Scala analysis: tripenta
6/31 generator supermajor seconds tripentatonic scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 38.710 cents 38.709677 2: 193.548 cents 193.548387 3: 232.258 cents 232.258065 4: 270.968 cents 270.967742 5: 425.806 cents 425.806452 6: 464.516 cents 464.516129 7: 503.226 cents 503.225806 8: 696.774 cents 696.774194 9: 735.484 cents 735.483871 10: 774.194 cents 774.193548 11: 929.032 cents 929.032258 12: 967.742 cents 967.741935 13: 1006.452 cents 1006.451613 14: 1161.290 cents 1161.290323 15: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 38.7097 cents 38.7097 1: 38.7097 cents 38.7097 2: 154.8387 cents 154.8387 3: 38.7097 cents 38.7097 4: 38.7097 cents 38.7097 5: 154.8387 cents 154.8387 6: 38.7097 cents 38.7097 7: 38.7097 cents 38.7097 8: 193.5484 cents 193.5484 9: 38.7097 cents 38.7097 10: 38.7097 cents 38.7097 11: 154.8387 cents 154.8387 12: 38.7097 cents 38.7097 13: 38.7097 cents 38.7097 14: 154.8387 cents 154.8387 15: 38.7097 cents 38.7097
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 10 38.70968 cents 1: 4 154.83871 cents 1: 1 193.54839 cents 2: 5 77.41936 cents 2: 8 193.54839 cents 2: 2 232.25807 cents 3: 12 232.25807 cents 3: 3 270.96774 cents 4: 8 270.96774 cents 4: 2 309.67742 cents 4: 3 387.09677 cents 4: 2 425.80645 cents 5: 4 309.67742 cents 5: 1 348.38710 cents 5: 6 425.80645 cents 5: 4 464.51613 cents 6: 9 464.51613 cents 6: 6 503.22581 cents 7: 6 503.22581 cents 7: 4 541.93548 cents 7: 2 619.35484 cents 7: 3 658.06452 cents 8: 3 541.93548 cents 8: 2 580.64516 cents 8: 4 658.06452 cents 8: 6 696.77419 cents 9: 6 696.77419 cents 9: 9 735.48387 cents 10: 4 735.48387 cents 10: 6 774.19355 cents 10: 1 851.61290 cents 10: 4 890.32258 cents 11: 2 774.19355 cents 11: 3 812.90323 cents 11: 2 890.32258 cents 11: 8 929.03226 cents 12: 3 929.03226 cents 12: 12 967.74194 cents 13: 2 967.74194 cents 13: 8 1006.45161 cents 13: 5 1122.58065 cents 14: 1 1006.45161 cents 14: 4 1045.16129 cents 14: 10 1161.29032 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.14286 = 22/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 0.0 : 38.7 193.5 232.3 271.0 425.8 464.5 503.2 696.8 735.5 774.2 929.0 967.7 1006.5 1161.3 1200.0 38.7 : 154.8 193.5 232.3 387.1 425.8 464.5 658.1 696.8 735.5 890.3 929.0 967.7 1122.6 1161.3 1200.0 193.5 : 38.7 77.4 232.3 271.0 309.7 503.2 541.9 580.6 735.5 774.2 812.9 967.7 1006.5 1045.2 1200.0 232.3 : 38.7 193.5 232.3 271.0 464.5 503.2 541.9 696.8 735.5 774.2 929.0 967.7 1006.5 1161.3 1200.0 271.0 : 154.8 193.5 232.3 425.8 464.5 503.2 658.1 696.8 735.5 890.3 929.0 967.7 1122.6 1161.3 1200.0 425.8 : 38.7 77.4 271.0 309.7 348.4 503.2 541.9 580.6 735.5 774.2 812.9 967.7 1006.5 1045.2 1200.0 464.5 : 38.7 232.3 271.0 309.7 464.5 503.2 541.9 696.8 735.5 774.2 929.0 967.7 1006.5 1161.3 1200.0 503.2 : 193.5 232.3 271.0 