Semifourth-generated scales

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Semifourth-generated scales are scales in tuning systems where two generators of approximately 250 cents in size stack to a perfect fourth, defining a temperament archetype called alpha-dicot or omega-dicot, and notated [P8, P4/2] in pergen notation.

The semifourth-generated scales are characteristically 4L 1s, semiquartal (5L4s), and 5L9s. 4L 1s is structurally significant because it is the equal trichordal pentatonic.

Relevant tunings include Semaphore, Interganassismic temperament, and harmonic semiquartal where an exact 37/32 semifourth is used.

Intervals and notation

Alpha-dicot notation is complicated as it conventionally requires either the introduction of new "hemi-Pythagorean" ordinals or the use of scales other than the standard diatonic scale. As such, there is no universally accepted convention. An intuitive option, if one that takes getting used to, is to use KISS notation or diamond-mos notation for 5L 4s.