33ed4 - Revision history

Fredg999 category edits: Removing from Category:Ed4 using Cat-a-lot

2025-07-31T21:18:56Z

Removing from Category:Ed4 using Cat-a-lot

← Older revision		Revision as of 21:18, 31 July 2025
Line 233:		Line 233:

	[[Category:Equal-step tuning]]		[[Category:Equal-step tuning]]
	~~[[Category:Ed4]]~~

	{{todo\|expand}}		{{todo\|expand}}

ArrowHead294 at 18:25, 13 March 2025

2025-03-13T18:25:06Z

← Older revision		Revision as of 18:25, 13 March 2025
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	{{Infobox ET}}		{{Infobox ET}}
	'''33ed4''' is the [[ed4\|Equal Divisions of the Double Octave]] into 33 narrow chromatic semitones each of 72.727 [[cent]]s. It takes out every second step of [[33edo]] and falls between [[16edo]] and [[17edo]]. So even degree 16 or degree 17 can play the role of the [[octave]], depending on the actual melodic or harmonic situation in a given composition. So it can be seen as a kind of '''<span style="color: #080">Equivocal Tuning</span>'''.		'''33ed4''' is the [[ed4\|Equal Divisions of the Double Octave]] into 33 narrow chromatic semitones each of 72.727 [[cent]]s. It takes out every second step of [[33edo]] and falls between [[16edo]] and [[17edo]]. So even degree 16 or degree 17 can play the role of the [[octave]], depending on the actual melodic or harmonic situation in a given composition. So it can be seen as a kind of '''<span style="color: #080;">Equivocal Tuning</span>'''.

	It has a [[9/5]] which is 0.6 ~~cents~~ sharp, a [[7/5]] which is 0.7 ~~cents~~ flat, and a [[9/7]] which is 1.3 ~~cents~~ sharp. Therefore it is closely related to [[13edt]], the [[~~Bohlen-Pierce~~]] ~~scale~~, although it has no pure [[3/1]], which is 11.1 cents flat. The lack of a [[3/2\|pure fifth]] makes it also interesting.		It has a [[9/5]] which is 0.6{{c}} sharp, a [[7/5]] which is 0.7{{c}} flat, and a [[9/7]] which is 1.3{{c}} sharp. Therefore it is closely related to [[13edt]], the [[Bohlen–Pierce scale]], although it has no pure [[3/1]], which is 11.1 cents flat. The lack of a [[3/2\|pure fifth]] makes it also interesting.

	Furthermore it has some [[11-limit]], [[13-limit]], [[17-limit]] and even [[23-limit]] which are very close (most of them under or nearby 1 ~~cent~~).		Furthermore it has some [[11-limit]], [[13-limit]], [[17-limit]] and even [[23-limit]] which are very close (most of them under or nearby 1{{c}}).

