1080edo - Revision history

ArrowHead294 at 22:46, 20 February 2025

2025-02-20T22:46:52Z

← Older revision		Revision as of 22:46, 20 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|1080~~}}		{{ED intro}}

	== Theory ==		== Theory ==
Line 17:		Line 17:
	== Selected intervals ==		== Selected intervals ==
	{\| class="wikitable mw-collapsible mw-collapsed"		{\| class="wikitable mw-collapsible mw-collapsed"
	\|+		\|-
	! Step		! Step
	! Eliora's Naming System		! Eliora's Naming System
Line 23:		Line 23:
	! Comments		! Comments
	\|-		\|-
	\|0		\| 0
	\|Prime		\| Prime
	\|		\|
	\|		\|
	\|-		\|-
	\|3		\| 3
	\|Degree		\| Degree
	\|		\|
	\|Derives from 360edo.		\| Derives from 360edo.
	\|-		\|-
	\|4		\| 4
	\|Ducentiseptuagesima		\| Ducentiseptuagesima
	\|		\|
	\|Derives from 270edo		\| Derives from 270edo
	\|-		\|-
	\|7		\| 7
	\|Septimal kelisma		\| Septimal kelisma
	\|		\|
	\|		\|
	\|-		\|-
	\|15		\| 15
	\|Moria		\| Moria
	\|		\|
	\|Derives form 72edo.		\| Derives form 72edo.
	\|-		\|-
	\|90		\| 90
	\|Dodecaphonic semitone		\| Dodecaphonic semitone
	\|		\|
	\|		\|
	\|-		\|-
	\|94		\| 94
	\|Septendecimal semitone		\| Septendecimal semitone
	\|17/16		\| 17/16
	\|		\|
	\|-		\|-
	\|240		\| 240
	\|Septimal submajor second		\| Septimal submajor second
	\|7/6		\| 7/6
	\|Derives form 9edo.		\| Derives form 9edo.
	\|-		\|-
	\|360		\| 360
	\|Landscape major third		\| Landscape major third
	\|63/50		\| 63/50
	\|		\|
	\|-		\|-
	\|495		\| 495
	\|24-phonic superfourth		\| 24-phonic superfourth
	\|		\|
	\|Derives from 24edo.		\| Derives from 24edo.
	\|-		\|-
	\|496		\| 496
	\|Undecimal superfourth		\| Undecimal superfourth
	\|11/8		\| 11/8
	\|		\|
	\|-		\|-
	\|630		\| 630
	\|Dodecaphonic fifth		\| Dodecaphonic fifth
	\|		\|
	\|		\|
	\|-		\|-
	\|632		\| 632
	\|135-phonic Fifth		\| 135-phonic Fifth
	\|3/2		\| 3/2
	\|		\|
	\|-		\|-
	\|756		\| 756
	\|Tridecimal neutral sixth, 13th harmonic		\| Tridecimal neutral sixth, 13th harmonic
	\|13/8		\| 13/8
	\|Derives from 10edo.		\| Derives from 10edo.
	\|-		\|-
	\|1080		\| 1080
	\|Octave		\| Octave
	\|		\|
	\|		\|
	\|}		\|}

Francium: +music

2024-06-19T07:22:04Z

+music

← Older revision		Revision as of 07:22, 19 June 2024
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	\|		\|
	\|}		\|}

			== Music ==
			; [[No Clue Music]]
			* [https://www.youtube.com/watch?v=hQOvnQhAcKU ''Not Torture Music''] (2024)

	[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->		[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->

Eliora: /* Theory */

2023-10-21T15:29:17Z

Theory

← Older revision		Revision as of 15:29, 21 October 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	1080edo is [[enfactoring\|enfactored]] in the 13-limit, with the same tuning as [[270edo]]. Aside from the patent val, there are a number of mappings to be cosidered. The 1080e val, 1080 1712 2508 3032 ~~3737~~, [[Tempering out\|tempers out]] 114345/114244, and the 1080ef val, 1080 1712 2508 3032 3737 3997 it tempers out [[2080/2079]].		1080edo is [[enfactoring\|enfactored]] in the 13-limit, with the same tuning as [[270edo]]. Aside from the patent val, there are a number of mappings to be cosidered. The 1080e val, {{mapping\|1080 1712 2508 3032 '''3737'''}}, [[Tempering out\|tempers out]] 114345/114244, and the 1080ef val, {{mapping\|1080 1712 2508 3032 '''3737 3997'''}} it tempers out [[2080/2079]].

