Scala analysis: portent11
A distributionally even scale in portent temperament, abababababc
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 151.534 cents 151.534000 2: 233.784 cents 233.784000 3: 385.318 cents 385.318000 4: 467.568 cents 467.568000 5: 619.102 cents 619.102000 6: 701.352 cents 701.352000 7: 852.886 cents 852.886000 8: 935.136 cents 935.136000 9: 966.707 cents 966.707000 10: 1118.241 cents 1118.241000 11: 1200.491 cents 1200.491000
SHOW/INTERVAL
0: 82.2500 cents 82.2500 1: 151.5340 cents 151.5340 2: 82.2500 cents 82.2500 3: 151.5340 cents 151.5340 4: 82.2500 cents 82.2500 5: 151.5340 cents 151.5340 6: 82.2500 cents 82.2500 7: 151.5340 cents 151.5340 8: 82.2500 cents 82.2500 9: 31.5710 cents 31.5710 10: 151.5340 cents 151.5340 11: 82.2500 cents 82.2500
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 31.57100 cents 1: 5 82.25000 cents 1: 5 151.53400 cents 2: 1 113.82100 cents 2: 1 183.10500 cents 2: 9 233.78400 cents 3: 3 265.35500 cents 3: 4 316.03400 cents 3: 4 385.31800 cents 4: 2 347.60500 cents 4: 2 416.88900 cents 4: 7 467.56800 cents 5: 5 499.13900 cents 5: 3 549.81800 cents 5: 3 619.10200 cents 6: 3 581.38900 cents 6: 3 650.67300 cents 6: 5 701.35200 cents 7: 7 732.92300 cents 7: 2 783.60200 cents 7: 2 852.88600 cents 8: 4 815.17300 cents 8: 4 884.45700 cents 8: 3 935.13600 cents 9: 9 966.70700 cents 9: 1 1017.38600 cents 9: 1 1086.67000 cents 10: 5 1048.95700 cents 10: 5 1118.24100 cents 10: 1 1168.92000 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 0.0 : 151.5 233.8 385.3 467.6 619.1 701.4 852.9 935.1 966.7 1118.2 1200.5 151.5 : 82.3 233.8 316.0 467.6 549.8 701.4 783.6 815.2 966.7 1049.0 1200.5 233.8 : 151.5 233.8 385.3 467.6 619.1 701.4 732.9 884.5 966.7 1118.2 1200.5 385.3 : 82.3 233.8 316.0 467.6 549.8 581.4 732.9 815.2 966.7 1049.0 1200.5 467.6 : 151.5 233.8 385.3 467.6 499.1 650.7 732.9 884.5 966.7 1118.2 1200.5 619.1 : 82.2 233.8 316.0 347.6 499.1 581.4 732.9 815.2 966.7 1049.0 1200.5 701.4 : 151.5 233.8 265.4 416.9 499.1 650.7 732.9 884.5 966.7 1118.2 1200.5 852.9 : 82.2 113.8 265.4 347.6 499.1 581.4 732.9 815.2 966.7 1049.0 1200.5 935.1 : 31.6 183.1 265.4 416.9 499.1 650.7 732.9 884.5 966.7 1118.2 1200.5 966.7 : 151.5 233.8 385.3 467.6 619.1 701.4 852.9 935.1 1086.7 1168.9 1200.5 1118.2: 82.2 233.8 316.0 467.6 549.8 701.4 783.6 935.1 1017.4 1049.0 1200.5 1200.5
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 31.5710 .. 151.5340 cents 119.96300 cents 31.57100 cents 2: 113.8210 .. 233.7840 cents 119.96300 cents -37.71300 cents 3: 265.3550 .. 385.3180 cents 119.96300 cents 31.57100 cents 4: 347.6050 .. 467.5680 cents 119.96300 cents -37.71300 cents 5: 499.1390 .. 619.1020 cents 119.96300 cents 31.57100 cents 6: 581.3890 .. 701.3520 cents 119.96300 cents -37.71300 cents 7: 732.9230 .. 852.8860 cents 119.96300 cents 31.57100 cents 8: 815.1730 .. 935.1360 cents 119.96300 cents -37.71300 cents 9: 966.7070 .. 1086.6700 cents 119.96300 cents 31.57100 cents 10: 1048.9570 .. 