	== Intervals ==		== Intervals ==

	{\| class="wikitable right-all mw-collapsible"		{\| class="wikitable right-all mw-collapsible"
	\|+ Intervals of 33ed4		\|+ style="font-size: 105%;" \| Intervals of 33ed4
	\|-		\|-
	! ~~degree~~		! Degree
	! ~~in cents~~		! Cents
	! ~~nearest~~ JI <br> interval		! Nearest JI<br />interval
	! ~~in cents~~		! Cents
	! ~~difference~~ <br> in cents		! Difference<br />in cents
	\|-		\|-
	\| 1		\| 1
Line 21:		Line 20:
	\| 24/23		\| 24/23
	\| 73.7		\| 73.7
	\| -1.0		\| −1.0
	\|-		\|-
	\| 2		\| 2
Line 57:		Line 56:
	\| 51/38		\| 51/38
	\| 509.4		\| 509.4
	\| -0.3		\| −0.3
	\|- style="font-weight: bold"		\|- style="font-weight: bold"
	\| 8		\| 8
Line 63:		Line 62:
	\| 7/5		\| 7/5
	\| 582.5		\| 582.5
	\| -0.7		\| −0.7
	\|-		\|-
	\| 9		\| 9
Line 69:		Line 68:
	\| 19/13		\| 19/13
	\| 657.0		\| 657.0
	\| -2.5		\| −2.5
	\|-		\|-
	\| 10		\| 10
Line 81:		Line 80:
	\| 27/17		\| 27/17
	\| 800.9		\| 800.9
	\| -0.9		\| −0.9
	\|-		\|-
	\| 12		\| 12
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	\| 53/32		\| 53/32
	\| 873.5		\| 873.5
	\| -0.8		\| −0.8
	\|-		\|-
	\| 13		\| 13
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	\| 19/11		\| 19/11
	\| 946.2		\| 946.2
	\| -0.7		\| −0.7
	\|- style="font-weight: bold"		\|- style="font-weight: bold"
	\| 14		\| 14
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	\| 32/15		\| 32/15
	\| 1311.7		\| 1311.7
	\| -2.6		\| −2.6
	\|- style="font-weight: bold"		\|- style="font-weight: bold"
	\| 19		\| 19
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	\| 20/9		\| 20/9
	\| 1382.4		\| 1382.4
	\| -0.6		\| −0.6
	\|-		\|-
	\| 20		\| 20
Line 141:		Line 140:
	\| 29/12		\| 29/12
	\| 1527.6		\| 1527.6
	\| -0.3		\| −0.3
	\|-		\|-
	\| 22		\| 22
Line 177:		Line 176:
	\| 28/9		\| 28/9
	\| 1964.9		\| 1964.9
	\| -1.3		\| −1.3
	\|-		\|-
	\| 28		\| 28
Line 183:		Line 182:
	\| 13/4		\| 13/4
	\| 2040.5		\| 2040.5
	\| -4.1		\| −4.1
	\|-		\|-
	\| 29		\| 29
Line 189:		Line 188:
	\| 44/13		\| 44/13
	\| 2110.8		\| 2110.8
	\| -1.7		\| −1.7
	\|-		\|-
	\| 30		\| 30
Line 195:		Line 194:
	\| 60/17		\| 60/17
	\| 2183.3		\| 2183.3
	\| -1.5		\| −1.5
	\|-		\|-
	\| 31		\| 31
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	== Music ==		== Music ==

	* [http://soundcloud.com/ahornberg/sets/equivocal-tuning-33ed4 Equivocal Tuning] — Set of compositions by Ahornberg		* [http://soundcloud.com/ahornberg/sets/equivocal-tuning-33ed4 Equivocal Tuning] — Set of compositions by Ahornberg

BudjarnLambeth: /* Intervals */

2024-12-22T04:16:58Z

Intervals

← Older revision		Revision as of 04:16, 22 December 2024
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	{\| class="wikitable right-all mw-collapsible"		{\| class="wikitable right-all mw-collapsible"
			\|+ Intervals of 33ed4
	\|-		\|-
	! degree		! degree

BudjarnLambeth: {{todo|expand}} & collapsible

2024-12-22T04:16:36Z

{{todo|expand}} & collapsible

← Older revision		Revision as of 04:16, 22 December 2024
Line 8:		Line 8:
	== Intervals ==		== Intervals ==

	{\| class="wikitable right-all"		{\| class="wikitable right-all mw-collapsible"
	\|-		\|-
	! degree		! degree
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	[[Category:Equal-step tuning]]		[[Category:Equal-step tuning]]
	[[Category:Ed4]]		[[Category:Ed4]]

			{{todo\|expand}}

BudjarnLambeth: Harmonics

2024-10-05T02:32:47Z

Harmonics

@@ Line 214: / Line 214: @@
 | 0.0
 |}
 == Music ==

Plumtree: Infobox ET added

2022-10-05T20:16:16Z

Infobox ET added

← Older revision		Revision as of 20:16, 5 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	'''33ed4''' is the [[ed4\|Equal Divisions of the Double Octave]] into 33 narrow chromatic semitones each of 72.727 [[cent]]s. It takes out every second step of [[33edo]] and falls between [[16edo]] and [[17edo]]. So even degree 16 or degree 17 can play the role of the [[octave]], depending on the actual melodic or harmonic situation in a given composition. So it can be seen as a kind of '''<span style="color: #080">Equivocal Tuning</span>'''.		'''33ed4''' is the [[ed4\|Equal Divisions of the Double Octave]] into 33 narrow chromatic semitones each of 72.727 [[cent]]s. It takes out every second step of [[33edo]] and falls between [[16edo]] and [[17edo]]. So even degree 16 or degree 17 can play the role of the [[octave]], depending on the actual melodic or harmonic situation in a given composition. So it can be seen as a kind of '''<span style="color: #080">Equivocal Tuning</span>'''.