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

Eliora: /* Theory */

2023-10-21T15:28:45Z

Theory

← Older revision		Revision as of 15:28, 21 October 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	1080edo is [[enfactoring\|enfactored]] in the 13-limit, with the same tuning as [[270edo]]. In the 1080e val, ~~which puts the 11th harmonic on 3737 steps~~, it [[Tempering out\|tempers out]] 114345/114244, and in the 1080ef val it tempers out [[2080/2079]].		1080edo is [[enfactoring\|enfactored]] in the 13-limit, with the same tuning as [[270edo]]. Aside from the patent val, there are a number of mappings to be cosidered. The 1080e val, 1080 1712 2508 3032 3737, [[Tempering out\|tempers out]] 114345/114244, and the 1080ef val, 1080 1712 2508 3032 3737 3997 it tempers out [[2080/2079]].

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

FloraC: Rework

2023-10-19T15:19:12Z

Rework

← Older revision		Revision as of 15:19, 19 October 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	~~1080~~ is ~~a largely composite EDO, meaning it's notable for its divisors. Its~~ [[~~number of the divisors~~\|~~32 divisors~~]] ~~are 1~~, 2, 3, 4, ~~5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 90, 108, 120, 135, 180, 216, 270, 360, 540. 1080's abundancy index is 2.33..., or exactly 7~~/3.		1080edo is [[enfactoring\|enfactored]] in the 13-limit, with the same tuning as [[270edo]]. In the 1080e val, which puts the 11th harmonic on 3737 steps, it [[Tempering out\|tempers out]] 114345/114244, and in the 1080ef val it tempers out [[2080/2079]].

	~~Notable subsets of 1080edo are [[270edo]] and [[72edo]], as they both belong to [[The Riemann Zeta Function and Tuning#Zeta EDO lists~~\|the ''zeta peak edos'', ''zeta integral edos'' and ''zeta gap edos'' sequences]], however the patent val of 1080edo does not consist of their approximation alone, as the 17th harmonic comes from [[540edo]]. In addition, [[12edo]] is the dominant tuning system in the world, and [[360edo]] is a highly composite EDO.		=== Odd harmonics ===
			{{Harmonics in equal\|1080}}

	~~As every 4th step of [[4320edo]]~~, it is ~~a good tuning~~ for ~~the 2.5/3~~.~~7 subgroup, and has strong representation for~~ [[~~19/12~~]], ~~[[19/~~10]], ~~[[17/13]]~~, ~~[[23/13]]~~, and ~~[[23~~/~~17]]~~.		=== Subsets and supersets ===
			1080 is a largely composite edo, meaning it is notable for its divisors. Its 32 [[number of the divisors\|divisors]] are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 90, 108, 120, 135, 180, 216, 270, 360, 540, and 1080. 1080's abundancy index is 2.33…, or exactly 7/3.

	~~=== Regular temperament theory ===~~		Notable subsets of 1080edo are [[270edo]] and [[72edo]], as they both belong to the [[The Riemann zeta function and tuning #Zeta EDO lists\|zeta peak edos, zeta integral edos and zeta gap edos]]. However, the [[patent val]] of 1080edo does not consist of their approximation alone, as the 17th harmonic comes from [[540edo]]. In addition, [[12edo]] is the dominant tuning system in the world, and [[360edo]] is a highly composite edo.
	~~In the 13-limit,~~ 1080edo ~~is contorted order-4~~, ~~with~~ the ~~same tuning as~~ [[~~270edo~~]]. In the ~~1080e~~ val, ~~which puts~~ the ~~11th~~ harmonic ~~on 3737~~, ~~it tempers out 114345/114244~~, and ~~in the 1080ef val it tempers out~~ [[~~2080/2079~~]].

