Blackdye - Revision history

Inthar: /* Example */

2026-02-16T20:58:34Z

Example

← Older revision		Revision as of 20:58, 16 February 2026
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	[[File:Blackdye Aeolian Example 36edo.mp3]] [[36edo]] (L:m:s = 5:4:1)		[[File:Blackdye Aeolian Example 36edo.mp3]] [[36edo]] (L:m:s = 5:4:1)

			A fugue exposition:

			[[File:34edo blackdye fugue expo.mp3]]

	== Scala files ==		== Scala files ==

Inthar: /* External links */

2024-09-29T01:12:54Z

External links

← Older revision		Revision as of 01:12, 29 September 2024
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	== External links ==		== External links ==
	[https://sw3.lumipakkanen.com/scale/9kkCrGrsY ~~Play~~ 27edo blackdye in Scale Workshop]		* [https://sw3.lumipakkanen.com/scale/9kkiMRL__ 5-limit JI blackdye in Scale Workshop]
			* [https://sw3.lumipakkanen.com/scale/9kkCrGrsY 27edo blackdye in Scale Workshop]
			* [https://sw3.lumipakkanen.com/scale/9kkWpQX9k 32edo blackdye in Scale Workshop]
			* [https://sw3.lumipakkanen.com/scale/9kkLl2oWP 34edo blackdye in Scale Workshop]

	[[Category:GO scales]]		[[Category:GO scales]]
	[[Category:Rank-3 scales]]		[[Category:Rank-3 scales]]

Inthar: /* See also */ Add SW3 link for noodling in blackdye

2024-09-29T01:09:42Z

See also: Add SW3 link for noodling in blackdye

← Older revision		Revision as of 01:09, 29 September 2024
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	* [[Nicetone]], a subset of blackdye		* [[Nicetone]], a subset of blackdye

			== External links ==
			[https://sw3.lumipakkanen.com/scale/9kkCrGrsY Play 27edo blackdye in Scale Workshop]
	[[Category:GO scales]]		[[Category:GO scales]]
	[[Category:Rank-3 scales]]		[[Category:Rank-3 scales]]

Inthar: /* Example */

2024-09-29T00:55:59Z

Example

← Older revision		Revision as of 00:55, 29 September 2024
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	== Example ==		== Example ==
	An example in Blackdye Acute Aeolian, ~~SLMLSLMLSL~~ ([[:File:Blackdye Aeolian Example Score.pdf\|score]])		An example in Blackdye Acute Aeolian, sLmLsLmLsL ([[:File:Blackdye Aeolian Example Score.pdf\|score]])

	[[File:Blackdye Aeolian Example 22edo.mp3]] [[22edo]] (L:m:s = 3:2:1)		[[File:Blackdye Aeolian Example 22edo.mp3]] [[22edo]] (L:m:s = 3:2:1)

Inthar: /* By generator chain */

2024-08-12T16:14:06Z

By generator chain

← Older revision		Revision as of 16:14, 12 August 2024
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	Because blackdye has two chains of 5 fifth generators, it has two chains of 5 modes each separated by one generator:		Because blackdye has two chains of 5 fifth generators, it has two chains of 5 modes each separated by one generator:
	* Lydian > Ionian > Grave Mixo > Grave Dorian > Grave Aeolian		* Lydian > Ionian > Grave Mixo > Grave Dorian > Grave Aeolian
	# Acute Mixo > Acute Dorian > Acute Aeolian > Phrygian > Locrian		* Acute Mixo > Acute Dorian > Acute Aeolian > Phrygian > Locrian