425.8 464.5 503.2 658.1 696.8 735.5 890.3 929.0 967.7 1122.6 1161.3 1200.0 696.8 : 38.7 77.4 232.3 271.0 309.7 464.5 503.2 541.9 696.8 735.5 774.2 929.0 967.7 1006.5 1200.0 735.5 : 38.7 193.5 232.3 271.0 425.8 464.5 503.2 658.1 696.8 735.5 890.3 929.0 967.7 1161.3 1200.0 774.2 : 154.8 193.5 232.3 387.1 425.8 464.5 619.4 658.1 696.8 851.6 890.3 929.0 1122.6 1161.3 1200.0 929.0 : 38.7 77.4 232.3 271.0 309.7 464.5 503.2 541.9 696.8 735.5 774.2 967.7 1006.5 1045.2 1200.0 967.7 : 38.7 193.5 232.3 271.0 425.8 464.5 503.2 658.1 696.8 735.5 929.0 967.7 1006.5 1161.3 1200.0 1006.5: 154.8 193.5 232.3 387.1 425.8 464.5 619.4 658.1 696.8 890.3 929.0 967.7 1122.6 1161.3 1200.0 1161.3: 38.7 77.4 232.3 271.0 309.7 464.5 503.2 541.9 735.5 774.2 812.9 967.7 1006.5 1045.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.7097 .. 193.5484 cents 154.83871 cents 38.70968 cents 2: 77.4194 .. 232.2581 cents 154.83871 cents -116.12903 cents 3: 232.2581 .. 270.9677 cents 38.70968 cents 1/1, 0.0000 cents 4: 270.9677 .. 425.8065 cents 154.83871 cents 1/1, 0.0000 cents 5: 309.6774 .. 464.5161 cents 154.83871 cents -116.12903 cents 6: 464.5161 .. 503.2258 cents 38.70968 cents 1/1, 0.0000 cents 7: 503.2258 .. 658.0645 cents 154.83871 cents -0.00000 cents 8: 541.9355 .. 696.7742 cents 154.83871 cents -116.12903 cents 9: 696.7742 .. 735.4839 cents 38.70968 cents -0.00000 cents 10: 735.4839 .. 890.3226 cents 154.83871 cents 1/1, 0.0000 cents 11: 774.1935 .. 929.0323 cents 154.83871 cents -116.12903 cents 12: 929.0323 .. 967.7419 cents 38.70968 cents 1/1, 0.0000 cents 13: 967.7419 .. 1122.5806 cents 154.83871 cents 1/1, 0.0000 cents 14: 1006.4516 .. 1161.2903 cents 154.83871 cents -116.12903 cents
SHOW DATA
Number of notes : 15 -- Interval properties -- Smallest interval : 38.70968 cents, class 1 Average step (divided formal octave): 80.0000 cents Largest one step interval : 193.54839 cents Average / Smallest step : 2.066667 Largest / Average step : 2.419355 Largest / Smallest step : 5.000000 Median interval of one step : 38.70968 cents, amount: 10 Most common interval of one step : 38.70968 cents, amount: 10 Least squares average step : 80.44745 cents, oct.: 1206.71176 cents Scale is not proper Scale is a mode of a 31-tone equal temperament with octave 1200.000 cents degrees: 1 5 6 7 11 12 13 18 19 20 24 25 26 30 31 Least number of segments generator : 19 of 735.484 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 25 of 967.742 cents and inv. generated superset size: 15 = 0 more = 100.000% Number of contiguous 1-step segments: 5 Step pattern alph. order: ABAABAACAABAABA Step pattern size order : SMSSMSSLSSMSSMS Interval vector is [ 10 5 0 4 9 14 11 6 1 3 8 13 12 7 2 ] Scale is not a Constant Structure Scale diversity : 1.223251 Lumma stability : 0.064516 Lumma impropriety factor : 0.483871 