Scala analysis: met12
Milder Extended Temperament, 5ths average 703.711 cents
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 126.563 cents 126.562500 2: 207.422 cents 207.421870 3: 289.453 cents 289.453130 4: 414.844 cents 414.843750 5: 496.875 cents 496.875000 6: 622.266 cents 622.265630 7: 704.297 cents 704.296880 8: 829.687 cents 829.687500 9: 911.719 cents 911.718750 10: 992.578 cents 992.578130 11: 1119.141 cents 1119.140630 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 80.8594 cents 80.8594 1: 126.5625 cents 126.5625 2: 80.8594 cents 80.8594 3: 82.0313 cents 82.0313 4: 125.3906 cents 125.3906 5: 82.0313 cents 82.0313 6: 125.3906 cents 125.3906 7: 82.0312 cents 82.0312 8: 125.3906 cents 125.3906 9: 82.0313 cents 82.0313 10: 80.8594 cents 80.8594 11: 126.5625 cents 126.5625 12: 80.8594 cents 80.8594
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 80.85937 cents 1: 4 82.03126 cents 1: 3 125.39062 cents 1: 2 126.56250 cents 2: 2 162.89063 cents 2: 10 207.42187 cents 3: 4 288.28125 cents 3: 5 289.45313 cents 3: 2 332.81250 cents 3: 1 333.98437 cents 4: 4 370.31250 cents 4: 8 414.84375 cents 5: 5 495.70313 cents 5: 6 496.87500 cents 5: 1 540.23437 cents 6: 6 577.73438 cents 6: 6 622.26563 cents 7: 1 659.76563 cents 7: 6 703.12500 cents 7: 5 704.29688 cents 8: 8 785.15625 cents 8: 4 829.68750 cents 9: 1 866.01563 cents 9: 2 867.18750 cents 9: 5 910.54687 cents 9: 4 911.71875 cents 10: 10 992.57813 cents 10: 2 1037.10937 cents 11: 2 1073.43750 cents 11: 3 1074.60938 cents 11: 4 1117.96874 cents 11: 3 1119.14063 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 2.90909 = 32/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 126.6 207.4 289.5 414.8 496.9 622.3 704.3 829.7 911.7 992.6 1119.1 1200.0 126.6 : 80.9 162.9 288.3 370.3 495.7 577.7 703.1 785.2 866.0 992.6 1073.4 1200.0 207.4 : 82.0 207.4 289.5 414.8 496.9 622.3 704.3 785.2 911.7 992.6 1119.1 1200.0 289.5 : 125.4 207.4 332.8 414.8 540.2 622.3 703.1 829.7 910.5 1037.1 1118.0 1200.0 414.8 : 82.0 207.4 289.5 414.8 496.9 577.7 704.3 785.2 911.7 992.6 1074.6 1200.0 496.9 : 125.4 207.4 332.8 414.8 495.7 622.3 703.1 829.7 910.5 992.6 1118.0 1200.0 622.3 : 82.0 207.4 289.5 370.3 496.9 577.7 704.3 785.2 867.2 992.6 1074.6 1200.0 704.3 : 125.4 207.4 288.3 414.8 495.7 622.3 703.1 785.2 910.5 992.6 1118.0 1200.0 829.7 : 82.0 162.9 289.5 370.3 496.9 577.7 659.8 785.2 867.2 992.6 1074.6 1200.0 911.7 : 80.9 207.4 288.3 414.8 495.7 577.7 703.1 785.2 910.5 992.6 1118.0 1200.0 992.6 : 126.6 207.4 334.0 414.8 496.9 622.3 704.3 829.7 911.7 1037.1 1119.1 1200.0 1119.1: 80.9 207.4 288.3 370.3 495.7 577.7 703.1 785.2 910.5 992.6 1073.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.8594 .. 126.5625 cents 45.70313 cents 80.85937 cents 2: 162.8906 .. 207.4219 cents 44.53124 cents 36.32813 cents 3: 288.2812 .. 333.9844 cents 45.70312 cents 80.85938 cents 4: 370.3125 .. 414.8438 cents 44.53125 cents 36.32813 cents 5: 495.7031 .. 540.2344 cents 44.53124 cents 80.85938 cents 6: 577.7344 .. 622.2656 cents 44.53125 cents 37.50001 cents 7: 659.7656 .. 704.2969 cents 44.53125 cents 37.50000 cents 8: 785.1562 .. 829.6875 cents 44.53125 cents 80.85937 cents 9: 866.0156 .. 911.7187 cents 45.70312 cents 36.32813 cents 10: 992.5781 .. 1037.1094 cents 44.53124 cents 80.85938 cents 11: 1073.4375 .. 