User:BudjarnLambeth/Tailwind comma: Difference between revisions
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{{editable user page|Do not remove anything, but feel free to add stuff (e.g. music, instruments, modes, subsets, tables, diagrams, any other observations.)}} | {{editable user page|Do not remove anything, but feel free to add stuff (e.g. music, instruments, modes, subsets, tables, diagrams, any other observations.)}} | ||
Latest revision as of 09:53, 17 October 2026
This page is about Budjarn Lambeth’s idiosyncratic use of this comma. For mainstream xenharmonic uses see 89/88.
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reduced
89/88, a.k.a. the tailwind comma, is an 89-limit superparticular comma tempered out by two of the Batch 89 temperaments.
Tempering this comma on its own gives the tailwind temperament, a rank-2 2.11.89 subgroup temperament.
Tempering out 89/88 equates the harmonics 11/8 and 89/64.
If not tempered out, then 89/88 is very well approximated by 1 step of 36edf.
Etymology
The name is meant to invoke a vast and beautiful sky, to fit with the theming of the other Batch 89 temperaments.
Tailwind
Equal Temperament Mappings 2 11 89 [ ⟨ 2 7 13 ] ⟨ 9 31 58 ] ⟩ Reduced Mapping 2 11 89 [ ⟨ 1 4 7 ] ⟨ 0 -1 -1 ] ⟩ TE Generator Tunings (cents) ⟨1200.9330, 648.6921] TE Step Tunings (cents) ⟨166.43584, 96.45125] TE Tuning Map (cents) ⟨1200.933, 4155.040, 7757.839] TE Mistunings (cents) ⟨0.933, 3.722, -13.041] 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. Complexity 0.118010 Adjusted Error 9.221690 cents TE Error 1.424038 cents/octave Unison Vector [-3, -1, 1⟩ (89:88) Scala Files Number of notes per octave TE 2 9 Pure octaves 2 9