Scala analysis: porcupine15
Porcupine[15] in 22et tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 54.545 cents 54.545450 2: 163.636 cents 163.636360 3: 218.182 cents 218.181820 4: 327.273 cents 327.272730 5: 381.818 cents 381.818180 6: 490.909 cents 490.909090 7: 545.455 cents 545.454550 8: 654.545 cents 654.545450 9: 709.091 cents 709.090910 10: 818.182 cents 818.181820 11: 872.727 cents 872.727270 12: 981.818 cents 981.818180 13: 1036.364 cents 1036.363640 14: 1145.455 cents 1145.454550 15: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 54.5455 cents 54.5455 1: 54.5455 cents 54.5455 2: 109.0909 cents 109.0909 3: 54.5455 cents 54.5455 4: 109.0909 cents 109.0909 5: 54.5454 cents 54.5454 6: 109.0909 cents 109.0909 7: 54.5455 cents 54.5455 8: 109.0909 cents 109.0909 9: 54.5455 cents 54.5455 10: 109.0909 cents 109.0909 11: 54.5455 cents 54.5455 12: 109.0909 cents 109.0909 13: 54.5455 cents 54.5455 14: 109.0909 cents 109.0909 15: 54.5455 cents 54.5455
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 8 54.54545 cents 1: 7 109.09091 cents 2: 1 109.09090 cents 2: 14 163.63636 cents 3: 9 218.18182 cents 3: 6 272.72728 cents 4: 2 272.72727 cents 4: 13 327.27273 cents 5: 10 381.81818 cents 5: 5 436.36364 cents 6: 3 436.36363 cents 6: 12 490.90909 cents 7: 11 545.45455 cents 7: 4 600.00000 cents 8: 4 600.00000 cents 8: 11 654.54545 cents 9: 12 709.09091 cents 9: 3 763.63637 cents 10: 5 763.63636 cents 10: 10 818.18182 cents 11: 13 872.72727 cents 11: 2 927.27273 cents 12: 6 927.27272 cents 12: 9 981.81818 cents 13: 14 1036.36364 cents 13: 1 1090.90910 cents 14: 7 1090.90909 cents 14: 8 1145.45455 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 : 54.5 163.6 218.2 327.3 381.8 490.9 545.5 654.5 709.1 818.2 872.7 981.8 1036.4 1145.5 1200.0 54.5 : 109.1 163.6 272.7 327.3 436.4 490.9 600.0 654.5 763.6 818.2 927.3 981.8 1090.9 1145.5 1200.0 163.6 : 54.5 163.6 218.2 327.3 381.8 490.9 545.5 654.5 709.1 818.2 872.7 981.8 1036.4 1090.9 1200.0 218.2 : 109.1 163.6 272.7 327.3 436.4 490.9 600.0 654.5 763.6 818.2 927.3 981.8 1036.4 1145.5 1200.0 327.3 : 54.5 163.6 218.2 327.3 381.8 490.9 545.5 654.5 709.1 818.2 872.7 927.3 1036.4 1090.9 1200.0 381.8 : 109.1 163.6 272.7 327.3 436.4 490.9 600.0 654.5 763.6 818.2 872.7 981.8 1036.4 1145.5 1200.0 490.9 : 54.5 163.6 218.2 327.3 381.8 490.9 545.5 654.5 709.1 763.6 872.7 927.3 1036.4 1090.9 1200.0 545.5 : 109.1 163.6 272.7 327.3 436.4 490.9 600.0 654.5 709.1 818.2 872.7 981.8 1036.4 1145.5 1200.0 654.5 : 54.5 163.6 218.2 327.3 381.8 490.9 545.5 600.0 709.1 763.6 872.7 927.3 1036.4 1090.9 1200.0 709.1 : 109.1 163.6 272.7 327.3 436.4 490.9 545.5 654.5 709.1 818.2 872.7 981.8 1036.4 1145.5 1200.0 818.2 : 54.5 163.6 218.2 327.3 381.8 436.4 545.5 600.0 709.1 763.6 872.7 927.3 1036.4 1090.9 1200.0 872.7 : 109.1 163.6 272.7 327.3 381.8 490.9 545.5 654.5 709.1 818.2 872.7 981.8 1036.4 1145.5 1200.0 981.8 : 54.5 163.6 218.2 272.7 381.8 436.4 545.5 600.0 709.1 763.6 872.7 927.3 1036.4 1090.9 1200.0 1036.4: 109.1 163.6 218.2 327.3 381.8 490.9 545.5 654.5 709.1 818.2 872.7 981.8 1036.4 1145.5 1200.0 1145.5: 54.5 109.1 218.2 272.7 381.8 436.4 545.5 600.0 709.1 763.6 872.7 927.3 1036.4 1090.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 54.5455 .. 109.0909 cents 54.54546 cents 54.54545 cents 2: 109.0909 .. 163.6364 cents 54.54546 cents -0.00001 cents 3: 218.1818 .. 272.7273 cents 54.54546 cents 54.54546 cents 4: 272.7273 .. 