Scala analysis: xen18-erlich-porcupine-15
7L 8s MOS for Porcupine, L=101.65, s=60.67
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 60.670 cents 60.670000 2: 162.320 cents 162.320000 3: 222.990 cents 222.990000 4: 324.640 cents 324.640000 5: 385.310 cents 385.310000 6: 486.960 cents 486.960000 7: 547.630 cents 547.630000 8: 649.280 cents 649.280000 9: 709.950 cents 709.950000 10: 811.600 cents 811.600000 11: 872.270 cents 872.270000 12: 973.920 cents 973.920000 13: 1034.590 cents 1034.590000 14: 1136.240 cents 1136.240000 15: 1196.910 cents 1196.910000
SHOW/INTERVAL
0: 60.6700 cents 60.6700 1: 60.6700 cents 60.6700 2: 101.6500 cents 101.6500 3: 60.6700 cents 60.6700 4: 101.6500 cents 101.6500 5: 60.6700 cents 60.6700 6: 101.6500 cents 101.6500 7: 60.6700 cents 60.6700 8: 101.6500 cents 101.6500 9: 60.6700 cents 60.6700 10: 101.6500 cents 101.6500 11: 60.6700 cents 60.6700 12: 101.6500 cents 101.6500 13: 60.6700 cents 60.6700 14: 101.6500 cents 101.6500 15: 60.6700 cents 60.6700
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 8 60.67000 cents 1: 7 101.65000 cents 2: 1 121.34000 cents 2: 14 162.32000 cents 3: 9 222.99000 cents 3: 6 263.97000 cents 4: 2 283.66000 cents 4: 13 324.64000 cents 5: 10 385.31000 cents 5: 5 426.29000 cents 6: 3 445.98000 cents 6: 12 486.96000 cents 7: 11 547.63000 cents 7: 4 588.61000 cents 8: 4 608.30000 cents 8: 11 649.28000 cents 9: 12 709.95000 cents 9: 3 750.93000 cents 10: 5 770.62000 cents 10: 10 811.60000 cents 11: 13 872.27000 cents 11: 2 913.25000 cents 12: 6 932.94000 cents 12: 9 973.92000 cents 13: 14 1034.59000 cents 13: 1 1075.57000 cents 14: 7 1095.26000 cents 14: 8 1136.24000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0.0 : 60.7 162.3 223.0 324.6 385.3 487.0 547.6 649.3 710.0 811.6 872.3 973.9 1034.6 1136.2 1196.9 60.7 : 101.6 162.3 264.0 324.6 426.3 487.0 588.6 649.3 750.9 811.6 913.2 973.9 1075.6 1136.2 1196.9 162.3 : 60.7 162.3 223.0 324.6 385.3 487.0 547.6 649.3 709.9 811.6 872.3 973.9 1034.6 1095.3 1196.9 223.0 : 101.6 162.3 264.0 324.6 426.3 487.0 588.6 649.3 750.9 811.6 913.2 973.9 1034.6 1136.2 1196.9 324.6 : 60.7 162.3 223.0 324.6 385.3 487.0 547.6 649.3 709.9 811.6 872.3 932.9 1034.6 1095.3 1196.9 385.3 : 101.7 162.3 264.0 324.6 426.3 487.0 588.6 649.3 750.9 811.6 872.3 973.9 1034.6 1136.2 1196.9 487.0 : 60.7 162.3 223.0 324.6 385.3 487.0 547.6 649.3 709.9 770.6 872.3 932.9 1034.6 1095.3 1196.9 547.6 : 101.7 162.3 264.0 324.6 426.3 487.0 588.6 649.3 710.0 811.6 872.3 973.9 1034.6 1136.2 1196.9 649.3 : 60.7 162.3 223.0 324.6 385.3 487.0 547.6 608.3 709.9 770.6 872.3 932.9 1034.6 1095.3 1196.9 710.0 : 101.6 162.3 264.0 324.6 426.3 487.0 547.6 649.3 709.9 811.6 872.3 973.9 1034.6 1136.2 1196.9 811.6 : 60.7 162.3 223.0 324.6 385.3 446.0 547.6 