	~~=== Harmonics ===~~		As every 4th step of [[4320edo]], it is a good tuning for the 2.5/3.7 subgroup, and has strong representation for [[19/12]], [[19/10]], [[17/13]], [[23/13]], and [[23/17]].
	~~{{Harmonics in equal\|1080}}~~

	== ~~Table of~~ intervals ==		== Selected intervals ==
	{\| class="wikitable"		{\| class="wikitable mw-collapsible mw-collapsed"
	\|+		\|+
	!Step		! Step
	!~~Name~~		! Eliora's Naming System
	!~~Associated ratio~~		! Approximate Ratio
	!Comments		! Comments
	\|-		\|-
	\|0		\|0

Eliora: /* Theory */

2023-09-14T18:34:50Z

Theory

← Older revision		Revision as of 18:34, 14 September 2023
Line 6:		Line 6:

	Notable subsets of 1080edo are [[270edo]] and [[72edo]], as they both belong to [[The Riemann Zeta Function and Tuning#Zeta EDO lists\|the ''zeta peak edos'', ''zeta integral edos'' and ''zeta gap edos'' sequences]], however the patent val of 1080edo does not consist of their approximation alone, as the 17th harmonic comes from [[540edo]]. In addition, [[12edo]] is the dominant tuning system in the world, and [[360edo]] is a highly composite EDO.		Notable subsets of 1080edo are [[270edo]] and [[72edo]], as they both belong to [[The Riemann Zeta Function and Tuning#Zeta EDO lists\|the ''zeta peak edos'', ''zeta integral edos'' and ''zeta gap edos'' sequences]], however the patent val of 1080edo does not consist of their approximation alone, as the 17th harmonic comes from [[540edo]]. In addition, [[12edo]] is the dominant tuning system in the world, and [[360edo]] is a highly composite EDO.

			As every 4th step of [[4320edo]], it is a good tuning for the 2.5/3.7 subgroup, and has strong representation for [[19/12]], [[19/10]], [[17/13]], [[23/13]], and [[23/17]].

	=== Regular temperament theory ===		=== Regular temperament theory ===

BudjarnLambeth at 06:50, 9 July 2023

2023-07-09T06:50:09Z

← Older revision		Revision as of 06:50, 9 July 2023
Line 1:		Line 1:
	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|1080}}		{{EDO intro\|1080}}

BudjarnLambeth at 05:21, 9 July 2023

2023-07-09T05:21:37Z

← Older revision		Revision as of 05:21, 9 July 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	{{EDO intro\|1080}}		{{EDO intro\|1080}}

Eliora: /* Theory */

2022-11-29T19:03:38Z

Theory

← Older revision		Revision as of 19:03, 29 November 2022
Line 5:		Line 5:
	1080 is a largely composite EDO, meaning it's notable for its divisors. Its [[number of the divisors\|32 divisors]] are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 90, 108, 120, 135, 180, 216, 270, 360, 540. 1080's abundancy index is 2.33..., or exactly 7/3.		1080 is a largely composite EDO, meaning it's notable for its divisors. Its [[number of the divisors\|32 divisors]] are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 90, 108, 120, 135, 180, 216, 270, 360, 540. 1080's abundancy index is 2.33..., or exactly 7/3.

	Notable subsets of 1080edo are [[270edo]] and [[72edo]], as they both belong to [[The Riemann Zeta Function and Tuning#Zeta EDO lists\|the ''zeta peak edos'', ''zeta integral edos'' and ''zeta gap edos'' sequences]], however ~~1080 itself cannot be consistently read through~~ their approximation alone. In addition, [[12edo]] is the dominant tuning system in the world, and [[360edo]] is a highly composite EDO.		Notable subsets of 1080edo are [[270edo]] and [[72edo]], as they both belong to [[The Riemann Zeta Function and Tuning#Zeta EDO lists\|the ''zeta peak edos'', ''zeta integral edos'' and ''zeta gap edos'' sequences]], however the patent val of 1080edo does not consist of their approximation alone, as the 17th harmonic comes from [[540edo]]. In addition, [[12edo]] is the dominant tuning system in the world, and [[360edo]] is a highly composite EDO.

