5edt - Revision history

Xenllium at 09:47, 26 February 2026

2026-02-26T09:47:56Z

← Older revision		Revision as of 09:47, 26 February 2026
Line 53:		Line 53:

	== See also ==		== See also ==
	* [~~https://en.xen.wiki/w/Equal-step_tuning#~~Alpha-beta~~-gamma_family_of_equal_divisions Alpha-beta-gamma_family_of_equal_divisions~~]		* [[Alpha, beta, and gamma family of equal divisions]]

	[[Category:Todo:add sound example]]		[[Category:Todo:add sound example]]

Contribution: /* See also */

2025-10-28T01:45:09Z

Contribution at 01:43, 28 October 2025

2025-10-28T01:43:38Z

← Older revision		Revision as of 01:43, 28 October 2025
Line 51:		Line 51:
	\| [[3/1]]		\| [[3/1]]
	\|}		\|}

			=== See also ===
			* [https://en.xen.wiki/w/Equal-step_tuning#Alpha-beta-gamma_family_of_equal_divisions Alpha-beta-gamma_family_of_equal_divisions]

	[[Category:Todo:add sound example]]		[[Category:Todo:add sound example]]

FloraC: +subsets and supersets

2025-02-23T13:37:37Z

+subsets and supersets

← Older revision		Revision as of 13:37, 23 February 2025
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	=== Harmonics ===		=== Harmonics ===
	{{Harmonics in equal\|5\|3\|1\|columns=15}}		{{Harmonics in equal\|5\|3\|1\|columns=15}}

			=== Subsets and supersets ===
			5edt is the 3rd [[prime equal division\|prime edt]], after [[3edt]] and before [[7edt]].

	== Intervals ==		== Intervals ==

FloraC: Cleanup

2025-02-23T13:18:37Z

Cleanup

← Older revision		Revision as of 13:18, 23 February 2025
Line 5:		Line 5:
	5edt has steps too large to be used melodically, though it has some notable harmonic properties shared by other 5''n''-edts (such as [[10edt]], [[15edt]], etc.). It has a surprisingly accurate [[5/4]] major third (only 5.92{{cent}} flat), five of them making a tritave. (This phenomenon cannot be seen in single-digit [[edo]]s, and it is not until [[19edo]] that an approximation of 5/4 to within 10{{c}} can be seen.) 5edt therefore tempers out [[3125/3072]], the magic comma. Two of these major thirds give a septimal minor sixth, meaning that it also tempers out the marvel comma [[225/224]].		5edt has steps too large to be used melodically, though it has some notable harmonic properties shared by other 5''n''-edts (such as [[10edt]], [[15edt]], etc.). It has a surprisingly accurate [[5/4]] major third (only 5.92{{cent}} flat), five of them making a tritave. (This phenomenon cannot be seen in single-digit [[edo]]s, and it is not until [[19edo]] that an approximation of 5/4 to within 10{{c}} can be seen.) 5edt therefore tempers out [[3125/3072]], the magic comma. Two of these major thirds give a septimal minor sixth, meaning that it also tempers out the marvel comma [[225/224]].

	5edt is the ~~lowest equal division of the tritave~~ to encompass elements of [[5-limit]] harmony. The available chords are 4:5:12 and 5:12:15; being inversions of each other, they essentially act as "major" and "minor" chords. This is similar to [[6edt]], which contains the same chords but with the major thirds transposed an octave higher, and vice versa. Also available is the chord 9:14:27, which can express the single [[7-limit]] consonance found in 5edt.		5edt is the first edt to encompass elements of [[5-limit]] harmony. The available chords are 4:5:12 and 5:12:15; being inversions of each other, they essentially act as "major" and "minor" chords. This is similar to [[6edt]], which contains the same chords but with the major thirds transposed an octave higher, and vice versa. Also available is the chord 9:14:27, which can express the single [[7-limit]] consonance found in 5edt.

