Ploidacot/Diploid tricot: Difference between revisions
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|+ style="font-size: 105%;" | Diploid tricot intervals (assuming pure fifth and octave) | |||
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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]]. | 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]]. | ||
[[Category:Ploidacots]] | [[Category:Ploidacots|Diploid tricot]] | ||
Latest revision as of 12:58, 7 January 2026
| 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 tricot 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 | ||||
A notable feature of diploid tricot is encountering the following small intervals:
- 1/3 of a diatonic semitone (encountered after 5 steps)
- half of an inversed diminished second (encountered after 18 steps, representing a half of Pythagorean comma)
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.