Archytas and ares: Difference between revisions

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{{Infobox regtemp

| Title = Archytas; ares

| Subgroups = 2.3.5.7, 2.3.5.7.11

| Comma basis = [[64/63]] (7-limit); <br>[[64/63]], [[100/99]] (11-limit)

| Edo join 1 = 12 | Edo join 2 = 15 | Edo join 3 = 22

| Mapping = 1; 1 0 -2 -2; 0 1 0 2

| Generators = 3/2, 5/4

| Generators tuning = 709.7, 390.0

| Optimization method = CWE

| Odd limit 1 = 9 | Mistuning 1 = 13.6 | Complexity 1 = ?

| Odd limit 2 = 11 | Mistuning 2 = 13.6 | Complexity 2 = ?

}}

{{Redirect|Archytas|the ancient Greek Pythagorean|Wikipedia: Archytas}}

'''Archytas''' is the [[rank-3]] [[regular temperament|temperament]] [[tempering out]] [[64/63]], with the same 2.3.7-[[subgroup]] structure as [[archy]] but giving [[prime harmonic|prime]] [[5/1|5]] an independent generator. It has an obvious extension to the 11-limit tempering out [[100/99]] and [[176/175]], called '''ares''', as 64/63 = (100/99)(176/175).

These temperaments are named after the ancient Greek mathematician {{w|Archytas}} and the Greek god {{w|Ares}} respectively, the latter being most likely related to the fact that Archytas was Greek, in addition to the pattern of naming rank-2 temperaments after deities.

These temperaments are named after the ancient Greek mathematician {{w|Archytas}} and the Greek god {{w|Ares}} respectively, the latter being most likely related to the fact that Archytas was Greek, in addition to the pattern of naming rank-3 temperaments after deities.

See [[Archytas family #Archytas]] and [[Archytas family #Ares|#Ares]] for technical data.

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+{{Infobox regtemp
+| Title = Archytas; ares
+| Subgroups = 2.3.5.7, 2.3.5.7.11
+| Comma basis = [[64/63]] (7-limit); <br>[[64/63]], [[100/99]] (11-limit)
+| Edo join 1 = 12 | Edo join 2 = 15 | Edo join 3 = 22
+| Mapping = 1; 1 0 -2 -2; 0 1 0 2
+| Generators = 3/2, 5/4
+| Generators tuning = 709.7, 390.0
+| Optimization method = CWE
+| Odd limit 1 = 9 | Mistuning 1 = 13.6 | Complexity 1 = ?
+| Odd limit 2 = 11 | Mistuning 2 = 13.6 | Complexity 2 = ?
+}}
 {{Redirect|Archytas|the ancient Greek Pythagorean|Wikipedia: Archytas}}
 '''Archytas''' is the [[rank-3]] [[regular temperament|temperament]] [[tempering out]] [[64/63]], with the same 2.3.7-[[subgroup]] structure as [[archy]] but giving [[prime harmonic|prime]] [[5/1|5]] an independent generator. It has an obvious extension to the 11-limit tempering out [[100/99]] and [[176/175]], called '''ares''', as 64/63 = (100/99)(176/175).
-These temperaments are named after the ancient Greek mathematician {{w|Archytas}} and the Greek god {{w|Ares}} respectively, the latter being most likely related to the fact that Archytas was Greek, in addition to the pattern of naming rank-2 temperaments after deities.
+These temperaments are named after the ancient Greek mathematician {{w|Archytas}} and the Greek god {{w|Ares}} respectively, the latter being most likely related to the fact that Archytas was Greek, in addition to the pattern of naming rank-3 temperaments after deities.
 See [[Archytas family #Archytas]] and [[Archytas family #Ares|#Ares]] for technical data.