89/88: Difference between revisions

← Older edit Newer edit →

VisualWikitext

@@ Line 2: / Line 2: @@
 {{Infobox Interval
-| Name = sky comma
+| Name = tailwind comma
 | Color name = 89o1u1
 | Comma = yes
 }}
-'''89/88''', a.k.a. the '''sky comma''', is an [[89-limit]] [[superparticular]] [[comma]] tempered out by two of the [[Batch 89 temperaments]]. Tempering out this comma equates the harmonics [[11/8]] and [[89/64]].
+'''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 sky temperament, a 2.11.89 [[subgroup]] temperament.
+Tempering this comma on its own gives the tailwind temperament, a 2.11.89 [[subgroup]] temperament.
-It is very well approximated by 1 step of [[36edf]].
+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 ==
+<pre>
+Equal Temperament Mappings
+	11	89
+[ ⟨	2	7	13	]
+⟨	9	31	58	] ⟩
+Reduced Mapping
+	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]]