Ploidacot/Diploid alpha-tricot: Difference between revisions
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== Intervals and notation == | == Intervals and notation == | ||
Diploid alpha-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 alpha- | Diploid alpha-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 alpha-tricot intervals align with standard monocot intervals (which use [[chain-of-fifths notation]]). | ||
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|+ style="font-size: 105%;" | Diploid alpha-tricot intervals (assuming pure fifth and octave) | |||
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The larger generator is equated to [[9/7]] and the smaller one to [[11/10]], treating the period as [[99/70]]. This is also equated to [[17/12]], which leads to the stack of three large generators being [[17/8]]. | The larger generator is equated to [[9/7]] and the smaller one to [[11/10]], treating the period as [[99/70]]. This is also equated to [[17/12]], which leads to the stack of three large generators being [[17/8]]. | ||
[[Category:Ploidacots]] | [[Category:Ploidacots|Diploid alpha-tricot]] | ||
Latest revision as of 13:00, 7 January 2026
| Pergen | [P8/2, P4/3] |
| Numeral form | 2-ploid 1-sheared 3-cot |
| Pure generator size | 166.01 ¢ |
| Pure period size | 600 ¢ |
| Forms | 6, 8, 14, 22 |
| Characteristic multival entry | 6 |
Diploid alpha-tricot is a temperament archetype with a half-octave period, and a generator that is a third of the size of a stack of a period and a perfect fifth (433.98 ¢), but the alternative generator with size a third of a perfect fourth is rather easier to grasp.
Diploid alpha-tricot temperaments usually generate the 2L 4s, 6L 2s, and 8L 6s MOS structures.
Intervals and notation
Diploid alpha-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 alpha-tricot intervals align with standard monocot intervals (which use chain-of-fifths notation).
| # | Ploid 1 | Ploid 2 | ||||
|---|---|---|---|---|---|---|
| Cents | Notation | Name | Cents | Notation | Name | |
| −12 | 407.820 | E | major third | 1007.820 | ||
| −11 | 573.835 | 1173.835 | ||||
| −10 | 139.850 | 739.850 | ||||
| −9 | 305.865 | 905.865 | A | major sixth | ||
| −8 | 471.880 | 1071.880 | ||||
| −7 | 37.895 | 637.895 | ||||
| −6 | 203.910 | D | major second | 803.910 | ||
| −5 | 369.925 | 969.925 | ||||
| −4 | 535.940 | 1135.940 | ||||
| -3 | 101.955 | 701.955 | G | perfect fifth | ||
| −2 | 267.970 | 867.970 | ||||
| −1 | 433.985 | 1033.985 | ||||
| 0 | 0 | C | perfect unison | 600 | ||
| 1 | 166.015 | 766.015 | ||||
| 2 | 332.030 | 932.030 | ||||
| 3 | 498.045 | F | perfect fourth | 1098.045 | ||
| 4 | 64.060 | 664.060 | ||||
| 5 | 230.075 | 830.075 | ||||
| 6 | 396.090 | 996.090 | Bb | minor seventh | ||
| 7 | 562.105 | 1162.105 | ||||
| 8 | 128.120 | 728.120 | ||||
| 9 | 294.135 | Eb | minor third | 894.135 | ||
| 10 | 460.150 | 1060.150 | ||||
| 11 | 26.165 | 626.165 | ||||
| 12 | 192.180 | 792.180 | Ab | minor sixth | ||
Temperament interpretations
Here, there is one obvious temperament, which is a 2.3.7.11/5.17 restriction of echidna.
The larger generator is equated to 9/7 and the smaller one to 11/10, treating the period as 99/70. This is also equated to 17/12, which leads to the stack of three large generators being 17/8.