1168.9200 cents 119.96300 cents -37.71300 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 31.57100 cents, class 1 Average step (divided formal octave): 109.1355 cents Largest one step interval : 151.53400 cents Average / Smallest step : 3.456829 Largest / Average step : 1.388494 Largest / Smallest step : 4.799785 Median interval of one step : 82.25000 cents, amount: 5 Least squares average step : 113.61347 cents, oct.: 1249.74813 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABABABABCAB Step pattern size order : LMLMLMLMSLM Scale is a Constant Structure, by a margin of 31.57100 cents Scale diversity : 1.412081 Lumma stability : 0.157790 Lumma impropriety factor : 0.157073 Rothenberg efficiency : 0.513420 redundancy: 0.486580 Efficiency x scale size : 5.647619 Number of different interval sizes : 30 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 31.57100 cents Most common intervals : 233.78400 cents & inv., amount: 9 Scale is a chain of 5 triads 0.0 151.534 233.784 cents Most common triad is 0.0 233.784 966.707 cents, amount: 7 Number of recognisable fifths : 5, average 701.3520 cents Number of recognisable fourths : 5, average 499.1390 cents Scale contains two identical conjunct pentachords Formal octave complements present : 3 = 27.2727% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
11: 1 1 1 1 1 1 1 1 0 2 1 N T3 SD: 56.5363 c. M: 93.6226 c. 12: 1 1 1 1 2 1 1 1 0 2 1 N D3 SD: 47.3231 c. M: 85.1952 c. 13: 1 1 2 1 1 1 2 1 0 2 1 N D3 SD: 38.1759 c. M: 65.0292 c. 14: 2 1 1 1 2 1 2 1 0 2 1 N D3 SD: 22.3372 c. M: 42.3206 c. 15: 2 1 2 1 2 1 2 1 0 2 1 N T3 SD: 15.7728 c. M:-27.4741 c. 21: 3 1 3 1 3 1 3 1 1 3 1 N M DE S SD: 14.0659 c. M:-25.0838 c. Spartan-11 24: 3 2 3 1 3 2 3 2 0 3 2 N SD: 13.3813 c. M: 18.8565 c. 25: 3 2 3 2 3 2 3 1 1 3 2 N S SD: 11.7613 c. M: 22.7628 c. 26: 3 2 3 2 3 2 3 2 1 3 2 P T3 SD: 12.1336 c. M: 21.7768 c. 27: 3 2 4 2 3 2 3 2 1 3 2 N SD: 11.6794 c. M:-21.5209 c. 29: 4 2 3 2 4 2 4 2 0 4 2 N SD: 11.6882 c. M:-16.9776 c. 31: 4 2 4 2 4 2 4 2 1 4 2 N T3 SD: 3.0557 c. M: 5.7236 c. 41: 5 3 5 3 5 3 5 3 1 5 3 N T3 SD: 3.2733 c. M: 5.5908 c. 72: 9 5 9 5 9 5 9 5 2 9 5 N T3 SD: 1.4103 c. M: 2.5382 c. 103: 13 7 13 7 13 7 13 7 3 13 7 N T3 SD: 1.3920 c. M: 2.7158 c. 118: 15 8 15 8 15 8 15 8 3 15 8 N T3 SD: 0.9540 c. M:-1.7008 c. 149: 19 10 19 10 19 10 19 10 4 19 10 N T3 SD: 0.9887 c. M:-1.6801 c. 159: 20 11 20 11 20 11 20 11 4 20 11 N T3 SD: 0.5562 c. M:-1.0960 c. 190: 24 13 24 13 24 13 24 13 5 24 13 N T3 SD: 0.0698 c. M:-0.1111 c. 1022: 129 70 129 70 129 70 129 70 27 129 70 N T3 SD: 0.0601 c. M: 0.1156 c. 1181: 149 81 149 81 149 81 149 81 31 149 81 N T3 SD: 0.0483 c. M: 0.0868 c. 1212: 153 83 153 83 153 83 153 83 32 153 83 N T3 SD: 0.0490 c. M: 0.1001 c. 1371: 173 94 173 94 173 94 173 94 36 173 94 N T3 SD: 0.0328 c. M: 0.0594 c. 1561: 197 107 197 107 197 107 197 107 41 197 107 N T3 SD: 0.0217 c. M: 0.0386 c. 1751: 221 120 221 120 221 120 221 120 46 221 120 N T3 SD: 0.0142 c. M:-0.0266 c. 1941: 245 133 245 133 245 133 245 133 51 245 133 N T3 SD: 0.0109 c. M:-0.0224 c. 2131: 269 146 269 146 269 146 269 146 56 269 146 N T3 SD: 0.0117 c. M:-0.0203 c.
