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Tetracot family: Difference between revisions

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Re-added POTE tunings
BudjarnLambeth (talk | contribs)
autopatrolled, emailconfirmed
21,295 edits
m Made consistent with the formatting of other temperament pages
Line 12: Line 12:
{{Mapping|legend=1| 1 1 1 | 0 4 9 }}
{{Mapping|legend=1| 1 1 1 | 0 4 9 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~10/9 = 176.028
[[Optimal tuning]]s:
 
* [[CTE]]: ~2 = 1\1, ~10/9 = 176.028
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~10/9 = 176.160
* [[POTE]]:~2 = 1\1, ~10/9 = 176.160


[[Minimax tuning]]:  
[[Minimax tuning]]:  
Line 51: Line 51:
Sval mapping: {{mapping| 1 1 1 2 | 0 4 9 10 }}
Sval mapping: {{mapping| 1 1 1 2 | 0 4 9 10 }}


Optimal tuning (CTE): ~2 = 1\1, ~10/9 = 175.7765
Optimal tunings:
 
* CTE: ~2 = 1\1, ~10/9 = 175.7765
Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 175.985
* POTE ~2 = 1\1, ~10/9 = 175.985


Optimal ET sequence: {{Optimal ET sequence| 7, 20ce, 27e, 34, 41, 75e }}
Optimal ET sequence: {{Optimal ET sequence| 7, 20ce, 27e, 34, 41, 75e }}
Line 66: Line 66:
Sval mapping: {{mapping| 1 1 1 2 4 | 0 4 9 10 -2 }}
Sval mapping: {{mapping| 1 1 1 2 4 | 0 4 9 10 -2 }}


Optimal tuning (CTE): ~2 = 1\1, ~10/9 = 175.8150
Optimal tunings:
 
* CTE: ~2 = 1\1, ~10/9 = 175.8150
Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 176.196
* POTE ~2 = 1\1, ~10/9 = 176.196


Optimal ET sequence: {{Optimal ET sequence| 7, 20ce, 27e, 34, 41, 75e, 109ef }}
Optimal ET sequence: {{Optimal ET sequence| 7, 20ce, 27e, 34, 41, 75e, 109ef }}
Line 85: Line 85:
{{Multival|legend=1| 4 9 -15 5 -35 -60 }}
{{Multival|legend=1| 4 9 -15 5 -35 -60 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~10/9 = 175.676
Optimal tunings:
 
* CTE: ~2 = 1\1, ~10/9 = 175.676
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~10/9 = 175.659
* POTE:~2 = 1\1, ~10/9 = 175.659


{{Optimal ET sequence|legend=1| 7, 34, 41 }}
{{Optimal ET sequence|legend=1| 7, 34, 41 }}
Line 100: Line 100:
Mapping: {{mapping| 1 1 1 5 2 | 0 4 9 -15 10 }}
Mapping: {{mapping| 1 1 1 5 2 | 0 4 9 -15 10 }}


Optimal tuning (CTE): ~2 = 1\1, ~10/9 = 175.598
Optimal tunings:
 
* CTE: ~2 = 1\1, ~10/9 = 175.598
Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 175.570
* POTE ~2 = 1\1, ~10/9 = 175.570


Optimal ET sequence: {{Optimal ET sequence| 7, 34, 41 }}
Optimal ET sequence: {{Optimal ET sequence| 7, 34, 41 }}
Line 115: Line 115:
Mapping: {{mapping| 1 1 1 5 2 4 | 0 4 9 -15 10 -2 }}
Mapping: {{mapping| 1 1 1 5 2 4 | 0 4 9 -15 10 -2 }}


Optimal tuning (CTE): ~2 = 1\1, ~10/9 = 175.618
Optimal tunings:
 
* CTE: ~2 = 1\1, ~10/9 = 175.618
Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 175.622
* POTE ~2 = 1\1, ~10/9 = 175.622


Optimal ET sequence: {{Optimal ET sequence| 7, 34, 41 }}
Optimal ET sequence: {{Optimal ET sequence| 7, 34, 41 }}
Line 160: Line 160:
{{Multival|legend=1| 4 9 26 5 30 35 }}
{{Multival|legend=1| 4 9 26 5 30 35 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~10/9 = 175.785
Optimal tunings:
 
* CTE: ~2 = 1\1, ~10/9 = 175.785
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~10/9 = 175.741
* POTE:~2 = 1\1, ~10/9 = 175.741


