and [[Quartisma\|117440512/117406179]], in the [[13-limit\|13-limit]] 196/195 and 325/324, in the [[17-limit\|17-limit]] 136/135 and 154/153, in the [[19-limit\|19-limit]] 286/285 and 343/342. These commas make for 114edo being an excellent tuning for [[Diaschismic_family\|shrutar temperament]]; it is in fact the [[Optimal_patent_val\|optimal patent val]] for [[Shrutar\|shrutar]] in the 11- 13- 17- and 19-limit, as well as the rank three bisector temperament.		'''114edo''' is the [[Equal_division_of_the_octave\|equal division of the octave]] into 114 parts, each of 10.52632 [[cent]]s. In the [[5-limit\|5-limit]] it [[tempering_out\|tempers out]] 2048/2025, in the [[7-limit\|7-limit]] 245/243, in the [[11-limit\|11-limit]] 121/120, 176/175 and [[Quartisma\|117440512/117406179]], in the [[13-limit\|13-limit]] 196/195 and 325/324, in the [[17-limit\|17-limit]] 136/135 and 154/153, in the [[19-limit\|19-limit]] 286/285 and 343/342. These commas make for 114edo being an excellent tuning for [[Diaschismic_family\|shrutar temperament]]; it is in fact the [[Optimal_patent_val\|optimal patent val]] for [[Shrutar\|shrutar]] in the 11- 13- 17- and 19-limit, as well as the rank three bisector temperament.

	===Period of 19-limit Shrutar===		== Prime harmonics ==
			{{Harmonics in equal\|114}}

			== Period of 19-limit Shrutar ==

	{\| class="wikitable"		{\| class="wikitable"
Line 142:		Line 145:
	\| -3.40557¢		\| -3.40557¢
	\|}		\|}

			== Circulating temperaments ==

	Since 114edo has a step of 10.52632 cents, it also allows one to use its MOS scales as circulating temperaments.		Since 114edo has a step of 10.52632 cents, it also allows one to use its MOS scales as circulating temperaments.
	{\| class="wikitable"		{\| class="wikitable"

Aura at 18:51, 4 October 2022

2022-10-04T18:51:32Z

← Older revision		Revision as of 18:51, 4 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	'''114edo''' is the [[Equal_division_of_the_octave\|equal division of the octave]] into 114 parts, each of 10.52632 [[cent]]s. In the [[5-limit\|5-limit]] it [[tempering_out\|tempers out]] 2048/2025, in the [[7-limit\|7-limit]] 245/243, in the [[11-limit\|11-limit]] 121/120, 176/175 and [[Quartisma\|117440512/117406179]], in the [[13-limit\|13-limit]] 196/195 and 325/324, in the [[17-limit\|17-limit]] 136/135 and 154/153, in the [[19-limit\|19-limit]] 286/285 and 343/342. These commas make for 114edo being an excellent tuning for [[Diaschismic_family\|shrutar temperament]]; it is in fact the [[Optimal_patent_val\|optimal patent val]] for [[Shrutar\|shrutar]] in the 11- 13- 17- and 19-limit, as well as the rank three bisector temperament.		'''114edo''' is the [[Equal_division_of_the_octave\|equal division of the octave]] into 114 parts, each of 10.52632 [[cent]]s. In the [[5-limit\|5-limit]] it [[tempering_out\|tempers out]] 2048/2025, in the [[7-limit\|7-limit]] 245/243, in the [[11-limit\|11-limit]] 121/120, 176/175 and [[Quartisma\|117440512/117406179]], in the [[13-limit\|13-limit]] 196/195 and 325/324, in the [[17-limit\|17-limit]] 136/135 and 154/153, in the [[19-limit\|19-limit]] 286/285 and 343/342. These commas make for 114edo being an excellent tuning for [[Diaschismic_family\|shrutar temperament]]; it is in fact the [[Optimal_patent_val\|optimal patent val]] for [[Shrutar\|shrutar]] in the 11- 13- 17- and 19-limit, as well as the rank three bisector temperament.

