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'''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]]).
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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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== 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)


[[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 ==
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* [[Diasem]], a similar diatonic-like mos detempering but for 2.3.7
* [[Diasem]], a similar diatonic-like mos detempering but for 2.3.7
* [[Nicetone]], a subset of blackdye
* [[Nicetone]], a subset of blackdye
== External links ==
* [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]]
Retrieved from "https://en.xen.wiki/w/Blackdye"