A-team: Difference between revisions

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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 470.78¢ (the pure value for 21/16) if you don't care about tempering out 81/80 or avoiding quartertone-sized steps. Three 21/16's are equated to one 9/8, which means that the [[color notation|latrizo]] comma (1029/1024) is tempered out. Hence, any EDO that equates three 8/7's with one 3/2 will support A-Team with its 21/16.

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 470.78¢ (the pure value for 21/16) if you don't care about tempering out 81/80 or avoiding quartertone-sized steps. Three 21/16's are equated to one 9/8, which means that the [[color notation|latrizo]] comma (1029/1024) is tempered out. Hence, any EDO that equates three 8/7's with one 3/2 will support A-Team with its 21/16. Its name is a pun on the 18 notes in its proper scale, which is a [[13L_5s|13L 5s]] MOS.

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 [[3L 2s]], [[5L 3s]], and [[5L 8s]] MOSes, most notably the 8-note "oneirotonic" MOS; see also [[13edo#Modes_and_Harmony_in_the_Oneirotonic_Scale]].

[[13edo]], [[18edo]], [[31edo]], and [[44edo]] (with generators 5\13, 7\18, 12\31, and 17\44 respectively) all support 2.9.21.5 A-Team with their closest approximations to 9/8 and 21/16. 13edo, while representing the 2.9.21.5 subgroup less accurately, gives some chords extra interpretations; for example, the chord O#-J-K-M (in Kentaku notation) represents both 8:10:11:13 and 13:16:18:21 in 13edo. 31edo gives the [[optimal patent val]] for 2.9.21.5 A-Team and tunes the 13:17:19 chord very accurately. 44edo is similar to 31edo but better approximates 11, 13, 17, 19 and 23 as harmonics with the generator chain.

~~Its name is a pun on the 18 notes in its proper scale, which is a [[13L_5s|13L 5s]] MOS.~~

==Notation==

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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 470.78¢ (the pure value for 21/16) if you don't care about tempering out 81/80 or avoiding quartertone-sized steps. Three 21/16's are equated to one 9/8, which means that the [[color notation|latrizo]] comma (1029/1024) is tempered out. Hence, any EDO that equates three 8/7's with one 3/2 will support A-Team with its 21/16.
+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 470.78¢ (the pure value for 21/16) if you don't care about tempering out 81/80 or avoiding quartertone-sized steps. Three 21/16's are equated to one 9/8, which means that the [[color notation|latrizo]] comma (1029/1024) is tempered out. Hence, any EDO that equates three 8/7's with one 3/2 will support A-Team with its 21/16. Its name is a pun on the 18 notes in its proper scale, which is a [[13L_5s|13L 5s]] MOS.
 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 [[3L 2s]], [[5L 3s]], and [[5L 8s]] MOSes, most notably the 8-note "oneirotonic" MOS; see also [[13edo#Modes_and_Harmony_in_the_Oneirotonic_Scale]].
 [[13edo]], [[18edo]], [[31edo]], and [[44edo]] (with generators 5\13, 7\18, 12\31, and 17\44 respectively) all support 2.9.21.5 A-Team with their closest approximations to 9/8 and 21/16.  13edo, while representing the 2.9.21.5 subgroup less accurately, gives some chords extra interpretations; for example, the chord O#-J-K-M (in Kentaku notation) represents both 8:10:11:13 and 13:16:18:21 in 13edo. 31edo gives the [[optimal patent val]] for 2.9.21.5 A-Team and tunes the 13:17:19 chord very accurately. 44edo is similar to 31edo but better approximates 11, 13, 17, 19 and 23 as harmonics with the generator chain.
-Its name is a pun on the 18 notes in its proper scale, which is a [[13L_5s|13L 5s]] MOS.
 ==Notation==