Ploidacot/Omega-enneacot

Omega-enneacot is a temperament archetype where the generator is a quartertone, nine of which make a perfect fourth of 4/3, and the period is a 2/1 octave. Omega-enneacot temperaments also include all omega-tricot intervals, as the omega-tricot generator is split further into three.

Omega-enneacot
Pergen [P8, P4/9]
Numeral form 8-sheared 9-cot
Pure generator size 55.34 ¢
Pure period size 1200 ¢
Forms 21, 22, 43
Characteristic multival entry 9

Omega-enneacot temperaments generate the 21L 1s MOS scale, and are mostly famous in the form of the Noleta scale, which is usually perceived as multiple independent chains of omega-enneacot generators offset by octaves.

Intervals and notation

Due to dividing the fourth into so many steps, standard notation becomes almost useless for omega-enneacot. Regardless, notation has been provided for where monocot intervals appear in this system.

Omega-enneacot intervals (assuming pure fifth and octave)
# Cents Notation Name
−11 591.278
−10 646.617
−9 701.955 G perfect fifth
−8 757.293
−7 812.632
−6 867.970
−5 923.308
−4 978.647
−3 1033.985
−2 1089.323
−1 1144.662
0 0.000 C perfect unison
1 55.338
2 110.677
3 166.015
4 221.353
5 276.692
6 332.030
7 387.368
8 442.707
9 498.045 F perfect fourth
10 553.383
11 608.722

Temperament interpretations

Escapade

Escapade is the standard regular temperament interpretation of the Noleta scale as an ET. The generator represents 33/32, two of them give 16/15, three of them give 11/10, seven of them give 5/4, and ten of them give 11/8.