No-twos subgroup temperaments: Difference between revisions

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Classified by focusing on the mapping of 5th harmonic, similar to [[Rank-2 temperaments by mapping of 3]].

* Arcturus, aldebaran and polaris have a 3/1 period and ~5/3 generator. There is one-to-one correspondence between the 3.5 subgroup and mapped intervals.

* Arcturus, antares aldebaran and polaris have a 3/1 period and ~5/3 generator. There is one-to-one correspondence between the 3.5 subgroup and mapped intervals.

* BPS has a ~9/7 generator, two of which give the ~5/3.

* Sirius has a ~25/21 generator, three of which give the ~5/3.

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Badness (Sintel): 2.51

== Antares ==

Antares tempers out [[21875/19683]], the amount by which, assuming [[tritave equivalence]], five [[5/3]]'s exceed [[9/7]], or equivalently the amount by which five [[9/5]]'s fall short of [[7/3]]. It is basically to [[#Arcturus|arcturus]] what [[mavila family #Mavila|mavila]] is to [[meantone family #Meantone|meantone]], and is even more inaccurate than mavila. It falls into [[exotemperament]] range with the "comma" it tempers out (~182.8{{cent}}) being greater than a [[Bohlen–Pierce]] step. In terms of diatonic interval regions, the ~[[9/5]] is extremely sharp and becomes a [[neutral seventh]], and the ~[[7/5]] becomes a [[supermajor third]].

Antares was named by {{u|CompactStar}} after the star {{w|Antares}}, following a series of non-octave temperaments that were named after stars.

[[Subgroup]]: 3.5.7

[[Comma list]]: 21875/19683

: mapping generators: ~3, ~5

[[Optimal tuning]]s:

* [[WE]]: ~3 = 1913.7665{{c}}, ~5/3 = 858.1255{{c}}

: [[error map]]: {{val| +11.811 -14.422 -4.388 }}

* [[CWE]]: ~3 = 1901.9550{{c}}, ~5/3 = 851.8677{{c}}

: error map: {{val| 0.000 -32.391 -20.844 }}

[[Optimal ET sequence]]: [[9edt|b9]], [[20edt|b20]], [[29edt|b29]]

[[Badness]] (Sintel): 2.95

== BPS ==

@@ Line 7: / Line 7: @@
 Classified by focusing on the mapping of 5th harmonic, similar to [[Rank-2 temperaments by mapping of 3]].
-* Arcturus, aldebaran and polaris have a 3/1 period and ~5/3 generator. There is one-to-one correspondence between the 3.5 subgroup and mapped intervals.
+* Arcturus, antares aldebaran and polaris have a 3/1 period and ~5/3 generator. There is one-to-one correspondence between the 3.5 subgroup and mapped intervals.
 * BPS has a ~9/7 generator, two of which give the ~5/3.
 * Sirius has a ~25/21 generator, three of which give the ~5/3.
@@ Line 58: / Line 58: @@
 Badness (Sintel): 2.51
+== Antares ==
+Antares tempers out [[21875/19683]], the amount by which, assuming [[tritave equivalence]], five [[5/3]]'s exceed [[9/7]], or equivalently the amount by which five [[9/5]]'s fall short of [[7/3]]. It is basically to [[#Arcturus|arcturus]] what [[mavila family #Mavila|mavila]] is to [[meantone family #Meantone|meantone]], and is even more inaccurate than mavila. It falls into [[exotemperament]] range with the "comma" it tempers out (~182.8{{cent}}) being greater than a [[Bohlen–Pierce]] step. In terms of diatonic interval regions, the ~[[9/5]] is extremely sharp and becomes a [[neutral seventh]], and the ~[[7/5]] becomes a [[supermajor third]].
+Antares was named by {{u|CompactStar}} after the star {{w|Antares}}, following a series of non-octave temperaments that were named after stars.
+[[Subgroup]]: 3.5.7
+[[Comma list]]: 21875/19683
+{{Mapping|legend=3| 1 0 9 | 0 1 -5 }}
+: mapping generators: ~3, ~5
+[[Optimal tuning]]s:
+* [[WE]]: ~3 = 1913.7665{{c}}, ~5/3 = 858.1255{{c}}
+: [[error map]]: {{val| +11.811 -14.422 -4.388 }}
+* [[CWE]]: ~3 = 1901.9550{{c}}, ~5/3 = 851.8677{{c}}
+: error map: {{val| 0.000 -32.391 -20.844 }}
+[[Optimal ET sequence]]: [[9edt|b9]], [[20edt|b20]], [[29edt|b29]]
+[[Badness]] (Sintel): 2.95
 == BPS ==