{{Optimal ET sequence|legend=1| 7d, …, 34d, 41, 116, 157c, 198c }}
{{Optimal ET sequence|legend=1| 7d, …, 34d, 41, 116, 157c, 198c }}
Line 175: Line 175:
Mapping: {{mapping| 1 1 1 -1 2 | 0 4 9 26 10 }}
Mapping: {{mapping| 1 1 1 -1 2 | 0 4 9 26 10 }}


Optimal tuning (CTE): ~2 = 1\1, ~10/9 = 175.738
Optimal tunings:
 
* CTE: ~2 = 1\1, ~10/9 = 175.738
Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 175.777
* POTE ~2 = 1\1, ~10/9 = 175.777


Optimal ET sequence: {{Optimal ET sequence| 7d, …, 34d, 41, 116e }}
Optimal ET sequence: {{Optimal ET sequence| 7d, …, 34d, 41, 116e }}
Line 190: Line 190:
Mapping: {{mapping| 1 1 1 -1 2 4 | 0 4 9 26 10 -2 }}
Mapping: {{mapping| 1 1 1 -1 2 4 | 0 4 9 26 10 -2 }}


Optimal tuning (CTE): ~2 = 1\1, ~10/9 = 175.748
Optimal tunings:
 
* CTE: ~2 = 1\1, ~10/9 = 175.748
Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 175.886
* POTE ~2 = 1\1, ~10/9 = 175.886


Optimal ET sequence: {{Optimal ET sequence| 7d, 34d, 41, 116ef }}
Optimal ET sequence: {{Optimal ET sequence| 7d, 34d, 41, 116ef }}
Line 235: Line 235:
{{Mapping|legend=1| 1 1 1 4 | 0 4 9 -8 }}
{{Mapping|legend=1| 1 1 1 4 | 0 4 9 -8 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~10/9 = 176.818
Optimal tunings:
 
* CTE: ~2 = 1\1, ~10/9 = 176.818
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~10/9 = 177.203
* POTE:~2 = 1\1, ~10/9 = 177.203


{{Optimal ET sequence|legend=1| 7, 20c, 27, 34d, 61d, 95dd }}
{{Optimal ET sequence|legend=1| 7, 20c, 27, 34d, 61d, 95dd }}
Line 250: Line 250:
Mapping: {{mapping| 1 1 1 4 2 | 0 4 9 -8 10 }}
Mapping: {{mapping| 1 1 1 4 2 | 0 4 9 -8 10 }}


Optimal tuning (CTE): ~2 = 1\1, ~10/9 = 176.446
Optimal tunings:
 
* CTE: ~2 = 1\1, ~10/9 = 176.446
Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 177.053
* POTE ~2 = 1\1, ~10/9 = 177.053


Optimal ET sequence: {{Optimal ET sequence| 7, 20ce, 27e, 34d }}
Optimal ET sequence: {{Optimal ET sequence| 7, 20ce, 27e, 34d }}
Line 265: Line 265:
Mapping: {{mapping| 1 1 1 4 2 4 | 0 4 9 -8 10 -2 }}
Mapping: {{mapping| 1 1 1 4 2 4 | 0 4 9 -8 10 -2 }}


Optimal tuning (CTE): ~2 = 1\1, ~10/9 = 176.471
Optimal tunings:
 
* CTE: ~2 = 1\1, ~10/9 = 176.471
Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 176.953
* POTE ~2 = 1\1, ~10/9 = 176.953


Optimal ET sequence: {{Optimal ET sequence| 7, 20ce, 27e, 34d }}
Optimal ET sequence: {{Optimal ET sequence| 7, 20ce, 27e, 34d }}
Line 313: Line 313:
Mapping: {{mapping| 1 1 1 4 3 | 0 4 9 -8 3 }}
Mapping: {{mapping| 1 1 1 4 3 | 0 4 9 -8 3 }}


Optimal tuning (CTE): ~2 = 1\1, ~10/9 = 176.990
Optimal tunings:
 
* CTE: ~2 = 1\1, ~10/9 = 176.990
Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 177.200
* POTE ~2 = 1\1, ~10/9 = 177.200


Optimal ET sequence: {{Optimal ET sequence| 7, 20c, 27, 34de, 61dee }}
Optimal ET sequence: {{Optimal ET sequence| 7, 20c, 27, 34de, 61dee }}
Line 328: Line 328:
Mapping: {{mapping| 1 1 1 4 3 4 | 0 4 9 -8 3 -2 }}
Mapping: {{mapping| 1 1 1 4 3 4 | 0 4 9 -8 3 -2 }}


Optimal tuning (CTE): ~2 = 1\1, ~10/9 = 177.017
Optimal tunings:
 
* CTE: ~2 = 1\1, ~10/9 = 177.017
Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 177.197
* POTE ~2 = 1\1, ~10/9 = 177.197


