Ploidacot/Triploid monocot: Difference between revisions
Created page with "{{Breadcrumb}}{{Infobox ploidacot|Ploids=3|Shears=0|Cots=1|Pergen=[P8/3, P5]|Forms=9, 12, 15|Title=Triploid monocot|Wedgie=3}} '''Triploid monocot''' is a temperament archetype where the generator is a 3/2 perfect fifth and the period is 1/3 of a 2/1 octave, or 400{{c}}. The generator can also be characterized as a perfect fourth 4/3, or as a "perfect semitone" <math>\frac{2\sqrt[3]{4}}{3}</math>. Triploid monocot temperaments usually generate the 3L 6..." Tags: Mobile edit Mobile web edit |
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== Notation == | == Notation == | ||
Triploid monocot notation is complicated as it conventionally requires either the introduction of new "1/3-pythagorean" 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 triploid monocot intervals align with standard monocot intervals. | Triploid monocot notation is complicated as it conventionally requires either the introduction of new "1/3-pythagorean" 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 triploid monocot intervals align with standard monocot intervals. | ||
While there is no agreed-upon notation system for triploid monocot, the following is based on interpreting the generator as a semitone (1/3 of a minor third), allowing for an ^ or v to stand for a 1/3 of of an ''inversed'' diminished second (equivalent to the [[Pythagorean comma]]), so vvC# and ^Db are enharmonic. | |||
{| class="wikitable" | {| class="wikitable" | ||
|+ style="font-size: 105%;" | Triploid monocot intervals (assuming pure fifth and octave) | |+ style="font-size: 105%;" | Triploid monocot intervals (assuming pure fifth and octave) | ||
|- | |- | ||
! rowspan="2" |# | ! rowspan="2" | # | ||
! colspan="3" | Ploid 1 | ! colspan="3" | Ploid 1 | ||
! colspan="3" | Ploid 2 | ! colspan="3" | Ploid 2 | ||
| Line 22: | Line 24: | ||
! Name | ! Name | ||
! Notation | ! Notation | ||
|- | |||
| −6 | |||
| 188.27 | |||
| — | |||
| ^Ebb | |||
| 588.27 | |||
| diminished fifth | |||
| Gb | |||
| 988.27 | |||
| — | |||
| vBb | |||
|- | |- | ||
| −5 | | −5 | ||
| Line 29: | Line 42: | ||
| 490.22 | | 490.22 | ||
| — | | — | ||
| | | vF | ||
| 890.22 | | 890.22 | ||
| — | | — | ||
| | | ^Bbb | ||
|- | |- | ||
| −4 | | −4 | ||
| 392.18 | | 392.18 | ||
| — | | — | ||
| | | ^Fb | ||
| 792.18 | | 792.18 | ||
| minor sixth | | minor sixth | ||
| Line 43: | Line 56: | ||
| 1192.18 | | 1192.18 | ||
| — | | — | ||
| | | vC | ||
|- | |- | ||
| −3 | | −3 | ||
| Line 51: | Line 64: | ||
| 694.13 | | 694.13 | ||
| — | | — | ||
| | | vG | ||
| 1094.13 | | 1094.13 | ||
| — | | — | ||
| | | ^Cb | ||
|- | |- | ||
| −2 | | −2 | ||
| 196.09 | | 196.09 | ||
| — | | — | ||
| | | vD | ||
| 596.09 | | 596.09 | ||
| — | | — | ||
| | | ^Gb | ||
| 996.09 | | 996.09 | ||
| minor seventh | | minor seventh | ||
| Line 70: | Line 83: | ||
| 98.04 | | 98.04 | ||
| — | | — | ||
| | | ^Db | ||
| 498.04 | | 498.04 | ||
| perfect fourth | | perfect fourth | ||
| Line 76: | Line 89: | ||
| 898.04 | | 898.04 | ||
| — | | — | ||
| | | vA | ||
|- | |- | ||
| 0 | | 0 | ||
| Line 84: | Line 97: | ||
| 400 | | 400 | ||
| — | | — | ||
| | | vE | ||
| 800 | | 800 | ||
| — | | — | ||
| | | ^Ab | ||
|- | |- | ||
| 1 | | 1 | ||
| 301.96 | | 301.96 | ||
| — | | — | ||
| | | ^Eb | ||
| 701.96 | | 701.96 | ||
| perfect fifth | | perfect fifth | ||
| Line 98: | Line 111: | ||
| 1101.96 | | 1101.96 | ||
| — | | — | ||
| | | vB | ||
|- | |- | ||
| 2 | | 2 | ||
| Line 106: | Line 119: | ||
| 603.91 | | 603.91 | ||
| — | | — | ||
| | | vF# | ||
| 1003.91 | | 1003.91 | ||
| — | | — | ||
| | | ^Bb | ||
|- | |- | ||
| 3 | | 3 | ||
| 105.87 | | 105.87 | ||
| — | | — | ||
| | | vC# | ||
| 505.87 | | 505.87 | ||
| — | | — | ||
| | | ^F | ||
| 905.87 | | 905.87 | ||
| major sixth | | major sixth | ||
| Line 125: | Line 138: | ||
| 7.82 | | 7.82 | ||
