Scala analysis: 10_serpent2
Two pentatonic chains of 3:2's rooted a 7:4 apart, tuned in 31-tet.
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 154.839 cents 154.839000 2: 193.548 cents 193.548000 3: 387.097 cents 387.097000 4: 464.516 cents 464.516000 5: 658.065 cents 658.065000 6: 696.774 cents 696.774000 7: 890.323 cents 890.323000 8: 967.742 cents 967.742000 9: 1161.290 cents 1161.290000 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 38.7100 cents 38.7100 1: 154.8390 cents 154.8390 2: 38.7090 cents 38.7090 3: 193.5490 cents 193.5490 4: 77.4190 cents 77.4190 5: 193.5490 cents 193.5490 6: 38.7090 cents 38.7090 7: 193.5490 cents 193.5490 8: 77.4190 cents 77.4190 9: 193.5480 cents 193.5480 10: 38.7100 cents 38.7100
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 38.70900 cents 1: 1 38.71000 cents 1: 2 77.41900 cents 1: 1 154.83900 cents 1: 1 193.54800 cents 1: 3 193.54900 cents 2: 1 193.54800 cents 2: 1 193.54900 cents 2: 4 232.25800 cents 2: 1 270.96700 cents 2: 3 270.96800 cents 3: 1 232.25800 cents 3: 4 309.67700 cents 3: 2 387.09700 cents 3: 1 425.80700 cents 3: 1 464.51600 cents 3: 1 464.51700 cents 4: 1 425.80600 cents 4: 1 425.80700 cents 4: 2 464.51600 cents 4: 1 503.22500 cents 4: 5 503.22600 cents 5: 1 503.22500 cents 5: 1 503.22600 cents 5: 2 541.93500 cents 5: 1 580.64500 cents 5: 1 619.35500 cents 5: 2 658.06500 cents 5: 1 696.77400 cents 5: 1 696.77500 cents 6: 5 696.77400 cents 6: 1 696.77500 cents 6: 2 735.48400 cents 6: 1 774.19300 cents 6: 1 774.19400 cents 7: 1 735.48300 cents 7: 1 735.48400 cents 7: 1 774.19300 cents 7: 2 812.90300 cents 7: 4 890.32300 cents 7: 1 967.74200 cents 8: 3 929.03200 cents 8: 1 929.03300 cents 8: 4 967.74200 cents 8: 1 1006.45100 cents 8: 1 1006.45200 cents 9: 3 1006.45100 cents 9: 1 1006.45200 cents 9: 1 1045.16100 cents 9: 2 1122.58100 cents 9: 1 1161.29000 cents 9: 2 1161.29100 cents Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 5.77778 = 52/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 154.8 193.5 387.1 464.5 658.1 696.8 890.3 967.7 1161.3 1200.0 154.8 : 38.7 232.3 309.7 503.2 541.9 735.5 812.9 1006.5 1045.2 1200.0 193.5 : 193.5 271.0 464.5 503.2 696.8 774.2 967.7 1006.5 1161.3 1200.0 387.1 : 77.4 271.0 309.7 503.2 580.6 774.2 812.9 967.7 1006.5 1200.0 464.5 : 193.5 232.3 425.8 503.2 696.8 735.5 890.3 929.0 1122.6 1200.0 658.1 : 38.7 232.3 309.7 503.2 541.9 696.8 735.5 929.0 1006.5 1200.0 696.8 : 193.5 271.0 464.5 503.2 658.1 696.8 890.3 967.7 1161.3 1200.0 890.3 : 77.4 271.0 309.7 464.5 503.2 696.8 774.2 967.7 1006.5 1200.0 967.7 : 193.5 232.3 387.1 425.8 619.4 696.8 890.3 929.0 1122.6 1200.0 1161.3: 38.7 193.5 232.3 425.8 503.2 696.8 735.5 929.0 1006.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.7090 .. 193.5490 cents 154.84000 cents 38.70900 cents 2: 193.5480 .. 