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 : 3 Highest interval variety : 4 Mean interval variety : 3.14286 = 22/7 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 38.70968 cents Most common intervals : 232.25807 cents & inv., amount: 14 Scale has Generated (pseudo-Myhill) property, generator: 967.742 cents and inv. Scale is a Winograd/Gamer deep scale Scale is a chain of 7 triads 0.0 425.806 967.742 cents Most common triad is 0.0 232.258 967.742 cents, amount: 13 Number of recognisable fifths : 12, average 696.7742 cents Formal octave complements present : 15 = 100.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 7-8 -- Rational properties --
FIT/MODE
15: 0 2 0 1 2 0 1 2 1 0 2 1 0 2 1 N T3 SD: 42.3467 c. M: 72.2581 c. 16: 0 2 1 0 2 1 0 3 0 1 2 0 1 2 1 N SD: 39.7000 c. M: 67.7419 c. 17: 1 2 0 1 2 1 0 3 0 1 2 1 0 2 1 N I SD: 19.5348 c. M:-31.8786 c. 19: 1 2 1 0 3 0 1 3 1 0 3 0 1 2 1 N I SD: 16.8826 c. M: 24.4482 c. 21: 1 2 1 1 2 1 1 3 1 1 2 1 1 2 1 N D3 I SD: 15.9281 c. M: 25.8065 c. 23: 1 3 0 1 3 1 1 3 1 1 3 1 0 3 1 N I SD: 14.1748 c. M: 23.5624 c. 25: 1 3 1 1 3 1 0 5 0 1 3 1 1 3 1 N I SD: 12.9424 c. M: 23.2258 c. 26: 1 3 1 1 3 1 1 4 1 1 3 1 1 3 1 N I SD: 6.4325 c. M:-10.4218 c. 31: 1 4 1 1 4 1 1 5 1 1 4 1 1 4 1 N G 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 3 x x x x x x 4 S SD: 2.5904 cents 3 x x x x x x 4 x x x 5 x x x 6 S SD: 14.9910 cents 4 x x x x 5 x x 6 x x x 7 x x 8 S SD: 9.9615 cents 5 x x x 6 x x 7 x x 8 x x 9 x 10 S SD: 19.9659 cents 6 x x x 7 x x 8:9 x x 10 x 11 x 12 S SD: 10.4184 cents 7 x x 8 x 9 x x 10 x 11:12 x 13 x 14 S SD: 14.7889 cents 8 x 9 x x 10 x 11:12 x 13 x 14 x x 16 S SD: 13.0994 cents 9 x 10 x 11 x x 12:13 x 14:15 x 16 x 18 S SD: 13.5797 cents 10 x 11 x 12 x 13 x 15 x 16:17 x 18 x 20 SD: 8.6017 cents 11 x 12 x 13:14 x 15:16:17 x 19 x 20 x 22 SD: 9.3835 cents 12 x 13 x 14:15 x 16:18 x 19 x 21 x 23:24 SD: 8.8423 cents 13 x x 15 x x 17 x 19:20 x 22 x 23:25:26 SD: 7.3567 cents 14 x x 16 x 18 x 19:21 x 22:24 x 25:27:28 SD: 4.2210 cents 15:16 x 17:18:19 x 20:22:23 x x 26:27:29:30 SD: 8.9961 cents 16:17:18 x 19:20:21 x 24 x 25:27:28:29:31:32 SD: 7.5303 cents 17:18:19 x 20 x 22:23:25:26:27:29:30 x 33:34 SD: 6.6992 cents 18:19:20 x 21:23 x 24:27 x 28:31 x 32:35:36 SD: 5.4930 cents 19:20:21 x 22:24:25 x 28:29:30:32:33:34:37:38 SD: 5.7681 cents 20:21:22:23 x x 26:27:30 x 31:34:35:36:39:40 SD: 5.2049 cents 21:22:23:24:25:27 x 28:31:32:33:36:37:38:41:42 SD: 5.2167 cents 22:23 x 25:26:28:29 x 33:34 x 38 x 39:43:44 SD: 5.0280 cents 23:24:26 x 27:29:30:31:34:35:36:39:40:41:45:46 SD: 4.0704 cents 24:25:27 x 28:31 x 32:36:37:38:41:42:43:47:48 SD: 3.5811 cents 25:26:28 x 29:32:33 x 37:38:39:43:44:45:49:50 SD: 3.5507 cents 26:27:29:30 x 33:34:35:39:40:41:44:45:47:51:52 SD: 3.6669 cents 27:28:30:31:32 x 35:36:40:41:42:46:47:48:53:54 SD: 3.4380 cents 