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 (5L 4s), and 5L 9s. 4L 1s is structurally significant because it is the equal trichordal pentatonic.

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.

Temperaments

Semifourth-generated temperaments have the edo join 5 & 9 (ignoring warts).

• Interseptimal or Semaphore is a 2.3.7 temperament that tempers out 49/48, often considered inaccurate.
• Island temperament is a 2.3.15/13 temperament that tempers out 676/675, equating the semifourth to 15/13.

See also

• Chthonic harmony