608.3 709.9 770.6 872.3 932.9 1034.6 1095.3 1196.9 872.3 : 101.7 162.3 264.0 324.6 385.3 487.0 547.6 649.3 709.9 811.6 872.3 973.9 1034.6 1136.2 1196.9 973.9 : 60.7 162.3 223.0 283.7 385.3 446.0 547.6 608.3 710.0 770.6 872.3 932.9 1034.6 1095.3 1196.9 1034.6: 101.6 162.3 223.0 324.6 385.3 487.0 547.6 649.3 709.9 811.6 872.3 973.9 1034.6 1136.2 1196.9 1136.2: 60.7 121.3 223.0 283.7 385.3 446.0 547.6 608.3 710.0 770.6 872.3 932.9 1034.6 1095.3 1196.9 1196.9
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 60.6700 .. 101.6500 cents 40.98000 cents 60.67000 cents 2: 121.3400 .. 162.3200 cents 40.98000 cents 19.69000 cents 3: 222.9900 .. 263.9700 cents 40.98000 cents 60.67000 cents 4: 283.6600 .. 324.6400 cents 40.98000 cents 19.69000 cents 5: 385.3100 .. 426.2900 cents 40.98000 cents 60.67000 cents 6: 445.9800 .. 486.9600 cents 40.98000 cents 19.69000 cents 7: 547.6300 .. 588.6100 cents 40.98000 cents 60.67000 cents 8: 608.3000 .. 649.2800 cents 40.98000 cents 19.69000 cents 9: 709.9500 .. 750.9300 cents 40.98000 cents 60.67000 cents 10: 770.6200 .. 811.6000 cents 40.98000 cents 19.69000 cents 11: 872.2700 .. 913.2500 cents 40.98000 cents 60.67000 cents 12: 932.9400 .. 973.9200 cents 40.98000 cents 19.69000 cents 13: 1034.5900 .. 1075.5700 cents 40.98000 cents 60.67000 cents 14: 1095.2600 .. 1136.2400 cents 40.98000 cents 19.69000 cents
SHOW DATA
Number of notes : 15 -- Interval properties -- Smallest interval : 60.67000 cents, class 1 Average step (divided formal octave): 79.7940 cents Largest one step interval : 101.65000 cents Average / Smallest step : 1.315213 Largest / Average step : 1.273905 Largest / Smallest step : 1.675457 Median interval of one step : 60.67000 cents, amount: 8 Most common interval of one step : 60.67000 cents, amount: 8 Least squares average step : 80.10245 cents, oct.: 1201.53677 cents Scale is strictly proper Scale has Myhill's property chromas: 40.98000 cents and 19.69000 cents, ratio: 2.081260 generators: 2 of 162.32000 cents and 13 of 1034.59000 cents ET pair of linear temperament : 15&22 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 730-tone equal temperament with octave 1196.910 cents degrees: 37 99 136 198 235 297 334 396 433 495 532 594 631 693 730 generators: 99 and 631 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABABABABABABA Step pattern size order : SLSLSLSLSLSLSLS Scale is a Constant Structure, by a margin of 19.69000 cents Scale diversity : 1.201727 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.520666 Rothenberg efficiency : 0.711111 redundancy: 0.288889 Efficiency x scale size : 10.666667 Number of different interval sizes : 28 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 19.69000 cents Most common intervals : 162.32000 cents & inv., amount: 