Ploidacot/Diploid tricot

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Revision as of 08:10, 4 January 2026 by Xenllium (talk | contribs) (Created page with "{{Breadcrumb}} {{Infobox ploidacot|Ploids=2|Shears=0|Cots=3|Pergen=[P8/2, P5/3]|Forms=10, 16, 26, 36|Title=Diploid tricot|Wedgie=6}} '''Diploid tricot''' is a temperament archetype with a half-octave period, and a generator that is a third of the size of a perfect fifth (233.98{{c}}). Diploid tricot temperaments usually generate the 4L 2s, 6L 4s, and 10L 6s MOS structures. == Intervals and notation == Diploid tricot notation is complicated a...")
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Diploid tricot
Pergen [P8/2, P5/3]
Numeral form 2-ploid 3-cot
Pure generator size 233.99 ¢
Pure period size 600 ¢
Forms 10, 16, 26, 36
Characteristic multival entry 6

Diploid tricot is a temperament archetype with a half-octave period, and a generator that is a third of the size of a perfect fifth (233.98 ¢).

Diploid tricot temperaments usually generate the 4L 2s, 6L 4s, and 10L 6s MOS structures.

Intervals and notation

Diploid tricot notation is complicated as it conventionally requires either the introduction of new "hemipythagorean" ordinals or the use of scales other than the standard diatonic scale. Note and interval names are provided where diploid dicot intervals align with standard monocot intervals (which use chain-of-fifths notation).

# Ploid 1 Ploid 2
Cents Notation Name Cents Notation Name
-13 558.195 1158.195
-12 192.180 792.180 Ab minor sixth
-11 426.165 1026.165
-10 60.150 660.150
-9 294.135 Eb minor third 894.135
-8 528.120 1128.120
-7 162.105 762.105
-6 396.090 996.090 Bb minor seventh
-5 30.075 630.075
-4 264.060 864.060
-3 498.045 F perfect fourth 1098.045
-2 132.030 732.030
-1 366.015 966.015
0 0 C perfect unison 600
1 233.985 833.985
2 467.970 1067.970
3 101.955 701.955 G perfect fifth
4 335.940 935.940
5 569.925 1169.925
6 203.910 D major second 803.910
7 437.895 1037.895
8 71.880 671.880
9 305.865 905.865 A major sixth
10 539.850 1139.850
11 173.835 773.835
12 407.820 E major third 1007.820
13 41.805 641.805

Temperament interpretations

Here, there is one obvious temperament, baladic, which is useful for the 2.3.7.13.17 subgroup. It tempers out 169/168, which splits 7/6 in half (13/12~14/13) and one finds that the octave is therefore split in half via the interval 91/64, which is then equated to 17/12.