Diasem: Difference between revisions

Line 5:

|ja =

}}

'''Diasem''' is a 9-note [[Maximum variety|max-variety-3]], [[generator-offset]] scale with step pattern 5L 2M 2s, equivalent to the [[semiquartal]] ([[5L 4s]]) mos with two of the small steps made larger and the other two made smaller. Diasem is [[chiral]], with two rotationally non-equivalent variants: ''right-handed diasem'' LMLSLMLSL and ''left-handed diasem'' LSLMLSLML; these are mirror images. The fact that the small step of diatonic is made smaller results in [[26edo]] and [[31edo]] diasem having better melodic properties than the respective diatonic scales. The scale has two chains of fifth generators (with 5 notes and 4 notes, respectively) with offset a subminor third or a supermajor second. [[21edo]] is the smallest edo to support a non-degenerate diasem.

'''Diasem''' (also known as '''Tas''', from Archytas) is a 9-note [[Maximum variety|max-variety-3]], [[generator-offset]] scale with step pattern 5L 2M 2s, equivalent to the [[semiquartal]] ([[5L 4s]]) mos with two of the small steps made larger and the other two made smaller. Diasem is [[chiral]], with two rotationally non-equivalent variants: ''right-handed diasem'' LMLSLMLSL and ''left-handed diasem'' LSLMLSLML; these are mirror images. The fact that the small step of diatonic is made smaller results in [[26edo]] and [[31edo]] diasem having better melodic properties than the respective diatonic scales. The scale has two chains of fifth generators (with 5 notes and 4 notes, respectively) with offset a subminor third or a supermajor second. [[21edo]] is the smallest edo to support a non-degenerate diasem.

Diasem can be tuned as a [[Just intonation subgroup|2.3.7 subgroup]] JI scale or a tempered version thereof, where L represents [[9/8]], M represents [[28/27]], and S represents [[64/63]].

Line 804:

[[File:Diasem Phrygian Example 31edo.mp3]] [[31edo]], L:M:S = 5:2:1

== ~~Extensions~~ ==

== Supersets ==

The diasem scale extends to a 14-note AG scale: LmLsLmLsL and LsLmLsLmL both extend to the scale mcmcmsmcmcmsmc (c = L − m), with two 7-note mosses generated by the diasem's fifths separated by m. This scale is not chiral. This scale extends diasem like how [[blackdye]] is a 10-note non-chiral AG extension of the [[Zarlino]] scale's AG pattern 3L 2m 2s, LmsLmLs. The 14-note extension is one of:

* 5L 7m 2s (if m < c < L)

Line 813:

5L 7m 2s must have a diatonic fifth, since L > 2m > m + s. The 31edo tuning (c = 3\31, m = 2\31, s = 1\31) of the scale is ideal for the 81/80-tempering 2.3.5.7 interpretation.

Another ~~extension~~ is scscsmscscsmsc, with c = L - s (5L 2m 7s if c > m). 31edo diasem yields 5L 2m 7s with step ratio 4:2:1.

Another superset is scscsmscscsmsc, with c = L - s (5L 2m 7s if c > m). 31edo diasem yields 5L 2m 7s with step ratio 4:2:1.

Both these tunings, 5L 7m 2s and 5L 2m 7s, have been named '''crossdye''' ("crossed eyes" referring to the two copies of 5L 2s diatonic + "blackdye", courtesy of [[User:CellularAutomaton|cellularAutomaton]]). 5L 7m 2s could be called ''chromatic crossdye'' and 5L 2m 7s could be called ''dietic crossdye''.

2.3.7 JI diasem also has

* a 19-note superset: mLsmsLmsmLsmsLmsmLs (5L 7m 7s), with L = 2187/2048, m = 28/27, and s = 64/63,

* a 24-note superset: mLsmLmLsmLmLmsLmLmLsmLmLmsLmL (12L 12m 5s), with L = 28/27, s = 64/63, and s = 531441/524188.

