A-team: Difference between revisions
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Trivia: A-Team can be tuned by ear, by tuning a chain of pure harmonic sevenths and taking every other note. This corresponds to using a generator of 64/49 = 462.34819 cents. A chain of fourteen 7/4's are needed to tune the 8-note oneirotonic MOS. This produces a tuning close to 13edo. | Trivia: A-Team can be tuned by ear, by tuning a chain of pure harmonic sevenths and taking every other note. This corresponds to using a generator of 64/49 = 462.34819 cents. A chain of fourteen 7/4's are needed to tune the 8-note oneirotonic MOS. This produces a tuning close to 13edo. | ||
=== Temperament data === | |||
Subgroup: 2.5.9.21 | |||
Period: 1\1 | |||
Optimal ([[POTE]]) generator: 464.3865 | |||
EDO generators: [[13edo|5\13]], [[18edo|7\18]], [[31edo|12\31]], [[44edo|17\44]] | |||
<div class="toccolours mw-collapsible mw-collapsed" style="width:600px; overflow:auto;"> | |||
<div style="line-height:1.6;">Technical data</div> | |||
<div class="mw-collapsible-content"> | |||
[[Comma]] list: 81/80, 1029/1024 | |||
[[Mapping]] (for 2, 5, 9, 21): [{{val|1 0 2 4}}, {{val|0 6 3 1}}] | |||
Mapping generators: ~2, ~21/16 | |||
{{Vals|legend=1| 13, 18, 31, 44 }} | |||
</div></div> | |||
==== Intervals ==== | |||
Sortable table of intervals in the Dylathian mode and their A-Team interpretations: | |||
{| class="wikitable right-2 right-3 right-4 sortable" | |||
|- | |||
! Degree | |||
! Size in 13edo | |||
! Size in 18edo | |||
! Size in 31edo | |||
! Note name on Q | |||
! class="unsortable"| Approximate ratios<ref>The ratio interpretations that are not valid for 18edo are italicized.</ref> | |||
! #Gens up | |||
|- | |||
| 1 | |||
| 0\13, 0.00 | |||
| 0\18, 0.00 | |||
| 0\31, 0.00 | |||
| Q | |||
| 1/1 | |||
| 0 | |||
|- | |||
| 2 | |||
| 2\13, 184.62 | |||
| 3\18, 200.00 | |||
| 5\31, 193.55 | |||
| J | |||
| 9/8, 10/9 | |||
| +3 | |||
|- | |||
| 3 | |||
| 4\13, 369.23 | |||
| 6\18, 400.00 | |||
| 10\31, 387.10 | |||
| K | |||
| 5/4 | |||
| +6 | |||
|- | |||
| 4 | |||
| 5\13, 461.54 | |||
| 7\18, 466.67 | |||
| 12\31, 464.52 | |||
| L | |||
| 21/16, ''13/10'' | |||
| +1 | |||
|- | |||
| 5 | |||
| 7\13, 646.15 | |||
| 10\18, 666.66 | |||
| 17\31, 658.06 | |||
| M | |||
| ''13/9'', ''16/11'' | |||
| +4 | |||
|- | |||
| 6 | |||
| 9\13, 830.77 | |||
| 13\18, 866.66 | |||
| 22\31, 851.61 | |||
| N | |||
| ''13/8'', ''18/11'' | |||
| +7 | |||
|- | |||
| 7 | |||
| 10\13, 923.08 | |||
| 14\18, 933.33 | |||
| 24\31, 929.03 | |||
| O | |||
| 12/7 | |||
| +2 | |||
|- | |||
| 8 | |||
| 12\13, 1107.69 | |||
| 17\18, 1133.33 | |||
| 29\31, 1122.58 | |||
| P | |||
| | |||
| +5 | |||
|} | |||
<references/> | |||
== Basic theory == | == Basic theory == | ||