28:29:31:32:33:36:37 x 42:43:44:48:49:50:55:56 SD: 2.8648 cents 30:31 x 34:35:38:39:40:45:46:47:51:52:54:59:60 SD: 2.8691 cents 31:32:35 x 36:40 x 41:46:47:48:53:54:55:61:62 SD: 3.7298 cents 32:33:36:37 x 41:42:43:48:49:50:55:56:57:63:64 SD: 2.3595 cents 35:36:39:40:41:45:46:47:52:54:55:60:61:63:68:70 SD: 2.2115 cents 36:37:40:41:42:46:47:48:54:55:56:62:63:64:70:72 SD: 1.8584 cents 41:42:46:47:48:52:54:55:61:63:64:70:72:73:80:82 SD: 1.8142 cents 42:43:47:48:49:54:55:56:63:64:66:72:73:75:82:84 SD: 1.3741 cents 65:66:73:74:76:83:85:87:97:99:102:111:114:116:127:130 SD: 1.3673 cents 68:70:76:78:80:87:89:91:102:104:106:116:119:122:133:136 SD: 1.3024 cents 69:71:77:79:81:88:90:92:103:106:108:118:121:123:135:138 SD: 1.2890 cents 71:73:79:81:83:91:93:95:106:109:111:121:124:127:139:142 SD: 1.1623 cents 75:77:84:86:88:96:98:100:112:115:117:128:131:134:147:150 SD: 0.9912 cents 76:78:85:87:89:97:99:102:114:116:119:130:133:136:149:152 SD: 0.9589 cents 83:85:93:95:97:106:109:111:124:127:130:142:145:148:162:166 SD: 0.7696 cents 117:120:131:134:137:150:153:156:175:179:183:200:205:209:229:234 SD: 0.6852 cents 119:122:133:136:139:152:156:159:178:182:186:204:208:213:233:238 SD: 0.5752 cents 136:139:152:156:159:174:178:182:203:208:213:233:238:243:266:272 SD: 0.5341 cents 159:163:178:182:186:203:208:213:238:243:249:272:278:284:311:318 SD: 0.5032 cents 160:164:179:183:187:205:209:214:239:245:250:274:280:286:313:320 SD: 0.4778 cents 166:170:186:190:194:212:217:222:248:254:260:284:290:297:325:332 SD: 0.4517 cents 172:176:192:197:201:220:225:230:257:263:269:294:301:308:336:344 SD: 0.3849 cents 176:180:197:201:206:225:230:235:263:269:275:301:308:315:344:352 SD: 0.3592 cents 208:213:233:238:243:266:272:278:311:318:325:356:364:372:407:416 SD: 0.3403 cents 218:223:244:249:255:279:285:292:326:333:341:373:381:390:426:436 SD: 0.3362 cents 230:235:257:263:269:294:301:308:344:352:360:393:402:411:450:460 SD: 0.3091 cents 255:261:285:292:298:326:333:341:381:390:399:436:446:456:499:510 SD: 0.3070 cents 259:265:290:296:303:331:339:346:387:396:405:443:453:463:507:518 SD: 0.2962 cents 264:270:295:302:309:338:345:353:395:404:413:452:462:472:516:528 SD: 0.2860 cents 266:272:297:304:311:340:348:356:398:407:416:455:465:476:520:532 SD: 0.2607 cents 270:276:302:309:316:345:353:361:404:413:422:462:472:483:528:540 SD: 0.2137 cents 312:319:349:357:365:399:408:417:467:477:488:534:546:558:610:624 SD: 0.1951 cents 355:363:397:406:415:454:464:475:531:543:555:607:621:635:694:710 SD: 0.1262 cents 542:554:606:620:634:693:709:725:811:829:848:927:948:969:1060:1084 SD: 0.1254 cents 566:579:633:647:662:724:740:757:846:866:885:968:990:1012:1107:1132 SD: 0.1201 cents 573:586:641:655:670:733:749:766:857:876:896:980:1002:1025:1121:1146 SD: 0.1187 cents 585:598:654:669:684:748:765:782:875:895:915:1000:1023:1046:1144:1170 SD: 0.1140 cents