User:BudjarnLambeth/Tailwind comma - Revision history

BudjarnLambeth at 09:57, 17 April 2025

2025-04-17T09:57:49Z

← Older revision		Revision as of 09:57, 17 April 2025
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	If ''not'' tempered out, then 89/88 is very well approximated by 1 step of [[36edf]].		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 ==		== Tailwind ==

BudjarnLambeth at 05:32, 11 April 2025

2025-04-11T05:32:33Z

← Older revision		Revision as of 05:32, 11 April 2025
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	'''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]].

BudjarnLambeth at 05:27, 11 April 2025

2025-04-11T05:27:37Z

← Older revision		Revision as of 05:27, 11 April 2025
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	{{Novelty}}		{{Novelty}}
			{{editable user page\|Do not remove anything, but feel free to add stuff (e.g. music, instruments, modes, subsets, tables, diagrams, any other observations.)}}


	{{Infobox Interval		{{Infobox Interval

BudjarnLambeth at 05:26, 11 April 2025

2025-04-11T05:26:44Z

← Older revision		Revision as of 05:26, 11 April 2025
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			<div style="border: 1px green solid; background-color: #efe; padding: 0.5em 1em; margin-bottom: 1em">
			'''This page is about [[Budjarn Lambeth]]’s [[idiosyncratic]] use of this comma. For mainstream xenharmonic uses see [[89/88]].'''
			</div>

	{{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
	}}		}}

	~~'''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]].		'''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]].

BudjarnLambeth: 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..."

2025-04-11T04:12:47Z

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..."

New page

{{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]] 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 ==
<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 after mythology or literature]]