	=== Regular temperament theory ===		=== Regular temperament theory ===
	In the 13-limit, 1080edo is contorted order-4, with the same tuning as [[270edo]]. In the 1080e val, which puts the 11th harmonic on 3737, it tempers out 114345/114244, and in the 1080ef val it tempers out [[2080/2079]].		In the 13-limit, 1080edo is contorted order-4, with the same tuning as [[270edo]]. In the 1080e val, which puts the 11th harmonic on 3737, it tempers out 114345/114244, and in the 1080ef val it tempers out [[2080/2079]].

			=== Harmonics ===
			{{Harmonics in equal\|1080}}

	== Table of intervals ==		== Table of intervals ==

Eliora: /* Theory */ misc cleanup

2022-11-22T21:49:16Z

Theory: misc cleanup

← Older revision		Revision as of 21:49, 22 November 2022
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	~~'''1080 tone equal temperament''', also called '''1080-~~EDO~~''' divides the octave in~~ 1080 ~~equal steps of approximately 1.11 [[cent]]s.~~		{{EDO intro\|1080}}

	== Theory ==		== Theory ==
	~~{{primes in edo\|~~1080~~\|columns=15}}~~		1080 is a largely composite EDO, meaning it's notable for its divisors. Its [[number of the divisors\|32 divisors]] are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 90, 108, 120, 135, 180, 216, 270, 360, 540. 1080's abundancy index is 2.33..., or exactly 7/3.
	~~Since 1080 = 4 * 270 and 1080 = 15 * 72~~, it ~~contains~~ [[~~270edo~~]] ~~and [[72edo]] as subsets~~, ~~both belonging to [[The Riemann Zeta Function and Tuning#Zeta EDO lists\|the ''zeta peak edos'~~', ~~''zeta integral edos'' and ''zeta gap edos'' sequences]]~~.

			Notable subsets of 1080edo are [[270edo]] and [[72edo]], as they both belong to [[The Riemann Zeta Function and Tuning#Zeta EDO lists\|the ''zeta peak edos'', ''zeta integral edos'' and ''zeta gap edos'' sequences]], however 1080 itself cannot be consistently read through their approximation alone. In addition, [[12edo]] is the dominant tuning system in the world, and [[360edo]] is a highly composite EDO.

			=== Regular temperament theory ===
	In the 13-limit, 1080edo is contorted order-4, with the same tuning as [[270edo]]. In the 1080e val, which puts the 11th harmonic on 3737, it tempers out 114345/114244, and in the 1080ef val it tempers out [[2080/2079]].		In the 13-limit, 1080edo is contorted order-4, with the same tuning as [[270edo]]. In the 1080e val, which puts the 11th harmonic on 3737, it tempers out 114345/114244, and in the 1080ef val it tempers out [[2080/2079]].

	~~=== Divisors ===~~
	~~The prime factorization of 1080 is~~
	~~<math>1080 = 2^{3} \cdot 3^{3} \cdot 5</math>~~

	~~Its [[number of the divisors\|32 divisors]] are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 90, 108, 120, 135, 180, 216, 270, 360, 540, 1080.~~

	~~1080's abundancy index is 2.33333... = exactly 7/3.~~

	== Table of intervals ==		== Table of intervals ==
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	\|		\|
	\|Derives form 72edo.		\|Derives form 72edo.
	\|-
	~~\|21~~
	~~\|Pythagorean comma~~
	\|
	\|
	\|-		\|-
	\|90		\|90
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	\|-		\|-
	\|632		\|632
	\|~~270~~-phonic Fifth		\|135-phonic Fifth
	\|3/2		\|3/2
	\|		\|