270.9680 cents 77.42000 cents -0.00100 cents 3: 232.2580 .. 464.5170 cents 232.25900 cents -38.71000 cents 4: 425.8060 .. 503.2260 cents 77.42000 cents -38.71100 cents 5: 503.2250 .. 696.7750 cents 193.55000 cents -0.00100 cents 6: 696.7740 .. 774.1940 cents 77.42000 cents -0.00100 cents 7: 735.4830 .. 967.7420 cents 232.25900 cents -38.71100 cents 8: 929.0320 .. 1006.4520 cents 77.42000 cents -38.71000 cents 9: 1006.4510 .. 1161.2910 cents 154.84000 cents -0.00100 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 38.70900 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 193.54900 cents Average / Smallest step : 3.100054 Largest / Average step : 1.612908 Largest / Smallest step : 5.000103 Median interval of one step : 116.12900 cents, amount: 0 Most common interval of one step : 193.54900 cents, amount: 3 Least squares average step : 123.26770 cents, oct.: 1232.67704 cents Scale is not proper Scale is a mode of a 31-tone equal temperament with octave 2/1 degrees: 4 5 10 12 17 18 23 25 30 31 Least number of segments generator : 18 of 696.774 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 25 of 967.742 cents and inv. generated superset size: 14 = 4 more = 140.000% Number of contiguous 1-step segments: 3 Step pattern alph. order: ABCDCBCDEF Step pattern size order : DAFCFAFCEB Interval vector is [ 1 2 0 1 4 5 3 4 0 2 2 1 6 2 1 ] Scale is not a Constant Structure Scale diversity : 1.391664 Lumma stability : 0.064515 Lumma impropriety factor : 0.129038 Rothenberg efficiency : 0.362698 redundancy: 0.637302 Efficiency x scale size : 3.626984 Number of different interval sizes : 38 = 4.22222 / class Number of one step interval sizes : 6 Highest interval variety : 8 Mean interval variety : 5.77778 = 52/9 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 0.00100 cents Most common intervals : 503.22600 cents & inv., amount: 6 Number of recognisable fifths : 8, average 696.7742 cents Formal octave complements present : 1 = 10.0000% Limited inverse transpositions : 1 Inversional symmetry on intervals : 0-1 5-6 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
10: 1 1 1 1 1 1 1 1 2 0 N T3 SD: 35.1388 c. M: 58.0650 c. 11: 1 1 1 1 2 0 2 1 1 1 P D3 SD: 37.8524 c. M: 70.3809 c. 12: 2 0 2 1 2 0 2 1 2 0 N SD: 28.1218 c. M:-45.1610 c. 14: 2 0 3 0 3 0 2 1 3 0 N SD: 28.0750 c. M:-41.4744 c. 15: 2 0 3 1 2 1 2 1 3 0 N SD: 20.2215 c. M:-38.7100 c. 18: 2 1 3 1 3 0 3 1 3 1 P SD: 20.4471 c. M: 34.4087 c. 19: 2 1 3 1 3 1 3 1 3 1 P G SD: 17.7613 c. M: 28.5232 c. 20: 3 0 3 2 3 1 3 1 3 1 N SD: 17.1484 c. M: 27.0970 c. 22: 3 1 3 2 3 1 3 2 3 1 P SD: 15.2685 c. M:-26.3931 c. 23: 3 1 3 2 4 0 4 2 3 1 N SD: 14.9496 c. M:-23.5623 c. 24: 3 1 4 1 4 1 4 1 4 1 P G SD: 10.2644 c. M: 17.7420 c. 26: 3 1 4 2 4 1 4 2 4 1 N SD: 10.3687 c. M: 17.8662 c. 31: 4 1 5 2 5 1 5 2 5 1 N SD: 0.0003 c. M: 0.0005 c.