	=== Harmonics ===		=== Harmonics ===
	{{Harmonics in equal\|5\|3\|1\|columns=15}}		{{Harmonics in equal\|5\|3\|1\|columns=15}}

	== ~~Steps~~ ==		== Intervals ==
	{\| class="wikitable right-all left-4"		{\| class="wikitable right-all left-4"
	\|-		\|-
	! ~~Degrees~~		! #
	! Cents		! Cents
	! Hekts		! Hekts
	! Approximate ~~Ratios~~		! Approximate ratios
	\|-		\|-
	\| 0		\| 0
	\| 0.000		\| 0
	\| 0		\| 0
	\| [[1/1]]		\| [[1/1]]
	\|-		\|-
	\| 1		\| 1
	\| 380~~.391~~		\| 380
	\| 260		\| 260
	\| [[5/4]]		\| [[5/4]]
	\|-		\|-
	\| 2		\| 2
	\| ~~760.782~~		\| 761
	\| 520		\| 520
	\| [[14/9]]		\| [[14/9]]
	\|-		\|-
	\| 3		\| 3
	\| 1141~~.173~~		\| 1141
	\| 780		\| 780
	\| [[27/14]]		\| [[27/14]]
	\|-		\|-
	\| 4		\| 4
	\| ~~1521.564~~		\| 1522
	\| 1040		\| 1040
	\| [[12/5]] ~~([[6/5]] plus an octave)~~		\| [[12/5]]
	\|-		\|-
	\| 5		\| 5
	\| ~~1901.955~~		\| 1902
	\| 1300		\| 1300
	\| [[3/1]]		\| [[3/1]]
	\|}		\|}

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

	[[Category:Todo:add sound example]]		[[Category:Todo:add sound example]]

ArrowHead294 at 15:40, 20 February 2025

2025-02-20T15:40:16Z

← Older revision		Revision as of 15:40, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	== Theory ==		== Theory ==
			5edt has steps too large to be used melodically, though it has some notable harmonic properties shared by other 5''n''-edts (such as [[10edt]], [[15edt]], etc.). It has a surprisingly accurate [[5/4]] major third (only 5.92{{cent}} flat), five of them making a tritave. (This phenomenon cannot be seen in single-digit [[edo]]s, and it is not until [[19edo]] that an approximation of 5/4 to within 10{{c}} can be seen.) 5edt therefore tempers out [[3125/3072]], the magic comma. Two of these major thirds give a septimal minor sixth, meaning that it also tempers out the marvel comma [[225/224]].
	5edt has steps too large to be used melodically, though it has some notable harmonic properties shared by other 5n-edts (such as [[10edt]], [[15edt]], etc.). It has a surprisingly accurate [[5/4]] major third (only 5.92 ~~[[cents]]~~ flat), five of them making a tritave. (This phenomenon cannot be seen in single-digit [[edo]]s, and it is not until [[19edo]] that an approximation of 5/4 to within 10 ~~cents~~ can be seen.) 5edt therefore tempers out [[3125/3072]], the magic comma. Two of these major thirds give a septimal minor sixth, meaning that it also tempers out the marvel comma [[225/224]].

	5edt is the lowest equal division of the tritave to encompass elements of [[5-limit]] harmony. The available chords are 4:5:12 and 5:12:15; being inversions of each other, they essentially act as "major" and "minor" chords. This is similar to [[6edt]], which contains the same chords but with the major thirds transposed an octave higher, and vice versa. Also available is the chord 9:14:27, which can express the single [[7-limit]] consonance found in 5edt.		5edt is the lowest equal division of the tritave to encompass elements of [[5-limit]] harmony. The available chords are 4:5:12 and 5:12:15; being inversions of each other, they essentially act as "major" and "minor" chords. This is similar to [[6edt]], which contains the same chords but with the major thirds transposed an octave higher, and vice versa. Also available is the chord 9:14:27, which can express the single [[7-limit]] consonance found in 5edt.
Line 12:		Line 11:

