95ed5 - Revision history

ArrowHead294 at 14:00, 20 June 2025

2025-06-20T14:00:20Z

← Older revision		Revision as of 14:00, 20 June 2025
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	* [[41edo]] – relative edo		* [[41edo]] – relative edo
	* [[65edt]] – relative edt		* [[65edt]] – relative edt
	* [[95ed5]] – relative ed5
	* [[106ed6]] – relative ed6		* [[106ed6]] – relative ed6
	* [[147ed12]] – relative ed12		* [[147ed12]] – relative ed12

ArrowHead294 at 14:00, 20 June 2025

2025-06-20T14:00:12Z

← Older revision		Revision as of 14:00, 20 June 2025
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	== As a generator ==		== As a generator ==
	95ed5 can also be thought of as a [[generator]] of the 2.3.5.7.11.19-subgroup temperament which tempers out 1540/1539, 3025/3024, 6875/6859, and 184877/184320, which is a [[cluster temperament]] with 41 clusters of notes in an octave. While the small chroma interval between adjacent notes in each cluster represents 385/384 ~ 441/440 ~ 1479016/1476225 ~ 194579/194400 ~ 204800/204687 ~ 176000/175959 tempered together, the step interval is very versatile, representing 16807/16500 ~ 19551/19200 ~ 18000/17689 ~ 72900/71687 ~ 273375/268912 ~ 295245/290521 ~ 12100/11907 ~ 64/63 all tempered together. This temperament is supported by [[41edo]], [[491edo]] (491e val), and [[532edo]] (532d val) among others.		95ed5 can also be thought of as a [[generator]] of the 2.3.5.7.11.19-subgroup temperament which tempers out 1540/1539, 3025/3024, 6875/6859, and 184877/184320, which is a [[cluster temperament]] with 41 clusters of notes in an octave. While the small chroma interval between adjacent notes in each cluster represents 385/384 ~ 441/440 ~ 1479016/1476225 ~ 194579/194400 ~ 204800/204687 ~ 176000/175959 tempered together, the step interval is very versatile, representing 16807/16500 ~ 19551/19200 ~ 18000/17689 ~ 72900/71687 ~ 273375/268912 ~ 295245/290521 ~ 12100/11907 ~ 64/63 all tempered together. This temperament is supported by [[41edo]], [[491edo]] (491e val), and [[532edo]] (532d val) among others.

			== See also ==
			* [[24edf]] – relative edf
			* [[41edo]] – relative edo
			* [[65edt]] – relative edt
			* [[95ed5]] – relative ed5
			* [[106ed6]] – relative ed6
			* [[147ed12]] – relative ed12
			* [[361ed448]] – close to the zeta-optimized tuning for 41edo

			[[Category:41edo]]

FloraC: /* Theory */ cleanup

2025-06-20T13:16:49Z

Theory: cleanup

← Older revision		Revision as of 13:16, 20 June 2025
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	== Theory ==		== Theory ==
	95ed5 is related to [[41edo]], but with the ~~5/1~~ rather than the [[2/1]] being just. The octave is about 2.~~5143~~ cents stretched. This tuning has a generally sharp tendency for ~~harmonics~~ up to 12. Unlike 41edo, it is only consistent up to the [[integer limit\|12-integer-limit]], with discrepancy for the [[13/1\|13th~~]] [[~~harmonic]].		95ed5 is related to [[41edo]], but with the 5th harmonic rather than the [[2/1\|octave]] being just. The octave is about 2.51 cents stretched. This tuning has a generally sharp tendency for [[harmonic]]s up to 12. Unlike 41edo, it is only [[consistent]] up to the [[integer limit\|12-integer-limit]], with discrepancy for the [[13/1\|13th harmonic]].

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

FloraC: /* Intervals */ fix

2025-06-20T13:15:55Z

Intervals: fix

← Older revision		Revision as of 13:15, 20 June 2025
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	\| 5		\| 5
	\| 146.6		\| 146.6
	\| [[12/11], [[13/12]]		\| [[12/11]], [[13/12]]
	\|-		\|-
	\| 6		\| 6

FloraC: /* Theory */ +subsets and supersets

2025-03-20T17:48:52Z

Theory: +subsets and supersets

← Older revision		Revision as of 17:48, 20 March 2025
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	{{Harmonics in equal\|95\|5\|1\|intervals=integer}}		{{Harmonics in equal\|95\|5\|1\|intervals=integer}}
	{{Harmonics in equal\|95\|5\|1\|intervals=integer\|columns=12\|start=12\|collapsed=1\|title=Approximation of harmonics in 95ed5 (continued)}}		{{Harmonics in equal\|95\|5\|1\|intervals=integer\|columns=12\|start=12\|collapsed=1\|title=Approximation of harmonics in 95ed5 (continued)}}

			=== Subsets and supersets ===
			Since 95 factors into primes as {{nowrap\| 5 × 19 }}, 95ed5 contains [[5ed5]] and [[19ed5]] as subset ed5's.

