18edt - Revision history

Lucius Chiaraviglio: /* Harmonics */ Don't oversell closeness to 1ed17/16

2025-11-03T03:22:00Z

Harmonics: Don't oversell closeness to 1ed17/16

← Older revision		Revision as of 03:22, 3 November 2025
Line 17:		Line 17:
	\| intervals = integer		\| intervals = integer
	}}		}}
	Note that this tuning is ~~very~~ close to [[1ed17/16]], although by [[patent val]] [[mapping]] 18edt maps ~[[17/16]] inconsistently to 2\18edt instead of 1\18edt, while 1ed17/16 maps its own [[equave]] even more inconsistently, to 3\1ed17/16.		Note that this tuning is fairly close to [[1ed17/16]], although by [[patent val]] [[mapping]] 18edt maps ~[[17/16]] inconsistently to 2\18edt instead of 1\18edt, while 1ed17/16 maps its own [[equave]] even more inconsistently, to 3\1ed17/16.

	== Intervals ==		== Intervals ==

Lucius Chiaraviglio: Link to 1ed17/16 (this includes adding section See also)

2025-11-03T03:16:19Z

Link to 1ed17/16 (this includes adding section See also)

← Older revision		Revision as of 03:16, 3 November 2025
Line 17:		Line 17:
	\| intervals = integer		\| intervals = integer
	}}		}}
			Note that this tuning is very close to [[1ed17/16]], although by [[patent val]] [[mapping]] 18edt maps ~[[17/16]] inconsistently to 2\18edt instead of 1\18edt, while 1ed17/16 maps its own [[equave]] even more inconsistently, to 3\1ed17/16.

	== Intervals ==		== Intervals ==
Line 143:		Line 144:

	18edt can also be used for the [[Electra]] temperament based on [[15/11]], although in this case its approximation to [[13/11]] is very sharp.		18edt can also be used for the [[Electra]] temperament based on [[15/11]], although in this case its approximation to [[13/11]] is very sharp.

			== See also ==
			[[1ed17/16]] — relative ed17/16

	[[category:macrotonal]]		[[category:macrotonal]]
	[[category:tritave]]		[[category:tritave]]

Lucius Chiaraviglio: Move Harmonics up and Temperaments down to be consistent with most other equal temperament pages

2025-11-02T21:25:02Z

Move Harmonics up and Temperaments down to be consistent with most other equal temperament pages

← Older revision		Revision as of 21:25, 2 November 2025
Line 2:		Line 2:
	'''18edt''' is the division of the tritave into 18 equal parts of size 105.664 cents each. It has a decent 7 and an excellent 13, but a 5 which is 39 cents flat; if octaves were added and it was a sixth, it would count as a neutral sixth. The corresponding 5/3 is 845 cents, which is a neutral sixth between 8/5 and 5/3, which is really more of a 13/8, though this is allegedly a no-twos tuning. With octaves added, it also has a minor third and a major tenth which are both excellent as well as a minor thirteenth and major seventeenth which are still decent even though it skips actual octaves (in fact it is the non-octave semitone scale of 34edo). On the 3.7.13 subgroup it tempers out 351/343 and 2197/2187.		'''18edt''' is the division of the tritave into 18 equal parts of size 105.664 cents each. It has a decent 7 and an excellent 13, but a 5 which is 39 cents flat; if octaves were added and it was a sixth, it would count as a neutral sixth. The corresponding 5/3 is 845 cents, which is a neutral sixth between 8/5 and 5/3, which is really more of a 13/8, though this is allegedly a no-twos tuning. With octaves added, it also has a minor third and a major tenth which are both excellent as well as a minor thirteenth and major seventeenth which are still decent even though it skips actual octaves (in fact it is the non-octave semitone scale of 34edo). On the 3.7.13 subgroup it tempers out 351/343 and 2197/2187.

