Ploidacot/Enneacot: Difference between revisions

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+{{Infobox ploidacot|Ploids=1|Shears=0|Cots=9|Pergen=[P8, P5/9]|Forms=15, 16, 31|Title=Enneacot|Wedgie=9}}
+'''Enneacot''' is a temperament archetype where the generator is a small semitone, nine of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Enneacot temperaments also include all [[Ploidacot/Tricot|tricot]] intervals, as the tricot generator is split further into three.
-'''Enneacot''' is a temperament archetype where the generator is a small semitone, nine of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave.
+Enneacot temperaments generate the [[15L&nbsp;1s]] MOS scale, and are mostly famous in the form of the [[Carlos Alpha]] scale, which is usually perceived as multiple independent chains of enneacot generators offset by octaves.
-Enneacot temperaments generate the [[15L 1s]] MOS scale, and are mostly famous in the form of the [[Carlos Alpha]] scale, which is usually perceived as multiple independent chains of enneacot generators offset by octaves.
 == Intervals and notation ==
 Due to dividing the fifth into so many steps, standard notation becomes almost useless for enneacot. Regardless, notation has been provided for where [[Ploidacot/Monocot|monocot]] intervals appear in this system.
 {| class="wikitable"
-|+Enneacot intervals (assuming pure fifth and octave)
+|+ style="font-size: 105%;" | Enneacot intervals (assuming pure fifth and octave)
-!#
-!Cents
-!Notation
-!Name
 |-
-| -9
+! #
-|498.045
+! Cents
-|F
+! Notation
-|perfect fourth
+! Name
 |-
-| -8
+| −9
-|576.04
+| 498.045
-|
+| F
-|
+| perfect fourth
 |-
-| -7
+| −8
-|654.035
+| 576.040
 |
 |
 |-
-| -6
+| −7
-|732.03
+| 654.035
 |
 |
 |-
-| -5
+| −6
-|810.025
+| 732.030
 |
 |
 |-
-| -4
+| −5
-|888.02
+| 810.025
 |
 |
 |-
-| -3
+| −4
-|966.015
+| 888.020
 |
 |
 |-
-| -2
+| −3
-|1044.01
+| 966.015
 |
 |
 |-
-| -1
+| −2
-|1122.005
+| 1044.010
 |
 |
 |-
-|0
+| −1
-|0
+| 1122.005
-|C
+|
-|perfect unison
+|
 |-
-|1
+| 0
-|77.995
+| 0.000
-|
+| C
-|
+| perfect unison
 |-
-|2
+| 1
-|155.99
+| 77.995
 |
 |
 |-
-|3
+| 2
-|233.985
+| 155.990
 |
 |
 |-
-|4
+| 3
-|311.98
+| 233.985
 |
 |
 |-
-|5
+| 4
-|389.975
+| 311.980
 |
 |
 |-
-|6
+| 5
-|467.97
+| 389.975
 |
 |
 |-
-|7
+| 6
-|545.965
+| 467.970
 |
 |
 |-
-|8
+| 7
-|623.96
+| 545.965
 |
 |
 |-
-|9
+| 8
-|701.955
+| 623.960
-|G
+|
-|perfect fifth
+|
+|-
+| 9
+| 701.955
+| G
+| perfect fifth
 |}
 == Temperament interpretations ==
 === Valentine ===
-Valentine is the standard [[regular temperament]] interpretation of the Carlos Alpha scale as an ET. 5 generators is 5/4, 4 is 6/5, and 3 is 8/7. It can be extended to the 11-limit by setting 7 steps to 11/8, and to the 13-limit by setting 11 steps to 13/8.
+[[Valentine]] is the standard [[regular temperament]] interpretation of the Carlos Alpha scale as an ET. 5 generators is [[5/4]], 4 is [[6/5]], and 3 is [[8/7]]. It can be extended to the 11-limit by setting 7 steps to [[11/8]]; [[Valentine extensions|a few mappings]] of 13 are possible, the most accurate of which maps 20 generators to [[32/13]].
-{{Todo| unify precision }}