20edf - Revision history

Xenllium at 07:07, 22 February 2026

2026-02-22T07:07:49Z

← Older revision		Revision as of 07:07, 22 February 2026
Line 180:		Line 180:

	== 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]]

	{{stub}}		{{stub}}

Contribution at 01:47, 28 October 2025

2025-10-28T01:47:38Z

← Older revision		Revision as of 01:47, 28 October 2025
Line 178:		Line 178:
	\|'''1403.91'''		\|'''1403.91'''
	\|}		\|}

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

	{{stub}}		{{stub}}

FloraC: Carlos Gamma as we know today is non-octave, even tho it was originally intended to include the octaves

2025-08-06T11:40:26Z

Carlos Gamma as we know today is non-octave, even tho it was originally intended to include the octaves

← Older revision		Revision as of 11:40, 6 August 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	20edf corresponds to 34.1902edo. It is closely related to [[Carlos Gamma]]~~, where Carlos Gamma,~~ and ~~similarly~~ the [[gammic]] temperament, ~~can be seen as 20edf with~~ an independent dimension for 2 (although strictly speaking, the "canonical" optimized Carlos Gamma tuning is not exactly 20edf, with its fifth stretched by the microscopic amount of 0.016{{c}}). It very accurately represents the intervals [[5/4]], with 11 steps, and [[17/16]], with 3 steps.		20edf corresponds to 34.1902edo. It is closely related to [[Carlos Gamma]] and the [[gammic]] temperament, which adds an independent dimension for the [[2/1\|octave]] (although strictly speaking, the "canonical" optimized Carlos Gamma tuning is not exactly 20edf, with its fifth stretched by the microscopic amount of 0.016{{c}}). It very accurately represents the intervals [[5/4]], with 11 steps, and [[17/16]], with 3 steps.

	=== Harmonics ===		=== Harmonics ===

Lériendil: /* Intervals */

2025-08-06T00:03:25Z

Intervals

← Older revision		Revision as of 00:03, 6 August 2025
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	\|-		\|-
	\|5		\|5
	\|425/384		\|320/289, 425/384
	\|175.49		\|175.49
	\|-		\|-
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	\|-		\|-
	\|15		\|15
	\|576/425		\|576/425, 867/640
	\|526.47		\|526.47
	\|-		\|-
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	\|-		\|-
	\|25		\|25
	\|425/256		\|425/256, 480/289
	\|877.44		\|877.44
	\|-		\|-

Lériendil at 00:02, 6 August 2025

2025-08-06T00:02:07Z

← Older revision		Revision as of 00:02, 6 August 2025
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	\|-		\|-
	\|16		\|16
	\|864/625~~, 400/289~~		\|400/289, 864/625
	\|561.56		\|561.56
	\|-		\|-

Lériendil: filled in some more complex intervals

2025-08-06T00:01:45Z

filled in some more complex intervals

← Older revision		Revision as of 00:01, 6 August 2025
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	\|-		\|-
	\|4		\|4
	\|		\|625/576, 867/800
	\|140.39		\|140.39
	\|-		\|-
	\|5		\|5
	\|		\|425/384
	\|175.49		\|175.49
	\|-		\|-
Line 75:		Line 75:
	\|-		\|-
	\|15		\|15
	\|		\|576/425
	\|526.47		\|526.47
	\|-		\|-
	\|16		\|16
	\|		\|864/625, 400/289
	\|561.56		\|561.56
	\|-		\|-
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	\|-		\|-
	\|24		\|24
	\|		\|625/384
	\|842.35		\|842.35
	\|-		\|-
	\|25		\|25
	\|		\|425/256
	\|877.44		\|877.44
	\|-		\|-
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	\|-		\|-
	\|35		\|35
	\|		\|864/425
	\|1228.42		\|1228.42
	\|-		\|-
	\|36		\|36
	\|		\|600/289
	\|1263.52		\|1263.52
	\|-		\|-

Lériendil at 22:41, 5 August 2025

2025-08-05T22:41:18Z

Show changes

Lériendil at 20:00, 5 August 2025

2025-08-05T20:00:05Z

← Older revision		Revision as of 20:00, 5 August 2025
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	{{Infobox ET}}		{{Infobox ET}}
	~~'''20edf''' is very close to the [[Carlos Gamma]] tuning.~~		{{ED intro}}

	==Intervals==		== Theory ==
			20edf corresponds to 34.1902edo. It is closely related to [[Carlos Gamma]], where Carlos Gamma, and similarly the [[gammic]] temperament, can be seen as 20edf with an independent dimension for 2 (although strictly speaking, the "canonical" optimized Carlos Gamma tuning is not exactly 20edf, with its fifth stretched by the microscopic amount of 0.016{{c}}). It very accurately represents the intervals [[5/4]], with 11 steps, and [[17/16]], with 3 steps.

