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'''Blackdye''' is a 10-note, [[dipentatonic scale|dipentatonic]], [[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]]. The scale can be generated by an alternating chain of [[10/9]] and [[6/5]]. Blackdye can, of course, be used in 5-limit edos 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.
'''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 Zarlino pattern 3L 2m 2s, LmsLmLs.
Blackdye is a 10-note extension of the [[nicetone]] scale 3L 2M 2s, LMsLMLs.


"Blackdye" is a name given by [[User:ks26|ks26]]. The name 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]]).
 
[[Category:AG scales]]


== Intervals ==
== Intervals ==
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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¢
Line 31: Line 29:
| 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¢
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== Modes ==
== Modes ==
=== Cyclic order ===
The modes arranged in cyclic order: (Note: The mode names are based on the 5-limit JI interpretation; modes in a less JI-like tuning may differ greatly from what these names suggest.)
The modes arranged in cyclic order: (Note: The mode names are based on the 5-limit JI interpretation; modes in a less JI-like tuning may differ greatly from what these names suggest.)
{| class="wikitable"
{| class="wikitable"
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! style="text-align:center;" |Name
! style="text-align:center;" |Name
|-
|-
| | SLMLSLMLSL
| | sLmLsLmLsL
| | Blackdye Bright Aeolian
| | Blackdye Acute Aeolian
|-
|-
| | LMLSLMLSLS
| | LmLsLmLsLs
| | Blackdye Dark Aeolian
| | Blackdye Grave Aeolian
|-
|-
| | MLSLMLSLSL
| | mLsLmLsLsL
| | Blackdye Locrian
| | Blackdye Locrian
|-
|-
| | LSLMLSLSLM
| | LsLmLsLsLm
| | Blackdye Ionian
| | Blackdye Ionian
|-
|-
| | SLMLSLSLML
| | sLmLsLsLmL
| | Blackdye Bright Dorian
| | Blackdye Acute Dorian
|-
|-
| | LMLSLSLMLS
| | LmLsLsLmLs
| | Blackdye Dark Dorian
| | Blackdye Grave Dorian
|-
|-
| | MLSLSLMLSL
| | mLsLsLmLsL
| | Blackdye Phrygian
| | Blackdye Phrygian
|-
|-
| | LSLSLMLSLM
| | LsLsLmLsLm
| | Blackdye Lydian
| | Blackdye Lydian
|-
|-
| | SLSLMLSLML
| | sLsLmLsLmL
| | Blackdye Bright Mixo
| | Blackdye Acute Mixo
|-
|-
| | LSLMLSLMLS
| | LsLmLsLmLs
| | Blackdye Dark Mixo
| | Blackdye Grave Mixo
|}
|}
=== By generator chain ===
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
* Acute Mixo > Acute Dorian > Acute Aeolian > Phrygian > Locrian


== Properties ==
== Properties ==
# 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.)-->
# 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
Line 204: Line 207:


== Example ==
== Example ==
An example in Blackdye Bright 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 27edo.mp3]] [[27edo]] (L:m:s = 4:2:1)


[[File:Blackdye Aeolian Example 22edo.mp3]] [[22edo]] (L:M:S = 3:2:1)
[[File:Blackdye Aeolian Example 29edo.mp3]] [[29edo]] (L:m:s = 4:3:1)


[[File:Blackdye Aeolian Example 27edo.mp3]] [[27edo]] (L:M:S = 4:2:1)
[[File:Blackdye Aeolian Example 32edo 5_2_1.mp3]] [[32edo]] (L:m:s = 5:2:1)


[[File:Blackdye Aeolian Example 29edo.mp3]] [[29edo]] (L:M:S = 4:3:1)
[[File:Blackdye Aeolian Example 34edo.mp3]] [[34edo]] (L:m:s = 5:3:1)


[[File:Blackdye Aeolian Example 32edo 5_2_1.mp3]] [[32edo]] (L:M:S = 5:2:1)
[[File:Blackdye Aeolian Example 36edo.mp3]] [[36edo]] (L:m:s = 5:4:1)


[[File:Blackdye Aeolian Example 34edo.mp3]] [[34edo]] (L:M:S = 5:3:1)
== Scala files ==
* [[SNS ((2/1, 3/2)-5, 10/9)-10]]


[[File:Blackdye Aeolian Example 36edo.mp3]] [[36edo]] (L:M:S = 5:4:1)
== Music ==
* [https://www.youtube.com/watch?v=HGaiFU_S2WI ''squid''] (2024) by [[Abnormality]]


== See also ==
== See also ==
* [[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
== 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]]
[[Category:Rank-3 scales]]
[[Category:Rank-3 scales]]
[[Category:Dipentatonic scales]]
[[Category:Step-nested scales]]
[[Category:Listen]]
[[Category:bipentatonic scales]]
[[Category:Flought scales]]
[[Category:Aberrismic theory]]
Retrieved from "https://en.xen.wiki/w/Blackdye"