A-team: Difference between revisions
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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 [[color notation|latrizo]] comma (1029/1024) is tempered out. It's natural to consider A-Team a 2.9.21.5.11 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]]. | 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 [[color notation|latrizo]] comma (1029/1024) is tempered out. It's natural to consider A-Team a 2.9.21.5.11 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]] all support 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 | [[13edo]], [[18edo]], [[31edo]], and [[44edo]] all support 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 13, 17, 19 and 23. | ||
Its name is a pun on the 18 notes in its proper scale, which is a [[13L_5s|13L 5s]] MOS. | Its name is a pun on the 18 notes in its proper scale, which is a [[13L_5s|13L 5s]] MOS. | ||
Revision as of 01:48, 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 2.9.21.5.11 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 all support 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 13, 17, 19 and 23.
Its name is a pun on the 18 notes in its proper scale, which is a 13L 5s MOS.
Generator chain
| Generators | Cents (*) | Ratios (**) | Generators | 2/1 inverse (*) | Ratios (**) |
|---|---|---|---|---|---|
| 0 | 0.00 | 1/1 | 0 | 1200.00 | 2/1 |
| 1 | 463.5 | 21/16 | -1 | 736.5 | 32/21 |
| 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 | close to 17/16 | -8 | 1092.0 | close to 15/8 |
| 9 | 571.5 | -9 | 628.5 | very close to 23/16 (within 0.2 cents) | |
| 10 | 1035.0 | 20/11 | -10 | 165.0 | 11/10 |
| 11 | 298.5 | 13/11, close to 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