95ed5: Difference between revisions

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~~'''[[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.

== 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]].

=== Harmonics ===

{{Harmonics in equal|95|5|1|intervals=integer|columns=12|start=12|collapsed=1|title=Approximation of harmonics in 95ed5 (continued)}}

== Intervals ==

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|}

== ~~Harmonics ==~~

== As a generator ==

~~{{Harmonics in equal~~

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.

~~| steps = 95~~

~~| num = 5~~

~~| denom = 1~~

}}

~~{{Harmonics in equal~~

~~| steps = 95~~

~~| num = 5~~

~~| denom = 1~~

~~| start = 12~~

~~| collapsed = 1~~

}}

~~==95ed5 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.

~~[[Category:Ed5]]~~

~~[[Category:Edonoi]]~~

~~{{todo|expand}}~~

@@ 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}}
+== Theory ==
+ed5 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]].
+=== Harmonics ===
+{{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)}}
 == 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.
-| steps = 95
-| num = 5
-| denom = 1
-}}
-{{Harmonics in equal
-| steps = 95
-| num = 5
-| denom = 1
-| start = 12
-| collapsed = 1
-}}
-==95ed5 as a generator==
-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.
-[[Category:Ed5]]
-[[Category:Edonoi]]
-{{todo|expand}}