A-team: Difference between revisions

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'''A-Team''' is a 2.9.21 temperament generated by a tempered zo fourth ([[21/16]]) with a size ranging from 461.54¢ (5\13) to 470.78¢ (the pure value for 21/16). It can be viewed as every other note of 2.3.7 latrizo or "[[slendric]]" temperament. Any EDO that has an interval within the range 461.54¢ to 470.78¢ will support A-Team. Three 21/16's are equated to one 9/8, which means that the [[color notation|latrizo]] comma (1029/1024) is tempered out. 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. Generators optimized for tempering out 81/80 also tend to generate the melodically best scales. ~~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]]. Any EDO with an interval between 461.54¢ and 466.67¢ can be reasonably said to support 2.9.21.5 A-Team.

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. Generators optimized for tempering out 81/80 also tend to generate the melodically best scales. This temperament 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]]. Any EDO with an interval between 461.54¢ and 466.67¢ can be reasonably said to support 2.9.21.5 A-Team.

[[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 P1-d4-m5-m7 (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 to within 1.1 cents. 44edo is similar to 31edo but better approximates 11, 13, 17, and 19 as harmonics with the generator chain, and additionally provides the 23th harmonic.

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 '''A-Team''' is a 2.9.21 temperament generated by a tempered zo fourth ([[21/16]]) with a size ranging from 461.54¢ (5\13) to 470.78¢ (the pure value for 21/16). It can be viewed as every other note of 2.3.7 latrizo or "[[slendric]]" temperament. Any EDO that has an interval within the range 461.54¢ to 470.78¢ will support A-Team. Three 21/16's are equated to one 9/8, which means that the [[color notation|latrizo]] comma (1029/1024) is tempered out. 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. Generators optimized for tempering out 81/80 also tend to generate the melodically best scales. 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]]. Any EDO with an interval between 461.54¢ and 466.67¢ can be reasonably said to support 2.9.21.5 A-Team.
+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. Generators optimized for tempering out 81/80 also tend to generate the melodically best scales. This temperament 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]]. Any EDO with an interval between 461.54¢ and 466.67¢ can be reasonably said to support 2.9.21.5 A-Team.
 [[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 P1-d4-m5-m7 (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 to within 1.1 cents. 44edo is similar to 31edo but better approximates 11, 13, 17, and 19 as harmonics with the generator chain, and additionally provides the 23th harmonic.