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Quartismic family: Difference between revisions

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Remove non-existent extensions; various corrections (e.g. meanquarter can't be extended (recte tempered) to godzilla, also those are individual temperaments not clans)
m Edo lists reviewed
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[[POTE generator]]s: ~3/2 = 701.9826, ~5/4 = 386.3427, ~33/32 = 53.3748
[[POTE generator]]s: ~3/2 = 701.9826, ~5/4 = 386.3427, ~33/32 = 53.3748


{{Val list|legend=1| 21, 22, 24, 25, 43, 45, 46, 67, 68, 89, 90, 91, 92, 110, 111, 113, 114, 132, 134, 135, 138, 156, 157, 159, 178, 179, 180, 181, 202, 224, 270, 313, 359, 494, 629, 653, 742, 877, 1012, 1236, 1506, 2159, 2248, 2383, 2518, 3125, 7419 }}
{{Val list|legend=1| 21, 22, 43, 46, 65d, 68, 89, 111, 159, 202, 224, 270, 494, 742, 764, 966, 1236, 1506, 2159, 2653, 3125, 3395, 7060, 7554, 10949e, 14614e, 15850ee, 22168bdee, 23404bcdee, 26799bcdeee, 34353bcdeeee }}


[[Badness]]: 0.274 × 10<sup>-6</sup>
[[Badness]]: 0.274 × 10<sup>-6</sup>
Line 33: Line 33:
[[POTE generator]]s: ~3/2 = 701.9826, ~33/32 = 53.3748
[[POTE generator]]s: ~3/2 = 701.9826, ~33/32 = 53.3748


{{Val list|legend=1| 21, 22, 24, 43, 46, 89, 135, 270, 359, 494, 629, 653, 742, 877, 1012, 1236, 1506, 2159, 2248, 2383, 2518, 7419 }}
{{Val list|legend=1| 21, 22, 24, 43, 46, 89, 135, 359, 494, 629, 742, 877, 1012, 1506, 2248, 2383, 2518, 7419, 8431e, 10949e, 13467e }}


The following unnamed rank-2 quartismic temperament MOS scales have been found
The following unnamed rank-2 quartismic temperament MOS scales have been found
* [https://sevish.com/scaleworkshop/?name=Rank%202%20scale%20(106.71461627796054%2C%201200.0)%2C%205%7C5&data=106.714616%0A213.429233%0A320.143849%0A426.858465%0A533.573081%0A666.426919%0A773.141535%0A879.856151%0A986.570767%0A1093.285384%0A1200.000000&freq=440&midi=69&vert=9&horiz=1&colors=&waveform=triangle&ampenv=organ Rank 2 scale (106.71461627796054, 1200.0), 5|5]   
* [https://sevish.com/scaleworkshop/?name=Rank%202%20scale%20(106.71461627796054%2C%201200.0)%2C%205%7C5&data=106.714616%0A213.429233%0A320.143849%0A426.858465%0A533.573081%0A666.426919%0A773.141535%0A879.856151%0A986.570767%0A1093.285384%0A1200.000000&freq=440&midi=69&vert=9&horiz=1&colors=&waveform=triangle&ampenv=organ Rank 2 scale (106.71461627796054, 1200.0), 5|5]   
* The following scale tree has been found: [http://www.microtonalsoftware.com/scale-tree.html?left=12&right=11&rr=1200&ioi=106.71461627796054 1200-106.71461627796054-12-11 Scale Tree]
* The following scale tree has been found: [http://www.microtonalsoftware.com/scale-tree.html?left=12&right=11&rr=1200&ioi=106.71461627796054 1200-106.71461627796054-12-11 Scale Tree]


== Altierran ==
== Altierran ==
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[[POTE generator]]s: ~3/2 = 701.7299, ~33/32 = 53.3889  
[[POTE generator]]s: ~3/2 = 701.7299, ~33/32 = 53.3889  


{{Val list|legend=1| 135, 159, 224, 248, 313, 472 }}
{{Val list|legend=1| 24, 46c, 65d, 89, 135, 159, 224, 383, 472, 696, 1168, 1327, 1551, 2023e }}


=== 13-limit ===
=== 13-limit ===
Line 79: Line 79:
[[POTE generator]]s: ~3/2 = 697.3325, ~33/32 = 54.1064
[[POTE generator]]s: ~3/2 = 697.3325, ~33/32 = 54.1064


{{Val list|legend=1| 24, 43, 45, 67 }}
{{Val list|legend=1| 24, 43, 67, 110c }}


== Coin ==
== Coin ==
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[[POTE generator]]s: ~5/4 = 380.3623, ~9/7 = 433.3120
[[POTE generator]]s: ~5/4 = 380.3623, ~9/7 = 433.3120


{{Val list|legend=1| 22, 25, 139cdd }}
{{Val list|legend=1| 19d, 22 }}


== Escapismic ==
== Escapismic ==
Line 107: Line 107:
[[POTE generator]]s: ~33/32 = 55.3538
[[POTE generator]]s: ~33/32 = 55.3538


{{Val list|legend=1| 21, 22, 43 }}
{{Val list|legend=1| 21, 22, 43, 65d, 521d, 543, 564, 586, 629c, 651 }}


== Dietismic ==
== Dietismic ==
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[[Mapping]]: [{{val| 2 3 5 5 7 }}, {{val| 0 2 -4 7 -1 }}]
[[Mapping]]: [{{val| 2 3 5 5 7 }}, {{val| 0 2 -4 7 -1 }}]


{{Val list|legend=1| 22, 24, 38cdde, 46, 68, 114 }}
{{Val list|legend=1| 22, 46, 68, 114 }}


Scales:  
Scales:  
Line 141: Line 141:
[[POTE generator]]s: ~6/5 = 317.0291, ~68/55 = 370.2940
[[POTE generator]]s: ~6/5 = 317.0291, ~68/55 = 370.2940


{{Val list|legend=1| 159, 178, 246 }}
{{Val list|legend=1| 68, 91, 159, 246, 337, 405 }}


== Doublefour ==
== Doublefour ==
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[[POTE generator]]s: ~425/384 = 175.9566, ~33/32 = 52.9708
[[POTE generator]]s: ~425/384 = 175.9566, ~33/32 = 52.9708


{{Val list|legend=1| 48d, 68, 89c }}
{{Val list|legend=1| 48d, 68, 116d, 157c, 225 }}


[[Category:Regular temperament theory]]
[[Category:Regular temperament theory]]
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