| — | | — | ||
| | | ^C | ||
| 407.82 | | 407.82 | ||
| major third | | major third | ||
| Line 131: | Line 144: | ||
| 807.82 | | 807.82 | ||
| — | | — | ||
| | | vG# | ||
|- | |- | ||
| 5 | | 5 | ||
| 309.78 | | 309.78 | ||
| — | | — | ||
| | | vD# | ||
| 709.78 | | 709.78 | ||
| — | | — | ||
| | | ^G | ||
| 1109.78 | | 1109.78 | ||
| major seventh | | major seventh | ||
| B | | B | ||
|- | |||
| 6 | |||
| 211.73 | |||
| — | |||
| ^D | |||
| 611.73 | |||
| augmented fourth | |||
| F# | |||
| 1011.73 | |||
| — | |||
| vA# | |||
|} | |} | ||
A notable feature of triploid monocot is the small comma, encountered after 4 steps, which represents 1/3 of a Pythagorean comma (or its equivalence, ''inversed'' diminished second). This makes triploid monocot scales cluster around 12edo. | |||
== Temperament interpretations == | == Temperament interpretations == | ||
By definition, triploid monocot temperaments | By definition, triploid monocot temperaments split the octave in three. | ||
=== Augmented === | === Augmented === | ||
Revision as of 03:30, 4 January 2026
| Pergen | [P8/3, P5] |
| Numeral form | 3-ploid 1-cot |
| Pure generator size | 98.04 ¢ |
| Pure period size | 400 ¢ |
| Forms | 9, 12, 15 |
| Characteristic multival entry | 3 |
Triploid monocot is a temperament archetype where the generator is a 3/2 perfect fifth and the period is 1/3 of a 2/1 octave, or 400 ¢. The generator can also be characterized as a perfect fourth 4/3, or as a "perfect semitone" [math]\displaystyle{ \frac{2\sqrt[3]{4}}{3} }[/math]. Triploid monocot temperaments usually generate the 3L 6s MOS structure and either 3L 9s (and thus 12L 3s) or 9L 3s as children.
Notation
Triploid monocot notation is complicated as it conventionally requires either the introduction of new "1/3-pythagorean" 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 triploid monocot intervals align with standard monocot intervals.
While there is no agreed-upon notation system for triploid monocot, the following is based on interpreting the generator as a semitone (1/3 of a minor third), allowing for an ^ or v to stand for a 1/3 of of an inversed diminished second (equivalent to the Pythagorean comma), so vvC# and ^Db are enharmonic.
| # | Ploid 1 | Ploid 2 | Ploid 3 | ||||||
|---|---|---|---|---|---|---|---|---|---|
| Cents | Name | Notation | Cents | Name | Notation | Cents | Name | Notation | |
| −6 | 188.27 | — | ^Ebb | 588.27 | diminished fifth | Gb | 988.27 | — | vBb |
| −5 | 90.22 | minor second | Db | 490.22 | — | vF | 890.22 | — | ^Bbb |
| −4 | 392.18 | — | ^Fb | 792.18 | minor sixth | Ab | 1192.18 | — | vC |
| −3 | 294.13 | minor third | Eb | 694.13 | — | vG | 1094.13 | — | ^Cb |
| −2 | 196.09 | — | vD | 596.09 | — | ^Gb | 996.09 | minor seventh | Bb |
| −1 | 98.04 | — | ^Db | 498.04 | perfect fourth | F | 898.04 | — | vA |
| 0 | 0 | unison | C | 400 | — | vE | 800 | — | ^Ab |
| 1 | 301.96 | — | ^Eb | 701.96 | perfect fifth | G | 1101.96 | — | vB |
| 2 | 203.91 | major second | D | 603.91 | — | vF# | 1003.91 | — | ^Bb |
| 3 | 105.87 | — | vC# | 505.87 | — | ^F | 905.87 | major sixth | A |
| 4 | 7.82 | — | ^C | 407.82 | major third | E | 807.82 | — | vG# |
| 5 | 309.78 | — | vD# | 709.78 | — | ^G | 1109.78 | major seventh | B |
| 6 | 211.73 | — | ^D | 611.73 | augmented fourth | F# | 1011.73 | — | vA# |
A notable feature of triploid monocot is the small comma, encountered after 4 steps, which represents 1/3 of a Pythagorean comma (or its equivalence, inversed diminished second). This makes triploid monocot scales cluster around 12edo.
Temperament interpretations
By definition, triploid monocot temperaments split the octave in three.
Augmented
Augmented sets 5/4 as a period, and uses a fifth as a free generator. There are some extensions for 7-limit or higher prime limits: augene (12 & 15), august (9 & 12), inflated (3d & 15), and deflated (3 & 9).