A-team: Difference between revisions

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[[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.

It is also possible to tune A-Team by ear, by tuning a chain of harmonic sevenths and taking every other note. This corresponds to using a generator of (8/7)^2 = 462.34819 cents. A chain of fourteen 7/4's are needed to tune the 8-note oneirotonic MOS.

It is also possible to tune A-Team by ear, by tuning a chain of pure harmonic sevenths and taking every other note. This corresponds to using a generator of (8/7)^2 = 462.34819 cents. A chain of fourteen 7/4's are needed to tune the 8-note oneirotonic MOS.

==Notation==

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 [[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.
-It is also possible to tune A-Team by ear, by tuning a chain of harmonic sevenths and taking every other note. This corresponds to using a generator of (8/7)^2 =  462.34819 cents. A chain of fourteen 7/4's are needed to tune the 8-note oneirotonic MOS.
+It is also possible to tune A-Team by ear, by tuning a chain of pure harmonic sevenths and taking every other note. This corresponds to using a generator of (8/7)^2 =  462.34819 cents. A chain of fourteen 7/4's are needed to tune the 8-note oneirotonic MOS.
 ==Notation==