Optimal ET sequence: {{Optimal ET sequence| 7, 20c, 27, 34de, 61dee }}
Optimal ET sequence: {{Optimal ET sequence| 7, 20c, 27, 34de, 61dee }}
Line 373: Line 373:
{{Multival|legend=1| 4 9 19 5 19 19 }}
{{Multival|legend=1| 4 9 19 5 19 19 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~10/9 = 176.900
Optimal tunings:
 
* CTE: ~2 = 1\1, ~10/9 = 176.900
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~10/9 = 177.357
* POTE:~2 = 1\1, ~10/9 = 177.357


{{Optimal ET sequence|legend=1| 7d, 20cd, 27, 34, 61, 95d, 156bcd }}
{{Optimal ET sequence|legend=1| 7d, 20cd, 27, 34, 61, 95d, 156bcd }}
Line 388: Line 388:
Mapping: {{mapping| 1 1 1 0 2 | 0 4 9 19 10 }}
Mapping: {{mapping| 1 1 1 0 2 | 0 4 9 19 10 }}


Optimal tuning (CTE): ~2 = 1\1, ~10/9 = 176.704
Optimal tunings:
 
* CTE: ~2 = 1\1, ~10/9 = 176.704
Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 177.413
* POTE ~2 = 1\1, ~10/9 = 177.413


Optimal ET sequence: {{Optimal ET sequence| 7d, 20cde, 27e, 34, 95dee }}
Optimal ET sequence: {{Optimal ET sequence| 7d, 20cde, 27e, 34, 95dee }}
Line 403: Line 403:
Mapping: {{mapping| 1 1 1 0 2 4 | 0 4 9 19 10 -2 }}
Mapping: {{mapping| 1 1 1 0 2 4 | 0 4 9 19 10 -2 }}


Optimal tuning (CTE): ~2 = 1\1, ~10/9 = 176.716
Optimal tunings:
 
* CTE: ~2 = 1\1, ~10/9 = 176.716
Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 177.231
* POTE ~2 = 1\1, ~10/9 = 177.231


Optimal ET sequence: {{Optimal ET sequence| 7d, 20cde, 27e, 34, 95dee }}
Optimal ET sequence: {{Optimal ET sequence| 7d, 20cde, 27e, 34, 95dee }}
Line 452: Line 452:
{{Multival|legend=1| 8 18 11 10 -5 -25 }}
{{Multival|legend=1| 8 18 11 10 -5 -25 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~21/20 = 88.023
Optimal tunings:
 
* CTE: ~2 = 1\1, ~21/20 = 88.023
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~21/20 = 88.076
* POTE:~2 = 1\1, ~21/20 = 88.076


{{Optimal ET sequence|legend=1| 14c, 27, 41, 68, 109, 150, 259, 409bc, 668bbcc }}
{{Optimal ET sequence|legend=1| 14c, 27, 41, 68, 109, 150, 259, 409bc, 668bbcc }}
Line 467: Line 467:
Mapping: {{mapping| 1 1 1 2 2 | 0 8 18 11 20 }}
Mapping: {{mapping| 1 1 1 2 2 | 0 8 18 11 20 }}


Optimal tuning (CTE): ~2 = 1\1, ~21/20 = 87.910
Optimal tunings:
 
* CTE: ~2 = 1\1, ~21/20 = 87.910
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 87.975
* POTE ~2 = 1\1, ~21/20 = 87.975


Optimal ET sequence: {{Optimal ET sequence| 14c, 27e, 41, 150ee, 191ee, 232cee }}
Optimal ET sequence: {{Optimal ET sequence| 14c, 27e, 41, 150ee, 191ee, 232cee }}
Line 482: Line 482:
Mapping: {{mapping| 1 1 1 2 2 4 | 0 8 18 11 20 -4 }}
Mapping: {{mapping| 1 1 1 2 2 4 | 0 8 18 11 20 -4 }}


Optimal tuning (CTE): ~2 = 1\1, ~21/20 = 87.926
Optimal tunings:
 
* CTE: ~2 = 1\1, ~21/20 = 87.926
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 88.106
* POTE ~2 = 1\1, ~21/20 = 88.106


Optimal ET sequence: {{Optimal ET sequence| 14c, 27e, 41, 150eef, 191eeff, 232ceeff }}
Optimal ET sequence: {{Optimal ET sequence| 14c, 27e, 41, 150eef, 191eeff, 232ceeff }}
Line 497: Line 497:
Mapping: {{mapping| 1 1 1 2 2 4 3 | 0 8 18 11 20 -4 15 }}
Mapping: {{mapping| 1 1 1 2 2 4 3 | 0 8 18 11 20 -4 15 }}


