Ploidacot/Omega-tetracot

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Omega-tetracot (gamma-tetracot)
Pergen [P8, P4/4]
Numeral form 3-sheared 4-cot
Pure generator size 124.51 ¢
Pure period size 1200 ¢
Forms 9, 10, 19, 29
Characteristic multival entry 4

Omega-tetracot is a temperament archetype where the generator is a wide semitone, four of which make a perfect fourth of 4/3, and the period is a 2/1 octave. Omega-tetracot temperaments typically generate the 9L 1s and 10L 9s MOS scales, and containing all alpha-dicot intervals.

Intervals and notation

There is no agreed-upon notation for omega-tetracot, and constructing one by extending Pythagorean notation is complicated due to the fact that it does not split the chromatic or diatonic semitone, but rather the inversed double-diminished second (the difference between two chromatic semitones and one diatonic semitone). Note and interval names are provided where omega-tetracot intervals align with standard monocot intervals (which use chain-of-fifths notation).

Omega-tetracot intervals (assuming pure fifth and octave)
# Cents Notation Name
−12 905.87 A major sixth
−11 1030.38
−10 1154.89
−9 79.40
−8 203.91 D major second
−7 328.42
−6 452.93
−5 577.44
−4 701.96 G perfect fifth
−3 826.47
−2 950.98
−1 1075.49
0 0.00 C perfect unison
1 124.51
2 249.02
3 373.53
4 498.04 F perfect fourth
5 622.56
6 747.07
7 871.58
8 996.09 Bb minor seventh
9 1120.60
10 45.11
11 169.62
12 294.13 Eb minor third

Temperament interpretations

An obvious interpretation for omega-tetracot is negri, where the generator is 16/15~15/14 and four of them make a perfect fourth. There are some extensions for full 11- and 13-limit: negri (10 & 19), negril (10e & 19), negric (9 & 19e), and negroni (10 & 19e).