14 Scale is a chain of 7 triads 0.0 162.320 324.640 cents Most common triad is 0.0 162.320 1034.590 cents, amount: 13 Number of recognisable fifths : 12, average 709.9500 cents Number of recognisable fourths : 12, average 486.9600 cents Scale contains two identical disjunct heptachords Best minor thirds form a closed circle Formal octave complements present : 15 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 7-8 -- Rational properties --
FIT/MODE
15: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 11.8036 c. M:-19.1240 c. 22: 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 P M ME I SD: 3.8668 c. M:-6.2650 c. 37: 2 3 2 3 2 3 2 3 2 3 2 3 2 3 2 SP M ME I SD: 2.4860 c. M:-4.0278 c. 59: 3 5 3 5 3 5 3 5 3 5 3 5 3 5 3 SP M DE I SD: 0.1172 c. M: 0.1898 c. 376: 19 32 19 32 19 32 19 32 19 32 19 32 19 32 19 SP M DE I SD: 0.1159 c. M: 0.1878 c. 435: 22 37 22 37 22 37 22 37 22 37 22 37 22 37 22 SP M DE I SD: 0.0843 c. M: 0.1366 c. 494: 25 42 25 42 25 42 25 42 25 42 25 42 25 42 25 SP M DE I SD: 0.0603 c. M:-0.0976 c. 553: 28 47 28 47 28 47 28 47 28 47 28 47 28 47 28 SP M DE I SD: 0.0413 c. M:-0.0670 c. 612: 31 52 31 52 31 52 31 52 31 52 31 52 31 52 31 SP M DE I SD: 0.0261 c. M:-0.0422 c. 671: 34 57 34 57 34 57 34 57 34 57 34 57 34 57 34 SP M DE I SD: 0.0135 c. M:-0.0218 c. 730: 37 62 37 62 37 62 37 62 37 62 37 62 37 62 37 SP M DE I SD: 0.0029 c. M: 0.0047 c. 1519: 77 129 77 129 77 129 77 129 77 129 77 129 77 129 77 SP M DE I SD: 0.0018 c. M: 0.0029 c. 2249: 114 191 114 191 114 191 114 191 114 191 114 191 114 191 114 SP M DE I SD: 0.0002 c. M:-0.0004 c.
FIT/HARMONIC
1 x x x x x x x x x x x x x x 2 S SD: 3.0900 cents 2 x x x x x x x x 3 x x x x x 4 S SD: 4.2857 cents 3 x x x x x 4 x x x x 5 x x x 6 S SD: 5.5634 cents 4 x x x x 5 x x x 6 x x 7 x x 8 S SD: 2.5053 cents 5 x x x 6 x x 7 x x 8 x x 9 x 10 S SD: 8.0011 cents 6 x x 7 x x 8 x x 9 x 10 x 11 x 12 S SD: 8.3104 cents 7 x x 8 x 9 x x 10 x 11 x 12:13 x 14 S SD: 12.3331 cents 8 x x 9 x 10 x 11 x 12:13 x 14 x 15:16 S SD: 7.5168 cents 9 x 10 x 11 x 12 x 13 x 14:15:16 x 17:18 S SD: 8.0662 cents 10 x 11 x 12 x 13:14 x 15:16:17 x 18:19:20 S SD: 7.4305 cents 11 x 12 x 13:14 x 15:16:17 x 18:19:20:21:22 S SD: 6.9820 cents 12 x 13:14 x 15:16 x 17:18:19:20:21:22:23:24 S SD: 6.2220 cents 13 x 14:15 x 16:17:18:19:20:21:22:23:24:25:26 S SD: 6.5755 cents 14 x 15:16:17 x x 19:20:21:22:23:25 x 27:28 SD: 6.6716 cents 15 x 16:17:18:19:20:21:22:23:24:25:26:27:29:30 SD: 5.8156 cents 16:17 x 18:19:20:21:22:23:24:26 x 28:29:31:32 SD: 5.3391 cents 17:18:19 x x 21 x 23:25:26:27:28:30:31:33:34 SD: 5.7760 cents 18:19:20 x 22 x 24:25:26:27:29:30:32:33:35:36 SD: 4.9171 cents 20:21:22:23:24:25 x 27:29:30:32:33:35:36:39:40 SD: 3.6825 cents 22:23:24:25:27 x 29:30:32:33:35:36:39:40:42:44 