Ploidacot/Diploid alpha-tricot: Difference between revisions

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{{Infobox ploidacot|Ploids=2|Shears=1|Cots=3|Pergen=[P8/2, P4/3]|Forms=6, 8, 14|Title=Diploid alpha-tricot|Wedgie=6}}
{{Infobox ploidacot|Ploids=2|Shears=1|Cots=3|Pergen=[P8/2, P4/3]|Forms=6, 8, 14, 22|Title=Diploid alpha-tricot|Wedgie=6}}


'''Diploid alpha-tricot''' is a temperament archetype with a half-octave period, and a generator that is a third of the size of a stack of a period and a perfect fifth (433.98{{c}}), but the alternative generator with size a third of a perfect fourth is rather easier to grasp.
'''Diploid alpha-tricot''' is a temperament archetype with a half-octave period, and a generator that is a third of the size of a stack of a period and a perfect fifth (433.98{{c}}), but the alternative generator with size a third of a perfect fourth is rather easier to grasp.
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== Intervals and notation ==
== Intervals and notation ==
Diploid alpha-tricot 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.
Diploid alpha-tricot 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. Note and interval names are provided where diploid alpha-dicot intervals align with standard monocot intervals (which use [[chain-of-fifths notation]]).


 
{| class="wikitable"
<!-- TODO - actually do the notation -->
|-
! rowspan="2" | #
! colspan="3" | Ploid 1
! colspan="3" | Ploid 2
|-
! Cents
! Notation
! Name
! Cents
! Notation
! Name
|-
| −12
| 407.820
| E
| major third
| 1007.820
|
|
|-
| −11
| 573.835
|
|
| 1173.835
|
|
|-
| −10
| 139.850
|
|
| 739.850
|
|
|-
| −9
| 305.865
|
|
| 905.865
| A
| major sixth
|-
| −8
| 471.880
|
|
| 1071.880
|
|
|-
| −7
| 37.895
|
|
| 637.895
|
|
|-
| −6
| 203.910
| D
| major second
| 803.910
|
|
|-
| −5
| 369.925
|
|
| 969.925
|
|
|-
| −4
| 535.940
|
|
| 1135.940
|
|
|-
| -3
| 101.955
|
|
| 701.955
| G
| perfect fifth
|-
| −2
| 267.970
|
|
| 867.970
|
|
|-
| −1
| 433.985
|
|
| 1033.985
|
|
|-
| 0
| 0
| C
| perfect unison
| 600
|
|
|-
| 1
| 166.015
|
|
| 766.015
|
|
|-
| 2
| 332.030
|
|
| 932.030
|
|
|-
| 3
| 498.045
| F
| perfect fourth
| 1098.045
|
|
|-
| 4
| 64.060
|
|
| 664.060
|
|
|-
| 5
| 230.075
|
|
| 830.075
|
|
|-
| 6
| 396.090
|
|
| 996.090
| Bb
| minor seventh
|-
| 7
| 562.105
|
|
| 1162.105
|
|
|-
| 8
| 128.120
|
|
| 728.120
|
|
|-
| 9
| 294.135
| Eb
| minor third
| 894.135
|
|
|-
| 10
| 460.150
|
|
| 1060.150
|
|
|-
| 11
| 26.165
|
|
| 626.165
|
|
|-
| 12
| 192.180
|
|
| 792.180
| Ab
| minor sixth
|}


== Temperament interpretations ==
== Temperament interpretations ==
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The larger generator is equated to [[9/7]] and the smaller one to [[11/10]], treating the period as [[99/70]]. This is also equated to [[17/12]], which leads to the stack of three large generators being [[17/8]].
The larger generator is equated to [[9/7]] and the smaller one to [[11/10]], treating the period as [[99/70]]. This is also equated to [[17/12]], which leads to the stack of three large generators being [[17/8]].
[[Category:Ploidacot]]