← Older revision		Revision as of 06:23, 4 June 2024
Line 10:		Line 10:
	{{Interval table}}		{{Interval table}}

	~~== Period of 19-limit Shrutar ==~~

	~~{\| class="wikitable"~~
	\|-
	~~! \|Degree~~
	~~! \|Cents~~
	~~!Difference from 68edo~~
	\|-
	~~\| \|2~~
	~~\| \|21.05263~~
	~~\|3.40557¢~~
	\|-
	~~\| \|3~~
	~~\| \|31.57895~~
	~~\| -3.71517¢~~
	\|-
	~~\| \| 5~~
	~~\| \| 52.63158~~
	~~\| -0.3096¢~~
	\|-
	~~\| \|7~~
	~~\| \|73.68421~~
	~~\|3.096¢~~
	\|-
	~~\| \|8~~
	~~\| \|84.21053~~
	~~\| -4.02477¢~~
	\|-
	~~\| \|10~~
	~~\| \|105.26316~~
	~~\| -0.619195¢~~
	\|-
	~~\| \|12~~
	~~\| \| 126.31579~~
	~~\|2.78638¢~~
	\|-
	~~\| \|13~~
	~~\| \|136.842105~~
	~~\| -4.334365¢~~
	\|-
	~~\| \|15~~
	~~\| \|157.89474~~
	~~\| -0.9288¢~~
	\|-
	~~\| \| 17~~
	~~\| \|178.94737~~
	~~\|2.47678¢~~
	\|-
	~~\| \|18~~
	~~\| \| 189.47369~~
	~~\| -4.644¢~~
	\|-
	~~\| \|20~~
	~~\| \|210.52632~~
	~~\| -1.23839¢~~
	\|-
	~~\| \|22~~
	~~\| \|231.57895~~
	~~\|2.16718¢~~
	\|-
	~~\| \|23~~
	~~\| \|242.10526~~
	~~\| -4.953560372~~
	\|-
	~~\| \|25~~
	~~\| \|263.157895~~
	~~\| -1.548¢~~
	\|-
	~~\| \|27~~
	~~\| \|284.21053~~
	~~\|1.857585¢~~
	\|-
	~~\| \|29~~
	~~\| \|305.26316~~
	~~\|5.26316¢~~
	\|-
	~~\| \|30~~
	~~\| \|315.78947~~
	~~\| -1.857585¢~~
	\|-
	~~\| \|32~~
	~~\| \|336.842105~~
	~~\|1.548¢~~
	\|-
	~~\| \|34~~
	~~\| \|357.89474~~
	~~\|4.95356¢~~
	\|-
	~~\| \|35~~
	~~\| \| 368.42105~~
	~~\| -2.16718¢~~
	\|-
	~~\| \|37~~
	~~\| \|389.47368~~
	~~\|1.23839¢~~
	\|-
	~~\| \|39~~
	~~\| \|410.52632~~
	~~\|4.64396¢~~
	\|-
	~~\| \|40~~
	~~\| \|421.05263~~
	~~\| -2.47678¢~~
	\|-
	~~\| \|42~~
	~~\| \|442.10526~~
	~~\|0.92879¢~~
	\|-
	~~\| \|44~~
	~~\| \|463.157895~~
	~~\|4.334365¢~~
	\|-
	~~\| \|45~~
	~~\| \|473.68421~~
	~~\| -2.78638¢~~
	\|-
	~~\| \|47~~
	~~\| \|494.73684~~
	~~\|0.619195¢~~
	\|-
	~~\| \|49~~
	~~\| \|515.78947~~
	~~\|4.02477¢~~
	\|-
	~~\| \|50~~
	~~\| \|526.31579~~
	~~\| -3.095975¢~~
	\|-
	~~\| \|52~~
	~~\| \|547.36842~~
	~~\|0.3096¢~~
	\|-
	~~\| \|54~~
	~~\| \|568.42105~~
	~~\|3.71517¢~~
	\|-
	~~\| \|55~~
	~~\| \|578.94737~~
	~~\| -3.40557¢~~
	\|}

	~~[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->~~
	[[Category:Shrutar]]		[[Category:Shrutar]]