SD: 3.6347 cents 24:25:26:27:29:30:32:33:35:36:38:40:42:44:46:48 SD: 2.9883 cents 28:29:31:32:34:35:37:38:41:42:45:46:49:51:54:56 SD: 2.3704 cents 29:30:32:33:35:36:38:40:42:44:46:48:51:53:56:58 SD: 2.2355 cents 37:38:41:42:45:46:49:51:54:56:59:61:65:67:71:74 SD: 2.1688 cents 40:41:44:46:48:50:53:55:58:60:64:66:70:73:77:80 SD: 2.1138 cents 43:45:47:49:52:54:57:59:63:65:69:71:75:78:83:86 SD: 1.9898 cents 44:46:48:50:53:55:58:60:64:66:70:73:77:80:85:88 SD: 1.8776 cents 49:51:54:56:59:61:65:67:71:74:78:81:86:89:94:98 SD: 1.4316 cents 52:54:57:59:63:65:69:71:76:78:83:86:91:95:100:104 SD: 1.4099 cents 53:55:58:60:64:66:70:73:77:80:85:88:93:96:102:106 SD: 1.2733 cents 59:61:65:67:71:74:78:81:86:89:94:98:104:107:114:118 SD: 1.1547 cents 73:76:80:83:88:91:97:100:106:110:117:121:128:133:141:146 SD: 1.0137 cents 81:84:89:92:98:101:107:111:118:122:129:134:142:147:156:162 SD: 0.8024 cents 108:112:119:123:130:135:143:148:157:163:173:179:190:196:208:216 SD: 0.7596 cents 110:114:121:125:133:137:146:151:160:166:176:182:193:200:212:220 SD: 0.6263 cents 132:137:145:150:159:165:175:181:192:199:211:218:232:240:254:264 SD: 0.5423 cents 160:166:176:182:193:200:212:220:233:241:256:265:281:291:308:319 SD: 0.4858 cents 164:170:180:187:198:205:217:225:239:247:262:271:288:298:316:327 SD: 0.4824 cents 169:175:186:192:204:211:224:232:246:255:270:280:297:307:326:337 SD: 0.4328 cents 191:198:210:217:230:239:253:262:278:288:305:316:335:347:368:381 SD: 0.4007 cents 194:201:213:221:234:242:257:266:282:292:310:321:341:353:374:387 SD: 0.3908 cents 197:204:216:224:238:246:261:270:287:297:315:326:346:358:380:393 SD: 0.3723 cents 204:211:224:232:246:255:270:280:297:307:326:338:358:371:393:407 SD: 0.3210 cents 224:232:246:255:270:280:297:307:326:338:358:371:393:407:432:447 SD: 0.2948 cents 252:261:277:287:304:315:334:346:367:380:403:417:442:458:486:503 SD: 0.2770 cents 253:262:278:288:305:316:335:347:368:381:404:419:444:460:488:505 SD: 0.2225 cents 306:317:336:348:369:382:405:420:445:461:489:506:537:556:590:611 SD: 0.2097 cents 314:325:345:357:379:392:416:431:457:473:502:520:551:571:605:627 SD: 0.1987 cents 336:348:369:382:405:420:445:461:489:506:537:556:590:611:648:671 SD: 0.1794 cents 416:431:457:473:502:520:551:571:605:627:665:689:730:756:802:831 SD: 0.1778 cents 428:443:470:487:516:535:567:587:623:645:684:708:751:778:825:854 SD: 0.1675 cents 446:462:490:507:538:557:591:612:649:672:713:738:783:811:860:890 SD: 0.1350 cents 481:498:528:547:580:601:637:660:700:725:769:796:844:874:927:960 SD: 0.1350 cents 510:528:560:580:615:637:676:700:742:769:815:844:895:927:983:1018 SD: 0.1251 cents 530:549:582:603:639:662:702:727:771:799:847:877:930:963:1022:1058 SD: 0.1227 cents 538:557:591:612:649:672:713:738:783:811:860:890:944:978:1037:1074 SD: 0.1114 cents