89/88

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Interval information

Ratio

89/88

Subgroup monzo

2.11.89 [-3 -1 1⟩

Size in cents

19.56217¢

Name

tailwind comma

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, 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 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