	== Properties ==		== Properties ==

Inthar: Step label casing

2024-08-12T16:13:55Z

Step label casing

← Older revision		Revision as of 16:13, 12 August 2024
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	! style="text-align:center;" \|Name		! style="text-align:center;" \|Name
	\|-		\|-
	\| \| ~~SLMLSLMLSL~~		\| \| sLmLsLmLsL
	\| \| Blackdye Acute Aeolian		\| \| Blackdye Acute Aeolian
	\|-		\|-
	\| \| ~~LMLSLMLSLS~~		\| \| LmLsLmLsLs
	\| \| Blackdye Grave Aeolian		\| \| Blackdye Grave Aeolian
	\|-		\|-
	\| \| ~~MLSLMLSLSL~~		\| \| mLsLmLsLsL
	\| \| Blackdye Locrian		\| \| Blackdye Locrian
	\|-		\|-
	\| \| ~~LSLMLSLSLM~~		\| \| LsLmLsLsLm
	\| \| Blackdye Ionian		\| \| Blackdye Ionian
	\|-		\|-
	\| \| ~~SLMLSLSLML~~		\| \| sLmLsLsLmL
	\| \| Blackdye Acute Dorian		\| \| Blackdye Acute Dorian
	\|-		\|-
	\| \| ~~LMLSLSLMLS~~		\| \| LmLsLsLmLs
	\| \| Blackdye Grave Dorian		\| \| Blackdye Grave Dorian
	\|-		\|-
	\| \| ~~MLSLSLMLSL~~		\| \| mLsLsLmLsL
	\| \| Blackdye Phrygian		\| \| Blackdye Phrygian
	\|-		\|-
	\| \| ~~LSLSLMLSLM~~		\| \| LsLsLmLsLm
	\| \| Blackdye Lydian		\| \| Blackdye Lydian
	\|-		\|-
	\| \| ~~SLSLMLSLML~~		\| \| sLsLmLsLmL
	\| \| Blackdye Acute Mixo		\| \| Blackdye Acute Mixo
	\|-		\|-
	\| \| ~~LSLMLSLMLS~~		\| \| LsLmLsLmLs
	\| \| Blackdye Grave Mixo		\| \| Blackdye Grave Mixo
	\|}		\|}
	=== By generator chain ===		=== By generator chain ===
	Because blackdye has two chains of 5 fifth generators, it has two chains of 5 modes each separated by one generator:		Because blackdye has two chains of 5 fifth generators, it has two chains of 5 modes each separated by one generator:
	~~# LSLSLMLSLM (~~Lydian) > ~~LSLMLSLSLM (~~Ionian) > ~~LSLMLSLMLS (~~Grave Mixo) > ~~LMLSLSLMLS (~~Grave Dorian) > ~~LMLSLMLSLS (~~Grave Aeolian)		* Lydian > Ionian > Grave Mixo > Grave Dorian > Grave Aeolian
	# ~~SLSLMLSLML (~~Acute Mixo) > ~~SLMLSLSLML (~~Acute Dorian) > ~~SLMLSLMLSL (~~Acute Aeolian) > ~~MLSLSLMLSL (~~Phrygian) > ~~MLSLMLSLSL (~~Locrian)		# Acute Mixo > Acute Dorian > Acute Aeolian > Phrygian > Locrian

	== Properties ==		== Properties ==
	# Assuming positive step sizes, the fifth (3L + M + 2S) of blackdye must be a diatonic fifth.<!--		# Assuming positive step sizes, the fifth (3L + m + 2s) of blackdye must be a diatonic fifth.<!--
	#* (To see this: Consider the chain of fifths generated by the fifth. The diatonic chroma = 7 fifths - 4 octaves = 21L + 7M + ~~14S~~ - (20L + 8M + ~~12S~~) = L - M + 2S. Since L - M >= 0, this must always be nonnegative, so the fifth must be >= 4\7. The fifth cannot be sharper than 3\5, since it generates the [[2L 3s\|2L' 3s']] subset of blackdye with L' = ML and s' = SL.)-->		#* (To see this: Consider the chain of fifths generated by the fifth. The diatonic chroma = 7 fifths - 4 octaves = 21L + 7m + 14s - (20L + 8m + 12s) = L - m + 2s. Since L - m >= 0, this must always be nonnegative, so the fifth must be >= 4\7. The fifth cannot be sharper than 3\5, since it generates the [[2L 3s\|2L' 3s']] subset of blackdye with L' = mL and s' = sL.)-->
	# Assuming positive step sizes, the fifth is:		# Assuming positive step sizes, the fifth is:
	#* sharper than 700¢, if L + 3S > 2M		#* sharper than 700¢, if L + 3s > 2m
	#* equal to 700¢, if L + 3S = 2M		#* equal to 700¢, if L + 3s = 2m
	#* flatter than 700¢, if L + 3S < 2M		#* flatter than 700¢, if L + 3s < 2m

	== Tunings ==		== Tunings ==
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	\|+ Blackdye tunings		\|+ Blackdye tunings
	! rowspan="2" \|Tuning		! rowspan="2" \|Tuning
	! rowspan="2" \|L:M:S		! rowspan="2" \|L:m:s
	! colspan="9" \|Degrees of the mode ~~SLMLSLMLSL~~		! colspan="9" \|Degrees of the mode sLmLsLmLsL
	\|-		\|-
	!1!!2!!3!!4!!5!!6!!7!!8!!9		!1!!2!!3!!4!!5!!6!!7!!8!!9
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	An example in Blackdye Acute Aeolian, SLMLSLMLSL ([[:File:Blackdye Aeolian Example Score.pdf\|score]])		An example in Blackdye Acute Aeolian, SLMLSLMLSL ([[:File:Blackdye Aeolian Example Score.pdf\|score]])

