A-team: Difference between revisions
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==Generator chain== | ==Generator chain== | ||
{| class="wikitable" | |||
|- | |||
! | Generators | |||
! | Cents | |||
! | Ratios* | |||
notation | |||
! | Generators | |||
! | 2/1 inverse | |||
! | Ratios | |||
notation | |||
|- | |||
| style="text-align:center;" | 0 | |||
| style="text-align:right;" | 0.00 | |||
| style="text-align:center;" | 1/1 | |||
| style="text-align:center;" | 0 | |||
| style="text-align:right;" | 1200.00 | |||
| style="text-align:center;" | 2/1 | |||
|- | |||
| style="text-align:center;" | 1 | |||
| style="text-align:right;" | 464.39 | |||
| style="text-align:center;" | 21/16 | |||
| style="text-align:center;" | -1 | |||
| style="text-align:right;" | 735.61 | |||
| style="text-align:center;" | 32/21 | |||
|- | |||
| style="text-align:center;" | 2 | |||
| style="text-align:right;" | 928.77 | |||
| style="text-align:center;" | 12/7 | |||
| style="text-align:center;" | -2 | |||
| style="text-align:right;" | 271.23 | |||
| style="text-align:center;" | 7/6 | |||
|- | |||
| style="text-align:center;" | 3 | |||
| style="text-align:right;" | 193.16 | |||
| style="text-align:center;" | 9/8, 10/9 | |||
| style="text-align:center;" | -3 | |||
| style="text-align:right;" | 1006.84 | |||
| style="text-align:center;" | 16/9, 9/5 | |||
|- | |||
| style="text-align:center;" | 4 | |||
| style="text-align:right;" | 651.00 | |||
| style="text-align:center;" | 16/11~22/15 | |||
| style="text-align:center;" | -4 | |||
| style="text-align:right;" | 549.00 | |||
| style="text-align:center;" | 15/11~11/8 | |||
|- | |||
| style="text-align:center;" | 5 | |||
| style="text-align:right;" | 1121.93 | |||
| style="text-align:center;" | 40/21 | |||
| style="text-align:center;" | -5 | |||
| style="text-align:right;" | 78.07 | |||
| style="text-align:center;" | 21/20 | |||
|- | |||
| style="text-align:center;" | 6 | |||
| style="text-align:right;" | 386.32 | |||
| style="text-align:center;" | 5/4 | |||
| style="text-align:center;" | -6 | |||
| style="text-align:right;" | 813.68 | |||
| style="text-align:center;" | 8/5 | |||
<!-- | |||
|- | |||
| style="text-align:center;" | 7 | |||
| style="text-align:right;" | 1139.25 | |||
| style="text-align:center;" | 48/25~160/81 | |||
| style="text-align:center;" | -7 | |||
| style="text-align:right;" | 60.75 | |||
| style="text-align:center;" | 81/80~25/24 | |||
|- | |||
| style="text-align:center;" | 8 | |||
| style="text-align:right;" | 102.00 | |||
| style="text-align:center;" | 16/15~21/20 | |||
| style="text-align:center;" | -8 | |||
| style="text-align:right;" | 1098.00 | |||
| style="text-align:center;" | 40/21~15/8 | |||
|- | |||
| style="text-align:center;" | 9 | |||
| style="text-align:right;" | 264.75 | |||
| style="text-align:center;" | 7/6 | |||
| style="text-align:center;" | -9 | |||
| style="text-align:right;" | 935.25 | |||
| style="text-align:center;" | 12/7 | |||
|- | |||
| style="text-align:center;" | 10 | |||
| style="text-align:right;" | 427.50 | |||
| style="text-align:center;" | 14/11 | |||
| style="text-align:center;" | -10 | |||
| style="text-align:right;" | 772.50 | |||
| style="text-align:center;" | 11/7 | |||
|- | |||
| style="text-align:center;" | 11 | |||
| style="text-align:right;" | 590.25 | |||
| style="text-align:center;" | 7/5 | |||
| style="text-align:center;" | -11 | |||
| style="text-align:right;" | 609.75 | |||
| style="text-align:center;" | 10/7 | |||
|- | |||
| style="text-align:center;" | 12 | |||
| style="text-align:right;" | 753.00 | |||
| style="text-align:center;" | 14/9 | |||
| style="text-align:center;" | -12 | |||
| style="text-align:right;" | 447.00 | |||
| style="text-align:center;" | 9/7 | |||
--> | |||
|} | |||
2.9.21.5.11 ratio interpretations | |||
Revision as of 00:29, 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, and 31edo all support A-Team; 31edo gives the optimal patent val for the 2.9.21.5 subgroup interpretation, with the 12\31 generator only 0.13 cents sharper than the POTE generator of 464.3865 cents.
Its name is a pun on the 18 notes in its proper scale, which is a 13L 5s MOS.
Generator chain
| Generators | Cents | Ratios*
notation |
Generators | 2/1 inverse | Ratios
notation |
|---|---|---|---|---|---|
| 0 | 0.00 | 1/1 | 0 | 1200.00 | 2/1 |
| 1 | 464.39 | 21/16 | -1 | 735.61 | 32/21 |
| 2 | 928.77 | 12/7 | -2 | 271.23 | 7/6 |
| 3 | 193.16 | 9/8, 10/9 | -3 | 1006.84 | 16/9, 9/5 |
| 4 | 651.00 | 16/11~22/15 | -4 | 549.00 | 15/11~11/8 |
| 5 | 1121.93 | 40/21 | -5 | 78.07 | 21/20 |
| 6 | 386.32 | 5/4 | -6 | 813.68 | 8/5 |
2.9.21.5.11 ratio interpretations