A-team: Difference between revisions
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| Line 10: | Line 10: | ||
! | Generators | ! | Generators | ||
! | Cents | ! | Cents | ||
! | Ratios* | ! | Ratios (*) | ||
notation | notation | ||
! | Generators | ! | Generators | ||
! | 2/1 inverse | ! | 2/1 inverse | ||
! | Ratios | ! | Ratios (*) | ||
notation | notation | ||
| Line 27: | Line 27: | ||
|- | |- | ||
| style="text-align:center;" | 1 | | style="text-align:center;" | 1 | ||
| style="text-align:right;" | | | style="text-align:right;" | 463.96 | ||
| style="text-align:center;" | 21/16 | | style="text-align:center;" | 21/16 | ||
| style="text-align:center;" | -1 | | style="text-align:center;" | -1 | ||
| Line 34: | Line 34: | ||
|- | |- | ||
| style="text-align:center;" | 2 | | style="text-align:center;" | 2 | ||
| style="text-align:right;" | | | style="text-align:right;" | 927.91 | ||
| style="text-align:center;" | 12/7 | | style="text-align:center;" | 12/7 | ||
| style="text-align:center;" | -2 | | style="text-align:center;" | -2 | ||
| style="text-align:right;" | | | style="text-align:right;" | 272.09 | ||
| style="text-align:center;" | 7/6 | | style="text-align:center;" | 7/6 | ||
|- | |- | ||
| style="text-align:center;" | 3 | | style="text-align:center;" | 3 | ||
| style="text-align:right;" | | | style="text-align:right;" | 191.87 | ||
| style="text-align:center;" | 9/8, 10/9 | | style="text-align:center;" | 9/8, 10/9 | ||
| style="text-align:center;" | -3 | | style="text-align:center;" | -3 | ||
| style="text-align:right;" | | | style="text-align:right;" | 1008.13 | ||
| style="text-align:center;" | 16/9, 9/5 | | style="text-align:center;" | 16/9, 9/5 | ||
|- | |- | ||
| style="text-align:center;" | 4 | | style="text-align:center;" | 4 | ||
| style="text-align:right;" | | | style="text-align:right;" | 655.82 | ||
| style="text-align:center;" | 16/11 | | style="text-align:center;" | 16/11 | ||
| style="text-align:center;" | -4 | | style="text-align:center;" | -4 | ||
| style="text-align:right;" | | | style="text-align:right;" | 544.18 | ||
| style="text-align:center;" | 11/8 | | style="text-align:center;" | 11/8 | ||
|- | |- | ||
| style="text-align:center;" | 5 | | style="text-align:center;" | 5 | ||
| style="text-align:right;" | | | style="text-align:right;" | 1119.78 | ||
| style="text-align:center;" | 40/21 | | style="text-align:center;" | 40/21 | ||
| style="text-align:center;" | -5 | | style="text-align:center;" | -5 | ||
| style="text-align:right;" | | | style="text-align:right;" | 80.22 | ||
| style="text-align:center;" | 21/20 | | style="text-align:center;" | 21/20 | ||
|- | |- | ||
| style="text-align:center;" | 6 | | style="text-align:center;" | 6 | ||
| style="text-align:right;" | | | style="text-align:right;" | 383.73 | ||
| style="text-align:center;" | 5/4 | | style="text-align:center;" | 5/4 | ||
| style="text-align:center;" | -6 | | style="text-align:center;" | -6 | ||
| style="text-align:right;" | | | style="text-align:right;" | 816.27 | ||
| style="text-align:center;" | 8/5 | | style="text-align:center;" | 8/5 | ||
|- | |- | ||
| style="text-align:center;" | 7 | | style="text-align:center;" | 7 | ||
| style="text-align:right;" | | | style="text-align:right;" | 847.68 | ||
| style="text-align:center;" | 18/11 | | style="text-align:center;" | 18/11 | ||
| style="text-align:center;" | -7 | | style="text-align:center;" | -7 | ||
| style="text-align:right;" | | | style="text-align:right;" | 352.31 | ||
| style="text-align:center;" | 11/9 | | style="text-align:center;" | 11/9 | ||
|} | |} | ||
2.9.21.5.11 ratio interpretations | (*) 2.9.21.5.11 ratio interpretations | ||
Revision as of 00:41, 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 | 463.96 | 21/16 | -1 | 735.61 | 32/21 |
| 2 | 927.91 | 12/7 | -2 | 272.09 | 7/6 |
| 3 | 191.87 | 9/8, 10/9 | -3 | 1008.13 | 16/9, 9/5 |
| 4 | 655.82 | 16/11 | -4 | 544.18 | 11/8 |
| 5 | 1119.78 | 40/21 | -5 | 80.22 | 21/20 |
| 6 | 383.73 | 5/4 | -6 | 816.27 | 8/5 |
| 7 | 847.68 | 18/11 | -7 | 352.31 | 11/9 |
(*) 2.9.21.5.11 ratio interpretations