	== Steps ==		== Steps ==

	{\| class="wikitable right-all left-4"		{\| class="wikitable right-all left-4"
	\|-		\|-

Lériendil at 02:02, 25 September 2024

2024-09-25T02:02:18Z

← Older revision		Revision as of 02:02, 25 September 2024
Line 9:		Line 9:

	=== Harmonics ===		=== Harmonics ===
	{{Harmonics in equal\|5\|3\|1}}		{{Harmonics in equal\|5\|3\|1\|columns=15}}

	== Steps ==		== Steps ==

Akselai: clean up

2024-04-28T13:39:37Z

clean up

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-'''5edt''' (5 Equal Divisions of the Tritave) subdivides the interval of the [[tritave]], frequency ratio 3:1, into 5 equal-sized parts, each 380.391 [[Cent]]s in size.
+{{EDO intro}}
 == Steps ==
@@ Line 34: / Line 43: @@
 | 1521.564
 | 1040
-| [[12/5]] ([[6/5|6/5]] plus an octave)
+| [[12/5]] ([[6/5]] plus an octave)
 |-
 | 5
@@ Line 41: / Line 50: @@
 | [[3/1]]
 |}
 [[Category:Edt]]

Plumtree: Infobox ET added

2022-10-05T19:42:21Z

Infobox ET added

← Older revision		Revision as of 19:42, 5 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	'''5edt''' (5 Equal Divisions of the Tritave) subdivides the interval of the [[tritave]], frequency ratio 3:1, into 5 equal-sized parts, each 380.391 [[Cent]]s in size.		'''5edt''' (5 Equal Divisions of the Tritave) subdivides the interval of the [[tritave]], frequency ratio 3:1, into 5 equal-sized parts, each 380.391 [[Cent]]s in size.

Xenwolf: /* Steps */ fix table formatting

2021-05-30T18:13:31Z

Steps: fix table formatting

← Older revision		Revision as of 18:13, 30 May 2021
Line 3:		Line 3:
	== Steps ==		== Steps ==

	{\| class="wikitable"		{\| class="wikitable right-all left-4"
	\|-		\|-
	! Degrees		! Degrees
	! Cents		! Cents
	!~~hekts~~		! Hekts
	! Approximate Ratios		! Approximate Ratios
	\|-		\|-
	~~! colspan="3"~~ \| 0		\| 0
			\| 0.000
			\| 0
	\| [[1/1]]		\| [[1/1]]
	\|-		\|-
	\| 1		\| 1
	\| 380.391		\| 380.391
	\|260		\| 260
	\| [[5/4]]		\| [[5/4]]
	\|-		\|-
	\| 2		\| 2
	\| 760.782		\| 760.782
	\|520		\| 520
	\| [[14/9]]		\| [[14/9]]
	\|-		\|-
	\| 3		\| 3
	\| 1141.173		\| 1141.173
	\|780		\| 780
	\| [[27/14]]		\| [[27/14]]
	\|-		\|-
	\| 4		\| 4
	\| 1521.564		\| 1521.564
	\|1040		\| 1040
	\| [[12/5]] ([[6/5\|6/5]] plus an octave)		\| [[12/5]] ([[6/5\|6/5]] plus an octave)
	\|-		\|-
	\| 5		\| 5
	\| 1901.955		\| 1901.955
	\|1300		\| 1300
	\| [[3/1]]		\| [[3/1]]
	\|}		\|}

← Older revision		Revision as of 01:45, 28 October 2025
Line 52:		Line 52:
	\|}		\|}

	=== See also ===		== See also ==
	* [https://en.xen.wiki/w/Equal-step_tuning#Alpha-beta-gamma_family_of_equal_divisions Alpha-beta-gamma_family_of_equal_divisions]		* [https://en.xen.wiki/w/Equal-step_tuning#Alpha-beta-gamma_family_of_equal_divisions Alpha-beta-gamma_family_of_equal_divisions]

	[[Category:Todo:add sound example]]		[[Category:Todo:add sound example]]