10edt - Revision history

FloraC: Interval table

2026-05-31T07:14:29Z

Interval table

← Older revision		Revision as of 07:14, 31 May 2026
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	{{Harmonics in equal\|10\|3\|1\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 10edt (continued)}}		{{Harmonics in equal\|10\|3\|1\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 10edt (continued)}}

	== ~~Interval table~~ ==		== Intervals ==
	{\| class="wikitable"		{\| class="wikitable center-1 right-2 right-3"
	\|-		\|-
	! ~~Degrees~~		! #
	! [[Cent]]s		! [[Cent]]s
	! [[Hekt]]s		! [[Hekt]]s
	! Approximate ~~Ratios~~		! Approximate ratios
	\|-		\|-
	\| ~~colspan="3"~~ \| 0		\| 0
	\| ~~<span style="color: #660000;">~~[[1/1]]~~</span>~~		\| 0
			\| 0
			\| [[1/1]]
	\|-		\|-
	\| 1		\| 1
	\| 190~~.196~~		\| 190
	\| 130		\| 130
	\| [[10/9]], [[28/25]]		\| [[10/9]], [[28/25]]
	\|-		\|-
	\| 2		\| 2
	\| 380~~.391~~		\| 380
	\| 260		\| 260
	\| ~~<span style="color: #660000;">~~[[5/4]]~~</span>~~		\| [[5/4]]
	\|-		\|-
	\| 3		\| 3
	\| ~~570.587~~		\| 571
	\| 390		\| 390
	\| [[7/5]]		\| [[7/5]]
	\|-		\|-
	\| 4		\| 4
	\| ~~760.782~~		\| 761
	\| 520		\| 520
	\| ~~<span style="color: #660000;">~~[[14/9]]~~</span>~~		\| [[14/9]]
	\|-		\|-
	\| 5		\| 5
	\| ~~950.978~~		\| 951
	\| 650		\| 650
	\| 45/26, [[26~~/15~~]]		\| [[26/15]], [[45/26]]
	\|-		\|-
	\| 6		\| 6
	\| 1141~~.173~~		\| 1141
	\| 780		\| 780
	\| ~~<span style="color: #660000;">~~[[27/14]]~~</span>~~		\| [[27/14]]
	\|-		\|-
	\| 7		\| 7
	\| 1331~~.369~~		\| 1331
	\| 910		\| 910
	\| [[15/7]] ~~([[15/14]] plus an octave)~~		\| [[15/7]]
	\|-		\|-
	\| 8		\| 8
	\| ~~1521.564~~		\| 1522
	\| 1040		\| 1040
	\| [[12/5]] ~~(<span style="color: #660000;">[[6/5]]</span> plus an octave)~~		\| [[12/5]]
	\|-		\|-
	\| 9		\| 9
	\| ~~1711.760~~		\| 1712
	\| 1170		\| 1170
	\| [[27/20\|27/10]]		\| [[27/20\|27/10]]
	\|-		\|-
	\| 10		\| 10
	\| ~~1901.955~~		\| 1902
	\| 1300		\| 1300
	\| [[3/1]]		\| [[3/1]]

FloraC: "Very accurate 5-limit harmony" what?

2026-05-31T07:12:36Z

"Very accurate 5-limit harmony" what?

← Older revision		Revision as of 07:12, 31 May 2026
Line 3:		Line 3:

	== Theory ==		== Theory ==
	10edt ~~has very accurate 5-limit harmony for such a small number of steps per tritave,~~ most notably the [[5/4]] ~~inherited~~ from 5edt~~. 10edt~~ introduces some new harmonic ~~properties though —~~ such as the 571 cent tritone, which can function as [[7/5]]. We can use this to readily construct chords such as 4:5:7:12, although the [[7/4]], being 18 cents flat, does considerable damage to the consonance of this chord.		10edt most notably inherits the [[5/4]] from 5edt, and introduces some new harmonic elements, such as the 571-cent tritone, which can function as [[7/5]]. We can use this to readily construct chords such as 4:5:7:12, although the [[7/4]], being 18 cents flat, does considerable damage to the consonance of this chord.

	10edt also splits the ~~major third~~ in half, categorizing this tuning as a fringe variety of "meantone~~" temperament~~.		10edt also splits the 5/4 in half, categorizing this tuning as a fringe variety of meantone.

	~~One step of~~ 10edt can serve as the generator for [[pocus]] temperament, a [[~~Temperament~~ merging\|merge]] of [[sensamagic]] and 2.3.5.7.13 [[catakleismic]], which tempers out [[169/168]], [[225/224]], and [[245/243]] in the 2.3.5.7.13 subgroup.		10edt can serve as the generator chain for the [[pocus]] temperament, a [[temperament merging\|merge]] of [[sensamagic]] and 2.3.5.7.13 [[catakleismic]], which tempers out [[169/168]], [[225/224]], and [[245/243]] in the 2.3.5.7.13 subgroup.

