|
|
| (305 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 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]], 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. | | [[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*
| |
| | |
| 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;" | 657.546
| |
| | style="text-align:center;" | 16/11~22/15
| |
| | style="text-align:center;" | -4
| |
| | style="text-align:right;" | 542.454
| |
| | 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
| |