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x x x 4 S SD: 2.5905 cents 3 x x x 4 x x 5 x x 6 S SD: 11.3518 cents 4 x x 5 x x 6 x 7 x 8 S SD: 1.3377 cents 5 x x 6 x 7 x 8:9 x 10 S SD: 27.6932 cents 6 x 7 x 8 x 9:10:11 x 12 S SD: 19.1665 cents 7 x 8 x 9:10 x x 12 x 14 S SD: 14.3199 cents 8 x 9:10 x x 12:13:14 x 16 S SD: 8.5238 cents 9 x 10:11:12:13 x 15:16 x 18 SD: 9.1727 cents 10:11 x x 13 x 15:17 x x 20 SD: 6.4444 cents 11:12 x 14 x 16 x 18:19 x 22 SD: 9.0037 cents 12:13 x 15:16 x 18:20:21:23:24 SD: 6.4662 cents 13:14:15:16:17:19 x 22:23:25:26 SD: 8.6615 cents 14:15:16 x 18:20:21:23:24:27:28 SD: 9.9055 cents 15:16:17:19:20:22 x 25:26:29:30 SD: 7.6237 cents 16 x 18:20:21:23:24:27:28:31:32 SD: 4.4005 cents 17 x 19:21:22:25 x 28:30:33:34 SD: 5.5703 cents 18 x 20:23:24:26:27:30:31:35:36 SD: 7.0003 cents 19:21 x 24:25:28 x 32:33:37:38 SD: 4.4642 cents 20:22 x 25:26:29:30:33:35:39:40 SD: 3.5647 cents 21:23 x 26:27:31 x 35:37:41:42 SD: 5.0705 cents 23:25:26:29:30:34 x 38:40:45:46 SD: 4.3995 cents 24:26:27:30:31:35:36:40:42:47:48 SD: 3.0407 cents 25:27:28:31:33 x 37:42:44:49:50 SD: 4.2612 cents 27 x 30:34:35:39:40:45:47:53:54 SD: 4.1101 cents 28 x 31:35:37:41:42:47:49:55:56 SD: 3.0529 cents 29:32 x 36:38:42:43:49:51:57:58 SD: 4.1617 cents 30:33:34:38:39:44:45:50:52:59:60 SD: 4.0679 cents 31:34:35:39:41:45:46:52:54:61:62 SD: 3.6369 cents 32:35:36:40:42:47:48:54:56:63:64 SD: 2.4562 cents 38:42 x 48:50:56:57:64:66:74:76 SD: 4.0097 cents 39:43:44:49:51:57:58:65:68:76:78 SD: 2.6415 cents 40:44:45:50:52:59:60:67:70:78:80 SD: 2.4447 cents 41:45:46:51:54:60:61:69:72:80:82 SD: 2.3966 cents 43:47:48:54:56:63:64:72:75:84:86 SD: 1.4963 cents 52:57:58:65:68:76:78:87:91:102:104 SD: 0.9657 cents 84:92:94:105:110:123:126:140:147:164:168 SD: 0.9584 cents 85:93:95:106:111:124:127:142:149:166:170 SD: 0.8861 cents 95:104:106:119:124:139:142:159:166:186:190 SD: 0.6827 cents 117:128:131:146:153:171:175:196:205:229:234 SD: 0.6371 cents 119:130:133:149:156:174:178:199:208:233:238 SD: 0.5586 cents 143:156:160:179:187:209:214:239:250:280:286 SD: 0.5419 cents 152:166:170:190:199:222:227:254:266:297:304 SD: 0.5153 cents 159:174:178:199:208:233:238:266:278:311:318 SD: 0.4741 cents 160:175:179:200:209:234:239:268:280:313:320 SD: 0.4230 cents 192:210:215:240:251:281:287:321:336:376:384 SD: 0.3936 cents 195:213:218:244:255:285:292:326:341:381:390 SD: 0.3829 cents 204:223:228:255:267:298:305:341:357:399:408 SD: 0.3180 cents 244:267:273:305:319:357:365:408:427:477:488 SD: 0.2351 cents 279:305:312:349:365:408:417:467:488:546:558 SD: 0.2321 cents 311:340:348:389:407:455:465:520:544:608:622 SD: 0.2079 cents 331:362:370:414:433:484:495:554:579:647:662 SD: 0.1950 cents 355:388:397:444:464:519:531:594:621:694:710 SD: 0.1922 cents 363:397:406:454:475:531:543:607:635:710:726 SD: 0.1335 cents 406:444:454:508:531:594:607:679:710:794:812 SD: 0.1300 cents 491:537:549:614:642:718:734:821:859:960:982 SD: 0.1196 cents 523:572:585:654:684:765:782:875:915:1023:1046 SD: 0.1133 cents