Scala analysis: mir11
Mir11
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 83.872 cents 83.871500 2: 233.431 cents 233.431200 3: 317.303 cents 317.302700 4: 466.862 cents 466.862400 5: 550.734 cents 550.733900 6: 700.294 cents 700.293600 7: 784.165 cents 784.165100 8: 933.725 cents 933.724800 9: 1017.596 cents 1017.596300 10: 1167.156 cents 1167.155900 11: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 32.8441 cents 32.8441 1: 83.8715 cents 83.8715 2: 149.5597 cents 149.5597 3: 83.8715 cents 83.8715 4: 149.5597 cents 149.5597 5: 83.8715 cents 83.8715 6: 149.5597 cents 149.5597 7: 83.8715 cents 83.8715 8: 149.5597 cents 149.5597 9: 83.8715 cents 83.8715 10: 149.5596 cents 149.5596 11: 32.8441 cents 32.8441
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 32.84410 cents 1: 5 83.87150 cents 1: 5 149.55970 cents 2: 1 116.71560 cents 2: 1 182.40370 cents 2: 9 233.43120 cents 3: 3 266.27520 cents 3: 4 317.30270 cents 3: 4 382.99090 cents 4: 2 350.14670 cents 4: 2 415.83490 cents 4: 7 466.86240 cents 5: 5 499.70640 cents 5: 3 550.73390 cents 5: 3 616.42210 cents 6: 3 583.57790 cents 6: 3 649.26610 cents 6: 5 700.29360 cents 7: 7 733.13760 cents 7: 2 784.16510 cents 7: 2 849.85330 cents 8: 4 817.00910 cents 8: 4 882.69730 cents 8: 3 933.72480 cents 9: 9 966.56880 cents 9: 1 1017.59630 cents 9: 1 1083.28440 cents 10: 5 1050.44030 cents 10: 5 1116.12850 cents 10: 1 1167.15590 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 : 83.9 233.4 317.3 466.9 550.7 700.3 784.2 933.7 1017.6 1167.2 1200.0 83.9 : 149.6 233.4 383.0 466.9 616.4 700.3 849.9 933.7 1083.3 1116.1 1200.0 233.4 : 83.9 233.4 317.3 466.9 550.7 700.3 784.2 933.7 966.6 1050.4 1200.0 317.3 : 149.6 233.4 383.0 466.9 616.4 700.3 849.9 882.7 966.6 1116.1 1200.0 466.9 : 83.9 233.4 317.3 466.9 550.7 700.3 733.1 817.0 966.6 1050.4 1200.0 550.7 : 149.6 233.4 383.0 466.9 616.4 649.3 733.1 882.7 966.6 1116.1 1200.0 700.3 : 83.9 233.4 317.3 466.9 499.7 583.6 733.1 817.0 966.6 1050.4 1200.0 784.2 : 149.6 233.4 383.0 415.8 499.7 649.3 733.1 882.7 966.6 1116.1 1200.0 933.7 : 83.9 233.4 266.3 350.1 499.7 583.6 733.1 817.0 966.6 1050.4 1200.0 1017.6: 149.6 182.4 266.3 415.8 499.7 649.3 733.1 882.7 966.6 1116.1 1200.0 1167.2: 32.8 116.7 266.3 350.1 499.7 583.6 733.1 817.0 966.6 1050.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 32.8441 .. 149.5597 cents 116.71560 cents 32.84410 cents 2: 116.7156 .. 233.4312 cents 116.71560 cents -32.84410 cents 3: 266.2752 .. 382.9909 cents 116.71570 cents 32.84400 cents 4: 350.1467 .. 466.8624 cents 116.71570 cents -32.84420 cents 5: 499.7064 .. 616.4221 cents 116.71570 cents 32.84400 cents 6: 583.5779 .. 700.2936 cents 116.71570 cents -32.84420 cents 7: 733.1376 .. 849.8533 cents 116.71570 cents 32.84400 cents 8: 817.0091 .. 933.7248 cents 116.71570 cents -32.84420 cents 9: 966.5688 .. 