	== ~~Temperaments~~ ==		== Harmonics ==
	~~As the double of [[9edt]], it is the analog of 14edo insofar if treating as it has a doubled harmonic chain. However, it, like [[8edt]], is not schismatic because~~ 3~~:5:7 is a redundant chord. As a multiple of 9edt, it is the widest variety of 'White-Extraterrestrial-Tree' temperament.~~		{{Harmonics in equal
			\| steps = 18
			\| num = 3
			\| denom = 1
			\| intervals = integer
			}}
			{{Harmonics in equal
			\| steps = 18
			\| num = 3
			\| denom = 1
			\| start = 12
			\| collapsed = 1
			\| intervals = integer
			}}

	~~18edt can also be used for the [[Electra]] temperament based on [[15/11]], although in this case its approximation to [[13/11]] is very sharp.~~
	== Intervals ==		== Intervals ==
	{\| class="wikitable"		{\| class="wikitable"
Line 127:		Line 139:
	\|}		\|}

	== ~~Harmonics~~ ==		== Temperaments ==
	~~{{Harmonics in equal~~		As the double of [[9edt]], it is the analog of 14edo insofar if treating as it has a doubled harmonic chain. However, it, like [[8edt]], is not schismatic because 3:5:7 is a redundant chord. As a multiple of 9edt, it is the widest variety of 'White-Extraterrestrial-Tree' temperament.
	~~\| steps = 18~~
	~~\| num =~~ 3		18edt can also be used for the [[Electra]] temperament based on [[15/11]], although in this case its approximation to [[13/11]] is very sharp.
	~~\| denom = 1~~
	~~\| intervals = integer~~
	}}
	~~{{Harmonics~~ in ~~equal~~
	~~\| steps = 18~~
	~~\| num = 3~~
	~~\| denom = 1~~
	~~\| start = 12~~
	~~\| collapsed = 1~~
	~~\| intervals = integer~~
	}}

	[[category:macrotonal]]		[[category:macrotonal]]
	[[category:tritave]]		[[category:tritave]]

Fredg999 category edits: Removing from Category:Edt using Cat-a-lot

2025-07-31T15:31:27Z

Removing from Category:Edt using Cat-a-lot

← Older revision		Revision as of 15:31, 31 July 2025
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	[[category:macrotonal]]		[[category:macrotonal]]
	[[category:tritave]]		[[category:tritave]]
	~~[[category:edt]]~~

BudjarnLambeth: Add table of harmonics

2024-10-06T06:35:42Z

Add table of harmonics

@@ Line 126: / Line 126: @@
 | J
 |}
 [[category:macrotonal]]
 [[category:tritave]]
 [[category:edt]]

CompactStar at 02:31, 5 March 2023

2023-03-05T02:31:26Z

← Older revision		Revision as of 02:31, 5 March 2023
Line 5:		Line 5:
	As the double of [[9edt]], it is the analog of 14edo insofar if treating as it has a doubled harmonic chain. However, it, like [[8edt]], is not schismatic because 3:5:7 is a redundant chord. As a multiple of 9edt, it is the widest variety of 'White-Extraterrestrial-Tree' temperament.		As the double of [[9edt]], it is the analog of 14edo insofar if treating as it has a doubled harmonic chain. However, it, like [[8edt]], is not schismatic because 3:5:7 is a redundant chord. As a multiple of 9edt, it is the widest variety of 'White-Extraterrestrial-Tree' temperament.

	18edt can also be used for the [[Electra]] temperament based on [[15/11]], although in this case ~~it's~~ approximation to [[13/11]] is very sharp.		18edt can also be used for the [[Electra]] temperament based on [[15/11]], although in this case its approximation to [[13/11]] is very sharp.
	== Intervals ==		== Intervals ==
	{\| class="wikitable"		{\| class="wikitable"

CompactStar at 02:31, 5 March 2023

2023-03-05T02:31:22Z

← Older revision		Revision as of 02:31, 5 March 2023
Line 5:		Line 5:
	As the double of [[9edt]], it is the analog of 14edo insofar if treating as it has a doubled harmonic chain. However, it, like [[8edt]], is not schismatic because 3:5:7 is a redundant chord. As a multiple of 9edt, it is the widest variety of 'White-Extraterrestrial-Tree' temperament.		As the double of [[9edt]], it is the analog of 14edo insofar if treating as it has a doubled harmonic chain. However, it, like [[8edt]], is not schismatic because 3:5:7 is a redundant chord. As a multiple of 9edt, it is the widest variety of 'White-Extraterrestrial-Tree' temperament.

