Ploidacot/Diploid dicot: Difference between revisions
Created page with "'''Diploid dicot''' is a temperament archetype where the generator is a neutral third, two of which stack to a 3/2 perfect fifth, and the period is half a 2/1 octave, or 600 cents. In other words, this is the same as the hemipythagorean structure. The generator can also be characterized as an inframinor third or ultramajor second, two of which reach a perfect fourth. Diploid dicot temperaments usually generate the decatonic scale 4L 6s and the 14-note sca..." |
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'''Diploid dicot''' is a temperament archetype where the generator is a neutral third, two of which stack to a [[3/2]] perfect fifth, and the period is half a [[2/1]] octave, or 600 cents. In other words, this is the same as the [[hemipythagorean]] structure. The generator can also be characterized as an inframinor third or ultramajor second, two of which reach a perfect fourth. Diploid dicot temperaments usually generate the decatonic scale [[4L 6s]] and the 14-note scale [[10L 4s]]. | {{Breadcrumb}}{{Infobox ploidacot|Ploids=2|Shears=0|Cots=2|Pergen=[P8/2, P4/2]|Forms=6, 10, 14|Title=Diploid dicot}}'''Diploid dicot''' is a temperament archetype where the generator is a neutral third, two of which stack to a [[3/2]] perfect fifth, and the period is half a [[2/1]] octave, or 600 cents. In other words, this is the same as the [[hemipythagorean]] structure. The generator can also be characterized as an inframinor third or ultramajor second, two of which reach a perfect fourth. Diploid dicot temperaments usually generate the decatonic scale [[4L 6s]] and the 14-note scale [[10L 4s]]. | ||
== Notation == | == Notation == | ||
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== Temperament interpretations == | == Temperament interpretations == | ||
A diploid dicot temperament must temper out at least two commas: one to equate an interval to its octave-complement, and one to equate another interval to its fifth-complement. As a result, diploid dicot temperaments must be at least in the 7-limit or another 4-prime subgroup. As such, there are few specifically defined interpretations of diploid dicot as a temperament, and instead they may be found by combining [[Ploidacot/Dicot|dicot]] and [[Ploidacot/Diploid monocot|diploid monocot]] temperaments. | A diploid dicot temperament must temper out at least two commas: one to equate an interval to its octave-complement, and one to equate another interval to its fifth-complement. As a result, diploid dicot temperaments must be at least in the 7-limit or another 4-prime subgroup. As such, there are few specifically defined interpretations of diploid dicot as a temperament, and instead they may be found by combining [[Ploidacot/Dicot|dicot]] and [[Ploidacot/Diploid monocot|diploid monocot]] temperaments. | ||
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Latest revision as of 00:26, 2 September 2025
| Pergen | [P8/2, P4/2] |
| Numeral form | 2-ploid 2-cot |
| Pure generator size | 249.03 ¢ |
| Pure period size | 600 ¢ |
| Forms | 6, 10, 14 |
Diploid dicot is a temperament archetype where the generator is a neutral third, two of which stack to a 3/2 perfect fifth, and the period is half a 2/1 octave, or 600 cents. In other words, this is the same as the hemipythagorean structure. The generator can also be characterized as an inframinor third or ultramajor second, two of which reach a perfect fourth. Diploid dicot temperaments usually generate the decatonic scale 4L 6s and the 14-note scale 10L 4s.
Notation
Diploid dicot 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. As such, there is no universally accepted convention. Note and interval names are provided where diploid dicot intervals align with standard dicot intervals (which use neutral chain-of-fifths notation).
| Ploid 1 | Ploid 2 | ||||||
|---|---|---|---|---|---|---|---|
| # | Cents | Name | Notation | # | Cents | Name | Notation |
| -6 | 294.135 | Eb | minor third | -6 | 894.135 | ||
| -5 | 45.1125 | -5 | 645.1125 | Gd | semidiminished fifth | ||
| -4 | 396.09 | -4 | 996.09 | Bb | minor seventh | ||
| -3 | 147.0675 | Dd | neutral second | -3 | 747.0675 | ||
| -2 | 498.045 | F | perfect fourth | -2 | 1098.045 | ||
| -1 | 249.0225 | -1 | 849.0225 | Ad | neutral sixth | ||
| 0 | 0 | C | perfect unison | 0 | 600 | ||
| 1 | 350.9775 | Ed | neutral third | 1 | 950.9775 | ||
| 2 | 101.955 | 2 | 701.955 | G | perfect fifth | ||
| 3 | 452.9325 | 3 | 1052.9325 | Bd | neutral seventh | ||
| 4 | 203.91 | D | major second | 4 | 803.91 | ||
| 5 | 554.8875 | Ft | semiaugmented fourth | 5 | 1154.8875 | ||
| 6 | 305.865 | 6 | 905.865 | A | major sixth | ||
Temperament interpretations
A diploid dicot temperament must temper out at least two commas: one to equate an interval to its octave-complement, and one to equate another interval to its fifth-complement. As a result, diploid dicot temperaments must be at least in the 7-limit or another 4-prime subgroup. As such, there are few specifically defined interpretations of diploid dicot as a temperament, and instead they may be found by combining dicot and diploid monocot temperaments.