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 (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|]

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: 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|]

Vals: 130, 190, 320

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|]

Vals: 130, 190, 320

Badness: 0.023948