	=== Harmonics ===		=== Harmonics ===
	{{Harmonics in equal\|10\|3\|1}}		{{Harmonics in equal\|10\|3\|1\|columns=11}}
	{{Harmonics in equal\|10\|3\|1\|start=12}}		{{Harmonics in equal\|10\|3\|1\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 10edt (continued)}}

	=== Interval table ===		== Interval table ==
	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-

Overthink: /* Harmonics */ integer and prime harmonics side-by-side is nonstandard and potentially confusing

2026-05-31T02:48:13Z

Harmonics: integer and prime harmonics side-by-side is nonstandard and potentially confusing

← Older revision		Revision as of 02:48, 31 May 2026
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	=== Harmonics ===		=== Harmonics ===
	{{Harmonics in equal\|10\|3\|1}}		{{Harmonics in equal\|10\|3\|1}}
	{{Harmonics in equal\|10\|3\|1\|~~intervals~~=~~prime~~}}		{{Harmonics in equal\|10\|3\|1\|start=12}}

	=== Interval table ===		=== Interval table ===

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

2025-07-31T15:31:25Z

Removing from Category:Edt using Cat-a-lot

← Older revision		Revision as of 15:31, 31 July 2025
Line 75:		Line 75:
	\|}		\|}

	~~[[Category:Edt]]~~
	[[Category:Macrotonal]]		[[Category:Macrotonal]]

ArrowHead294 at 16:50, 18 February 2025

2025-02-18T16:50:23Z

← Older revision		Revision as of 16:50, 18 February 2025
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	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
	\| Degrees		! Degrees
	\| [[Cent]]s		! [[Cent]]s
	\| [[Hekt]]s		! [[Hekt]]s
	\| Approximate Ratios		! Approximate Ratios
	\|-		\|-
	! colspan="3" \| 0		\| colspan="3" \| 0
	\| <span style="color: #660000;">[[1/1]]</span>		\| <span style="color: #660000;">[[1/1]]</span>
	\|-		\|-

ArrowHead294 at 16:49, 18 February 2025

2025-02-18T16:49:57Z

← Older revision		Revision as of 16:49, 18 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	== Theory ==		== Theory ==
Line 16:		Line 16:
	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
	\| \| Degrees		\| Degrees
	\| \| [[Cent]]s		\| [[Cent]]s
	\| \| [[Hekt]]s		\| [[Hekt]]s
	\| \| Approximate Ratios		\| Approximate Ratios
	\|-		\|-
	! colspan="3" \| 0		! colspan="3" \| 0
	\| \| <span style="color: #660000;">[[1/1]]</span>		\| <span style="color: #660000;">[[1/1]]</span>
	\|-		\|-
	\| \| 1		\| 1
	\| \| 190.196		\| 190.196
	\|130		\| 130
	\| \| [[10/9]], [[28/25]]		\| [[10/9]], [[28/25]]
	\|-		\|-
	\| \| 2		\| 2
	\| \| 380.391		\| 380.391
	\|260		\| 260
	\| \| <span style="color: #660000;">[[5/4]]</span>		\| <span style="color: #660000;">[[5/4]]</span>
	\|-		\|-
	\| \| 3		\| 3
	\| \| 570.587		\| 570.587
	\|390		\| 390
	\| \| [[7/5]]		\| [[7/5]]
	\|-		\|-
	\| \| 4		\| 4
	\| \| 760.782		\| 760.782
	\|520		\| 520
	\| \| <span style="color: #660000;">[[14/9]]</span>		\| <span style="color: #660000;">[[14/9]]</span>
	\|-		\|-
	\| \| 5		\| 5
	\| \| 950.978		\| 950.978
	\|650		\| 650
	\| \| 45/26, [[26/15]]		\| 45/26, [[26/15]]
	\|-		\|-
	\| \| 6		\| 6
	\| \| 1141.173		\| 1141.173
	\|780		\| 780
	\| \| <span style="color: #660000;">[[27/14]]</span>		\| <span style="color: #660000;">[[27/14]]</span>
	\|-		\|-
	\| \| 7		\| 7
	\| \| 1331.369		\| 1331.369
	\|910		\| 910
	\| \| [[15/7]] ([[15/14]] plus an octave)		\| [[15/7]] ([[15/14]] plus an octave)
	\|-		\|-
	\| \| 8		\| 8
	\| \| 1521.564		\| 1521.564
	\|1040		\| 1040
	\| \| [[12/5]] (<span style="color: #660000;">[[6/5]]</span> plus an octave)		\| [[12/5]] (<span style="color: #660000;">[[6/5]]</span> plus an octave)
	\|-		\|-
	\| \| 9		\| 9
	\| \| 1711.760		\| 1711.760
	\|1170		\| 1170
	\| \| [[27/20\|27/10]]		\| [[27/20\|27/10]]
	\|-		\|-
	\| \| 10		\| 10
	\| \| 1901.955		\| 1901.955
	\|1300		\| 1300
	\| \| [[3/1]]		\| [[3/1]]
	\|}		\|}

	[[Category:Edt]]		[[Category:Edt]]
	[[Category:Macrotonal]]		[[Category:Macrotonal]]

Akselai: clean up

2024-05-20T10:00:27Z

clean up

← Older revision		Revision as of 10:00, 20 May 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	'''10EDT''' is the [[Edt\|equal division of the third harmonic (tritave)]] into ten parts of 190.1955 [[cent\|cents]] each, corresponding to 6.3093 [[edo]]. It is related to the pocus temperament, which tempers out 169/168, 225/224, and 245/243 in the 2.3.5.7.13 subgroup.		{{EDO intro}}

			== Theory ==
			10edt has very accurate 5-limit harmony for such a small number of steps per tritave, most notably the [[5/4]] inherited from 5edt. 10edt introduces some new harmonic properties though — such as the 571 cent tritone, which can function as [[7/5]]. We can use this to readily construct chords such as 4:5:7:12, although the [[7/4]], being 18 cents flat, does considerable damage to the consonance of this chord.