	[[File:Blackdye Aeolian Example 22edo.mp3]] [[22edo]] (L:M:S = 3:2:1)		[[File:Blackdye Aeolian Example 22edo.mp3]] [[22edo]] (L:m:s = 3:2:1)

	[[File:Blackdye Aeolian Example 27edo.mp3]] [[27edo]] (L:M:S = 4:2:1)		[[File:Blackdye Aeolian Example 27edo.mp3]] [[27edo]] (L:m:s = 4:2:1)

	[[File:Blackdye Aeolian Example 29edo.mp3]] [[29edo]] (L:M:S = 4:3:1)		[[File:Blackdye Aeolian Example 29edo.mp3]] [[29edo]] (L:m:s = 4:3:1)

	[[File:Blackdye Aeolian Example 32edo 5_2_1.mp3]] [[32edo]] (L:M:S = 5:2:1)		[[File:Blackdye Aeolian Example 32edo 5_2_1.mp3]] [[32edo]] (L:m:s = 5:2:1)

	[[File:Blackdye Aeolian Example 34edo.mp3]] [[34edo]] (L:M:S = 5:3:1)		[[File:Blackdye Aeolian Example 34edo.mp3]] [[34edo]] (L:m:s = 5:3:1)

	[[File:Blackdye Aeolian Example 36edo.mp3]] [[36edo]] (L:M:S = 5:4:1)		[[File:Blackdye Aeolian Example 36edo.mp3]] [[36edo]] (L:m:s = 5:4:1)

	== Scala files ==		== Scala files ==

Fredg999: Terms, step label casing

2024-08-12T16:00:32Z

Terms, step label casing

← Older revision		Revision as of 16:00, 12 August 2024
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	\|ja =		\|ja =
	}}		}}
	'''Blackdye''' (also denoted 3s in [[groundfault]]'s [[aberrismic theory]]) is a 10-note, [[bipentatonic scale\|bipentatonic]], [[generator-offset]] scale with step ~~pattern~~ 5L ~~2M 3S~~ (~~SLMLSLMLSL~~), equivalent to the [[5L 5s]] mos with two of the small steps made larger and the other three made smaller. Unlike [[diasem]], another diatonic-based scale with comma steps, blackdye is not [[chirality\|chiral]]. It can be tuned as a [[5-limit]] JI scale or a tempered version thereof, where L represents [[10/9]], M represents [[16/15]], and S represents [[81/80]]. Under this interpretation, the scale has two chains of [[3/2]] generators with an offset of [[10/9]]. Blackdye can, of course, be used in 5-limit [[equal temperament]]s that do not temper out [[81/80]], such as [[22edo]] and [[34edo]]; however, there are more exotic tunings of the scale, such as [[32edo]]'s 5:2:1 and [[37edo]]'s 6:2:1, which have [[neogothic]] thirds and [[naiadic]]s instead of 5-limit thirds and Pythagorean thirds, and [[29edo]]'s 4:3:1 and [[36edo]]'s 5:4:1, which have submajor and supraminor thirds instead of 5-limit thirds. One can even interpret diasem as a [[negative-s blackdye\|9-note subset of blackdye with a negative s step]].		'''Blackdye''' (also denoted 3s in [[groundfault]]'s [[aberrismic theory]]) is a 10-note, [[bipentatonic scale\|bipentatonic]], [[generator-offset]] scale with [[step signature]] 5L 2m 3s ([[step pattern]] sLmLsLmLsL), equivalent to the [[5L 5s]] mos with two of the small steps made larger and the other three made smaller. Unlike [[diasem]], another diatonic-based scale with comma steps, blackdye is not [[chirality\|chiral]]. It can be tuned as a [[5-limit]] JI scale or a tempered version thereof, where L represents [[10/9]], m represents [[16/15]], and s represents [[81/80]]. Under this interpretation, the scale has two chains of [[3/2]] generators with an offset of [[10/9]]. Blackdye can, of course, be used in 5-limit [[equal temperament]]s that do not temper out [[81/80]], such as [[22edo]] and [[34edo]]; however, there are more exotic tunings of the scale, such as [[32edo]]'s 5:2:1 and [[37edo]]'s 6:2:1, which have [[neogothic]] thirds and [[naiadic]]s instead of 5-limit thirds and Pythagorean thirds, and [[29edo]]'s 4:3:1 and [[36edo]]'s 5:4:1, which have submajor and supraminor thirds instead of 5-limit thirds. One can even interpret diasem as a [[negative-s blackdye\|9-note subset of blackdye with a negative s step]].

