Aberrismic theory

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In groundfault's aberrismic theory, an aberrisma is a type of scale step which can be added to a scale pattern to turn it into a scale of one rank higher. Aberrismas are a new category of melodic steps that are smaller than the steps in the original scale, which are prototypically whole tones and semitones; the typical range for an aberrisma is 20 to 60 cents, with optimal size approximately 40 cents according to groundfault. Examples of ternary patterns that can be made by adding aberrismas to diatonic scales are:

Aberrismic theory and RTT

Certain scales with aberrismas may be endowed with JI interpretations via RTT temperaments, such as equal temperaments. Under groundfault's RTT interpretation, the aberrisma tends to become 81/80 in a 2.3.5 context and a 64/63 in a 2.3.7 context. Thus aberrismic scales that admit more accurate 2.3.5.7 temperament interpretations and temper neither 81/80 nor 64/63, such as 5L2m5s, tend to identify 81/80 and 64/63, tempering out 5120/5103.

At times, a scale pattern has varying interpretations according to the tuning. For example, 5L2m5s is tempered differently for 2.3.5.7 and 2.3.7.11.13.