Xenwolf: Fix span. I also made the accent color a bit darker for better readability, without saying that I think it's generally a good idea to color font however you want.

2022-10-04T06:28:26Z

Fix span. I also made the accent color a bit darker for better readability, without saying that I think it's generally a good idea to color font however you want.

← Older revision		Revision as of 06:28, 4 October 2022
Line 1:		Line 1:
	'''33ed4''' is the [[ed4\|Equal Divisions of the Double Octave]] into 33 narrow chromatic semitones each of 72.727 [[cent]]s. It takes out every second step of [[33edo]] and falls between [[16edo]] and [[17edo]]. So even degree 16 or degree 17 can play the role of the [[octave]], depending on the actual melodic or harmonic situation in a given composition. So it can be seen as a kind of '''<span style="color: #~~00cc00;~~">~~E</span><span style="color: #00cc00;">quivocal~~ Tuning</span>'''.		'''33ed4''' is the [[ed4\|Equal Divisions of the Double Octave]] into 33 narrow chromatic semitones each of 72.727 [[cent]]s. It takes out every second step of [[33edo]] and falls between [[16edo]] and [[17edo]]. So even degree 16 or degree 17 can play the role of the [[octave]], depending on the actual melodic or harmonic situation in a given composition. So it can be seen as a kind of '''<span style="color: #080">Equivocal Tuning</span>'''.

	It has a [[9/5]] which is 0.6 cents sharp, a [[7/5]] which is 0.7 cents flat, and a [[9/7]] which is 1.3 cents sharp. Therefore it is closely related to [[13edt]], the [[Bohlen-Pierce]] scale, although it has no pure [[3/1]], which is 11.1 cents flat. The lack of a [[3/2\|pure fifth]] makes it also interesting.		It has a [[9/5]] which is 0.6 cents sharp, a [[7/5]] which is 0.7 cents flat, and a [[9/7]] which is 1.3 cents sharp. Therefore it is closely related to [[13edt]], the [[Bohlen-Pierce]] scale, although it has no pure [[3/1]], which is 11.1 cents flat. The lack of a [[3/2\|pure fifth]] makes it also interesting.
Line 104:		Line 104:
	\| 1088.3		\| 1088.3
	\| 2.6		\| 2.6
	\|- style="font-weight: bold; color: #~~00cc00;~~"		\|- style="font-weight: bold; color: #080"
	\| 16		\| 16
	\| 1163.6		\| 1163.6
Line 110:		Line 110:
	\| 1161.9		\| 1161.9
	\| 1.7		\| 1.7
	\|- style="font-weight: bold; color: #~~00cc00;~~"		\|- style="font-weight: bold; color: #080"
	\| 17		\| 17
	\| 1236.4		\| 1236.4

Xenwolf: recat

2021-12-04T13:32:00Z

recat

← Older revision		Revision as of 13:32, 4 December 2021
Line 218:		Line 218:
	* [http://soundcloud.com/ahornberg/sets/equivocal-tuning-33ed4 Equivocal Tuning] — Set of compositions by Ahornberg		* [http://soundcloud.com/ahornberg/sets/equivocal-tuning-33ed4 Equivocal Tuning] — Set of compositions by Ahornberg

	[[Category:~~31edo~~]]		[[Category:Equal-step tuning]]
			[[Category:Ed4]]

Xenwolf: cleanup after import from wikispaces (I respect the green text)

2021-12-04T13:09:35Z

cleanup after import from wikispaces (I respect the green text)

Show changes

Wikispaces>FREEZE at 00:00, 17 July 2018

2018-07-17T00:00:00Z

Show changes