|
|
| (286 intermediate revisions by 7 users not shown) |
| Line 1: |
Line 1: |
| 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]] |
|
| |
|
| [[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 more accurately represents primes 13, 17, 19 and 23. | | [[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.
| |
| | |
| ==Generator chain==
| |
| {| class="wikitable"
| |
| |-
| |
| ! | Generators
| |
| ! | Cents (*)
| |
| ! | Ratios (**)
| |
| ! | Generators
| |
| ! | 2/1 inverse (*)
| |
| ! | Ratios (**)
| |
| |-
| |
| | 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;" | 463.5
| |
| | style="text-align:center;" | 21/16
| |
| | style="text-align:center;" | -1
| |
| | style="text-align:right;" | 736.5
| |
| | style="text-align:center;" | 32/21
| |
| |-
| |
| | style="text-align:center;" | 2
| |
| | style="text-align:right;" | 927.0
| |
| | style="text-align:center;" | 12/7
| |
| | style="text-align:center;" | -2
| |
| | style="text-align:right;" | 273.0
| |
| | style="text-align:center;" | 7/6
| |
| |-
| |
| | style="text-align:center;" | 3
| |
| | style="text-align:right;" | 190.5
| |
| | style="text-align:center;" | 9/8, 10/9
| |
| | style="text-align:center;" | -3
| |
| | style="text-align:right;" | 1009.5
| |
| | style="text-align:center;" | 16/9, 9/5
| |
| |-
| |
| | style="text-align:center;" | 4
| |
| | style="text-align:right;" | 654.0
| |
| | style="text-align:center;" | 16/11, 13/9
| |
| | style="text-align:center;" | -4
| |
| | style="text-align:right;" | 546.0
| |
| | style="text-align:center;" | 11/8, 18/13
| |
| |-
| |
| | style="text-align:center;" | 5
| |
| | style="text-align:right;" | 1117.5
| |
| | style="text-align:center;" | 40/21, 21/11
| |
| | style="text-align:center;" | -5
| |
| | style="text-align:right;" | 82.5
| |
| | style="text-align:center;" | 21/20, 22/21
| |
| |-
| |
| | style="text-align:center;" | 6
| |
| | style="text-align:right;" | 381.0
| |
| | style="text-align:center;" | 5/4
| |
| | style="text-align:center;" | -6
| |
| | style="text-align:right;" | 819.0
| |
| | style="text-align:center;" | 8/5
| |
| |-
| |
| | style="text-align:center;" | 7
| |
| | style="text-align:right;" | 844.5
| |
| | style="text-align:center;" | 18/11, 13/8
| |
| | style="text-align:center;" | -7
| |
| | style="text-align:right;" | 355.5
| |
| | style="text-align:center;" | 11/9, 16/13
| |
| |-
| |
| | style="text-align:center;" | 8
| |
| | style="text-align:right;" | 108.0
| |
| | style="text-align:center;" | close to 17/16
| |
| | style="text-align:center;" | -8
| |
| | style="text-align:right;" | 1092.0
| |
| | style="text-align:center;" | close to 15/8
| |
| |-
| |
| | style="text-align:center;" | 9
| |
| | style="text-align:right;" | 571.5
| |
| | style="text-align:center;" |
| |
| | style="text-align:center;" | -9
| |
| | style="text-align:right;" | 628.5
| |
| | style="text-align:center;" | very close to 23/16 (within 0.2 cents)
| |
| |-
| |
| | style="text-align:center;" | 10
| |
| | style="text-align:right;" | 1035.0
| |
| | style="text-align:center;" | 20/11
| |
| | style="text-align:center;" | -10
| |
| | style="text-align:right;" | 165.0
| |
| | style="text-align:center;" | 11/10
| |
| |-
| |
| | style="text-align:center;" | 11
| |
| | style="text-align:right;" | 298.5
| |
| | style="text-align:center;" | 13/11, close to 19/16
| |
| | style="text-align:center;" | -11
| |
| | style="text-align:right;" | 901.5
| |
| | style="text-align:center;" | 22/13
| |
| |-
| |
| | style="text-align:center;" | 12
| |
| | style="text-align:right;" | 762.0
| |
| | style="text-align:center;" | close to 14/9
| |
| | style="text-align:center;" | -12
| |
| | style="text-align:right;" | 438.0
| |
| | style="text-align:center;" | 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
| |