	18edt can also be used for the [[Electra]] temperament based on [[15/11]], although in this case it's approximation to [[13/11]] is ~~quite~~ sharp ~~being closer to [[6/5]]~~.		18edt can also be used for the [[Electra]] temperament based on [[15/11]], although in this case it's approximation to [[13/11]] is very sharp.
	== Intervals ==		== Intervals ==
	{\| class="wikitable"		{\| class="wikitable"

CompactStar at 02:28, 5 March 2023

2023-03-05T02:28:57Z

← Older revision		Revision as of 02:28, 5 March 2023
Line 5:		Line 5:
	As the double of [[9edt]], it is the analog of 14edo insofar if treating as it has a doubled harmonic chain. However, it, like [[8edt]], is not schismatic because 3:5:7 is a redundant chord. As a multiple of 9edt, it is the widest variety of 'White-Extraterrestrial-Tree' temperament.		As the double of [[9edt]], it is the analog of 14edo insofar if treating as it has a doubled harmonic chain. However, it, like [[8edt]], is not schismatic because 3:5:7 is a redundant chord. As a multiple of 9edt, it is the widest variety of 'White-Extraterrestrial-Tree' temperament.

	18edt can also be used for the [[Electra]] temperament based on [[15/11]], although in this case it's approximation to [[13/11] is ~~very~~ sharp being closer to [[6/5]].		18edt can also be used for the [[Electra]] temperament based on [[15/11]], although in this case it's approximation to [[13/11]] is quite sharp being closer to [[6/5]].
	== Intervals ==		== Intervals ==
	{\| class="wikitable"		{\| class="wikitable"

CompactStar at 02:28, 5 March 2023

2023-03-05T02:28:17Z

← Older revision		Revision as of 02:28, 5 March 2023
Line 16:		Line 16:
	! colspan="3" \| 0		! colspan="3" \| 0
	\| 1/1		\| 1/1
	~~\| [[1/1]]~~
	\| J		\| J
	\|-		\|-

CompactStar at 02:28, 5 March 2023

2023-03-05T02:28:06Z

← Older revision		Revision as of 02:28, 5 March 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	18edt ~~means~~ the division of the tritave into 18 equal parts of size 105.664 cents each. It has a decent 7 and an excellent 13, but a 5 which is 39 cents flat; if octaves were added and it was a sixth, it would count as a neutral sixth. The corresponding 5/3 is 845 cents, which is a neutral sixth between 8/5 and 5/3, which is really more of a 13/8, though this is allegedly a no-twos tuning. With octaves added, it also has a minor third and a major tenth which are both excellent as well as a minor thirteenth and major seventeenth which are still decent even though it skips actual octaves (in fact it is the non-octave semitone scale of 34edo). On the 3.7.13 subgroup it tempers out 351/343 and 2197/2187.		'''18edt''' is the division of the tritave into 18 equal parts of size 105.664 cents each. It has a decent 7 and an excellent 13, but a 5 which is 39 cents flat; if octaves were added and it was a sixth, it would count as a neutral sixth. The corresponding 5/3 is 845 cents, which is a neutral sixth between 8/5 and 5/3, which is really more of a 13/8, though this is allegedly a no-twos tuning. With octaves added, it also has a minor third and a major tenth which are both excellent as well as a minor thirteenth and major seventeenth which are still decent even though it skips actual octaves (in fact it is the non-octave semitone scale of 34edo). On the 3.7.13 subgroup it tempers out 351/343 and 2197/2187.

