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Ploidacot/Gamma-hexacot: Difference between revisions

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Created page with "{{Breadcrumb}} {{Infobox ploidacot|Ploids=1|Shears=3|Cots=6|Pergen=[P8, ccP4/6]|Forms=17, 22, 27, 32, 37|Title=Gamma-hexacot|Wedgie=6}} '''Gamma-hexacot ''' is a temperament archetype where the generator is a grave fourth of about 482–484{{c}}, six of which make 16/3 (perfect eighteenth, two octaves above a perfect fourth), and the period is a 2/1 octave. Gamma-hexacot temperaments also include all alpha-dicot and Ploidacot/Tricot|tr..."
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== Intervals and notation ==
== Intervals and notation ==
Due to dividing the eighteenth into so many steps, standard notation becomes almost useless for gamma-hexacot. Regardless, notation has been provided for where gamma-hexacot intervals align with standard monocot intervals (which use [[chain-of-fifths notation]]).
While there is no agreed-upon notation system for gamma-hexacot, the following is based on interpreting the generator as a grave fourth, and allowing for an ^ or v to stand for 1/6 of a diatonic semitone, so ^^^C and vvvDb are enharmonic.


{| class="wikitable"
{| class="wikitable"
Line 21: Line 21:
| −23
| −23
| 890.828
| 890.828
|  
| vA
|  
|  
|-
|-
| −22
| −22
| 173.835
| 173.835
|  
| vvD
|  
|  
|-
|-
| −21
| −21
| 656.843
| 656.843
|  
| ^^^F#/vvvG
|  
|  
|-
|-
| −20
| −20
| 1139.850
| 1139.850
|  
| ^^B
|  
|  
|-
|-
| −19
| −19
| 422.858
| 422.858
|  
| ^E
|  
|  
|-
|-
Line 51: Line 51:
| −17
| −17
| 188.873
| 188.873
|  
| vD
|  
|  
|-
|-
| −16
| −16
| 671.880
| 671.880
|  
| vvG
|  
|  
|-
|-
| −15
| −15
| 1154.888
| 1154.888
|  
| ^^^B/vvvC
|  
|  
|-
|-
| −14
| −14
| 437.895
| 437.895
|  
| ^^E
|  
|  
|-
|-
| −13
| −13
| 920.903
| 920.903
|  
| ^A
|  
|  
|-
|-
Line 81: Line 81:
| −11
| −11
| 686.918
| 686.918
|  
| vG
|  
|  
|-
|-
| −10
| −10
| 1169.925
| 1169.925
|  
| vvC
|  
|  
|-
|-
| −9
| −9
| 452.933
| 452.933
|  
| ^^^E/vvvF
|  
|  
|-
|-
| −8
| −8
| 935.940
| 935.940
|  
| ^^A
|  
|  
|-
|-
| −7
| −7
| 218.948
| 218.948
|  
| ^D
|  
|  
|-
|-
Line 111: Line 111:
| −5
| −5
| 1184.963
| 1184.963
|  
| vC
|  
|  
|-
|-
| −4
| −4
| 467.970
| 467.970
|  
| vvF
|  
|  
|-
|-
| −3
| −3
| 950.978
| 950.978
|  
| ^^^A/vvvBb
|  
|  
|-
|-
| −2
| −2
| 233.985
| 233.985
|  
| ^^D
|  
|  
|-
|-
| −1
| −1
| 716.993
| 716.993
|  
| ^G
|  
|  
|-
|-
Line 141: Line 141:
| 1
| 1
| 483.007
| 483.007
|  
| vF
|  
|  
|-
|-
| 2
| 2
| 966.015
| 966.015
|  
| vvBb
|  
|  
|-
|-
| 3
| 3
| 249.022
| 249.022
|  
| ^^^D/vvvEb
|  
|  
|-
|-
| 4
| 4
| 732.030
| 732.030
|  
| ^^G
|  
|  
|-
|-
| 5
| 5
| 15.037
| 15.037
|  
| ^C
|  
|  
|-
|-
Line 171: Line 171:
| 7
| 7
| 981.052
| 981.052
|  
| vBb
|  
|  
|-
|-
| 8
| 8
| 264.060
| 264.060
|  
| vvEb
|  
|  
|-
|-
| 9
| 9
| 747.067
| 747.067
|  
| ^^^G/vvvAb
|  
|  
|-
|-
| 10
| 10
| 30.075
| 30.075
|  
| ^^C
|  
|  
|-
|-
| 11
| 11
| 513.082
| 513.082
|  
| ^F
|  
|  
|-
|-
Line 201: Line 201:
| 13
| 13
| 279.097
| 279.097
|  
| vEb
|  
|  
|-
|-
| 14
| 14
| 762.105
| 762.105
|  
| vvAb
|  
|  
|-
|-
| 15
| 15
| 45.112
| 45.112
|  
| ^^^C/vvvDb
|  
|  
|-
|-
| 16
| 16
| 528.120
| 528.120
|  
| ^^F
|  
|  
|-
|-
| 17
| 17
| 1011.127
| 1011.127
|  
| ^Bb
|  
|  
|-
|-
Line 231: Line 231:
| 19
| 19
| 777.142
| 777.142
|  
| vAb
|  
|  
|-
|-
| 20
| 20
| 60.150
| 60.150
|  
| vvDb
|  
|  
|-
|-
| 21
| 21
| 543.157
| 543.157
|  
| ^^^F/vvvGb
|  
|  
|-
|-
| 22
| 22
| 1026.165
| 1026.165
|  
| ^^Bb
|  
|  
|-
|-
| 23
| 23
| 309.172
| 309.172
|  
| ^Eb
|  
|  
|-
|-
Line 261: Line 261:


== Temperament interpretations ==
== Temperament interpretations ==
An obvious interpretation for gamma-hexacot is [[hemiseven]], where the generator is [[45/34]], two of which make [[7/4]], four make {{nowrap|[[26/17]]~[[32/21]]}} above an octave, and six make [[4/3]] above two octaves.
An obvious interpretation for gamma-hexacot is [[hemiseven]], where the generator is [[45/34]], two of which make [[7/4]], three make [[15/13]] above an octave, four make {{nowrap|[[26/17]]~[[32/21]]}} above an octave, six make [[4/3]] above two octaves, seven make [[30/17]] above two octaves, seventeen make [[9/5]] above six octaves, and nineteen make [[11/7]] above seven octaves.


[[Category:Ploidacots|Gamma-hexacot]]
[[Category:Ploidacots|Gamma-hexacot]]
Retrieved from "https://en.xen.wiki/w/Ploidacot/Gamma-hexacot"