1119.1406 cents 45.70313 cents 36.32813 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 80.85937 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 126.56250 cents Average / Smallest step : 1.236715 Largest / Average step : 1.265625 Largest / Smallest step : 1.565217 Median interval of one step : 82.03126 cents, amount: 4 Most common interval of one step : 82.03126 cents, amount: 4 Least squares average step : 101.07151 cents, oct.: 1212.85818 cents Scale is strictly proper Scale is a mode of a 1024-tone equal temperament with octave 2/1 degrees: 108 177 247 354 424 531 601 708 778 847 955 1024 Least number of segments generator : 513 of 601.172 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 565 of 662.109 cents and inv. generated superset size: 74 = 62 more = 616.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDCDCDCBAB Step pattern size order : DABCBCBCBADA Scale is a Constant Structure, by a margin of 36.32813 cents Scale diversity : 1.225449 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.587891 Rothenberg efficiency : 0.514153 redundancy: 0.485847 Efficiency x scale size : 6.169841 Number of different interval sizes : 32 = 2.90909 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 2.90909 = 32/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 1.17187 cents Most common intervals : 207.42187 cents & inv., amount: 10 Most common triad is 0.0 207.422 992.578 cents, amount: 8 Number of recognisable fifths : 11, average 703.6577 cents Best fifths form a closed circle Formal octave complements present : 3 = 25.0000% Limited inverse transpositions : 11 Inversional symmetry on intervals : 5-6 11-12 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 15.9592 c. M: 29.6875 c. Twelve-tone Chromatic (1/11-comma) 17: 2 1 1 2 1 2 1 2 1 1 2 1 P M ME SD: 9.1260 c. M:-17.3713 c. Twelve-tone Chromatic (2/11-comma positive) 29: 3 2 2 3 2 3 2 3 2 2 3 2 SP M ME SD: 1.3164 c. M: 2.4246 c. Twelve-tone Chromatic (1/14-comma positive) 75: 8 5 5 8 5 8 5 8 5 5 8 5 SP M DE SD: 1.1623 c. M:-2.3125 c. Twelve-tone Chromatic (2/21-comma positive) 104: 11 7 7 11 7 11 7 11 7 7 11 7 SP M DE SD: 0.5877 c. M:-1.0817 c. Twelve-tone Chromatic (2/23-comma positive) 133: 14 9 9 14 9 14 9 14 9 9 14 9 SP M DE SD: 0.3969 c. M: 0.7313 c. Twelve-tone Chromatic (1/12-comma positive) 162: 17 11 11 17 11 17 11 17 11 11 17 11 SP M DE SD: 0.4255 c. M: 0.6366 c. 295: 31 20 20 31 20 31 20 31 20 20 31 20 SP M DE SD: 0.3956 c. M: 0.6396 c. 428: 45 29 29 45 29 45 29 45 29 29 45 29 SP M DE SD: 0.3914 c. M: 0.6681 c. 457: 48 31 31 48 31 48 31 48 31 31 48 31 SP M DE SD: 0.4032 c. M: 0.6129 c. 521: 55 35 36 54 36 54 36 54 36 35 55 35 SP SD: 0.4027 c. M:-0.7580 c. 538: 57 36 37 56 37 56 37 56 37 36 57 36 SP SD: 0.3844 c. M:-0.5750 c. 567: 60 38 39 59 39 59 39 59 39 38 60 38 SP SD: 0.3250 c. M:-0.4940 c. 596: 63 40 41 62 41 62 41 62 41 40 63 40 SP SD: 0.2811 c. M:-0.4798 c. 625: 66 42 43 65 43 65 43 65 43 42 66 42 SP SD: 0.2534 c. M:-0.4669 c. 654: 69 44 45 68 45 68 45 68 45 44 69 44 SP SD: 0.2418 c. M:-0.4551 c. 671: 71 45 46 70 46 70 46 70 46 45 71 45 SP SD: 0.2463 c. M:-0.4122 c. 683: 72 46 47 71 47 71 47 71 47 46 72 46 SP SD: 0.2444 c. M:-0.4444 c. 700: 74 47 48 73 48 73 48 73 48 47 74 47 SP SD: 0.1970 c. M:-0.2946 c. 729: 77 49 50 76 50 76 50 76 50 49 77 49 SP SD: 0.1601 c. M:-0.2588 c. 758: 80 51 52 79 52 79 52 79 52 51 80 51 SP SD: 0.1393 c. M:-0.2566 c. 787: 83 53 54 82 54 82 54 82 54 53 83 53 SP SD: 0.1368 c. M:-0.2546 c. 833: 88 56 57 87 57 87 57 87 57 56 88 56 SP