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| === A-Team (13&18) === | | === A-Team (13&18) === |
| :''Main article: [[A-Team]]'' | | :''Main article: [[A-Team]]'' |
| A-Team tunings (with generator between 5\13 and 7\18) have step ratios between 2/1 and 3/1.
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| A short definition of A-Team is "meantone oneirotonic". This is because A-Team tunings share the following features with [[meantone]] diatonic tunings:
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| * The large step is a "meantone", somewhere between near-10/9 (as in [[13edo]]) and near-9/8 (as in [[18edo]]). Thus A-Team tempers out [[81/80]] like meantone does.
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| * The major mosthird (made of two large steps) is a [[meantone]]- to [[flattone]]-sized major third, thus is a stand-in for the classical diatonic major third.
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| EDOs that support A-Team include [[13edo]], [[18edo]], and [[31edo]].
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| * 13edo has characteristically small major mosseconds of about 185c. It is uniformly compressed 12edo, so it has distorted versions of non-diatonic 12edo scales. It essentially has the best [[11/8]] out of all A-team tunings.
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| * 18edo can be used for a large step ratio of 3, (thus 18edo oneirotonic is distorted 17edo diatonic, or for its nearly pure 9/8 and 7/6. It also makes rising fifths (733.3c, a perfect mossixth) and falling fifths (666.7c, a major mosfifth) almost equally off from a just perfect fifth. 18edo is also more suited for conventionally jazz styles due to its 6-fold symmetry.
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| * 31edo is very close to the 2.9.5.21 POTE tuning, and can be used to make the major mos3rd a near-just 5/4.
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| * [[44edo]] (generator 17\44 = 463.64¢), [[57edo]] (generator 22\57 = 463.16¢), and [[70edo]] (generator 27\70 = 462.857¢) offer a compromise between 31edo's major third and 13edo's 11/8 and 13/8. In particular, 70edo has an essentially pure 13/8.
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| The sizes of the generator, large step and small step of oneirotonic are as follows in various A-Team tunings.
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| {| class="wikitable right-2 right-3 right-4 right-5"
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| |-
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| !
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| ! [[13edo]]
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| ! [[18edo]]
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| ! [[31edo]]
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| ! Optimal ([[POTE]]) tuning
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| ! JI intervals represented (2.9.5.21 subgroup)
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| |-
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| | generator (g)
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| | 5\13, 461.54
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| | 7\18, 466.67
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| | 12\31, 464.52
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| | 464.39
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| | 21/16
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| |-
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| | L (3g - octave)
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| | 2\13, 184.62
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| | 3\18, 200.00
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| | 5\31, 193.55
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| | 193.16
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| | 9/8, 10/9
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| |-
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| | s (-5g + 2 octaves)
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| | 1\13, 92.31
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| | 1\18, 66.67
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| | 2\31, 77.42
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| | 78.07
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| | 21/20
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| |}
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| Trivia: A-Team can be tuned by ear, by tuning a chain of pure harmonic sevenths and taking every other note. This corresponds to using a generator of 64/49 = 462.34819 cents. A chain of fourteen 7/4's are needed to tune the 8-note oneirotonic MOS. This produces a tuning close to 13edo.
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| === Petrtri (13&21) === | | === Petrtri (13&21) === |