	Blackdye is a 10-note extension of the [[nicetone]] scale 3L 2m 2s, ~~LmsLmLs~~.		Blackdye is a 10-note extension of the [[nicetone]] scale 3L 2M 2s, LMsLMLs.

	''Blackdye'', a name given by groundfault, is a pun on "Blackwood" and "diatonic" since its step sizes are intermediate between that of [[diatonic]] (5L 2s) and [[Blackwood]][10] ([[5L 5s]]).		''Blackdye'', a name given by groundfault, is a pun on "Blackwood" and "diatonic" since its step sizes are intermediate between that of [[diatonic]] (5L 2s) and [[Blackwood]][10] ([[5L 5s]]).

Francium: +music

2024-02-16T17:19:37Z

+music

← Older revision		Revision as of 17:19, 16 February 2024
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	== Scala files ==		== Scala files ==
	* [[SNS ((2/1, 3/2)-5, 10/9)-10]]		* [[SNS ((2/1, 3/2)-5, 10/9)-10]]

			== Music ==
			* [https://www.youtube.com/watch?v=HGaiFU_S2WI ''squid''] (2024) by [[Abnormality]]

	== See also ==		== See also ==
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	[[Category:Rank-3 scales]]		[[Category:Rank-3 scales]]
	[[Category:Step-nested scales]]		[[Category:Step-nested scales]]
			[[Category:Listen]]
	[[Category:bipentatonic scales]]		[[Category:bipentatonic scales]]
	[[Category:Flought scales]]		[[Category:Flought scales]]
	[[Category:Aberrismic theory]]		[[Category:Aberrismic theory]]