FIT/HARMONIC
1 x x x x x x x x x x 2 S SD: 0.4910 cents 2 x x x x x 3 x x x x 4 S SD: 0.3888 cents 3 x x x 4 x x 5 x x x 6 S SD: 14.6045 cents 4 x x 5 x x 6 x x 7 x 8 S SD: 0.6167 cents 5 x x 6 x 7 x 8 x 9 x 10 S SD: 20.3177 cents 6 x 7 x 8 x 9:10 x x 11:12 S SD: 14.6808 cents 7 x 8 x 9:10 x 11:12 x 13:14 S SD: 12.9285 cents 8 x 9:10 x 11:12:13 x 14:15:16 S SD: 10.1121 cents 9:10 x 11:12:13:14:15 x 16:17:18 S SD: 11.0084 cents 10:11 x x 13:14:15:16:17 x 19:20 SD: 7.4556 cents 11:12:13:14 x 16:17:18:19 x 21:22 SD: 9.8394 cents 12:13:14:15:16:17:18:20 x 21:23:24 SD: 5.9268 cents 13:14:15:16:17:19 x 21:22:23:25:26 SD: 6.7732 cents 14:15:16:17:18:20:21:23:24 x 27:28 SD: 7.0107 cents 15:16:17:19:20:21:22:25 x 26:29:30 SD: 8.8969 cents 16:17:18:20:21:23:24:26:27:28:31:32 SD: 6.3572 cents 17:19 x 21:22:24:25:28:29:30:32:34 SD: 7.1977 cents 18:20:21:22:24:26:27:29:31 x 34:36 SD: 7.6115 cents 19:21:22:24:25:27:28:31 x 33:36:38 SD: 5.1019 cents 20:22:23:25:26:29:30:33:34:35:38:40 SD: 3.5631 cents 22:24:25:27:29:31:33:36:38 x 42:44 SD: 4.4569 cents 23:25:26:29:30:33:34:38:39:40:44:46 SD: 4.3363 cents 24:26:27:30:31:34:36:39:41:42:46:48 SD: 4.2716 cents 25:27:29:31:33:36:37:41:43:44:48:50 SD: 4.2283 cents 26:28:30:32:34:37:39:43:45 x 50:52 SD: 4.7049 cents 27:29:31:34:35:39:40:44:46:47:52:54 SD: 4.6428 cents 28:31:32:35:37:40:42:46:48:49:53:56 SD: 2.9861 cents 32:35:37:40:42:46:48:52:55:56:61:64 SD: 2.1945 cents 42:46:48:52:55:60:63:69:72:73:80:84 SD: 1.9004 cents 44:48:50:55:58:63:66:72:76:77:84:88 SD: 1.8319 cents 52:57:60:65:68:74:78:85:89:91:99:104 SD: 1.7587 cents 55:60:63:69:72:79:82:90:94:96:105:110 SD: 1.5124 cents 56:61:64:70:73:80:84:92:96:98:107:112 SD: 1.1353 cents 68:74:78:85:89:97:102:111:117:119:130:136 SD: 0.9934 cents 77:84:88:96:101:110:115:126:132:135:147:154 SD: 0.9494 cents 84:92:96:105:110:120:126:137:144:147:160:168 SD: 0.9056 cents 88:96:101:110:115:126:132:144:151:154:168:176 SD: 0.6743 cents 96:105:110:120:126:137:144:157:165:168:183:192 SD: 0.6707 cents 110:120:126:137:144:157:165:180:189:192:210:220 SD: 0.6690 cents 116:127:133:145:152:166:174:190:199:203:221:232 SD: 0.6622 cents 130:142:149:162:170:186:195:213:223:227:248:260 SD: 0.6109 cents 132:144:151:165:173:189:198:216:227:231:252:264 SD: 0.4740 cents 152:166:174:190:199:217:228:249:261:266:290:304 SD: 0.3993 cents 207:226:237:259:271:296:310:339:355:362:395:414 SD: 0.3857 cents 209:228:239:261:274:299:313:342:359:365:399:418 SD: 0.3708 cents 228:249:261:285:299:326:342:373:391:399:435:456 SD: 0.3238 cents 242:264:277:302:317:346:363:396:415:423:462:484 SD: 0.2659 cents 261:285:299:326:342:373:391:427:448:456:498:522 SD: 0.2569 cents 284:310:325:355:372:406:426:465:487:496:542:568 SD: 0.2405 cents 317:346:363:396:415:453:475:519:544:554:605:634 SD: 0.2217 cents 325:355:372:406:426:465:487:532:558:568:620:650 SD: 0.2204 cents 338:369:387:422:443:483:507:553:580:591:645:676 SD: 0.2056 cents 361:394:413:451:473:516:541:591:620:631:689:722 SD: 0.1960 cents 381:416:436:476:499:545:571:624:654:666:727:762 SD: 0.1805 cents 416:454:476:520:545:595:624:681:714:727:794:832 SD: 0.1588 cents 493:538:564:616:646:705:739:807:846:862:941:986 SD: 0.1560 cents 512:559:586:640:671:732:768:838:879:895:977:1024 SD: 0.1529 cents 525:573:601:656:688:751:787:859:901:918:1002:1050 SD: 0.1507 cents 526:574:602:657:689:752:789:861:903:919:1003:1052 SD: 0.1419 cents 567:619:649:708:743:811:850:928:973:991:1082:1134 SD: 0.1296 cents