A-team: Difference between revisions
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| Line 73: | Line 73: | ||
| style="text-align:center;" | 8 | | style="text-align:center;" | 8 | ||
| style="text-align:right;" | 108.0 | | style="text-align:right;" | 108.0 | ||
| style="text-align:center;" | | | style="text-align:center;" | '''17/16''' | ||
| style="text-align:center;" | -8 | | style="text-align:center;" | -8 | ||
| style="text-align:right;" | 1092.0 | | style="text-align:right;" | 1092.0 | ||
| style="text-align:center;" | close to '''15/8''' | | style="text-align:center;" | (close to '''15/8''') | ||
|- | |- | ||
| style="text-align:center;" | 9 | | style="text-align:center;" | 9 | ||
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| style="text-align:center;" | -9 | | style="text-align:center;" | -9 | ||
| style="text-align:right;" | 628.5 | | style="text-align:right;" | 628.5 | ||
| style="text-align:center;" | | | style="text-align:center;" | '''23/16''' (within 0.2 cents) | ||
|- | |- | ||
| style="text-align:center;" | 10 | | style="text-align:center;" | 10 | ||
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| style="text-align:center;" | 11 | | style="text-align:center;" | 11 | ||
| style="text-align:right;" | 298.5 | | style="text-align:right;" | 298.5 | ||
| style="text-align:center;" | 13/11, | | style="text-align:center;" | 13/11, '''19/16''' | ||
| style="text-align:center;" | -11 | | style="text-align:center;" | -11 | ||
| style="text-align:right;" | 901.5 | | style="text-align:right;" | 901.5 | ||
Revision as of 02:06, 24 May 2020
A-Team is a 2.9.21 temperament generated by a tempered 21/16 with a size ranging from 5\13 (461.54¢) to 7\18 (466.67¢), or to about 470¢ if you don't care about tempering out 81/80. Three 21/16's are equated to one 9/8, which means that the latrizo comma (1029/1024) is tempered out. It's natural to consider A-Team a 2.9.21.5 temperament by also equating two 9/8's with one 5/4, tempering out 81/80. The generator generates 5-, 8-, and 13-note MOSes, most notably the 8-note "oneirotonic" MOS; see also 13edo#Modes_and_Harmony_in_the_Oneirotonic_Scale.
13edo, 18edo, 31edo, and 44edo (with generators 5\13, 7\18, 12\31, and 17\44 respectively) all support 2.9.21 A-Team with their closest approximations to 9/8 and 21/16. 13edo, while representing the 2.9.21.5 subgroup less accurately, gives the chords extra interpretations; for example, the chord H-C-D-F (in Cryptic Ruse's notation) represents both 8:10:11:13 and 13:16:18:21 in 13edo. 31edo gives the optimal patent val for the 2.9.21.5 subgroup interpretation. 44edo is similar to 31edo but better approximates primes 11, 13, 17, 19 and 23 with the generator chain.
Its name is a pun on the 18 notes in its proper scale, which is a 13L 5s MOS.
JI interpretations
| Generators | Cents (*) | Ratios (**) | Generators | 2/1 inverse (*) | Ratios (**) |
|---|---|---|---|---|---|
| 0 | 0.00 | 1/1 | 0 | 1200.00 | 2/1 |
| 1 | 463.5 | 21/16, 13/10 | -1 | 736.5 | 32/21, 20/13 |
| 2 | 927.0 | 12/7 | -2 | 273.0 | 7/6 |
| 3 | 190.5 | 9/8, 10/9 | -3 | 1009.5 | 16/9, 9/5 |
| 4 | 654.0 | 16/11, 13/9 | -4 | 546.0 | 11/8, 18/13 |
| 5 | 1117.5 | 40/21, 21/11 | -5 | 82.5 | 21/20, 22/21 |
| 6 | 381.0 | 5/4 | -6 | 819.0 | 8/5 |
| 7 | 844.5 | 18/11, 13/8 | -7 | 355.5 | 11/9, 16/13 |
| 8 | 108.0 | 17/16 | -8 | 1092.0 | (close to 15/8) |
| 9 | 571.5 | -9 | 628.5 | 23/16 (within 0.2 cents) | |
| 10 | 1035.0 | 20/11 | -10 | 165.0 | 11/10 |
| 11 | 298.5 | 13/11, 19/16 | -11 | 901.5 | 22/13 |
| 12 | 762.0 | close to 14/9 | -12 | 438.0 | close to 9/7 |
(*) using the 2.9.21.5.11.13 POTE generator; cf. the 463.64¢ generator in 44edo
(**) 2.9.21.5.11.13 ratio interpretations