Quintile family
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
The pentacloud temperament (5&60, named by Xenllium) tempers out the cloudy comma, 16807/16384 and the sensamagic comma, 245/243 in the 7-limit.
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
The hemipental temperament (125&130, named by Xenllium) tempers out the cataharry comma, 19683/19600 in the 7-limit, as well as 589824/588245 (satribiru-agu) and 5250987/5242880 (laquadzo-agu).
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
The decal temperament (130&190) tempers out the varunisma, 321489/320000 in the 7-limit, as well as 235298/234375 (tribizo-sepgu), 2460375/2458624 (laquadru-triyo), and the linus comma, |11 -10 -10 10>.
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