Scala analysis: as1511ms
Possible well-tempered interpretation of Arnold Schlick's tuning of 1555
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 88.270 cents 88.270000 2: 196.090 cents 196.090000 3: 303.910 cents 303.910000 4: 392.180 cents 392.180000 5: 501.955 cents 501.955000 6: 589.248 cents 589.247500 7: 698.045 cents 698.045000 8: 799.023 cents 799.022500 9: 894.135 cents 894.135000 10: 1002.933 cents 1002.932500 11: 1090.225 cents 1090.225000 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 109.7750 cents 109.7750 1: 88.2700 cents 88.2700 2: 107.8200 cents 107.8200 3: 107.8200 cents 107.8200 4: 88.2700 cents 88.2700 5: 109.7750 cents 109.7750 6: 87.2925 cents 87.2925 7: 108.7975 cents 108.7975 8: 100.9775 cents 100.9775 9: 95.1125 cents 95.1125 10: 108.7975 cents 108.7975 11: 87.2925 cents 87.2925 12: 109.7750 cents 109.7750
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 87.29250 cents 1: 2 88.27000 cents 1: 1 95.11250 cents 1: 1 100.97750 cents 1: 2 107.82000 cents 1: 2 108.79750 cents 1: 2 109.77500 cents 2: 5 196.09000 cents 2: 2 197.06750 cents 2: 2 198.04500 cents 2: 1 203.91000 cents 2: 1 209.77500 cents 2: 1 215.64000 cents 3: 2 285.33750 cents 3: 1 291.20250 cents 3: 1 297.06750 cents 3: 2 303.91000 cents 3: 2 304.88750 cents 3: 4 305.86500 cents 4: 3 392.18000 cents 4: 2 393.15750 cents 4: 2 394.13500 cents 4: 1 400.97750 cents 4: 1 406.84250 cents 4: 3 413.68500 cents 5: 1 489.24750 cents 5: 1 495.11250 cents 5: 4 500.97750 cents 5: 6 501.95500 cents 6: 1 588.27000 cents 6: 2 589.24750 cents 6: 2 590.22500 cents 6: 1 597.06750 cents 6: 1 602.93250 cents 6: 2 609.77500 cents 6: 2 610.75250 cents 6: 1 611.73000 cents 7: 6 698.04500 cents 7: 4 699.02250 cents 7: 1 704.88750 cents 7: 1 710.75250 cents 8: 3 786.31500 cents 8: 1 793.15750 cents 8: 1 799.02250 cents 8: 2 805.86500 cents 8: 2 806.84250 cents 8: 3 807.82000 cents 9: 4 894.13500 cents 9: 2 895.11250 cents 9: 2 896.09000 cents 9: 1 902.93250 cents 9: 1 908.79750 cents 9: 2 914.66250 cents 10: 1 984.36000 cents 10: 1 990.22500 cents 10: 1 996.09000 cents 10: 2 1001.95500 cents 10: 2 1002.93250 cents 10: 5 1003.91000 cents 11: 2 1090.22500 cents 11: 2 1091.20250 cents 11: 2 1092.18000 cents 11: 1 1099.02250 cents 11: 1 1104.88750 cents 11: 2 1111.73000 cents 11: 2 1112.70750 cents Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 6.00000 = 6
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 88.3 196.1 303.9 392.2 502.0 589.2 698.0 799.0 894.1 1002.9 1090.2 1200.0 88.3 : 107.8 215.6 303.9 413.7 501.0 609.8 710.8 805.9 914.7 1002.0 1111.7 1200.0 196.1 : 107.8 196.1 305.9 393.2 502.0 602.9 698.0 806.8 894.1 1003.9 1092.2 1200.0 303.9 : 88.3 198.0 285.3 394.1 495.1 590.2 699.0 786.3 896.1 984.4 1092.2 1200.0 392.2 : 109.8 197.1 305.9 406.8 502.0 610.8 698.0 807.8 896.1 1003.9 1111.7 1200.0 502.0 : 87.3 196.1 297.1 392.2 501.0 588.3 698.0 786.3 894.1 1002.0 1090.2 1200.0 589.2 : 108.8 209.8 304.9 413.7 501.0 610.8 699.0 806.8 914.7 1002.9 1112.7 1200.0 698.0 : 101.0 196.1 304.9 392.2 502.0 590.2 698.0 805.9 894.1 1003.9 1091.2 1200.0 799.0 : 95.1 203.9 291.2 401.0 489.2 597.1 704.9 793.2 902.9 990.2 1099.0 1200.0 894.1 : 108.8 196.1 305.9 394.1 502.0 609.8 698.0 807.8 895.1 1003.9 1104.9 1200.0 1002.9: 87.3 197.1 285.3 393.2 501.0 589.2 699.0 786.3 895.1 996.1 1091.2 1200.0 1090.2: 109.8 198.0 305.9 413.7 502.0 611.7 699.0 807.8 908.8 1003.9 1112.