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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]].
| | #redirect [[Subgroup temperaments #A-team]] |
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| [[13edo]], [[18edo]], [[31edo]], and [[44edo]] 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. | | [[Category:Rank-2 temperaments]] |
| | | [[Category:Subgroup temperaments]] |
| Its name is a pun on the 18 notes in its proper scale, which is a [[13L_5s|13L 5s]] MOS.
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| ==Generator chain==
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| {| class="wikitable"
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| |-
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| ! | Generators
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| ! | Cents (*)
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| ! | Ratios (**)
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| ! | Generators
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| ! | 2/1 inverse (*)
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| ! | Ratios (**)
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| |-
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| | style="text-align:center;" | 0
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| | style="text-align:right;" | 0.00
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| | style="text-align:center;" | 1/1
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| | style="text-align:center;" | 0
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| | style="text-align:right;" | 1200.00
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| | style="text-align:center;" | 2/1
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| |-
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| | style="text-align:center;" | 1
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| | style="text-align:right;" | 463.5
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| | style="text-align:center;" | '''21/16''', 13/10
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| | style="text-align:center;" | -1
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| | style="text-align:right;" | 736.5
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| | style="text-align:center;" | 32/21, 20/13
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| |-
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| | style="text-align:center;" | 2
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| | style="text-align:right;" | 927.0
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| | style="text-align:center;" | 12/7
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| | style="text-align:center;" | -2
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| | style="text-align:right;" | 273.0
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| | style="text-align:center;" | 7/6
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| |-
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| | style="text-align:center;" | 3
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| | style="text-align:right;" | 190.5
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| | style="text-align:center;" | '''9/8''', 10/9
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| | style="text-align:center;" | -3
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| | style="text-align:right;" | 1009.5
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| | style="text-align:center;" | 16/9, 9/5
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| |-
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| | style="text-align:center;" | 4
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| | style="text-align:right;" | 654.0
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| | style="text-align:center;" | 16/11, 13/9
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| | style="text-align:center;" | -4
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| | style="text-align:right;" | 546.0
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| | style="text-align:center;" | '''11/8''', 18/13
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| |-
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| | style="text-align:center;" | 5
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| | style="text-align:right;" | 1117.5
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| | style="text-align:center;" | 40/21, 21/11
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| | style="text-align:center;" | -5
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| | style="text-align:right;" | 82.5
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| | style="text-align:center;" | 21/20, 22/21
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| |-
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| | style="text-align:center;" | 6
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| | style="text-align:right;" | 381.0
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| | style="text-align:center;" | '''5/4'''
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| | style="text-align:center;" | -6
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| | style="text-align:right;" | 819.0
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| | style="text-align:center;" | 8/5
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| |-
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| | style="text-align:center;" | 7
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| | style="text-align:right;" | 844.5
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| | style="text-align:center;" | 18/11, '''13/8'''
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| | style="text-align:center;" | -7
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| | style="text-align:right;" | 355.5
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| | style="text-align:center;" | 11/9, 16/13
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| |-
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| | style="text-align:center;" | 8
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| | style="text-align:right;" | 108.0
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| | style="text-align:center;" | close to '''17/16'''
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| | style="text-align:center;" | -8
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| | style="text-align:right;" | 1092.0
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| | style="text-align:center;" | close to '''15/8'''
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| |-
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| | style="text-align:center;" | 9
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| | style="text-align:right;" | 571.5
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| | style="text-align:center;" |
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| | style="text-align:center;" | -9
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| | style="text-align:right;" | 628.5
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| | style="text-align:center;" | very close to '''23/16''' (within 0.2 cents)
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| |-
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| | style="text-align:center;" | 10
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| | style="text-align:right;" | 1035.0
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| | style="text-align:center;" | 20/11
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| | style="text-align:center;" | -10
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| | style="text-align:right;" | 165.0
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| | style="text-align:center;" | 11/10
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| |-
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| | style="text-align:center;" | 11
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| | style="text-align:right;" | 298.5
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| | style="text-align:center;" | 13/11, close to '''19/16'''
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| | style="text-align:center;" | -11
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| | style="text-align:right;" | 901.5
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| | style="text-align:center;" | 22/13
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| |-
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| | style="text-align:center;" | 12
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| | style="text-align:right;" | 762.0
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| | style="text-align:center;" | close to 14/9
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| | style="text-align:center;" | -12
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| | style="text-align:right;" | 438.0
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| | style="text-align:center;" | close to 9/7
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| |}
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| (*) using the 2.9.21.5.11.13 POTE generator; cf. the 463.64¢ generator in 44edo
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| (**) 2.9.21.5.11.13 ratio interpretations
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