Diaslen: Difference between revisions

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'''{{PAGENAME}}''' (also denoted 4s in [[groundfault]]'s [[aberrismic theory]]) is a family of quasi-diatonic ~~ternary~~ scale ~~patterns~~ with [[~~scale~~ signature]] ~~5L2m4s~~, so named by groundfault who considers [[33edo]]'s L:m:s = 5:2:1 a good tuning for it. The name ''diamech'' is a blend of ''dia-'' and the [[TAMNAMS]] prefix ''mech-'' for [[machinoid]]. [[23edo]] is the only edo without a diatonic fifth that has a ~~5L2mks~~ ternary scale pattern, namely ~~5L2m4s~~ with L:m:s = 3:2:1.

'''{{PAGENAME}}''' (also denoted 4s in [[groundfault]]'s [[aberrismic theory]]) is a family of quasi-[[diatonic]] [[scale pattern]]s with [[step signature]] 5L 2m 4s, so named by groundfault who considers [[33edo]]'s L:m:s = 5:2:1 a good tuning for it. The name ''diamech'' is a blend of ''dia-'' and the [[TAMNAMS]] prefix ''mech-'' for [[machinoid]]. [[23edo]] is the only edo without a diatonic fifth that has a 5L 2m ks [[ternary]] scale pattern, namely 5L 2m 4s with L:m:s = 3:2:1.

== Structure ==

The three standard diamech scale patterns, denoted 4sL (LsLsLmLsLsm), 4sC (LmLsLsLmLss), and 4sR (LsLmLsLsLms), may be constructed via [[MOS substitution]], giving [[generator sequence]]s for the three scales:

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|colspan=2| GS('''L'''+'''s''', '''L'''+'''s''', '''L'''+'''m''')

|}

== Tunings and interpretations ==

=== Untempered 2.3.7 ===

The standard untempered 2.3.7 interpretation for diamech has L = [[9/8]], m = [[49/48]], s = [[64/63]].

=== Huntmic (2.3.7.13/5[640/637]) ===

[[Huntmic]] is an important temperament for diamech offering an elegant combination of interordinals and making 7/4 sharper in systems exaggerating [[49/48]] and splitting it into two equal parts. Assuming the 2.3.7 interpretation above and the constraint m:s = 2:1 makes L + m = 147/128 exactly half of 2L + m + 2s = 4/3, making it natural to set 147/128 equal to 15/13, tempering out [[640/637]]. [[53edo]] (9:2:1) and [[58edo]] (10:2:1) offer particularly good tunings for this interpretation; while the 58edo tuning's s step is smaller than that of the 53edo tuning, 58edo has better 7/6, 9/7, 15/13, and 13/10 as well as giving you a free 11:13:15.

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-'''{{PAGENAME}}''' (also denoted 4s in [[groundfault]]'s [[aberrismic theory]]) is a family of quasi-diatonic ternary scale patterns with [[scale signature]] 5L2m4s, so named by groundfault who considers [[33edo]]'s L:m:s = 5:2:1 a good tuning for it. The name ''diamech'' is a blend of ''dia-'' and the [[TAMNAMS]] prefix ''mech-'' for [[machinoid]]. [[23edo]] is the only edo without a diatonic fifth that has a 5L2mks ternary scale pattern, namely 5L2m4s with L:m:s = 3:2:1.
+'''{{PAGENAME}}''' (also denoted 4s in [[groundfault]]'s [[aberrismic theory]]) is a family of quasi-[[diatonic]] [[scale pattern]]s with [[step signature]] 5L 2m 4s, so named by groundfault who considers [[33edo]]'s L:m:s = 5:2:1 a good tuning for it. The name ''diamech'' is a blend of ''dia-'' and the [[TAMNAMS]] prefix ''mech-'' for [[machinoid]]. [[23edo]] is the only edo without a diatonic fifth that has a 5L 2m ks [[ternary]] scale pattern, namely 5L 2m 4s with L:m:s = 3:2:1.
 == Structure ==
 The three standard diamech scale patterns, denoted 4sL (LsLsLmLsLsm), 4sC (LmLsLsLmLss), and 4sR (LsLmLsLsLms), may be constructed via [[MOS substitution]], giving [[generator sequence]]s for the three scales:
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 |colspan=2| GS('''L'''+'''s''', '''L'''+'''s''', '''L'''+'''m''')
 |}
 == Tunings and interpretations ==
 === Untempered 2.3.7 ===
 The standard untempered 2.3.7 interpretation for diamech has L = [[9/8]], m = [[49/48]], s = [[64/63]].
 === Huntmic (2.3.7.13/5[640/637]) ===
 [[Huntmic]] is an important temperament for diamech offering an elegant combination of interordinals and making 7/4 sharper in systems exaggerating [[49/48]] and splitting it into two equal parts. Assuming the 2.3.7 interpretation above and the constraint m:s = 2:1 makes L + m  = 147/128 exactly half of 2L + m + 2s = 4/3, making it natural to set 147/128 equal to 15/13, tempering out [[640/637]]. [[53edo]] (9:2:1) and [[58edo]] (10:2:1) offer particularly good tunings for this interpretation; while the 58edo tuning's s step is smaller than that of the 53edo tuning, 58edo has better 7/6, 9/7, 15/13, and 13/10 as well as giving you a free 11:13:15.