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| {{Novelty}}
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| {{Infobox Interval | | {{Infobox Interval |
| | Name = tailwind comma
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| | Color name = 89o1u1 | | | Color name = 89o1u1 |
| | Comma = yes | | | Comma = yes |
| }} | | }} |
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| '''89/88''', a.k.a. the '''tailwind comma''', is an [[89-limit]] [[superparticular]] [[comma]] tempered out by two of the [[Batch 89 temperaments]]. | | '''89/88''' is an [[89-limit]] [[superparticular]] [[comma]]. |
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| Tempering this comma on its own gives the tailwind temperament, a 2.11.89 [[subgroup]] temperament.
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| Tempering out 89/88 equates the harmonics [[11/8]] and [[89/64]].
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| If ''not'' tempered out, then 89/88 is very well approximated by 1 step of [[36edf]].
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| == Tailwind ==
| | For [[Budjarn Lambeth]]’s idiosyncratic uses for this comma, see [[User:BudjarnLambeth/Tailwind comma]]. |
| <pre>
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| Equal Temperament Mappings
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| 2 11 89
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| [ ⟨ 2 7 13 ] | |
| ⟨ 9 31 58 ] ⟩
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| Reduced Mapping
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| 2 11 89
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| [ ⟨ 1 4 7 ] | |
| ⟨ 0 -1 -1 ] ⟩
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| TE Generator Tunings (cents)
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| ⟨1200.9330, 648.6921]
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| TE Step Tunings (cents)
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| ⟨166.43584, 96.45125]
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| TE Tuning Map (cents)
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| ⟨1200.933, 4155.040, 7757.839]
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| TE Mistunings (cents)
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| ⟨0.933, 3.722, -13.041]
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| These calculations use inharmonic TE. Subgroup TE will not work because the basis is not a subgroup of the rational numbers or has a redundant entry or something else is wrong.
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| Complexity 0.118010
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| Adjusted Error 9.221690 cents
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| TE Error 1.424038 cents/octave
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| Unison Vector
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| [-3, -1, 1⟩ (89:88)
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| Scala Files
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| Number of notes per octave
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| TE 2 9
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| Pure octaves 2 9
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| </pre>
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| [[Category:Commas named for other reasons]]
| | {{Stub}} |