1083.2844 cents 116.71560 cents 32.84400 cents 10: 1050.4403 .. 1167.1559 cents 116.71560 cents -32.84410 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 32.84410 cents, class 1 Average step (divided formal octave): 109.0909 cents Largest one step interval : 149.55970 cents Average / Smallest step : 3.321477 Largest / Average step : 1.370964 Largest / Smallest step : 4.553625 Median interval of one step : 83.87150 cents, amount: 5 Least squares average step : 113.26957 cents, oct.: 1245.96527 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2046-tone equal temperament with octave 1200.000 cents degrees: 143 398 541 796 939 1194 1337 1592 1735 1990 2046 Least number of segments generator : 1025 of 601.173 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1847 of 1083.284 cents and inv. generated superset size: 20 = 9 more = 181.818% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABABABABC Step pattern size order : MLMLMLMLMLS Scale is a Constant Structure, by a margin of 32.84400 cents Scale diversity : 1.412445 Lumma stability : 0.164220 Lumma impropriety factor : 0.136851 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 : 32.84400 cents Most common intervals : 233.43120 cents & inv., amount: 9 Scale is a chain of 5 triads 0.0 83.872 233.431 cents Most common triad is 0.0 233.431 966.569 cents, amount: 7 Number of recognisable fifths : 5, average 700.2936 cents Scale contains two identical disjunct pentachords Formal octave complements present : 1 = 9.0909% -- Rational properties --
FIT/MODE
11: 1 1 1 1 1 1 1 2 0 2 0 N T3 SD: 28.7815 c. M:-48.0934 c. 12: 1 1 1 2 1 1 1 1 1 2 0 N D3 SD: 26.9325 c. M:-49.2661 c. 13: 1 2 1 1 1 2 1 1 1 2 0 N D3 SD: 29.4233 c. M:-51.9281 c. 14: 1 2 1 1 1 2 1 2 1 2 0 N SD: 22.7050 c. M: 38.2910 c. 15: 1 2 1 2 1 2 1 2 1 2 0 N T3 SD: 17.1464 c. M:-32.8441 c. 19: 1 3 1 2 2 2 1 3 1 2 1 N SD: 18.0952 c. M: 30.3138 c. 20: 1 3 1 3 1 3 1 3 1 2 1 N SD: 16.6228 c. M: 27.1559 c. 21: 1 3 2 2 2 2 2 2 2 2 1 N SD: 17.7505 c. M: 26.7286 c. 26: 2 3 2 3 2 3 2 3 2 3 1 P T3 SD: 6.8026 c. M: 13.3097 c. 31: 2 4 2 4 2 4 2 4 2 4 1 N T3 SD: 6.5818 c. M: 11.1447 c. 41: 3 5 3 5 3 5 3 5 3 5 1 N T3 SD: 4.0123 c. M:-6.7939 c. 46: 3 6 3 6 3 6 3 6 3 6 1 N T3 SD: 3.8256 c. M:-6.7571 c. 67: 5 8 5 8 5 8 5 8 5 8 2 N T3 SD: 3.3553 c. M:-5.6807 c. 72: 5 9 5 9 5 9 5 9 5 9 2 N T3 SD: 0.5490 c. M: 0.9296 c. 185: 13 23 13 23 13 23 13 23 13 23 5 N T3 SD: 0.4619 c. M:-0.7821 c. 257: 18 32 18 32 18 32 18 32 18 32 7 N T3 SD: 0.1787 c. M:-0.3025 c. 329: 23 41 23 41 23 41 23 41 23 41 9 N T3 SD: 0.0194 c. M:-0.0329 c. 1059: 74 132 74 132 74 132 74 132 74 132 29 N T3 SD: 0.0192 c. M: 0.0326 c. 1388: 97 173 97 173 97 173 97 173 97 173 38 N T3 SD: 0.0101 c. M: 0.0170 c. 1717: 120 214 120 214 120 214 120 214 120 214 47 N T3 SD: 0.0044 c. M: 0.0075 c. 2046: 143 255 143 255 143 255 143 255 143 255 56 N T3 SD: 0.0006 c. M: 0.0010 c.