SD: 0.1178 c. M:-0.2082 c. 862: 91 58 59 90 59 90 59 90 59 58 91 58 SP SD: 0.0800 c. M:-0.1196 c. 891: 94 60 61 93 61 93 61 93 61 60 94 60 SP SD: 0.0592 c. M:-0.1092 c. 995: 105 67 68 104 68 104 68 104 68 67 105 67 SP SD: 0.0384 c. M:-0.0707 c. 1024: 108 69 70 107 70 107 70 107 70 69 108 69 SP SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x x x x 4 S SD: 1.1709 cents 3 x x x x 4 x x x 5 x x 6 S SD: 9.1283 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 9.2992 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 11.2216 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 11.1678 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 11.0036 cents 8 x 9 x 10:11 x 12:13 x 14:15:16 S SD: 9.2115 cents 9 x 10:11 x 12:13:14 x 15:16:17:18 S SD: 10.5146 cents 10:11 x 12:13 x 14:15:16:17:18:19:20 S SD: 7.9324 cents 11:12 x 13:14:15:16:17:18:19:20:21:22 S SD: 8.5463 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.0133 cents 13:14:15 x x 17:19:20:21:22:23:25:26 SD: 7.6163 cents 14:15:16:17:18:19:20:21:23:24:25:27:28 SD: 6.4732 cents 15:16:17:18:19:20:21:23:24:25:27:29:30 SD: 6.4559 cents 16:17:18:19:20:21:23:24:26:27:28:31:32 SD: 4.9068 cents 21:23:24:25:27:28:30:32:34:36:37:40:42 SD: 4.8343 cents 22:24:25:26:28:29:32:33:36:37:39:42:44 SD: 4.1607 cents 23:25:26:27:29:31:33:35:37:39:41:44:46 SD: 3.4448 cents 26:28:29:31:33:35:37:39:42:44:46:50:52 SD: 2.9050 cents 32:34:36:38:41:43:46:48:52:54:57:61:64 SD: 2.8948 cents 36:39:41:43:46:48:52:54:58:61:64:69:72 SD: 2.8544 cents 37:40:42:44:47:49:53:56:60:63:66:71:74 SD: 2.5413 cents 39:42:44:46:50:52:56:59:63:66:69:74:78 SD: 1.9619 cents 48:52:54:57:61:64:69:72:78:81:85:92:96 SD: 1.8228 cents 49:53:55:58:62:65:70:74:79:83:87:94:98 SD: 1.7865 cents 54:58:61:64:69:72:77:81:87:91:96:103:108 SD: 1.4481 cents 55:59:62:65:70:73:79:83:89:93:98:105:110 SD: 1.2874 cents 66:71:74:78:84:88:95:99:107:112:117:126:132 SD: 1.2726 cents 70:75:79:83:89:93:100:105:113:119:124:134:140 SD: 1.2345 cents 76:82:86:90:97:101:109:114:123:129:135:145:152 SD: 1.1884 cents 77:83:87:91:98:103:110:116:124:130:137:147:154 SD: 1.1836 cents 78:84:88:92:99:104:112:117:126:132:138:149:156 SD: 0.7107 cents 111:119:125:131:141:148:159:167:179:188:197:212:222 SD: 0.6698 cents 120:129:135:142:152:160:172:180:194:203:213:229:240 SD: 0.6682 cents 132:142:149:156:168:176:189:198:213:224:234:252:264 SD: 0.5177 cents 159:171:179:188:202:212:228:239:257:269:282:303:318 SD: 0.4166 cents 187:201:211:221:238:249:268:281:302:317:332:357:374 SD: 0.3758 cents 199:214:224:235:253:265:285:299:321:337:353:380:398 SD: 0.3342 cents 241:259:272:285:306:321:345:362:389:408:428:460:482 SD: 0.3337 cents 252:271:284:298:320:336:361:379:407:427:447:481:504 SD: 0.2777 cents 291:313:328:344:370:388:417:437:470:493:516:555:582 SD: 0.2175 cents 307:330:346:363:390:409:440:461:496:520:545:586:614 SD: 0.2079 cents 329:354:371:389:418:438:471:494:531:557:584:628:658 SD: 0.2078 cents 340:366:383:402:432:453:487:511:549:576:603:649:680 SD: 0.1930 cents 384:413:433:454:488:512:550:577:620:650:681:733:768 SD: 0.1556 cents 462:497:521:546:587:616:662:694:746:782:820:882:924 SD: 0.1477 cents 472:508:532:558:600:629:676:709:762:799:837:901:944 SD: 0.1275 cents 488:525:550:577:620:650:699:733:788:826:866:931:976 SD: 0.1260 cents 550:592:620:650:699:733:788:826:888:931:976:1050:1100 SD: 0.1073 cents 566:609:638:669:719:754:811:850:914:958:1004:1080:1132 SD: 0.1073 cents