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{{Editable user page|This page is currently in user space since it uses slightly different formatting. See [[Talk:Ploidacot/Triploid monocot]].}}
{{Infobox ploidacot|Ploids=3|Shears=0|Cots=3|Pergen=[P8/3, P4/3]|Forms=6, 9, 15, 21|Title=Diploid dicot|Wedgie=9|debug=1}}'''Triploid tricot''' is a temperament archetype where the generator is a supermajor second, three of which stack to a [[3/2]] perfect fifth, and the period is a third of a [[2/1]] octave, or 400{{cent}}. Alternatively, the generator can be a submajor second, three of which stack to a [[4/3]] perfect fourth. Triploid tricot temperaments usually generate the [[3L 3s]], [[6L 3s]], and [[6L 9s]] [[mos scale]]s.

== Intervals and notation ==
There is no universally agreed apon notation for triploid tricot. The table below uses the following notation:

{| class="wikitable"
|+ style="font-size: 105% | Accidentals for triploid tricot
! Amount
! Sharp
! Flat
|-
! Chromatic semitone/3 (≈ 38{{C}})
| Lift (/)
| Drop (\)
|-
! Diatonic semitone/3 (≈ 30{{C}})
| Up (^)
| Down (v)
|-
! Pythagorean comma/3 (≈ 8{{C}})
| Plus (+)
| Minus (-)
|}

{| class="wikitable center-1 right-2 right-5 right-8"
|+ style="font-size: 105%;" | Triploid tricot intervals (assuming pure fifth and octave)
|-
! rowspan="2" | #
! colspan="3" | Ploid 0
! colspan="3" | Ploid 1
! colspan="3" | Ploid 2
|-
! Cents
! Notation
! Name
! Cents
! Notation
! Name
! Cents
! Notation
! Name
|-
| −6
| 203.91
| D
| Major second
| 603.91
| F#-
| —
| 1003.91
| Bb+
| —
|-
| −5
| 369.93
| \E
| —
| 769.93
| vAb+
| —
| 1169.93
| Cv
| —
|-
| −4
| 535.94
| /F
| —
| 935.94
| ^A
| —
| 135.94
| /Db+
| —
|-
| −3
| 701.96
| G
| Perfect fifth
| 1101.96
| B-
| —
| 301.96
| Eb+
| —
|-
| −2
| 867.97
| \A
| —
| 67.97
| vDb+
| —
| 467.97
| vF
| —
|-
| −1
| 1033.99
| /Bb
| —
| 233.99
| D^
| —
| 633.99
| ^F#-
| —
|-
| 0
| 0.00
| C
| Unison
| 400.00
| vE
| —
| 800.00
| ^Ab
| —
|-
| 1
| 166.01
| \D
| —
| 566.01
| vGb+
| —
| 966.01
| vBb
| —
|-
| 2
| 332.03
| /Eb
| —
| 732.03
| vF#
| —
| 1132.03
| ^B-
| —
|-
| 3
| 498.04
| F
| Perfect fourth
| 898.04
| A-
| —
| 98.04
| Db+
| —
|-
| 4
| 664.06
| \G
| —
| 1064.06
| \B-
| —
| 264.06
| vEb
| —
|-
| 5
| 830.07
| /Ab
| —
| 30.07
| ^C
| —
| 430.07
| ^E-
| —
|-
| 6
| 996.09
| Bb
| Minor seventh
| 196.09
| D-
| —
| 596.09
| Gb+
| —
|}

== Temperament interpretations ==
A third of 3/2 is close to [[8/7]], and a third of 4/3 is close to [[11/10]]. Making both of these equivalences in the 2.3.7.11/5 [[subgroup]], thus tempering out [[1029/1024]] and [[4000/3993]], leads to the subgroup temperament [[trisect]]. Prime [[13/1|13]] can then be added by setting [[13/9]] to be a third of [[3/1]], tempering out [[2197/2187]].

Extending this temperament to the full [[13-limit]] by setting the third-octave to [[5/4]] leads to the [[trisected]] temperament, though much accuracy is lost compared to the subgroup temperament.

User:Overthink/Ploidacot/Triploid Tricot - Revision history

Overthink: Start page (currently in userspace cause slightly different formatting)