Blackdye: Difference between revisions

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'''Blackdye''' is a 10-note ~~[[AG]], [[Maximum variety|MV4]]~~ 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 minor thirds and major thirds. 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 [[29edo]]'s 4:3:1, [[32edo]]'s 4:3:2 and 5:2:1, and [[36edo]]'s 5:4:1.

'''Blackdye''' is a 10-note 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 minor thirds and major thirds (however, the scale is not [[AG]] and not [[MV3]]). 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 [[29edo]]'s 4:3:1, [[32edo]]'s 4:3:2 and 5:2:1, and [[36edo]]'s 5:4:1.

"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]]).

== Intervals ==

The following is a table of blackdye intervals and their abstract sizes in terms of L, m and s. Given concrete sizes of L, m and s in edo steps or cents, you can compute the concrete size of any interval in blackdye using the following expressions.

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-'''Blackdye''' is a 10-note [[AG]], [[Maximum variety|MV4]] 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 minor thirds and major thirds. 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 [[29edo]]'s 4:3:1, [[32edo]]'s 4:3:2 and 5:2:1, and [[36edo]]'s 5:4:1.
+'''Blackdye''' is a 10-note 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 minor thirds and major thirds (however, the scale is not [[AG]] and not [[MV3]]). 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 [[29edo]]'s 4:3:1, [[32edo]]'s 4:3:2 and 5:2:1, and [[36edo]]'s 5:4:1.
 "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]]).
 == Intervals ==
 The following is a table of blackdye intervals and their abstract sizes in terms of L, m and s. Given concrete sizes of L, m and s in edo steps or cents, you can compute the concrete size of any interval in blackdye using the following expressions.