	As the double of [[9edt]], it is the analog of 14edo insofar as it has a doubled harmonic chain. However, it, like [[8edt]], is not schismatic because 3:5:7 is a redundant chord. As a multiple of 9edt, it is the widest variety of 'White-Extraterrestrial-Tree' temperament.		== Temperaments ==
			As the double of [[9edt]], it is the analog of 14edo insofar if treating as it has a doubled harmonic chain. However, it, like [[8edt]], is not schismatic because 3:5:7 is a redundant chord. As a multiple of 9edt, it is the widest variety of 'White-Extraterrestrial-Tree' temperament.

			18edt can also be used for the [[Electra]] temperament based on [[15/11]], although in this case it's approximation to [[13/11] is very sharp being closer to [[6/5]].
			== Intervals ==
	{\| class="wikitable"		{\| class="wikitable"
	! ~~step~~		! Step
	! ~~cents~~		! Cents
	!~~hekts~~		! Hekts
	! ~~approximated~~ interval		! Approximated interval
			! [[Electra]] notation (J = 1/1)
	\|-		\|-
	! colspan="3" \| 0		! colspan="3" \| 0
	\| 1/1		\| 1/1
			\| [[1/1]]
			\| J
	\|-		\|-
	\| 1		\| 1
Line 17:		Line 23:
	\|72.222		\|72.222
	\| 16/15		\| 16/15
			\| J#, Kbb
	\|-		\|-
	\| 2		\| 2
Line 22:		Line 29:
	\|144.444		\|144.444
	\| 9/8		\| 9/8
			\| Jx, Kb
	\|-		\|-
	\| 3		\| 3
Line 27:		Line 35:
	\|216.667		\|216.667
	\| 6/5		\| 6/5
			\| K
	\|-		\|-
	\| 4		\| 4
Line 32:		Line 41:
	\|288.889		\|288.889
	\| 9/7		\| 9/7
			\| K#, Lb
	\|-		\|-
	\| 5		\| 5
Line 37:		Line 47:
	\|361.111		\|361.111
	\| 27/20		\| 27/20
			\| L
	\|-		\|-
	\| 6		\| 6
Line 42:		Line 53:
	\|433.333		\|433.333
	\| 13/9		\| 13/9
			\| L#, Mbb
	\|-		\|-
	\| 7		\| 7
Line 47:		Line 59:
	\|505.556		\|505.556
	\| 17/13		\| 17/13
			\| Lx, Mb
	\|-		\|-
	\| 8		\| 8
Line 52:		Line 65:
	\|577.778		\|577.778
	\| 5/3		\| 5/3
			\| M
	\|-		\|-
	\| 9		\| 9
Line 57:		Line 71:
	\|650		\|650
	\| 19/11		\| 19/11
			\| M#, Nbb
	\|-		\|-
	\| 10		\| 10
Line 62:		Line 77:
	\|722.222		\|722.222
	\| 9/5		\| 9/5
			\| Mx, Nb
	\|-		\|-
	\| 11		\| 11
Line 67:		Line 83:
	\|794.444		\|794.444
	\| 49/25		\| 49/25
			\| N
	\|-		\|-
	\| 12		\| 12
Line 72:		Line 89:
	\|866.667		\|866.667
	\| 27/13		\| 27/13
			\| N#, Ob
	\|-		\|-
	\| 13		\| 13
Line 77:		Line 95:
	\|938.889		\|938.889
	\| 20/9		\| 20/9
			\| O
	\|-		\|-
	\| 14		\| 14
Line 82:		Line 101:
	\|1011.111		\|1011.111
	\| 7/3		\| 7/3
			\| O#, Pbb
	\|-		\|-
	\| 15		\| 15
Line 87:		Line 107:
	\|1083.333		\|1083.333
	\| 5/2		\| 5/2
			\| Ox, Pb
	\|-		\|-
	\| 16		\| 16
Line 92:		Line 113:
	\|1155.556		\|1155.556
	\| 8/3		\| 8/3
			\| P
	\|-		\|-
	\| 17		\| 17
Line 97:		Line 119:
	\|1227.778		\|1227.778
	\| 45/16		\| 45/16
			\| P#, Jb
	\|-		\|-
	\| 18		\| 18
Line 102:		Line 125:
	\|1300		\|1300
	\| 3/1		\| 3/1
			\| J
	\|}		\|}