Archytas family: Difference between revisions
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The '''archytas family''' of temperaments [[tempering out|tempers out]] [[64/63]], and thereby identifies the [[otonal]] [[tetrad]] with the [[dominant seventh chord]], which is familiar from [[12edo]] and also a feature of [[22edo]] and [[27edo]]. | The '''archytas family''' of temperaments [[tempering out|tempers out]] [[64/63]], and thereby identifies the [[otonal]] [[tetrad]] with the [[dominant seventh chord]], which is familiar from [[12edo]] and also a feature of [[22edo]] and [[27edo]]. | ||
== Archytas == | |||
== Archytas | |||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
[[Comma list]]: 64/63 | [[Comma list]]: [[64/63]] | ||
[[Mapping]]: [{{val| 1 0 0 6 }}, {{val| 0 1 0 -2 }}, {{val| 0 0 1 0 }}] | [[Mapping]]: [{{val| 1 0 0 6 }}, {{val| 0 1 0 -2 }}, {{val| 0 0 1 0 }}] | ||
| Line 37: | Line 34: | ||
* Joel Taylor – [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] | * Joel Taylor – [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] | ||
== Ares | == Ares == | ||
{{Main| Ares }} | |||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 66: | Line 64: | ||
Scales: [[ares12]] | Scales: [[ares12]] | ||
== Vulcan | == Vulcan == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 84: | Line 81: | ||
[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||
[[Category:Temperament family]] | [[Category:Temperament family]] | ||
[[Category:Archytas]] | [[Category:Archytas family| ]] <!-- main article --> | ||
[[Category:Rank 3]] | [[Category:Rank 3]] | ||
[[Category:Listen]] | |||
Revision as of 11:41, 8 August 2021
The archytas family of temperaments tempers out 64/63, and thereby identifies the otonal tetrad with the dominant seventh chord, which is familiar from 12edo and also a feature of 22edo and 27edo.
Archytas
Subgroup: 2.3.5.7
Mapping: [⟨1 0 0 6], ⟨0 1 0 -2], ⟨0 0 1 0]]
Mapping generators: ~2, ~3, ~5
Map to lattice: [⟨0 1 0 -2], ⟨0 0 1 0]]
Lattice basis:
- 3/2 length = 1.0508, 5/4 length = 2.3219
- Angle (3/2, 5/4) = 90 degrees
POTE generators: ~3/2 = 709.3213, ~5/4 = 393.3747
- [[1 0 0 0⟩, [2 1/3 0 -1/3⟩, [2 -2/3 1 -1/3⟩, [2 -2/3 0 2/3⟩]
- Eigenmonzos (unchanged intervals): 2, 6/5, 7/5
- [[1 0 0 0⟩, [3/2 1/2 0 -1/4⟩, [3/2 -1/2 1 -1/4⟩, [3 -1 0 1/2⟩]
- Eigenmonzos (unchanged intervals): 2, 6/5, 9/7
Scales: archytas12, archytas12synch
- Music
- Chris Vaisvil – 12 archytas hobbits with ale
- Joel Taylor – Portrait of a Tragedy (Death of a Son) - Archytas12 sync Study 3
Ares
Subgroup: 2.3.5.7.11
Comma list: 64/63, 100/99
Mapping: [⟨1 0 0 6 2], ⟨0 1 0 -2 -2], ⟨0 0 1 0 2]]
Mapping generators: ~2, ~3, ~5
Map to lattice: [⟨0 1 1 -2 0], ⟨0 0 -1 0 -2]]
Lattice basis:
- 3/2 length = 0.9878, 6/5 length = 1.4312
- Angle (3/2, 6/5) = 75.0475 degrees
POTE generators: ~3/2 = 709.6869, ~5/4 = 391.4507
- [[1 0 0 0 0⟩, [3/2 1/2 0 -1/4 0⟩, [2 0 0 -1/2 1/2⟩, [3 -1 0 1/2 0⟩, [3 -1 0 -1/2 1⟩]
- Eigenmonzos (unchanged intervals): 2, 11/9, 9/7
Badness: 0.469 × 10-3
Scales: ares12
Vulcan
Subgroup: 2.3.5.7.11
Comma list: 56/55, 64/63
Mapping: [⟨1 0 0 6 9], ⟨0 1 0 -2 -2], ⟨0 0 1 0 -1]]
Mapping generators: ~2, ~3, ~5
POTE generators: ~3/2 = 710.9720, ~5/4 = 401.2699
Badness: 0.577 × 10-3