	== Intervals ==		== Intervals ==

FloraC: Cleanup (2/2)

2025-03-20T17:47:32Z

Cleanup (2/2)

Show changes

FloraC: Cleanup (1/)

2025-03-20T17:24:50Z

Cleanup (1/)

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-'''[[Ed5|Division of the 5th harmonic]] into 95 equal parts''' (95ed5) is related to [[41edo|41 edo]], but with the 5/1 rather than the 2/1 being just. The octave is about 2.5143 cents stretched and the step size is about 29.3296 cents. This tuning has a generally sharp tendency for harmonics up to 12. Unlike 41edo, it is only consistent up to the [[11-odd-limit|12-integer-limit]], with discrepancy for the 13th harmonic.
+{{ED intro}}
 == Intervals ==
@@ Line 491: / Line 498: @@
 |}
-== Harmonics ==
+== As a generator ==
-{{Harmonics in equal
+ed5 can also be thought of as a [[generator]] of the 2.3.5.7.11.19-subgroup temperament which tempers out 1540/1539, 3025/3024, 6875/6859, and 184877/184320, which is a [[cluster temperament]] with 41 clusters of notes in an octave. While the small chroma interval between adjacent notes in each cluster represents 385/384 ~ 441/440 ~ 1479016/1476225 ~ 194579/194400 ~ 204800/204687 ~ 176000/175959 tempered together, the step interval is very versatile, representing 16807/16500 ~ 19551/19200 ~ 18000/17689 ~ 72900/71687 ~ 273375/268912 ~ 295245/290521 ~ 12100/11907 ~ 64/63 all tempered together. This temperament is supported by [[41edo]], [[491edo]] (491e val), and [[532edo]] (532d val) among others.

BudjarnLambeth: {{todo|expand}} & collapsible

2024-12-22T04:13:05Z

{{todo|expand}} & collapsible

← Older revision		Revision as of 04:13, 22 December 2024
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	== Intervals ==		== Intervals ==
	{\| class="wikitable"		{\| class="wikitable mw-collapsible"
	\|-		\|-
	! \| degree		! \| degree
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	[[Category:Ed5]]		[[Category:Ed5]]
	[[Category:Edonoi]]		[[Category:Edonoi]]
			{{todo\|expand}}

BudjarnLambeth: Harmonics

2024-10-06T01:32:58Z

Harmonics

@@ Line 2: / Line 2: @@
 '''[[Ed5|Division of the 5th harmonic]] into 95 equal parts''' (95ed5) is related to [[41edo|41 edo]], but with the 5/1 rather than the 2/1 being just. The octave is about 2.5143 cents stretched and the step size is about 29.3296 cents. This tuning has a generally sharp tendency for harmonics up to 12. Unlike 41edo, it is only consistent up to the [[11-odd-limit|12-integer-limit]], with discrepancy for the 13th harmonic.
 {| class="wikitable"
 |-
@@ Line 489: / Line 490: @@
 | | just major third plus two octaves
 |}
 ==95ed5 as a generator==

Plumtree: Infobox ET added

2022-10-05T20:43:27Z

Infobox ET added

← Older revision		Revision as of 20:43, 5 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	'''[[Ed5\|Division of the 5th harmonic]] into 95 equal parts''' (95ed5) is related to [[41edo\|41 edo]], but with the 5/1 rather than the 2/1 being just. The octave is about 2.5143 cents stretched and the step size is about 29.3296 cents. This tuning has a generally sharp tendency for harmonics up to 12. Unlike 41edo, it is only consistent up to the [[11-odd-limit\|12-integer-limit]], with discrepancy for the 13th harmonic.		'''[[Ed5\|Division of the 5th harmonic]] into 95 equal parts''' (95ed5) is related to [[41edo\|41 edo]], but with the 5/1 rather than the 2/1 being just. The octave is about 2.5143 cents stretched and the step size is about 29.3296 cents. This tuning has a generally sharp tendency for harmonics up to 12. Unlike 41edo, it is only consistent up to the [[11-odd-limit\|12-integer-limit]], with discrepancy for the 13th harmonic.