			=== Harmonics ===
			{{Harmonics in equal\|20\|3\|2\|columns=11}}
			{{Harmonics in equal\|20\|3\|2\|columns=12\|start=12\|collapsed=true\|title=Approximation of harmonics in 20edf (continued)}}

			== Intervals ==
	The first steps up to two just perfect fifths should give a feeling of the granularity of this system…		The first steps up to two just perfect fifths should give a feeling of the granularity of this system…
	{\| class="wikitable mw-collapsible"		{\| class="wikitable mw-collapsible"
Line 13:		Line 20:
	\|35.1		\|35.1
	\|-		\|-
	\| \|2		\|2
	\| \|70.2		\|70.2
	\|-		\|-
	\| \|3		\|3
	\| \|105.29		\|105.29
	\|-		\|-
	\| \|4		\|4
	\| \|140.39		\|140.39
	\|-		\|-
	\| \|5		\|5
	\| \|175.49		\|175.49
	\|-		\|-
	\| \|6		\|6
	\| \|210.59		\|210.59
	\|-		\|-
	\| \|7		\|7
	\| \|245.68		\|245.68
	\|-		\|-
	\| \|8		\|8
	\| \|280.78		\|280.78
	\|-		\|-
	\| \|9		\|9
	\| \|315.88		\|315.88
	\|-		\|-
	\| \|10		\|10
	\| \|350.98		\|350.98
	\|-		\|-
	\| \|11		\|11
	\| \|386.075		\|386.075
	\|-		\|-
	\| \|12		\|12
	\| \|421.17		\|421.17
	\|-		\|-
	\| \|13		\|13
	\| \|456.27		\|456.27
	\|-		\|-
	\| \|14		\|14
	\| \|491.37		\|491.37
	\|-		\|-
	\| \|15		\|15
	\| \|526.47		\|526.47
	\|-		\|-
	\| \|16		\|16
	\| \|561.56		\|561.56
	\|-		\|-
	\| \|17		\|17
	\| \|596.66		\|596.66
	\|-		\|-
	\| \|18		\|18
	\| \|631.76		\|631.76
	\|-		\|-
	\| \|19		\|19
	\| \|666.86		\|666.86
	\|-		\|-
	\| \|20		\|20
	\| \|701.955		\|701.955
	\|-		\|-
	\|21		\|21
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	\|1403.91		\|1403.91
	\|}		\|}

	~~== Harmonics ==~~
	~~{{Harmonics in equal\|20\|3\|2\|intervals=prime}}~~
	~~{{Harmonics in equal\|20\|3\|2\|start=12\|collapsed=1\|intervals=prime}}~~


	{{stub}}		{{stub}}

BudjarnLambeth: stub mbox, add harmonics, make table collapsible

2024-12-19T08:37:19Z

stub mbox, add harmonics, make table collapsible

← Older revision		Revision as of 08:37, 19 December 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	'''20edf''' is very close to the [[Carlos Gamma]] tuning.		'''20edf''' is very close to the [[Carlos Gamma]] tuning.

	==Intervals==		==Intervals==
	The first steps up to two just perfect fifths should give a feeling of the granularity of this system…		The first steps up to two just perfect fifths should give a feeling of the granularity of this system…
	{\| class="wikitable"		{\| class="wikitable mw-collapsible"
			\|+ Intervals of 20edf
			\|-
	!Degrees		!Degrees
	!		!Cents
	\|-		\|-
	\|1		\|1
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	\|1403.91		\|1403.91
	\|}		\|}

			== Harmonics ==
			{{Harmonics in equal\|20\|3\|2\|intervals=prime}}
			{{Harmonics in equal\|20\|3\|2\|start=12\|collapsed=1\|intervals=prime}}


			{{stub}}

BudjarnLambeth: Mentioned similarity to Gamma

2024-10-01T06:43:14Z

Mentioned similarity to Gamma

← Older revision		Revision as of 06:43, 1 October 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
			'''20edf''' is very close to the [[Carlos Gamma]] tuning.
	==Intervals==		==Intervals==
	The first steps up to two just perfect fifths should give a feeling of the granularity of this system…		The first steps up to two just perfect fifths should give a feeling of the granularity of this system…