Aberrismic theory: Difference between revisions

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* [[diachromedye]] (5L2m5s or 5s)
* [[diachromedye]] (5L2m5s or 5s)
== Edos with quasi-diatonic aberrismic scales ==
== Edos with quasi-diatonic aberrismic scales ==
All edo 20 and above have a quasi-diatonic aberrismic scale. If ''n''-edo is a diatonic edo with step ratio p:q, then (''n'' + ''k'')edo has a 5L2m''k''s scale with step ratio p:q:1 for 1 ≤ k &ke; q, and (''n'' + ''rk'')edo has a 5L2m''k''s scale with step ratio p:q:r if 1 ≤ r ≤ rk &ke; q.
All edo 20 and above have a quasi-diatonic aberrismic scale. If ''n''-edo is a diatonic edo with step ratio ''p'':''q'', then (''n'' + ''k'')edo has a 5L2m''k''s scale with step ratio ''p'':''q'':1 for 1 ≤ ''k'' ≤ ''q'', and (''n'' + ''rk'')edo has a 5L2m''k''s scale with step ratio ''p'':''q'':''r'' if 1 ≤ ''r'' ≤ ''rk'' ≤ ''q''.
 
== Aberrismic theory and RTT ==
== Aberrismic theory and RTT ==
Certain scales with aberrismas may be endowed with JI interpretations via [[RTT]] temperaments, such as [[equal temperament]]s. Under groundfault's use of edos (usually patent vals) as RTT temperaments, the aberrisma tends to become a [[81/80]] in a 2.3.5 context and a [[64/63]] in a 2.3.7 context. Some scales such as 5L2m5s and 5L2m7s admit a more accurate 2.3.5.7 interpretation that tempers neither 81/80 nor 64/63 but identifies the two commas, tempering out [[5120/5103]].
Certain scales with aberrismas may be endowed with JI interpretations via [[RTT]] temperaments, such as [[equal temperament]]s. Under groundfault's use of edos (usually patent vals) as RTT temperaments, the aberrisma tends to become a [[81/80]] in a 2.3.5 context and a [[64/63]] in a 2.3.7 context. Some scales such as 5L2m5s and 5L2m7s admit a more accurate 2.3.5.7 interpretation that tempers neither 81/80 nor 64/63 but identifies the two commas, tempering out [[5120/5103]].