327.2727 cents 54.54546 cents -0.00001 cents 5: 381.8182 .. 436.3636 cents 54.54546 cents 54.54545 cents 6: 436.3636 .. 490.9091 cents 54.54546 cents -0.00001 cents 7: 545.4546 .. 600.0000 cents 54.54545 cents 54.54546 cents 8: 600.0000 .. 654.5454 cents 54.54545 cents 1/1, 0.0000 cents 9: 709.0909 .. 763.6364 cents 54.54546 cents 54.54546 cents 10: 763.6364 .. 818.1818 cents 54.54546 cents -0.00001 cents 11: 872.7273 .. 927.2727 cents 54.54546 cents 54.54545 cents 12: 927.2727 .. 981.8182 cents 54.54546 cents -0.00001 cents 13: 1036.3636 .. 1090.9091 cents 54.54546 cents 54.54546 cents 14: 1090.9091 .. 1145.4545 cents 54.54546 cents -0.00001 cents
SHOW DATA
Number of notes : 15 -- Interval properties -- Smallest interval : 54.54545 cents, class 1 Average step (divided formal octave): 80.0000 cents Largest one step interval : 109.09091 cents Average / Smallest step : 1.466667 Largest / Average step : 1.363636 Largest / Smallest step : 2.000000 Median interval of one step : 54.54545 cents, amount: 8 Most common interval of one step : 54.54545 cents, amount: 8 Least squares average step : 80.41056 cents, oct.: 1206.15836 cents Scale is proper Scale has Myhill's property chromas: 54.54546 cents and 0.00001 cents, ratio: 5454546.127727 generators: 2 of 163.63636 cents and 13 of 1036.36364 cents Scale is maximally even in 22-tone equal temperament 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 22-tone equal temperament with octave 2/1 degrees: 1 3 4 6 7 9 10 12 13 15 16 18 19 21 22 generators: 3 and 19 Number of contiguous 1-step segments: 7 Scale is fully connected major-minor triadic in 22-tone equal temperament Step pattern alph. order: ABABABABABABABA Step pattern size order : SLSLSLSLSLSLSLS Interval vector is [ 8 8 14 9 8 13 10 8 12 11 4 ] Scale is not a Constant Structure Scale diversity : 1.141427 Rothenberg stability : 0.733333 = 11/15 Lumma stability : 0.363636 Number of different interval sizes : 21 = 1.50000 / 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 : 54.54545 cents Most common intervals : 163.63636 cents & inv., amount: 14 Scale is a chain of 7 triads 0.0 163.636 327.273 cents Most common triad is 0.0 163.636 1036.364 cents, amount: 13 Number of recognisable fifths : 12, average 709.0909 cents Scale contains two identical disjunct heptachords Best minor thirds form a closed circle Formal octave complements present : 15 = 100.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 7-8 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
15: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 15.7109 c. M: 25.4545 c. 22: 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 P M ME I SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x x x 3 x x x x x 4 S SD: 3.5680 cents 3 x x x x x 4 x x x x 5 x x x 6 S SD: 4.5486 cents 4 x x x x 5 x x x 6 x x 7 x x 8 S SD: 3.8724 cents 5 x x x 6 x x 7 x x 8 x x 9 x 10 S SD: 8.6741 cents 6 x x 7 x x 8 x x 9 x 10 x 11 x 12 S SD: 8.7825 cents 7 x x 8 x 9 x x 10 x 11 x 12:13 x 14 S SD: 13.7563 cents 8 x x 9 x 10 x 11 x 12:13 x 14:15 x 16 S SD: 7.5741 cents 9 x 10 x 11 x 12 x 13 x 14:15:16 x 17:18 S SD: 8.8040 cents 10 x 11 x 12 x 13:14 x 15:16:17 x 18:19:20 S SD: 8.1005 cents 11 x 12 x 13:14 x 15:16:17 x 18:19:20:21:22 S SD: 7.7856 cents 12 x 13:14 x 15:16 x x 18:19:20:21:22:23:24 S SD: 6.0793 cents 13 x 14:15 x 16:17:18:19:20:21:22:23:24:25:26 S SD: 6.6320 cents 14 x 15:16:17 x x 19:20:21:22:23:25 x 27:28 SD: 6.9887 cents 15 x 