120edo - Revision history

Lériendil: wtf is the "long hundred" thing doing here, pretty sure that's MMTM's doing

2025-06-29T06:28:38Z

wtf is the "long hundred" thing doing here, pretty sure that's MMTM's doing

← Older revision		Revision as of 06:28, 29 June 2025
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	=== Miscellaneous properties ===		=== Miscellaneous properties ===
	~~Being the simplest division of the octave by the Germanic {{w\|long hundred}}, it has a unit step which is the fine relative cent of [[1edo]].~~

	120edo also has a [[concoctic]] generator that resembles the leap day excess of earth, 29\120 corresponding to 5 hours and 48 minutes.		120edo also has a [[concoctic]] generator that resembles the leap day excess of earth, 29\120 corresponding to 5 hours and 48 minutes.

ArrowHead294 at 16:55, 18 February 2025

2025-02-18T16:55:46Z

← Older revision		Revision as of 16:55, 18 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|120~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294: /* Notation */

2025-02-06T19:19:47Z

Notation

← Older revision		Revision as of 19:19, 6 February 2025
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	120edo can be notated using [[ups and downs notation]] using [[Helmholtz–Ellis]] accidentals and Stein–Zimmerman [[24edo#Notation\|quarter-tone]] accidentals:		120edo can be notated using [[ups and downs notation]] using [[Helmholtz–Ellis]] accidentals and Stein–Zimmerman [[24edo#Notation\|quarter-tone]] accidentals:

	{{Sharpness-sharp10\|120}}		{{Sharpness-sharp10-qt1\|120}}

ArrowHead294: + Ups and downs notation

2025-02-06T19:19:30Z

+ Ups and downs notation

← Older revision		Revision as of 19:19, 6 February 2025
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	120edo shares the [[perfect fifth]] with 12edo, [[tempering out]] the [[Pythagorean comma]]. 120edo is an excellent tuning in the 2.3.7.11.13.23.29 [[subgroup]]. In the no-5's 11-limit, it tempers out [[243/242]]. In the patent val 120edo is also a tuning for the 7-limit [[decoid]] temperament.		120edo shares the [[perfect fifth]] with 12edo, [[tempering out]] the [[Pythagorean comma]]. 120edo is an excellent tuning in the 2.3.7.11.13.23.29 [[subgroup]]. In the no-5's 11-limit, it tempers out [[243/242]]. In the patent val 120edo is also a tuning for the 7-limit [[decoid]] temperament.

	The 120bdd val is a tuning for [[superpyth]] where 3/2 is tuned to exactly 710 ~~cents~~. It may be used as a ''de facto'' dual fifth in [[Substitute harmonic#Newcome\|newcome]] temperament.		The 120bdd val is a tuning for [[superpyth]] where 3/2 is tuned to exactly 710{{c}}. It may be used as a ''de facto'' dual fifth in [[Substitute harmonic#Newcome\|newcome]] temperament.

	=== Prime harmonics ===		=== Prime harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	120edo is the 10th highly composite edo and the 5th factorial edo (120 = 5! = 1 × 2 × 3 × 4 × 5). It has many subsets: {{EDOs\| 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 30, 40, and 60 }}.		120edo is the 10th highly composite edo and the 5th factorial edo (since {{nowrap\|120 {{=}} 5!}} {{nowrap\|{{=}} 1 × 2 × 3 × 4 × 5}}). It has many subsets: {{EDOs\| 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 30, 40, and 60 }}.

	=== Miscellaneous properties ===		=== Miscellaneous properties ===
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	== Intervals ==		== Intervals ==
	{{Interval table}}		{{Interval table}}

			== Notation ==
			=== Ups and downs notation ===
			120edo can be notated using [[ups and downs notation]] using [[Helmholtz–Ellis]] accidentals and Stein–Zimmerman [[24edo#Notation\|quarter-tone]] accidentals:

			{{Sharpness-sharp10\|120}}

ArrowHead294 at 23:45, 29 July 2024

2024-07-29T23:45:03Z

← Older revision		Revision as of 23:45, 29 July 2024
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	120edo also has a [[concoctic]] generator that resembles the leap day excess of earth, 29\120 corresponding to 5 hours and 48 minutes.		120edo also has a [[concoctic]] generator that resembles the leap day excess of earth, 29\120 corresponding to 5 hours and 48 minutes.

