View source for Ploidacot/Hexacot

{{Breadcrumb}}
{{Infobox ploidacot|Ploids=1|Shears=0|Cots=6|Pergen=[P8, P5/6]|Forms=10, 11, 21, 31|Title=Hexacot|Wedgie=6}}
'''Hexacot''' is a temperament archetype where the generator is a semitone of about 116–118¢, six of which make a perfect fifth of [[3/2]], and the period is a [[2/1]] octave. Hexacot temperaments also include all [[Ploidacot/Dicot|dicot]] and [[Ploidacot/Tricot|tricot]] intervals, as the dicot generator is split further into three, or the tricot generator is split further into two. Hexacot temperaments typically generate the [[1L&nbsp;9s]] and [[10L&nbsp;1s]] MOS scales.

== Intervals and notation ==
Due to dividing the fifth into so many steps, standard notation becomes almost useless for hexacot. Regardless, notation has been provided for where hexacot intervals align with standard dicot intervals (which use [[neutral chain-of-fifths notation]]).

{| class="wikitable"
|+ style="font-size: 105%;" | Hexacot intervals (assuming pure fifth and octave)
|-
! #
! Cents
! Notation
! Name
|-
| −24
| 792.180
| Ab
| minor sixth
|-
| −23
| 909.172
| 
| 
|-
| −22
| 1026.165
| 
| 
|-
| −21
| 1143.157
| Cd
| semidiminished octave
|-
| −20
| 60.150
| 
| 
|-
| −19
| 177.142
| 
| 
|-
| −18
| 294.135
| Eb
| minor third
|-
| −17
| 411.127
| 
| 
|-
| −16
| 528.120
| 
| 
|-
| −15
| 645.112
| Gd
| semidiminished fifth
|-
| −14
| 762.105
| 
| 
|-
| −13
| 879.097
| 
| 
|-
| −12
| 996.090
| Bb
| minor seventh
|-
| −11
| 1113.082
| 
| 
|-
| −10
| 30.075
| 
| 
|-
| −9
| 147.067
| Dd
| neutral second
|-
| −8
| 264.060
| 
| 
|-
| −7
| 381.052
| 
| 
|-
| −6
| 498.045
| F
| perfect fourth
|-
| −5
| 615.037
| 
| 
|-
| −4
| 732.030
| 
| 
|-
| −3
| 849.022
| Ad
| neutral sixth
|-
| −2
| 966.015
| 
| 
|-
| −1
| 1083.007
| 
| 
|-
| 0
| 0.000
| C
| perfect unison
|-
| 1
| 116.993
| 
| 
|-
| 2
| 233.985
| 
| 
|-
| 3
| 350.978
| Ed
| neutral third
|-
| 4
| 467.970
| 
| 
|-
| 5
| 584.963
| 
| 
|-
| 6
| 701.955
| G
| perfect fifth
|-
| 7
| 818.948
| 
| 
|-
| 8
| 935.940
| 
| 
|-
| 9
| 1052.933
| Bd
| neutral seventh
|-
| 10
| 1169.925
| 
| 
|-
| 11
| 86.918
| 
| 
|-
| 12
| 203.910
| D
| major second
|-
| 13
| 320.903
| 
| 
|-
| 14
| 437.895
| 
| 
|-
| 15
| 554.888
| Ft
| semiaugmented fourth
|-
| 16
| 671.880
| 
| 
|-
| 17
| 788.873
| 
| 
|-
| 18
| 905.865
| A
| major sixth
|-
| 19
| 1022.858
| 
| 
|-
| 20
| 1139.850
| 
| 
|-
| 21
| 56.843
| Ct
| semiaugmented unison
|-
| 22
| 173.835
| 
| 
|-
| 23
| 290.828
| 
| 
|-
| 24
| 407.820
| E
| major third
|}

A notable feature of hexacot is the small diesis, known as the [[quark]], encountered after 10 steps, which represents one-third of a diatonic semitone. This makes hexacot scales cluster around [[10edo]].

== Temperament interpretations ==
An obvious interpretation for hexacot is [[miracle]], where the generator is [[16/15]]~[[15/14]], three of them make [[11/9]], and six of them make a perfect fifth. See [[miracle extensions]] for extensions.

[[Category:Ploidacots|Hexacot]]