I wanted some simple intervals to test a microtonal score writing program. These ones only differ from 5-limit natural intervals by one or two commas, I think. They're 23-limit commas, but still.
Here is the full set of interval qualities: [P, M, m, A, d, Ac, Gr, AcM, Grm, Sp, Sb, SpM, Sbm, SpA, Sbd, As, De, Asm, DeM, AsGrm, DeAcM, Pr, Re, Prm, ReM, Ex, Hu, ExM, Hbm, Rs, Fa, Fam, RsM, Nb, NbM, Dsm, ReAsM, PrDem, RsAsM, FaDem. RsSbM, FaSpm, SbAcm, SpGrM].
Here are the intervals.
P1 # 1/1 @ 0c
SpA0 # 225/224 @ 8c
Rs1 # 96/95 @ 18c
Ac1 # 81/80 @ 22c
Pr1 # 65/64 @ 27c
Ex1 # 51/50 @ 34c
Nb1 # 46/45 @ 38c
d2 # 128/125 @ 41c
Sp1 # 36/35 @ 49c
As1 # 33/32 @ 53c
Sbm2 # 28/27 @ 63c
A1 # 25/24 @ 71c
Dsm2 # 24/23 @ 74c
Hbm2 # 160/153 @ 77c
SbAcm2 # 21/20 @ 84c
PrDem2 # 104/99 @ 85c
Grm2 # 256/243 @ 90c
Fam2 # 19/18 @ 94c
m2 # 16/15 @ 112c
SpA1 # 15/14 @ 119c
Prm2 # 13/12 @ 139c
FaSpm2 # 38/35 @ 142c
AsGrm2 # 88/81 @ 143c
DeAcM2 # 12/11 @ 151c
ReM2 # 128/117 @ 156c
Asm2 # 11/10 @ 165c
M2 # 10/9 @ 182c
Sbd3 # 28/25 @ 196c
RsM2 # 64/57 @ 201c
AcM2 # 9/8 @ 204c
ReAsM2 # 44/39 @ 209c
ExM2 # 17/15 @ 217c
NbM2 # 92/81 @ 220c
SpM2 # 8/7 @ 231c
d3 # 144/125 @ 245c
A2 # 125/108 @ 253c
RsAsM2 # 22/19 @ 254c
Sbm3 # 7/6 @ 267c
Dsm3 # 27/23 @ 278c
Hbm3 # 20/17 @ 281c
SbAcm3 # 189/160 @ 288c
PrDem3 # 13/11 @ 289c
Grm3 # 32/27 @ 294c
Fam3 # 19/16 @ 298c
SpA2 # 25/21 @ 302c
m3 # 6/5 @ 316c
DeM3 # 40/33 @ 333c
Prm3 # 39/32 @ 342c
FaSpm3 # 171/140 @ 346c
AsGrm3 # 11/9 @ 347c
DeAcM3 # 27/22 @ 355c
ReM3 # 16/13 @ 359c
Asm3 # 99/80 @ 369c
Sbd4 # 56/45 @ 379c
M3 # 5/4 @ 386c
RsM3 # 24/19 @ 404c
AcM3 # 81/64 @ 408c
ReAsM3 # 33/26 @ 413c
SpGrM3 # 80/63 @ 414c
ExM3 # 51/40 @ 421c
NbM3 # 23/18 @ 424c
d4 # 32/25 @ 427c
SpM3 # 9/7 @ 435c
De4 # 128/99 @ 445c
Sb4 # 35/27 @ 449c
A3 # 125/96 @ 457c
RsAsM3 # 99/76 @ 458c
Re4 # 256/195 @ 471c
Fa4 # 95/72 @ 480c
P4 # 4/3 @ 498c
SpA3 # 75/56 @ 506c
Rs4 # 128/95 @ 516c
Ac4 # 27/20 @ 520c
Pr4 # 65/48 @ 525c
Ex4 # 34/25 @ 532c
Nb4 # 184/135 @ 536c
Sp4 # 48/35 @ 547c
As4 # 11/8 @ 551c
A4 # 25/18 @ 569c
Sbd5 # 7/5 @ 583c
SpA4 # 10/7 @ 617c
d5 # 36/25 @ 631c
De5 # 16/11 @ 649c
Sb5 # 35/24 @ 653c
Re5 # 96/65 @ 675c
Gr5 # 40/27 @ 680c
Fa5 # 95/64 @ 684c
Sbd6 # 112/75 @ 694c
P5 # 3/2 @ 702c
Rs5 # 144/95 @ 720c
Ac5 # 243/160 @ 723c
Pr5 # 195/128 @ 729c
Ex5 # 153/100 @ 736c
Nb5 # 23/15 @ 740c
d6 # 192/125 @ 743c
Sp5 # 54/35 @ 751c
As5 # 99/64 @ 755c
Sbm6 # 14/9 @ 765c
A5 # 25/16 @ 773c
Dsm6 # 36/23 @ 776c
Hbm6 # 80/51 @ 779c
SbAcm6 # 63/40 @ 786c
PrDem6 # 52/33 @ 787c
Grm6 # 128/81 @ 792c
Fam6 # 19/12 @ 796c
m6 # 8/5 @ 814c
SpA5 # 45/28 @ 821c
DeM6 # 160/99 @ 831c
Prm6 # 13/8 @ 841c
FaSpm6 # 57/35 @ 844c
AsGrm6 # 44/27 @ 845c
DeAcM6 # 18/11 @ 853c
ReM6 # 64/39 @ 858c
Asm6 # 33/20 @ 867c
M6 # 5/3 @ 884c
Sbd7 # 42/25 @ 898c
RsM6 # 32/19 @ 902c
AcM6 # 27/16 @ 906c
ReAsM6 # 22/13 @ 911c
ExM6 # 17/10 @ 919c
NbM6 # 46/27 @ 922c
SpM6 # 12/7 @ 933c
d7 # 216/125 @ 947c
A6 # 125/72 @ 955c
RsAsM6 # 33/19 @ 956c
Sbm7 # 7/4 @ 969c
Dsm7 # 81/46 @ 980c
Hbm7 # 30/17 @ 983c
PrDem7 # 39/22 @ 991c
Grm7 # 16/9 @ 996c
Fam7 # 57/32 @ 999c
SpA6 # 25/14 @ 1004c
m7 # 9/5 @ 1018c
DeM7 # 20/11 @ 1035c
Prm7 # 117/64 @ 1044c
AsGrm7 # 11/6 @ 1049c
DeAcM7 # 81/44 @ 1057c
ReM7 # 24/13 @ 1061c
Sbd8 # 28/15 @ 1081c
M7 # 15/8 @ 1088c
RsM7 # 36/19 @ 1106c
AcM7 # 243/128 @ 1110c
ReAsM7 # 99/52 @ 1115c
SpGrM7 # 40/21 @ 1116c
ExM7 # 153/80 @ 1123c
NbM7 # 23/12 @ 1126c
d8 # 48/25 @ 1129c
SpM7 # 27/14 @ 1137c
De8 # 64/33 @ 1147c
Sb8 # 35/18 @ 1151c
A7 # 125/64 @ 1159c
Re8 # 128/65 @ 1173c
Gr8 # 160/81 @ 1178c
Fa8 # 95/48 @ 1182c
P8 # 2/1 @ 1200c
Nice.
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