Quintile family: Difference between revisions
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Comma: 847288609443/838860800000 | Comma: 847288609443/838860800000 | ||
POTE generator: ~3/2 = 701.210 | [[POTE tuning|POTE generator]]: ~3/2 = 701.210 | ||
Map: [<5 0 -28|, <0 1 5|] | [[Map]]: [<5 0 -28|, <0 1 5|] | ||
{{Vals|legend=1| 5, 60, 65, 190, 255, 575, 830b, 1405b }} | |||
Badness: 0. | [[Badness]]: 0.240050 | ||
=Pentacloud (5 & 60)= | |||
[[Comma list]]: 245/243, 16807/16384 | |||
[[POTE tuning|POTE generator]]: ~3/2 = 700.548 | |||
[[Map]]: [<5 0 -28 14|, <0 1 5 0|] | |||
{{Vals|legend=1| 5, 60, 65, 125d, 185cdd }} | |||
[[Badness]]: 0.120942 | |||
==11-limit== | |||
Comma list: 245/243, 385/384, 3087/3025 | |||
POTE generator: ~3/2 = 701.377 | |||
Map: [<5 0 -28 14 49|, <0 1 5 0 -4|] | |||
Vals: {{Vals| 5, 60, 65 }} | |||
Badness: 0.093248 | |||
==13-limit== | |||
Comma list: 105/104, 144/143, 245/243, 3087/3025 | |||
POTE generator: ~3/2 = 700.996 | |||
Map: [<5 0 -28 14 49 -29|, <0 1 5 0 -4 6|] | |||
Vals: {{Vals| 5, 60, 65, 125de, 190ddef }} | |||
Badness: 0.067549 | |||
=Hemipental (5 & 130)= | |||
[[Comma list]]: 19683/19600, 589824/588245 | |||
[[POTE tuning|POTE generator]]: ~8/7 = 230.654 | |||
[[Map]]: [<5 8 12 14|, <0 -2 -10 1|] | |||
{{Vals|legend=1| 5, 125, 130, 255, 385 }} | |||
[[Badness]]: 0.104163 | |||
==11-limit== | |||
Comma list: 540/539, 8019/8000, 180224/180075 | |||
POTE generator: ~8/7 = 230.634 | |||
Map: [<5 8 12 14 18|, <0 -2 -10 1 -18|] | |||
Vals: {{Vals| 5e, 125, 130, 255, 385, 640, 1025b }} | |||
Badness: 0.047624 | |||
==13-limit== | |||
Comma list: 540/539, 1575/1573, 4096/4095, 8019/8000 | |||
POTE generator: ~8/7 = 230.668 | |||
Map: [<5 8 12 14 18 18|, <0 -2 -10 1 -18 13|] | |||
Vals: {{Vals| 5ef, 125, 130, 255, 385, 515, 900ef }} | |||
Badness: 0.041043 | |||
=Decal= | =Decal= | ||
[[Comma list]]: 235298/234375, 321489/320000 | |||
POTE generator: ~3/2 = 701.303 | [[POTE tuning|POTE generator]]: ~3/2 = 701.303 | ||
Map: [<10 0 -56 -67|, <0 1 5 6|] | [[Map]]: [<10 0 -56 -67|, <0 1 5 6|] | ||
{{Vals|legend=1| 60, 130, 320, 450, 770d }} | |||
Badness: 0. | [[Badness]]: 0.104859 | ||
==11-limit== | ==11-limit== | ||
Comma list: 441/440, 8019/8000, 234375/234256 | |||
POTE generator: ~3/2 = 701.240 | POTE generator: ~3/2 = 701.240 | ||
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Map: [<10 0 -56 -67 -108|, <0 1 5 6 9|] | Map: [<10 0 -56 -67 -108|, <0 1 5 6 9|] | ||
Vals: {{Vals| 130, 190, 320 }} | |||
Badness: 0. | Badness: 0.040633 | ||
==13-limit== | ==13-limit== | ||
Comma list: 441/440, 729/728, 1001/1000, 4225/4224 | |||
POTE generator: ~3/2 = 701.252 | POTE generator: ~3/2 = 701.252 | ||
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Map: [<10 0 -56 -67 -108 37|, <0 1 5 6 9 0|] | Map: [<10 0 -56 -67 -108 37|, <0 1 5 6 9 0|] | ||
Vals: {{Vals| 130, 190, 320 }} | |||
Badness: 0.023948 | |||
[[Category:Temperament family]] | |||
Revision as of 05:14, 3 April 2021
The pental family tempers out the pental comma, 847288609443/838860800000 = |-28 25 -5>.
Pental
Comma: 847288609443/838860800000
POTE generator: ~3/2 = 701.210
Map: [<5 0 -28|, <0 1 5|]
Optimal ET sequence: 5, 60, 65, 190, 255, 575, 830b, 1405b
Badness: 0.240050
Pentacloud (5 & 60)
Comma list: 245/243, 16807/16384
POTE generator: ~3/2 = 700.548
Map: [<5 0 -28 14|, <0 1 5 0|]
Optimal ET sequence: 5, 60, 65, 125d, 185cdd
Badness: 0.120942
11-limit
Comma list: 245/243, 385/384, 3087/3025
POTE generator: ~3/2 = 701.377
Map: [<5 0 -28 14 49|, <0 1 5 0 -4|]
Badness: 0.093248
13-limit
Comma list: 105/104, 144/143, 245/243, 3087/3025
POTE generator: ~3/2 = 700.996
Map: [<5 0 -28 14 49 -29|, <0 1 5 0 -4 6|]
Vals: 5, 60, 65, 125de, 190ddef
Badness: 0.067549
Hemipental (5 & 130)
Comma list: 19683/19600, 589824/588245
POTE generator: ~8/7 = 230.654
Map: [<5 8 12 14|, <0 -2 -10 1|]
Optimal ET sequence: 5, 125, 130, 255, 385
Badness: 0.104163
11-limit
Comma list: 540/539, 8019/8000, 180224/180075
POTE generator: ~8/7 = 230.634
Map: [<5 8 12 14 18|, <0 -2 -10 1 -18|]
Vals: 5e, 125, 130, 255, 385, 640, 1025b
Badness: 0.047624
13-limit
Comma list: 540/539, 1575/1573, 4096/4095, 8019/8000
POTE generator: ~8/7 = 230.668
Map: [<5 8 12 14 18 18|, <0 -2 -10 1 -18 13|]
Vals: 5ef, 125, 130, 255, 385, 515, 900ef
Badness: 0.041043
Decal
Comma list: 235298/234375, 321489/320000
POTE generator: ~3/2 = 701.303
Map: [<10 0 -56 -67|, <0 1 5 6|]
Optimal ET sequence: 60, 130, 320, 450, 770d
Badness: 0.104859
11-limit
Comma list: 441/440, 8019/8000, 234375/234256
POTE generator: ~3/2 = 701.240
Map: [<10 0 -56 -67 -108|, <0 1 5 6 9|]
Badness: 0.040633
13-limit
Comma list: 441/440, 729/728, 1001/1000, 4225/4224
POTE generator: ~3/2 = 701.252
Map: [<10 0 -56 -67 -108 37|, <0 1 5 6 9 0|]
Badness: 0.023948