89/88: Difference between revisions

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{{Novelty}}
{{Infobox Interval
{{Infobox Interval
| Name = tailwind comma
| 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''' is an [[89-limit]] [[superparticular]] [[comma]].
 
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 ==
For [[Budjarn Lambeth]]’s idiosyncratic uses for this comma, see [[User:BudjarnLambeth/Tailwind comma]].
<pre>
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
</pre>


[[Category:Commas named for other reasons]]
{{Stub}}

Latest revision as of 04:37, 30 July 2025

Interval information
Ratio 89/88
Subgroup monzo 2.11.89 [-3 -1 1⟩
Size in cents 19.56217¢
Name(s) missing ? 
Color name 89o1u1
FJS name [math]\displaystyle{ \text{A1}^{89}_{11} }[/math]
Special properties superparticular,
reduced
Tenney height (log2 nd) 12.9352
Weil height (log2 max(n, d)) 12.9515
Wilson height (sopfr(nd)) 106
Comma size small
Open this interval in xen-calc

89/88 is an 89-limit superparticular comma.

For Budjarn Lambeth’s idiosyncratic uses for this comma, see User:BudjarnLambeth/Tailwind comma.


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