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Ploidacot/Triploid monocot: Difference between revisions

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{{Breadcrumb}}{{Infobox ploidacot|Ploids=3|Shears=0|Cots=1|Pergen=[P8/3, P5]|Forms=9, 12, 15|Title=Triploid monocot|Wedgie=3}}
{{Breadcrumb}}{{Infobox ploidacot|Ploids=3|Shears=0|Cots=1|Pergen=[P8/3, P5]|Forms=9, 12, 15, 27|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&nbsp;6s]] MOS structure and either [[3L&nbsp;9s]] (and thus [[12L&nbsp;3s]]) or [[9L&nbsp;3s]] as children.
'''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&nbsp;6s]] MOS structure and either [[3L&nbsp;9s]] (and thus [[12L&nbsp;3s]]) or [[9L&nbsp;3s]] (when the fifth is flatter than [[12edo|7\12]]) as children.


== Notation ==
== Intervals and 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 1/3 of an ''inversed'' diminished second (the difference between diatonic semitone and chromatic semitone, equivalent to the [[Pythagorean comma]]), so vvC# and ^Db are enharmonic.


{| class="wikitable"
{| class="wikitable center-1 right-2 right-5 right-8"
|+ 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 14: Line 14:
|-
|-
! Cents
! Cents
! Notation
! Name
! Name
! Cents
! Notation
! Notation
! Name
! Cents
! Cents
! Name
! Notation
! Notation
! Cents
! Name
! Name
! Notation
|-
| −6
| 188.27
| ^Ebb
| —
| 588.27
| Gb
| diminished fifth
| 988.27
| vBb
| —
|-
|-
| −5
| −5
| 90.22
| 90.22
| Db
| minor second
| minor second
| Db
| 490.22
| 490.22
| —
| vF
| —
| —
| 890.22
| 890.22
| —
| ^Bbb
| —
| —
|-
|-
| −4
| −4
| 392.18
| 392.18
| —
| ^Fb
| —
| —
| 792.18
| 792.18
| Ab
| minor sixth
| minor sixth
| Ab
| 1192.18
| 1192.18
| —
| vC
| —
| —
|-
|-
| −3
| −3
| 294.13
| 294.13
| Eb
| minor third
| minor third
| Eb
| 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
| Bb
| minor seventh
| minor seventh
| Bb
|-
|-
| −1
| −1
| 98.04
| 98.04
| —
| ^Db
| —
| —
| 498.04
| 498.04
| F
| perfect fourth
| perfect fourth
| F
| 898.04
| 898.04
| —
| vA
| —
| —
|-
|-
| 0
| 0
| 0
| 0.00
| C
| unison
| unison
| C
| 400.00
| 400
| vE
| —
| —
| 800
| —
| —
| 800.00
| ^Ab
| —
| —
|-
|-
| 1
| 1
| 301.96
| 301.96
| —
| ^Eb
| —
| —
| 701.96
| 701.96
| G
| perfect fifth
| perfect fifth
| G
| 1101.96
| 1101.96
| —
| vB
| —
| —
|-
|-
| 2
| 2
| 203.91
| 203.91
| D
| major second
| major second
| D
| 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
| A
| major sixth
| major sixth
| A
|-
|-
| 4
| 4
| 7.82
| 7.82
| —
| ^C
| —
| —
| 407.82
| 407.82
| E
| major third
| major third
| E
| 807.82
| 807.82
| —
| vG#
| —
| —
|-
|-
| 5
| 5
| 309.78
| 309.78
| —
| vD#
| —
| —
| 709.78
| 709.78
| —
| ^G
| —
| —
| 1109.78
| 1109.78
| B
| major seventh
| major seventh
| B
|-
| 6
| 211.73
| ^D
| —
| 611.73
| F#
| augmented fourth
| 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 equate some interval to its octave complement.
By definition, triploid monocot temperaments split the octave in three.


=== Augmented ===
=== Augmented ===
[[Augmented family|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 &amp; 15), august (9 &amp; 12), inflated (3d &amp; 15), and deflated (3 &amp; 9).
[[Augmented family|Augmented]] sets [[5/4]] as a period, and uses a fifth as a free generator. There are some extensions for 7-limit: augene (12 &amp; 15), august (9 &amp; 12), inflated (3d &amp; 15), and deflated (3 &amp; 9). In the 11-limit, these extensions equate 5/4 and [[14/11]] as a period.


[[Category:Ploidacot]]
[[Category:Ploidacots|Triploid monocot]]
Retrieved from "https://en.xen.wiki/w/Ploidacot/Triploid_monocot"