Ploidacot/Gamma-hexacot

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Gamma-hexacot
Pergen [P8, ccP4/6]
Numeral form 3-sheared 6-cot
Pure generator size 483.01 ¢
Pure period size 1200 ¢
Forms 17, 22, 27, 32, 37
Characteristic multival entry 6

Gamma-hexacot is a temperament archetype where the generator is a grave fourth of about 482–484 ¢, six of which make 16/3 (perfect eighteenth, two octaves above a perfect fourth), and the period is a 2/1 octave. Gamma-hexacot temperaments also include all alpha-dicot and tricot intervals. Gamma-hexacot temperaments typically generate the 5L 7s, 5L 12s, and 5L 17s MOS scales.

Intervals and notation

While there is no agreed-upon notation system for gamma-hexacot, the following is based on interpreting the generator as a grave fourth, and allowing for an ^ or v to stand for 1/6 of a diatonic semitone, so ^^^C and vvvDb are enharmonic.

Gamma-hexacot intervals (assuming pure fifth and octave)
# Cents Notation Name
−24 407.820 E major third
−23 890.828 vA
−22 173.835 vvD
−21 656.843 ^^^F#/vvvG
−20 1139.850 ^^B
−19 422.858 ^E
−18 905.865 A major sixth
−17 188.873 vD
−16 671.880 vvG
−15 1154.888 ^^^B/vvvC
−14 437.895 ^^E
−13 920.903 ^A
−12 203.910 D major second
−11 686.918 vG
−10 1169.925 vvC
−9 452.933 ^^^E/vvvF
−8 935.940 ^^A
−7 218.948 ^D
−6 701.955 G perfect fifth
−5 1184.963 vC
−4 467.970 vvF
−3 950.978 ^^^A/vvvBb
−2 233.985 ^^D
−1 716.993 ^G
0 0.000 C perfect unison
1 483.007 vF
2 966.015 vvBb
3 249.022 ^^^D/vvvEb
4 732.030 ^^G
5 15.037 ^C
6 498.045 F perfect fourth
7 981.052 vBb
8 264.060 vvEb
9 747.067 ^^^G/vvvAb
10 30.075 ^^C
11 513.082 ^F
12 996.090 Bb minor seventh
13 279.097 vEb
14 762.105 vvAb
15 45.112 ^^^C/vvvDb
16 528.120 ^^F
17 1011.127 ^Bb
18 294.135 Eb minor third
19 777.142 vAb
20 60.150 vvDb
21 543.157 ^^^F/vvvGb
22 1026.165 ^^Bb
23 309.172 ^Eb
24 792.180 Ab minor sixth

Temperament interpretations

An obvious interpretation for gamma-hexacot is hemiseven, where the generator is 45/34, two of which make 7/4, three make 15/13 above an octave, four make 26/17~32/21 above an octave, six make 4/3 above two octaves, seven make 30/17 above two octaves, seventeen make 9/5 above six octaves, and nineteen make 11/7 above seven octaves.