			10edt also splits the major third in half, categorizing this tuning as a fringe variety of "meantone" temperament.

			One step of 10edt can serve as the generator for [[pocus]] temperament, a [[Temperament merging\|merge]] of [[sensamagic]] and 2.3.5.7.13 [[catakleismic]], which tempers out [[169/168]], [[225/224]], and [[245/243]] in the 2.3.5.7.13 subgroup.

			=== Harmonics ===
			{{Harmonics in equal\|10\|3\|1}}
			{{Harmonics in equal\|10\|3\|1\|intervals=prime}}

			=== Interval table ===
	{\| class="wikitable"		{\| class="wikitable"
	\|-		\|-
	\| \| Degrees		\| \| Degrees
	\| \| ~~Cents~~		\| \| [[Cent]]s
	~~!Hekts~~		\| \| [[Hekt]]s
	\| \| Approximate Ratios		\| \| Approximate Ratios
	\|-		\|-
Line 63:		Line 75:
	\|}		\|}

	~~== Prime harmonics ==~~		[[Category:Edt]]
	~~{{Harmonics in equal\|10\|3\|1\|intervals=prime}}~~		[[Category:Macrotonal]]

	10edt, like [[5edt]], has very accurate 5-limit harmony for such a small number of steps per tritave. 10edt introduces some new harmonic properties though; notably the 571 cent tritone which can function as 7/5. It also splits the major third in half, categorizing this tuning as a fringe variety of "meantone" temperament.
	[[Category:~~edt~~]]
	[[~~category~~:~~macrotonal~~]]

Akselai: /* Prime harmonics */

2024-01-17T09:39:50Z

Prime harmonics

← Older revision		Revision as of 09:39, 17 January 2024
Line 64:		Line 64:

	== Prime harmonics ==		== Prime harmonics ==
	{{Harmonics in equal\|10\|3\|1}}		{{Harmonics in equal\|10\|3\|1\|intervals=prime}}

	10edt, like [[5edt]], has very accurate 5-limit harmony for such a small number of steps per tritave. 10edt introduces some new harmonic properties though; notably the 571 cent tritone which can function as 7/5. It also splits the major third in half, categorizing this tuning as a fringe variety of "meantone" temperament.		10edt, like [[5edt]], has very accurate 5-limit harmony for such a small number of steps per tritave. 10edt introduces some new harmonic properties though; notably the 571 cent tritone which can function as 7/5. It also splits the major third in half, categorizing this tuning as a fringe variety of "meantone" temperament.
	[[Category:edt]]		[[Category:edt]]
	[[category:macrotonal]]		[[category:macrotonal]]

Akselai: add harmonics in equal

2024-01-17T09:29:32Z

add harmonics in equal

← Older revision		Revision as of 09:29, 17 January 2024
Line 62:		Line 62:
	\| \| [[3/1]]		\| \| [[3/1]]
	\|}		\|}

			== Prime harmonics ==
			{{Harmonics in equal\|10\|3\|1}}

	10edt, like [[5edt]], has very accurate 5-limit harmony for such a small number of steps per tritave. 10edt introduces some new harmonic properties though; notably the 571 cent tritone which can function as 7/5. It also splits the major third in half, categorizing this tuning as a fringe variety of "meantone" temperament.		10edt, like [[5edt]], has very accurate 5-limit harmony for such a small number of steps per tritave. 10edt introduces some new harmonic properties though; notably the 571 cent tritone which can function as 7/5. It also splits the major third in half, categorizing this tuning as a fringe variety of "meantone" temperament.
	[[Category:edt]]		[[Category:edt]]
	[[category:macrotonal]]		[[category:macrotonal]]

Plumtree: Infobox ET added

2022-10-05T19:44:16Z

Infobox ET added

← Older revision		Revision as of 19:44, 5 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	'''10EDT''' is the [[Edt\|equal division of the third harmonic (tritave)]] into ten parts of 190.1955 [[cent\|cents]] each, corresponding to 6.3093 [[edo]]. It is related to the pocus temperament, which tempers out 169/168, 225/224, and 245/243 in the 2.3.5.7.13 subgroup.		'''10EDT''' is the [[Edt\|equal division of the third harmonic (tritave)]] into ten parts of 190.1955 [[cent\|cents]] each, corresponding to 6.3093 [[edo]]. It is related to the pocus temperament, which tempers out 169/168, 225/224, and 245/243 in the 2.3.5.7.13 subgroup.