Inthar: /* Intervals */

2024-02-11T12:56:11Z

Intervals

← Older revision		Revision as of 12:56, 11 February 2024
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	! [[34edo]] (L:m:s = 5:3:1)		! [[34edo]] (L:m:s = 5:3:1)
	\|-		\|-
	!\|[[TAMNAMS\|1-~~step~~]]		!\|[[TAMNAMS\|1-steps]]
	\| s<br/>m<br/>L		\| s<br/>m<br/>L
	\| 81/80, 21.51¢<br/>16/15, 111.73¢<br/>10/9, 182.40¢		\| 81/80, 21.51¢<br/>16/15, 111.73¢<br/>10/9, 182.40¢
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	\| 1\34, 35.29¢<br/>3\34, 105.88¢<br/>5\34, 176.47¢		\| 1\34, 35.29¢<br/>3\34, 105.88¢<br/>5\34, 176.47¢
	\|-		\|-
	!\|[[TAMNAMS\|2-~~step~~]]		!\|[[TAMNAMS\|2-steps]]
	\| L + s<br/>L + m		\| L + s<br/>L + m
	\| 9/8, 203.91¢<br/>32/27, 294.14¢		\| 9/8, 203.91¢<br/>32/27, 294.14¢
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	\| 6\34, 211.77¢<br/>8\34, 282.35¢		\| 6\34, 211.77¢<br/>8\34, 282.35¢
	\|-		\|-
	!\|[[TAMNAMS\|3-~~step~~]]		!\|[[TAMNAMS\|3-steps]]
	\| L + 2s<br/>L + m + s<br/>2L + s<br/>2L + m		\| L + 2s<br/>L + m + s<br/>2L + s<br/>2L + m
	\| 729/640‚ 225.42¢<br/>6/5, 315.64¢<br/>5/4, 386.31¢<br/>320/243, 476.54¢		\| 729/640‚ 225.42¢<br/>6/5, 315.64¢<br/>5/4, 386.31¢<br/>320/243, 476.54¢
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	\| 7\34, 247.06¢<br/>9\34, 317.65¢<br/>11\34, 388.24¢<br/>13\34, 458.82¢		\| 7\34, 247.06¢<br/>9\34, 317.65¢<br/>11\34, 388.24¢<br/>13\34, 458.82¢
	\|-		\|-
	!\|[[TAMNAMS\|4-~~step~~]]		!\|[[TAMNAMS\|4-steps]]
	\| 2L + 2s<br/>2L + m + s		\| 2L + 2s<br/>2L + m + s
	\| 81/64, 407.82¢<br/>4/3, 498.04¢		\| 81/64, 407.82¢<br/>4/3, 498.04¢
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	\| 12\34, 423.53¢<br/>14\34, 494.12¢		\| 12\34, 423.53¢<br/>14\34, 494.12¢
	\|-		\|-
	!\|[[TAMNAMS\|5-~~step~~]]		!\|[[TAMNAMS\|5-steps]]
	\| 2L + m + 2s<br/>2L + 2m + s<br/>3L + 2s<br/>3L + m + s		\| 2L + m + 2s<br/>2L + 2m + s<br/>3L + 2s<br/>3L + m + s
	\| 27/20, 519.55¢<br/>64/45, 609.78¢<br/>45/32, 590.22¢<br/>40/27, 680.45¢		\| 27/20, 519.55¢<br/>64/45, 609.78¢<br/>45/32, 590.22¢<br/>40/27, 680.45¢
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	\| 15\34, 529.41¢<br/>17\34, 600.00¢<br/>17\34, 600.00¢<br/>19\34, 670.59¢		\| 15\34, 529.41¢<br/>17\34, 600.00¢<br/>17\34, 600.00¢<br/>19\34, 670.59¢
	\|-		\|-
	!\|[[TAMNAMS\|6-~~step~~]]		!\|[[TAMNAMS\|6-steps]]
	\| 3L + m + 2s<br/>3L + 2m + s		\| 3L + m + 2s<br/>3L + 2m + s
	\| 3/2, 701.96¢<br/>128/81, 792.18¢		\| 3/2, 701.96¢<br/>128/81, 792.18¢
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	\| 20\34, 705.88¢<br/>22\34, 776.47¢		\| 20\34, 705.88¢<br/>22\34, 776.47¢
	\|-		\|-
	!\|[[TAMNAMS\|7-~~step~~]]		!\|[[TAMNAMS\|7-steps]]
	\| 3L + m + 3s<br/>3L + 2m + 2s<br/>4L + m + 2s<br/>4L + 2m + s		\| 3L + m + 3s<br/>3L + 2m + 2s<br/>4L + m + 2s<br/>4L + 2m + s
	\| 243/160, 723.46¢<br/>8/5, 813.69¢<br/>5/3, 884.36¢<br/>1280/729, 974.58¢		\| 243/160, 723.46¢<br/>8/5, 813.69¢<br/>5/3, 884.36¢<br/>1280/729, 974.58¢
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	\| 21\34, 741.18¢<br/>23\34, 811.77¢<br/>25\34, 882.35¢<br/>27\34, 952.94¢		\| 21\34, 741.18¢<br/>23\34, 811.77¢<br/>25\34, 882.35¢<br/>27\34, 952.94¢
	\|-		\|-
	!\|[[TAMNAMS\|8-~~step~~]]		!\|[[TAMNAMS\|8-steps]]
	\| 4L + m + 3s<br/>4L + 2m + 2s		\| 4L + m + 3s<br/>4L + 2m + 2s
	\| 27/16, 905.87¢<br/>16/9, 996.09¢		\| 27/16, 905.87¢<br/>16/9, 996.09¢
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	\| 26\34, 917.65¢<br/>28\34, 988.24¢		\| 26\34, 917.65¢<br/>28\34, 988.24¢
	\|-		\|-
	!\|[[TAMNAMS\|9-~~step~~]]		!\|[[TAMNAMS\|9-steps]]
	\| 5L + 2m + s<br/>5L + m + 2s<br/>4L + 2m + 2s		\| 5L + 2m + s<br/>5L + m + 2s<br/>4L + 2m + 2s
	\| 9/5, 1017.60¢<br/>15/8, 1088.27¢<br/>160/81, 1178.49¢		\| 9/5, 1017.60¢<br/>15/8, 1088.27¢<br/>160/81, 1178.49¢

Inthar: /* See also */

2024-02-09T21:21:29Z

← Older revision		Revision as of 21:21, 9 February 2024
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	[[Category:GO scales]]		[[Category:GO scales]]
	[[Category:Rank-3 scales]]		[[Category:Rank-3 scales]]
	[[Category:Step-nested ~~scale~~]]		[[Category:Step-nested scales]]
	[[Category:bipentatonic scales]]		[[Category:bipentatonic scales]]
	[[Category:Flought scales]]		[[Category:Flought scales]]
	[[Category:Aberrismic theory]]		[[Category:Aberrismic theory]]