Optimal tuning (CTE): ~2 = 1\1, ~18/17 = 87.842
Optimal tunings:
 
* CTE: ~2 = 1\1, ~18/17 = 87.842
Optimal tuning (POTE): ~2 = 1\1, ~18/17 = 88.102
* POTE ~2 = 1\1, ~18/17 = 88.102


Optimal ET sequence: {{Optimal ET sequence| 14c, 27eg, 41 }}
Optimal ET sequence: {{Optimal ET sequence| 14c, 27eg, 41 }}
Line 512: Line 512:
Mapping: {{mapping| 1 1 1 2 2 4 3 3 | 0 8 18 11 20 -4 15 17 }}
Mapping: {{mapping| 1 1 1 2 2 4 3 3 | 0 8 18 11 20 -4 15 17 }}


Optimal tuning (CTE): ~2 = 1\1, ~18/17 = 87.866
Optimal tunings:
 
* CTE: ~2 = 1\1, ~18/17 = 87.866
Optimal tuning (POTE): ~2 = 1\1, ~18/17 = 88.111
* POTE ~2 = 1\1, ~18/17 = 88.111


Optimal ET sequence: {{Optimal ET sequence| 14c, 27eg, 41 }}
Optimal ET sequence: {{Optimal ET sequence| 14c, 27eg, 41 }}
Line 527: Line 527:
Mapping: {{mapping| 1 1 1 2 2 2 | 0 8 18 11 20 23 }}
Mapping: {{mapping| 1 1 1 2 2 2 | 0 8 18 11 20 23 }}


Optimal tuning (CTE): ~2 = 1\1, ~21/20 = 88.090
Optimal tunings:
 
* CTE: ~2 = 1\1, ~21/20 = 88.090
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 88.179
* POTE ~2 = 1\1, ~21/20 = 88.179


Optimal ET sequence: {{Optimal ET sequence| 14cf, 27e, 41f, 68ef, 109eff }}
Optimal ET sequence: {{Optimal ET sequence| 14cf, 27e, 41f, 68ef, 109eff }}
Line 568: Line 568:
Mapping: {{mapping| 1 1 1 2 2 1 | 0 8 18 11 20 37 }}
Mapping: {{mapping| 1 1 1 2 2 1 | 0 8 18 11 20 37 }}


Optimal tuning (CTE): ~2 = 1\1, ~21/20 = 87.770
Optimal tunings:
 
* CTE: ~2 = 1\1, ~21/20 = 87.770
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 87.697
* POTE ~2 = 1\1, ~21/20 = 87.697


Optimal ET sequence: {{Optimal ET sequence| 14cf, 27eff, 41 }}
Optimal ET sequence: {{Optimal ET sequence| 14cf, 27eff, 41 }}
Line 609: Line 609:
Mapping: {{mapping| 1 9 19 13 22 19 | 0 -16 -36 -22 -40 -33 }}
Mapping: {{mapping| 1 9 19 13 22 19 | 0 -16 -36 -22 -40 -33 }}


Optimal tuning (CTE): ~2 = 1\1, ~13/9 = 643.916
Optimal tunings:
 
* CTE: ~2 = 1\1, ~13/9 = 643.916
Optimal tuning (POTE): ~2 = 1\1, ~13/9 = 643.989
* POTE ~2 = 1\1, ~13/9 = 643.989


Optimal ET sequence: {{Optimal ET sequence| 13cdeef, 28ccdef, 41 }}
Optimal ET sequence: {{Optimal ET sequence| 13cdeef, 28ccdef, 41 }}
Line 624: Line 624:
Mapping: {{mapping| 1 1 1 2 5 | 0 8 18 11 -21 }}
Mapping: {{mapping| 1 1 1 2 5 | 0 8 18 11 -21 }}


Optimal tuning (CTE): ~2 = 1\1, ~21/20 = 88.026
Optimal tunings:
 
* CTE: ~2 = 1\1, ~21/20 = 88.026
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 88.035
* POTE ~2 = 1\1, ~21/20 = 88.035


Optimal ET sequence: {{Optimal ET sequence| 27, 41, 68, 109, 150, 259 }}
Optimal ET sequence: {{Optimal ET sequence| 27, 41, 68, 109, 150, 259 }}
Line 639: Line 639:
Mapping: {{mapping| 1 1 1 2 5 4 | 0 8 18 11 -21 -4 }}
Mapping: {{mapping| 1 1 1 2 5 4 | 0 8 18 11 -21 -4 }}


