User:BudjarnLambeth/Tailwind comma: Difference between revisions
Created page with "{{Novelty}} {{Infobox Interval | Name = tailwind comma | Color name = 89o1u1 | Comma = yes }} '''This page is about Budjarn Lambeth’s idiosyncratic use of this comma. For mainstream xenharmonic uses see 89/88.''' '''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..." |
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'''This page is about [[Budjarn Lambeth]]’s [[idiosyncratic]] use of this comma. For mainstream xenharmonic uses see [[89/88]].''' | |||
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{{Novelty}} | {{Novelty}} | ||
{{Infobox Interval | {{Infobox Interval | ||
| Name = tailwind comma | | Name = tailwind comma | ||
| Ratio = 89/88 | |||
| Color name = 89o1u1 | | Color name = 89o1u1 | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
'''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''', 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 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]]. | Tempering out 89/88 equates the harmonics [[11/8]] and [[89/64]]. | ||
Revision as of 05:26, 11 April 2025
This page is about Budjarn Lambeth’s idiosyncratic use of this comma. For mainstream xenharmonic uses see 89/88.
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This page presents a novelty topic.
It may contain ideas which are less likely to find practical applications in music, or numbers or structures that are arbitrary or exceedingly small, large, or complex. Novelty topics are often developed by a single person or a small group. As such, this page may also contain idiosyncratic terms, notation, or conceptual frameworks. |
| Interval information |
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.
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