FIT/HARMONIC
1 x 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 x 4 S SD: 0.8307 cents 3 x x x 4 x x x 5 x x 6 S SD: 19.4633 cents 4 x x 5 x x 6 x 7 x x 8 S SD: 19.3607 cents 5 x x 6 x 7 x 8 x 9 x 10 S SD: 8.6813 cents 6 x 7 x 8 x 9 x 10:11 x 12 S SD: 12.4046 cents 7 x 8 x 9:10 x 11:12:13 x 14 S SD: 13.0943 cents 8 x 9:10 x 11:12:13:14 x x 16 S SD: 14.3185 cents 9 x 10:11:12 x 13:14:15:16 x 18 S SD: 13.5826 cents 10 x 11:12:13:14:15:16:17:18 x 20 S SD: 9.2674 cents 11:12 x 13:14:15:16:17:19:20 x 22 SD: 12.1343 cents 12:13:14 x 16:17:18:19:21:22 x 24 SD: 11.2153 cents 13:14:15:16:17:18:19:20:22:23 x 26 SD: 9.4277 cents 14:15:16:17:18:19:21:22:24:25:27:28 SD: 5.9084 cents 16:17:18:19:21:22:24:25:27:29:31:32 SD: 5.1972 cents 19:20:22:23:25:26:28:30:33:34:37:38 SD: 4.4515 cents 20:21:23:24:26:27:30:31:34:36:39:40 SD: 4.2703 cents 21:22:24:25:28:29:31:33:36:38:41:42 SD: 4.2014 cents 24:25:27:29:31:33:36:38:41:43:47:48 SD: 4.0370 cents 26:27:30:31:34:36:39:41:45:47:51:52 SD: 3.1622 cents 34:36:39:41:45:47:51:53:58:61:67:68 SD: 3.0682 cents 35:37:40:42:46:48:52:55:60:63:69:70 SD: 2.0387 cents 40:42:46:48:52:55:60:63:69:72:78:80 SD: 1.9679 cents 54:57:62:65:71:74:81:85:93:97:106:108 SD: 1.5464 cents 56:59:64:67:73:77:84:88:96:101:110:112 SD: 1.2084 cents 64:67:73:77:84:88:96:101:110:115:126:128 SD: 1.1748 cents 75:79:86:90:98:103:112:118:129:135:147:150 SD: 1.0630 cents 80:84:92:96:105:110:120:126:137:144:157:160 SD: 0.9324 cents 84:88:96:101:110:115:126:132:144:151:165:168 SD: 0.8193 cents 104:109:119:125:136:143:156:164:178:187:204:208 SD: 0.6519 cents 120:126:137:144:157:165:180:189:206:216:235:240 SD: 0.6204 cents 138:145:158:166:181:190:207:217:237:248:271:276 SD: 0.6072 cents 139:146:159:167:182:191:208:219:238:250:273:278 SD: 0.4799 cents 159:167:182:191:208:219:238:250:273:286:312:318 SD: 0.4781 cents 165:173:189:198:216:227:247:260:283:297:324:330 SD: 0.4641 cents 179:188:205:215:234:246:268:282:307:322:351:358 SD: 0.4539 cents 180:189:206:216:236:247:270:283:309:324:353:360 SD: 0.4452 cents 185:194:212:222:242:254:277:291:317:333:363:370 SD: 0.4338 cents 200:210:229:240:262:275:300:315:343:360:392:400 SD: 0.3773 cents 220:231:252:264:288:302:330:346:377:396:432:440 SD: 0.3748 cents 229:240:262:275:300:315:343:360:393:412:449:458 SD: 0.3609 cents 235:247:269:282:308:323:352:370:403:423:461:470 SD: 0.3462 cents 243:255:278:292:318:334:364:382:417:437:477:486 SD: 0.2573 cents 304:319:348:365:398:418:456:478:521:547:597:608 SD: 0.2548 cents 319:335:365:383:418:438:478:502:547:574:626:638 SD: 0.2421 cents 323:339:370:388:423:444:484:508:554:581:634:646 SD: 0.2006 cents 339:356:388:407:444:466:508:533:581:610:665:678 SD: 0.1797 cents 401:421:459:482:525:551:601:631:688:722:787:802 SD: 0.1775 cents 403:423:461:484:528:554:604:634:691:725:791:806 SD: 0.1417 cents 443:465:507:532:580:609:664:697:760:797:869:886 SD: 0.1416 cents 526:552:602:632:689:723:788:827:902:947:1032:1052 SD: 0.1232 cents 582:611:666:699:762:800:872:915:998:1048:1142:1164 SD: 0.1140 cents