Ploidacot/Delta-hexacot

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Delta-hexacot
Pergen [P8, P11/6]
Numeral form 4-sheared 6-cot
Pure generator size 283.01 ¢
Pure period size 1200 ¢
Forms 13, 17, 21, 38
Characteristic multival entry 6

Delta-hexacot is a temperament archetype where the generator is a minor third of about 282–284 ¢, six of which make a perfect eleventh of 8/3, and the period is a 2/1 octave. Delta-hexacot temperaments also include all dicot and alpha-tricot intervals. Delta-hexacot temperaments typically generate the 4L 5s, 4L 9s, and 4L 13s MOS scales.

Intervals and notation

Due to dividing the eleventh into so many steps, standard notation becomes almost useless for delta-hexacot. Regardless, notation has been provided for where delta-hexacot intervals align with standard dicot intervals (which use neutral chain-of-fifths notation).

Delta-hexacot intervals (assuming pure fifth and octave)
# Cents Notation Name
−24 407.820 E major third
−23 690.828
−22 973.835
−21 56.843 Ct semiaugmented unison
−20 339.850
−19 622.858
−18 905.865 A major sixth
−17 1188.873
−16 271.880
−15 554.888 Ft semiaugmented fourth
−14 837.895
−13 1120.903
−12 203.910 D major second
−11 486.918
−10 769.925
−9 1052.933 Bd neutral seventh
−8 135.940
−7 418.948
−6 701.955 G perfect fifth
−5 984.963
−4 67.970
−3 350.978 Ed neutral third
−2 633.985
−1 916.993
0 0.000 C perfect unison
1 283.007
2 566.015
3 849.022 Ad neutral sixth
4 1132.030
5 215.037
6 498.045 F perfect fourth
7 781.052
8 1064.060
9 147.067 Dd neutral second
10 430.075
11 713.082
12 996.090 Bb minor seventh
13 79.097
14 362.105
15 645.112 Gd semidiminished fifth
16 928.120
17 11.127
18 294.135 Eb minor third
19 577.142
20 860.150
21 1143.157 Cd semidiminished octave
22 226.165
23 509.172
24 792.180 Ab minor sixth

Temperament interpretations

An obvious interpretation for delta-hexacot is neominor, where the generator is 13/11~20/17, two of which make 18/13, three make 18/11 above an octave, six make a perfect eleventh, seven make 11/7 above an octave, eight make 13/7 above an octave, ten make 9/7 above two octaves, and nineteen make 7/5 above four octaves.