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{{Breadcrumb}}{{Infobox ploidacot|Ploids=1|Shears=2|Cots=3|Pergen=[P8, P4/3]|Forms=7, 8, 15, 22|Title=Omega-tricot (beta-tricot)|Wedgie=3}}
'''Omega-tricot''' is a temperament archetype where the generator is a submajor second, three of which stack to form a perfect fourth of [[4/3]], and the period is a [[2/1]] octave. Omega-tricot temperaments usually generate the [[1L 6s]] and [[7L 1s]] MOS structures. Omega-tricot temperaments produce "supraminor" and "submajor" intervals, splitting the chromatic semitone into three parts.


'''Omega-tricot''' is a temperament archetype where the generator is a submajor second, three of which stack to form a perfect fourth of [[4/3]], and the period is a [[2/1]] octave. Omega-tricot temperaments usually generate the [[1L 6s]] and [[7L 1s]] MOS structures. Omega-tricot temperaments produce "supraminor" and "submajor" intervals, splitting the chromatic semitone into three parts.
== Intervals and notation ==
While there is no agreed-upon notation system for omega-tricot, the following is based on interpreting the generator as a submajor second, allowing for an ^ or v to stand for 1/3 of a chromatic semitone, so ^^C and vC# are enharmonic.


== Notation ==
While there is no agreed-upon notation system for omega-tricot, the following is based on interpreting the generator as a submajor second. ^^C and vC# are enharmonic.
{| class="wikitable"
{| class="wikitable"
|+
|+ style="font-size: 105%;" | Omega-tricot intervals (assuming pure fifth and octave)
!#
!Cents
!Notation
!Name
|-
|-
| -9
! #
|905.865
! Cents
|A
! Notation
|major sixth
! Name
|-
|-
| -8
| −9
|1071.88
| 905.865
|vB
| A
|submajor seventh
| major sixth
|-
|-
| -7
| −8
|37.895
| 1071.88
|^C
| vB
|superunison
| submajor seventh
|-
|-
| -6
| −7
|203.91
| 37.895
|D
| ^C
|major second
| superunison
|-
|-
| -5
| −6
|369.925
| 203.91
|vE
| D
|submajor third
| major second
|-
|-
| -4
| −5
|535.94
| 369.925
|^F
| vE
|superfourth
| submajor third
|-
|-
| -3
| −4
|701.955
| 535.94
|G
| ^F
|perfect fifth
| superfourth
|-
|-
| -2
| −3
|867.97
| 701.955
|vA
| G
|submajor sixth
| perfect fifth
|-
|-
| -1
| −2
|1033.985
| 867.97
|^Bb
| vA
|supraminor seventh
| submajor sixth
|-
|-
|0
| −1
|0
| 1033.985
|C
| ^Bb
|perfect unison / perfect octave
| supraminor seventh
|-
|-
|1
| 0
|166.015
| 0
|vD
| C
|submajor second
| perfect unison
|-
|-
|2
| 1
|332.03
| 166.015
|^Eb
| vD
|supraminor third
| submajor second
|-
|-
|3
| 2
|498.045
| 332.03
|F
| ^Eb
|perfect fourth
| supraminor third
|-
|-
|4
| 3
|664.06
| 498.045
|vG
| F
|subfifth
| perfect fourth
|-
|-
|5
| 4
|830.075
| 664.06
|^Ab
| vG
|supraminor sixth
| subfifth
|-
|-
|6
| 5
|996.09
| 830.075
|Bb
| ^Ab
|minor seventh
| supraminor sixth
|-
|-
|7
| 6
|1162.105
| 996.09
|vC
| Bb
|suboctave
| minor seventh
|-
|-
|8
| 7
|128.12
| 1162.105
|^Db
| vC
|supraminor second
| suboctave
|-
|-
|9
| 8
|294.135
| 128.12
|Eb
| ^Db
|minor third
| supraminor second
|-
| 9
| 294.135
| Eb
| minor third
|}
|}


== Temperament interpretations ==
== Temperament interpretations ==
=== Porcupine ===
=== Porcupine ===
In [[porcupine]], the generator is [[11/10]], two generators make [[6/5]], and three make 4/3. This is tuned best with a considerably flat generator of about 162 cents or so, and naturally extends to the full 11-limit as in [[superpyth]], so the minor seventh is [[7/4]].
In [[porcupine]], the generator is [[11/10]], two generators make [[6/5]], and three make 4/3. This is tuned best with a considerably flat generator of about 162{{c}} or so, and naturally extends to the full 11-limit as in [[superpyth]], so the minor seventh is [[7/4]].


=== Superpine ===
=== Superpine ===
In [[superpine]], the subminor seventh (C-vBb, 13 generators up) is mapped to 7/4, and the mappings for 3 and 5 are as in meantone, so -3 generators is [[3/2]] and -12 generators is [[5/4]]. It is best tuned with a slightly sharp generator of about 168 cents.
In [[superpine]], the generator is again mapped to 11/10, and the mapping for 5 is as in [[meantone]], so [[5/4]] is found 12 generators down. The interval of two generators no longer represents a minor third, but more of a neutral one, as it is mapped to [[39/32]] (so that 5 generators span [[13/8]]). The canonical mapping of 7 places [[7/2]] at 13 generators, equating the generator to [[35/32]]. It is best tuned with a slightly sharp generator of about 168{{c}}.
 
[[Category:Ploidacots|Omega-tricot]]
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