			== JI approximation ==
			{{Q-odd-limit intervals\|120}}

	== Intervals ==		== Intervals ==
	{{Interval table}}		{{Interval table}}

FloraC: -surmarvelpyth (pointless in 120edo as prime 5 is more than 120 steps away)

2024-05-29T09:18:25Z

-surmarvelpyth (pointless in 120edo as prime 5 is more than 120 steps away)

← Older revision		Revision as of 09:18, 29 May 2024
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	== Theory ==		== Theory ==
	120edo is an excellent tuning in the 2.3.7.11.13.23.29 [[subgroup]]. In the no-5's 11-limit, it tempers out [[243/242]].		120edo shares the [[perfect fifth]] with 12edo, [[tempering out]] the [[Pythagorean comma]]. 120edo is an excellent tuning in the 2.3.7.11.13.23.29 [[subgroup]]. In the no-5's 11-limit, it tempers out [[243/242]]. In the patent val 120edo is also a tuning for the 7-limit [[decoid]] temperament.

	~~120edo shares the perfect fifth with 12edo, tempering out the [[Pythagorean comma]].~~ The ~~sharp fifth of 710 cents also has regular temperament interpretations. It~~ is ~~used in the 120b val~~ for ~~tuning the 5-limit~~ [[superpyth]] ~~temperament~~ where ~~it represents~~ 3/2~~, and in the 120g val as a tuning for the 19-limit [[surmarvelpyth]] temperament where it represents 675/448, which~~ is ~~[[marvel comma]] sharp of 3/2~~. It may be used as a ''de facto'' dual fifth in [[Substitute harmonic#Newcome\|newcome~~]] temperament. In the patent val 120edo is also a tuning for the 7-limit [[decoid~~]] temperament.		The 120bdd val is a tuning for [[superpyth]] where 3/2 is tuned to exactly 710 cents. It may be used as a ''de facto'' dual fifth in [[Substitute harmonic#Newcome\|newcome]] temperament.

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

FloraC: +subsets; misc. cleanup

2024-05-29T08:52:46Z

+subsets; misc. cleanup

← Older revision		Revision as of 08:52, 29 May 2024
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	120edo is the 10th highly composite edo and the 5th factorial edo (120 = 5! = 1 × 2 × 3 × 4 × 5).		120edo is the 10th highly composite edo and the 5th factorial edo (120 = 5! = 1 × 2 × 3 × 4 × 5). It has many subsets: {{EDOs\| 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 30, 40, and 60 }}.

	=== Miscellaneous properties ===		=== Miscellaneous properties ===
	Being the simplest division of the octave by the Germanic ~~[[wikipedia:Long_hundred~~\|long hundred]], it has a unit step which is the fine relative cent of [[1edo]].		Being the simplest division of the octave by the Germanic {{w\|long hundred}}, it has a unit step which is the fine relative cent of [[1edo]].

	120edo also has a concoctic generator that resembles the leap day excess of earth, 29\120 corresponding to 5 hours and 48 minutes.		120edo also has a [[concoctic]] generator that resembles the leap day excess of earth, 29\120 corresponding to 5 hours and 48 minutes.

	== Intervals ==		== Intervals ==
	{{Interval table}}		{{Interval table}}

FloraC: Anything about edostep size vs JND is useless due to how broad JND are interpreted (even the "upper bound" and "lower bound"); misc. cleanup

2024-05-29T08:49:57Z

Anything about edostep size vs JND is useless due to how broad JND are interpreted (even the "upper bound" and "lower bound"); misc. cleanup

← Older revision		Revision as of 08:49, 29 May 2024
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	== Theory ==		== Theory ==
	~~120edo is the 10th highly composite EDO and the 5th factorial EDO (120 = 12345 = 5!).~~		120edo is an excellent tuning in the 2.3.7.11.13.23.29 [[subgroup]]. In the no-5's 11-limit, it tempers out [[243/242]].

	120edo is an excellent tuning in the 2.3.7.11.13.23.29 subgroup. In the no-5s 11-limit, it tempers out [[243/242]].

