Ploidacot/Diploid dicot: Difference between revisions
m Removing from Category:Ploidacots using Cat-a-lot |
Expansion and slight rewriting - shouldn't add categories for temps here because there aren't many |
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== Temperament interpretations == | == Temperament interpretations == | ||
A diploid dicot temperament must temper out at least two commas: one to equate | A diploid dicot temperament must temper out at least two commas: one to equate a pair of intervals to the semioctave, and one to equate another pair of intervals to the hemififth. As a result, diploid dicot temperaments must have at least 4 primes. | ||
There are few temperaments that follow specifically the diploid dicot archetype, and those that do are often the lucky intersection of a diploid and an (alpha-)dicot temperament; lucky, because it's possible that the intersection of such a pair of temperaments produces a new one that cannot be expressed through diploid dicot, or any kind of chain of fifths. | |||
=== Sruti === | |||
The intersection of septimal [[diaschismic]] and [[namo]], which equates all of 16/13, 27/22, 11/9 and 39/32 to the neutral third, 45/32 and 64/45 with the semioctave. It is not very good for a diaschismic extension. | |||
=== Semihemi === | |||
The intersection of [[hemififths]] and [[kalismic]] and [[barbados]], which maps 15/13 to the hemifourth, 49/40 to the hemififth, and 99/70 to the semioctave. It is quite accurate, and solid as a hemififths extension, where primes 5 and 7 are along the dicot chain, and primes 11 and 13 are along the diploid chain. | |||
Latest revision as of 17:13, 23 July 2026
| Pergen | [P8/2, P4/2] |
| Numeral form | 2-ploid 2-cot |
| Pure generator size | 249.02 ¢ |
| Pure period size | 600 ¢ |
| Forms | 6, 10, 14, 24 |
| Characteristic multival entry | 4 |
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 ¢. 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.
Intervals and 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 | Notation | Name | Cents | Notation | Name | |
| −7 | 543.157 | – | 1143.157 | Cd | semidiminished octave | |
| −6 | 294.135 | Eb | minor third | 894.135 | – | |
| −5 | 45.112 | – | 645.112 | Gd | semidiminished fifth | |
| −4 | 396.090 | – | 996.090 | Bb | minor seventh | |
| −3 | 147.067 | Dd | neutral second | 747.067 | – | |
| −2 | 498.045 | F | perfect fourth | 1098.045 | – | |
| −1 | 249.022 | – | 849.022 | Ad | neutral sixth | |
| 0 | 0 | C | perfect unison | 600 | – | |
| 1 | 350.978 | Ed | neutral third | 950.978 | – | |
| 2 | 101.955 | – | 701.955 | G | perfect fifth | |
| 3 | 452.933 | – | 1052.933 | Bd | neutral seventh | |
| 4 | 203.910 | D | major second | 803.910 | – | |
| 5 | 554.888 | Ft | semiaugmented fourth | 1154.888 | – | |
| 6 | 305.865 | – | 905.865 | A | major sixth | |
| 7 | 56.843 | Ct | semiaugmented unison | 656.843 | – | |
Temperament interpretations
A diploid dicot temperament must temper out at least two commas: one to equate a pair of intervals to the semioctave, and one to equate another pair of intervals to the hemififth. As a result, diploid dicot temperaments must have at least 4 primes.
There are few temperaments that follow specifically the diploid dicot archetype, and those that do are often the lucky intersection of a diploid and an (alpha-)dicot temperament; lucky, because it's possible that the intersection of such a pair of temperaments produces a new one that cannot be expressed through diploid dicot, or any kind of chain of fifths.
Sruti
The intersection of septimal diaschismic and namo, which equates all of 16/13, 27/22, 11/9 and 39/32 to the neutral third, 45/32 and 64/45 with the semioctave. It is not very good for a diaschismic extension.
Semihemi
The intersection of hemififths and kalismic and barbados, which maps 15/13 to the hemifourth, 49/40 to the hemififth, and 99/70 to the semioctave. It is quite accurate, and solid as a hemififths extension, where primes 5 and 7 are along the dicot chain, and primes 11 and 13 are along the diploid chain.