Archytas and ares: Difference between revisions

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~~'''Ares''' is the rank-~~3 ~~temperament tempering out any two of~~ [[64/63]], [[~~100~~/99]] ~~and~~ [[~~176~~/~~175~~]]~~. It is one of the best extensions of '''archytas''', the rank~~-3 ~~temperament tempering out 64~~/63.

{{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}}

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

'''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-3 temperaments after deities.

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

== Interval lattice ==

[[File:Lattice_Ares.png]]

File:Lattice_Ares.png|11-limit ares

</gallery>

== Chords and harmony ==

Archytas enables the eponymous [[essentially tempered chord]]s of [[archytas chords]]. Ares further enables [[ptolemismic chords|ptolemismic]], [[valinorsmic chords|valinorsmic]], and [[ares chords]].

== Scales ==

=== Scala files ===

* [[Archytas12]]

* [[Archytas12synch]]

* [[Ares12]]

~~{{IoT}}~~

== Music ==

; [[Joel Taylor]]

* [https://web.archive.org/web/20201127013434/http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/Archytas12%20sync%20Study%203.mp3 ''Portrait of a Tragedy (Death of a Son) - Archytas12 sync Study 3'']

; [[Chris Vaisvil]]

* [https://web.archive.org/web/20201127012439/http://micro.soonlabel.com/hobbit_scales/daily201031--hobbit-archytas12.mp3 ''12 archytas hobbits with ale'']

[[Category:Archytas| ]]

[[Category:Ares| ]]

[[Category:Rank-3 temperaments]]

[[Category:Archytas family]]

[[Category:Ptolemismic clan]]

[[Category:Valinorsmic clan]]

[[Category:Listen]]

@@ Line 1: / Line 1: @@
-'''Ares''' is the rank-3 temperament tempering out any two of [[64/63]], [[100/99]] and [[176/175]]. It is one of the best extensions of '''archytas''', the rank-3 temperament tempering out 64/63.
+{{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}}
-See [[Archytas family #Ares]] for technical data.
+'''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-3 temperaments after deities.
+See [[Archytas family #Archytas]] and [[Archytas family #Ares|#Ares]] for technical data.
 == Interval lattice ==
-[[File:Lattice_Ares.png]]
+<gallery>
+File:Lattice_Ares.png|11-limit ares
+</gallery>
+== Chords and harmony ==
+Archytas enables the eponymous [[essentially tempered chord]]s of [[archytas chords]]. Ares further enables [[ptolemismic chords|ptolemismic]], [[valinorsmic chords|valinorsmic]], and [[ares chords]].
 == Scales ==
+=== Scala files ===
+* [[Archytas12]]
+* [[Archytas12synch]]
 * [[Ares12]]
-{{IoT}}
+== Music ==
+; [[Joel Taylor]]
+* [https://web.archive.org/web/20201127013434/http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/Archytas12%20sync%20Study%203.mp3 ''Portrait of a Tragedy (Death of a Son) - Archytas12 sync Study 3'']
+; [[Chris Vaisvil]]
+* [https://web.archive.org/web/20201127012439/http://micro.soonlabel.com/hobbit_scales/daily201031--hobbit-archytas12.mp3 ''12 archytas hobbits with ale'']
+[[Category:Archytas| ]] <!-- main article -->
 [[Category:Ares| ]] <!-- main article -->
+[[Category:Rank-3 temperaments]]
 [[Category:Archytas family]]
 [[Category:Ptolemismic clan]]
 [[Category:Valinorsmic clan]]
+[[Category:Listen]]