== See also ==

@@ Line 5: / Line 5: @@
 |ja =
 }}
-'''Diasem''' is a 9-note [[Maximum variety|max-variety-3]], [[generator-offset]] scale with step pattern 5L 2M 2s, equivalent to the [[semiquartal]] ([[5L 4s]]) mos with two of the small steps made larger and the other two made smaller. Diasem is [[chiral]], with two rotationally non-equivalent variants: ''right-handed diasem'' LMLSLMLSL and ''left-handed diasem'' LSLMLSLML; these are mirror images. The fact that the small step of diatonic is made smaller results in [[26edo]] and [[31edo]] diasem having better melodic properties than the respective diatonic scales. The scale has two chains of fifth generators (with 5 notes and 4 notes, respectively) with offset a subminor third or a supermajor second. [[21edo]] is the smallest edo to support a non-degenerate diasem.
+'''Diasem''' (also known as '''Tas''', from Archytas) is a 9-note [[Maximum variety|max-variety-3]], [[generator-offset]] scale with step pattern 5L 2M 2s, equivalent to the [[semiquartal]] ([[5L 4s]]) mos with two of the small steps made larger and the other two made smaller. Diasem is [[chiral]], with two rotationally non-equivalent variants: ''right-handed diasem'' LMLSLMLSL and ''left-handed diasem'' LSLMLSLML; these are mirror images. The fact that the small step of diatonic is made smaller results in [[26edo]] and [[31edo]] diasem having better melodic properties than the respective diatonic scales. The scale has two chains of fifth generators (with 5 notes and 4 notes, respectively) with offset a subminor third or a supermajor second. [[21edo]] is the smallest edo to support a non-degenerate diasem.
 Diasem can be tuned as a [[Just intonation subgroup|2.3.7 subgroup]] JI scale or a tempered version thereof, where L represents [[9/8]], M represents [[28/27]], and S represents [[64/63]].
@@ Line 804: / Line 804: @@
 [[File:Diasem Phrygian Example 31edo.mp3]] [[31edo]], L:M:S = 5:2:1
-== Extensions ==
+== Supersets ==
 The diasem scale extends to a 14-note AG scale: LmLsLmLsL and LsLmLsLmL both extend to the scale mcmcmsmcmcmsmc (c = L &minus; m), with two 7-note mosses generated by the diasem's fifths separated by m. This scale is not chiral. This scale extends diasem like how [[blackdye]] is a 10-note non-chiral AG extension of the [[Zarlino]] scale's AG pattern 3L 2m 2s, LmsLmLs. The 14-note extension is one of:
 * 5L 7m 2s (if m < c < L)
@@ Line 813: / Line 813: @@
 L 7m 2s must have a diatonic fifth, since L > 2m > m + s. The 31edo tuning (c = 3\31, m = 2\31, s = 1\31) of the scale is ideal for the 81/80-tempering 2.3.5.7 interpretation.
-Another extension is scscsmscscsmsc, with c = L - s (5L 2m 7s if c > m). 31edo diasem yields 5L 2m 7s with step ratio 4:2:1.
+Another superset is scscsmscscsmsc, with c = L - s (5L 2m 7s if c > m). 31edo diasem yields 5L 2m 7s with step ratio 4:2:1.
 Both these tunings, 5L 7m 2s and 5L 2m 7s, have been named '''crossdye''' ("crossed eyes" referring to the two copies of 5L 2s diatonic + "blackdye", courtesy of [[User:CellularAutomaton|cellularAutomaton]]). 5L 7m 2s could be called ''chromatic crossdye'' and 5L 2m 7s could be called ''dietic crossdye''.
+.3.7 JI diasem also has
+* a 19-note superset: mLsmsLmsmLsmsLmsmLs (5L 7m 7s), with L = 2187/2048, m = 28/27, and s = 64/63,
+* a 24-note superset: mLsmLmLsmLmLmsLmLmLsmLmLmsLmL (12L 12m 5s), with L = 28/27, s = 64/63, and s = 531441/524188.
 == See also ==