Blackdye: Difference between revisions

'''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'', 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]]).

!|[[TAMNAMS|1-steps]]

!|[[TAMNAMS|2-steps]]

!|[[TAMNAMS|3-steps]]

!|[[TAMNAMS|4-steps]]

!|[[TAMNAMS|5-steps]]

!|[[TAMNAMS|6-steps]]

!|[[TAMNAMS|7-steps]]

!|[[TAMNAMS|8-steps]]

!|[[TAMNAMS|9-steps]]

| | sLmLsLmLsL

| | Blackdye Acute Aeolian

| | LmLsLmLsLs

| | Blackdye Grave Aeolian

| | mLsLmLsLsL

| | LsLmLsLsLm

| | sLmLsLsLmL

| | Blackdye Acute Dorian

| | LmLsLsLmLs

| | Blackdye Grave Dorian

| | mLsLsLmLsL

| | LsLsLmLsLm

| | sLsLmLsLmL

| | Blackdye Acute Mixo

| | LsLmLsLmLs

| | Blackdye Grave Mixo

# 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.)-->

# Assuming positive step sizes, the fifth is:

#* sharper than 700¢, if L + 3s > 2m

#* equal to 700¢, if L + 3s = 2m

#* flatter than 700¢, if L + 3s < 2m

! rowspan="2" |L:m:s

! colspan="9" |Degrees of the mode sLmLsLmLsL

An example in Blackdye Acute Aeolian, sLmLsLmLsL ([[:File:Blackdye Aeolian Example Score.pdf|score]])

 

 

[[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 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 36edo.mp3]] [[36edo]] (L:m:s = 5:4:1)

* [[SNS ((2/1, 3/2)-5, 10/9)-10]]

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

[[Category:Step-nested scales]]

[[Category:Aberrismic theory]]