Diasem: Difference between revisions

Line 5:

|ja =

}}

'''Diasem''' is a 9-note [[Maximum variety|max-variety-3]], [[AG]] 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 has two [[chirality|rotationally non-equivalent variants]], ''right-handed diasem'' LMLSLMLSL and ''left-handed diasem'' LSLMLSLML; these are mirror images. It 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]]. 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 can be generated by an alternating chain of subminor thirds and supermajor seconds. [[21edo]] is the smallest edo to non-trivially support diasem.

'''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 has two [[chirality|rotationally non-equivalent variants]], ''right-handed diasem'' LMLSLMLSL and ''left-handed diasem'' LSLMLSLML; these are mirror images. It 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]]. 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 can be generated by an alternating chain of subminor thirds and supermajor seconds. [[21edo]] is the smallest edo to non-trivially support diasem.

"Diasem" is a name given by [[User:ks26|ks26]]. The name is a portmanteau of "diatonic" and "semiquartal" (or "[[semaphore]]") since its step sizes are intermediate between that of [[diatonic]] (5L 2s) and [[semiquartal]] (5L 4s); it is also a pun based on the [[diesis]], which appears as the small step in the scale in the [[31edo]] and [[36edo]] tunings.

Line 20:

| Diatonic || 5L2s || 10\62, 6\62 || ├─────────┼─────┼─────────╫─────────┼─────┼─────────╫─────────┤

|}

== Intervals ==

The following is a table of diasem 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 diasem using the following expressions.

@@ Line 5: / Line 5: @@
 |ja =
 }}
-'''Diasem''' is a 9-note [[Maximum variety|max-variety-3]], [[AG]] 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 has two [[chirality|rotationally non-equivalent variants]], ''right-handed diasem'' LMLSLMLSL and ''left-handed diasem'' LSLMLSLML; these are mirror images. It 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]]. 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 can be generated by an alternating chain of subminor thirds and supermajor seconds. [[21edo]] is the smallest edo to non-trivially support diasem.
+'''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 has two [[chirality|rotationally non-equivalent variants]], ''right-handed diasem'' LMLSLMLSL and ''left-handed diasem'' LSLMLSLML; these are mirror images. It 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]]. 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 can be generated by an alternating chain of subminor thirds and supermajor seconds. [[21edo]] is the smallest edo to non-trivially support diasem.
 "Diasem" is a name given by [[User:ks26|ks26]]. The name is a portmanteau of "diatonic" and "semiquartal" (or "[[semaphore]]") since its step sizes are intermediate between that of [[diatonic]] (5L 2s) and [[semiquartal]] (5L 4s); it is also a pun based on the [[diesis]], which appears as the small step in the scale in the [[31edo]] and [[36edo]] tunings.
@@ Line 20: / Line 20: @@
 | Diatonic || 5L2s || 10\62, 6\62 || ├─────────┼─────┼─────────╫─────────┼─────┼─────────╫─────────┤
 |}
 == Intervals ==
 The following is a table of diasem 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 diasem using the following expressions.