	120edo shares the perfect fifth with 12edo, tempering out the [[Pythagorean comma]]. The sharp fifth of 710 cents also has regular temperament interpretations. It is used in the 120b val for tuning the 5-limit [[superpyth]] temperament where it represents 3/2, and in the 120g val as a tuning for the 19-limit [[surmarvelpyth]] temperament where it represents 675/448, which is [[marvel comma]] sharp of 3/2. It may be used as a ''de facto'' dual fifth in [[Substitute harmonic#Newcome\|newcome]] temperament. In the patent val 120edo is also a tuning for the 7-limit [[decoid]] temperament.		120edo shares the perfect fifth with 12edo, tempering out the [[Pythagorean comma]]. The sharp fifth of 710 cents also has regular temperament interpretations. It is used in the 120b val for tuning the 5-limit [[superpyth]] temperament where it represents 3/2, and in the 120g val as a tuning for the 19-limit [[surmarvelpyth]] temperament where it represents 675/448, which is [[marvel comma]] sharp of 3/2. It may be used as a ''de facto'' dual fifth in [[Substitute harmonic#Newcome\|newcome]] temperament. In the patent val 120edo is also a tuning for the 7-limit [[decoid]] temperament.

	~~The step size of this EDO is near the upper boundary of the [[just noticeable difference]].~~

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|120}}		{{Harmonics in equal\|120}}

			=== Subsets and supersets ===
			120edo is the 10th highly composite edo and the 5th factorial edo (120 = 5! = 1 × 2 × 3 × 4 × 5).

	=== Miscellaneous properties ===		=== Miscellaneous properties ===
Line 19:		Line 18:
	120edo also has a concoctic generator that resembles the leap day excess of earth, 29\120 corresponding to 5 hours and 48 minutes.		120edo also has a concoctic generator that resembles the leap day excess of earth, 29\120 corresponding to 5 hours and 48 minutes.

	== ~~Interval list~~ ==		== Intervals ==
	{{Interval table}}		{{Interval table}}

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

BudjarnLambeth: /* Theory */ Mentioned Newcome

2024-02-03T23:08:42Z

Theory: Mentioned Newcome

← Older revision		Revision as of 23:08, 3 February 2024
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	120edo is an excellent tuning in the 2.3.7.11.13.23.29 subgroup. In the no-5s 11-limit, it tempers out [[243/242]].		120edo is an excellent tuning in the 2.3.7.11.13.23.29 subgroup. In the no-5s 11-limit, it tempers out [[243/242]].

	120edo shares the perfect fifth with 12edo, tempering out the [[Pythagorean comma]]. The sharp fifth of 710 cents also has regular temperament interpretations. It is used in the 120b val for tuning the 5-limit [[superpyth]] temperament where it represents 3/2, and in the 120g val as a tuning for the 19-limit [[surmarvelpyth]] temperament where it represents 675/448, which is [[marvel comma]] sharp of 3/2. In the patent val 120edo is also a tuning for the 7-limit [[decoid]] temperament.		120edo shares the perfect fifth with 12edo, tempering out the [[Pythagorean comma]]. The sharp fifth of 710 cents also has regular temperament interpretations. It is used in the 120b val for tuning the 5-limit [[superpyth]] temperament where it represents 3/2, and in the 120g val as a tuning for the 19-limit [[surmarvelpyth]] temperament where it represents 675/448, which is [[marvel comma]] sharp of 3/2. It may be used as a ''de facto'' dual fifth in [[Substitute harmonic#Newcome\|newcome]] temperament. In the patent val 120edo is also a tuning for the 7-limit [[decoid]] temperament.

	The step size of this EDO is near the upper boundary of the [[just noticeable difference]].		The step size of this EDO is near the upper boundary of the [[just noticeable difference]].

CompactStar at 07:47, 30 October 2023

2023-10-30T07:47:32Z

← Older revision		Revision as of 07:47, 30 October 2023
Line 8:		Line 8:

	120edo shares the perfect fifth with 12edo, tempering out the [[Pythagorean comma]]. The sharp fifth of 710 cents also has regular temperament interpretations. It is used in the 120b val for tuning the 5-limit [[superpyth]] temperament where it represents 3/2, and in the 120g val as a tuning for the 19-limit [[surmarvelpyth]] temperament where it represents 675/448, which is [[marvel comma]] sharp of 3/2. In the patent val 120edo is also a tuning for the 7-limit [[decoid]] temperament.		120edo shares the perfect fifth with 12edo, tempering out the [[Pythagorean comma]]. The sharp fifth of 710 cents also has regular temperament interpretations. It is used in the 120b val for tuning the 5-limit [[superpyth]] temperament where it represents 3/2, and in the 120g val as a tuning for the 19-limit [[surmarvelpyth]] temperament where it represents 675/448, which is [[marvel comma]] sharp of 3/2. In the patent val 120edo is also a tuning for the 7-limit [[decoid]] temperament.

			The step size of this EDO is near the upper boundary of the [[just noticeable difference]].

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