Optimal tuning (CTE): ~2 = 1\1, ~21/20 = 88.041
Optimal tunings:
 
* CTE: ~2 = 1\1, ~21/20 = 88.041
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 88.075
* POTE ~2 = 1\1, ~21/20 = 88.075


Optimal ET sequence: {{Optimal ET sequence| 27, 41, 68, 109f }}
Optimal ET sequence: {{Optimal ET sequence| 27, 41, 68, 109f }}
Line 654: Line 654:
Mapping: {{mapping| 1 1 1 2 5 4 6 | 0 8 18 11 -21 -4 -26 }}
Mapping: {{mapping| 1 1 1 2 5 4 6 | 0 8 18 11 -21 -4 -26 }}


Optimal tuning (CTE): ~2 = 1\1, ~21/20 = 88.093
Optimal tunings:
 
* CTE: ~2 = 1\1, ~21/20 = 88.093
Optimal tuning (POTE): ~2 = 1\1, ~21/20 = 88.104
* POTE ~2 = 1\1, ~21/20 = 88.104


Optimal ET sequence: {{Optimal ET sequence| 27, 41, 68, 109f }}
Optimal ET sequence: {{Optimal ET sequence| 27, 41, 68, 109f }}
Line 669: Line 669:
Mapping: {{mapping| 1 1 1 2 5 4 6 3 | 0 8 18 11 -21 -4 -26 17 }}
Mapping: {{mapping| 1 1 1 2 5 4 6 3 | 0 8 18 11 -21 -4 -26 17 }}


Optimal tuning (CTE): ~2 = 1\1, ~19/18 = 88.093
Optimal tunings:
 
* CTE: ~2 = 1\1, ~19/18 = 88.093
Optimal tuning (POTE): ~2 = 1\1, ~19/18 = 88.113
* POTE ~2 = 1\1, ~19/18 = 88.113


Optimal ET sequence: {{Optimal ET sequence| 27, 41, 68, 109f }}
Optimal ET sequence: {{Optimal ET sequence| 27, 41, 68, 109f }}
Line 686: Line 686:
{{Multival|legend=1| 12 27 37 15 25 10 }}
{{Multival|legend=1| 12 27 37 15 25 10 }}


[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~28/27 = 58.648
Optimal tunings:
 
* CTE: ~2 = 1\1, ~28/27 = 58.648
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~28/27 = 58.675
* POTE:~2 = 1\1, ~28/27 = 58.675


{{Optimal ET sequence|legend=1| 41, 143d, 184, 225, 266c }}
{{Optimal ET sequence|legend=1| 41, 143d, 184, 225, 266c }}
Line 701: Line 701:
Mapping: {{mapping| 1 1 1 1 2 | 0 12 27 37 30 }}
Mapping: {{mapping| 1 1 1 1 2 | 0 12 27 37 30 }}


Optimal tuning (CTE): ~2 = 1\1, ~28/27 = 58.602
Optimal tunings:
 
* CTE: ~2 = 1\1, ~28/27 = 58.602
Optimal tuning (POTE): ~2 = 1\1, ~28/27 = 58.665
* POTE ~2 = 1\1, ~28/27 = 58.665


Optimal ET sequence: {{Optimal ET sequence| 20cde, 41 }}
Optimal ET sequence: {{Optimal ET sequence| 20cde, 41 }}
Line 716: Line 716:
Mapping: {{mapping| 1 1 1 1 2 2 | 0 12 27 37 30 35 }}
Mapping: {{mapping| 1 1 1 1 2 2 | 0 12 27 37 30 35 }}


Optimal tuning (CTE): ~2 = 1\1, ~27/26 = 58.551
Optimal tunings:
 
* CTE: ~2 = 1\1, ~27/26 = 58.551
Optimal tuning (POTE): ~2 = 1\1, ~27/26 = 58.639
* POTE ~2 = 1\1, ~27/26 = 58.639


Optimal ET sequence: {{Optimal ET sequence| 20cdef, 21cdef, 41 }}
Optimal ET sequence: {{Optimal ET sequence| 20cdef, 21cdef, 41 }}
Line 737: Line 737:
{{Multival|legend=1| 8 18 18 10 6 -9 }}
{{Multival|legend=1| 8 18 18 10 6 -9 }}


[[Optimal tuning]] ([[CTE]]): ~7/5 = 1\2, ~10/9 = 175.472
Optimal tuning (CTE): ~7/5 = 1\2, ~10/9 = 175.472


{{Optimal ET sequence|legend=1| 14c, 34d, 48, 82d, 130cdd }}
{{Optimal ET sequence|legend=1| 14c, 34d, 48, 82d, 130cdd }}
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