16:17:18:19:20:21:22:23:24:25:26:27:29:30 SD: 6.1589 cents 16:17 x 18:19:20:21:22:23:24:26 x 28:29:31:32 SD: 5.7284 cents 17:18 x 19 x 21 x 23:25:26:27:28:30:31:33:34 SD: 5.6820 cents 18:19:20 x 22 x 24:25:26:27:29:30:32:33:35:36 SD: 4.7698 cents 20:21:22:23:24:25 x 27:29:30:32:33:35:36:39:40 SD: 4.0131 cents 21:22:23:24:25:26:28:29:31:32:34:35:37:38:41:42 SD: 3.8567 cents 22:23:24:25 x 27:29:30:32:33:35:36:39:40:43:44 SD: 3.6844 cents 24:25:26:27:29:30:32:33:35:36:39:40:42:44:47:48 SD: 3.3667 cents 26:27:29 x 31:32:35:36:38:39:42:43:46:47:50:52 SD: 4.0481 cents 27:28:30:31:33:34:36:37:39:41:43:45:48:49:52:54 SD: 3.5100 cents 28:29:31:32:34:35:37:38:41:42:45:46:49:51:54:56 SD: 2.4296 cents 30:31:33:34:36:37:40:41:44:45:48:50:53:55:58:60 SD: 2.1550 cents 37:38:41:42:45:46:49:51:54:56:59:61:65:67:72:74 SD: 2.0466 cents 43:44:47:49:52:54:57:59:63:65:69:71:76:78:83:86 SD: 1.8211 cents 51:53:56:58:62:64:68:70:74:77:82:84:90:93:99:102 SD: 1.7758 cents 52:54:57:59:63:65:69:71:76:78:83:86:92:95:101:104 SD: 1.4258 cents 59:61:65:67:71:74:78:81:86:89:95:98:104:107:114:118 SD: 1.3294 cents 61:63:67:69:74:76:81:84:89:92:98:101:108:111:118:122 SD: 0.9990 cents 81:84:89:92:98:101:108:111:118:122:130:134:143:147:157:162 SD: 0.8748 cents 89:92:98:101:108:111:118:122:130:134:143:147:157:162:172:178 SD: 0.7775 cents 101:104:111:115:122:126:134:138:147:152:162:167:178:184:196:202 SD: 0.7514 cents 111:115:122:126:134:138:147:152:162:167:178:184:196:202:215:222 SD: 0.7048 cents 119:123:131:135:144:148:158:163:174:179:191:197:210:217:231:238 SD: 0.6040 cents 122:126:134:138:147:152:162:167:178:184:196:202:215:222:236:244 SD: 0.5790 cents 134:138:147:152:162:167:178:184:196:202:215:222:236:244:260:268 SD: 0.5454 cents 149:154:164:169:180:186:198:204:217:224:239:247:263:271:289:298 SD: 0.5050 cents 150:155:165:170:181:187:199:206:219:226:241:248:264:273:291:300 SD: 0.4994 cents 159:164:175:180:192:198:211:218:232:239:255:263:280:289:308:318 SD: 0.4646 cents 162:167:178:184:196:202:215:222:236:244:260:268:286:295:314:324 SD: 0.3982 cents 192:198:211:218:232:239:255:263:280:289:308:318:339:349:372:384 SD: 0.3381 cents 211:218:232:239:255:263:280:289:308:318:338:349:372:384:409:422 SD: 0.3168 cents 222:229:244:252:268:277:295:304:324:334:356:368:391:404:430:444 SD: 0.3164 cents 244:252:268:277:295:304:324:334:356:368:391:404:430:444:473:488 SD: 0.3127 cents 253:261:278:287:306:315:336:347:369:381:406:419:446:460:490:506 SD: 0.2830 cents 259:267:285:294:313:323:344:355:378:390:415:429:457:471:502:518 SD: 0.2801 cents 275:284:302:312:332:343:365:377:401:414:441:455:485:500:533:550 SD: 0.2431 cents 283:292:311:321:342:353:376:388:413:426:454:469:499:515:548:566 SD: 0.2036 cents 342:353:376:388:413:426:454:469:499:515:549:566:603:622:663:684 SD: 0.1927 cents 351:362:386:398:424:438:466:481:512:529:563:581:619:639:680:702 SD: 0.1913 cents 372:384:409:422:449:464:494:510:543:560:597:616:656:677:721:744 SD: 0.1633 cents 381:393:419:432:460:475:506:522:556:574:611:631:672:693:738:762 SD: 0.1632 cents 433:447:476:491:523:540:575:593:632:652:695:717:763:788:839:866 SD: 0.1458 cents 470:485:517:533:568:586:624:644:686:708:754:778:829:855:911:940 SD: 0.1215 cents 583:602:641:661:704:727:774:799:851:878:935:965:1028:1061:1130:1166 SD: 0.1202 cents 595:614:654:675:719:742:790:815:868:896:954:985:1049:1083:1153:1190 SD: 0.1124 cents 596:615:655:676:720:743:791:817:870:898:956:987:1051:1084:1155:1192 SD: 0.1090 cents