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 87.2925 .. 109.7750 cents 22.48250 cents 87.29250 cents 2: 196.0900 .. 215.6400 cents 19.55000 cents 86.31500 cents 3: 285.3375 .. 305.8650 cents 20.52750 cents 69.69750 cents 4: 392.1800 .. 413.6850 cents 21.50500 cents 86.31500 cents 5: 489.2475 .. 501.9550 cents 12.70750 cents 75.56250 cents 6: 588.2700 .. 611.7300 cents 23.46000 cents 86.31500 cents 7: 698.0450 .. 710.7525 cents 12.70750 cents 86.31500 cents 8: 786.3150 .. 807.8200 cents 21.50500 cents 75.56250 cents 9: 894.1350 .. 914.6625 cents 20.52750 cents 86.31500 cents 10: 984.3600 .. 1003.9100 cents 19.55000 cents 69.69750 cents 11: 1090.2250 .. 1112.7075 cents 22.48250 cents 86.31500 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 87.29250 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 109.77500 cents Average / Smallest step : 1.145574 Largest / Average step : 1.097750 Largest / Smallest step : 1.257554 Median interval of one step : 104.39875 cents, amount: 0 Least squares average step : 99.62103 cents, oct.: 1195.45237 cents Scale is strictly proper Step pattern alph. order: ABBACDEFGEDC Step pattern size order : BEEBGAFDCFAG Scale is a Constant Structure, by a margin of 69.69750 cents Scale diversity : 1.151692 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.819162 Rothenberg efficiency : 0.254621 redundancy: 0.745379 Efficiency x scale size : 3.055447 Number of different interval sizes : 66 = 6.00000 / class Number of one step interval sizes : 7 Highest interval variety : 8 Mean interval variety : 6.00000 = 6 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 0.97750 cents Most common intervals : 501.95500 cents & inv., amount: 6 Most common triad is 0.0 501.955 698.045 cents, amount: 5 Number of recognisable fifths : 12, average 700.0000 cents Best fifths form a closed circle Formal octave complements present : 3 = 25.0000% Limited transpositions with margin 22.4825 cents: 5 7 8 Limited inverse transpositions with margin 22.4825 cents: 4 8 9 11 -- 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: 6.4037 c. M:-11.7300 c. Twelve-tone Chromatic (1/11-comma) 43: 3 4 4 3 4 3 4 4 3 4 3 4 SP M ME SD: 3.6132 c. M:-10.2798 c. 51: 4 4 5 4 4 4 5 4 4 5 3 5 SP D3 SD: 5.9564 c. M:-8.8322 c. 55: 4 5 5 4 5 4 5 5 4 5 4 5 SP M ME SD: 2.4667 c. M:-8.2502 c. 59: 4 6 5 4 6 4 5 5 5 5 5 5 SP D3 SD: 5.4795 c. M:-8.0801 c. 63: 5 5 6 5 5 5 6 5 5 6 4 6 SP D3 SD: 4.9971 c. M:-7.8200 c. 66: 5 6 6 5 6 4 6 6 5 6 5 6 SP D3 SD: 4.8965 c. M:-7.8200 c. 67: 5 6 6 5 6 5 6 6 5 6 5 6 SP M ME SD: 2.3353 c. M:-6.9476 c. 79: 6 7 7 6 7 6 7 7 6 7 6 7 SP M ME SD: 2.6055 c. M:-6.0408 c. 86: 6 8 8 6 8 6 8 7 7 8 6 8 SP D3 S SD: 2.3181 c. M: 4.5491 c. 98: 7 9 9 7 9 7 9 8 8 9 7 9 SP D3 S SD: 1.4440 c. M: 3.1041 c. 110: 8 10 10 8 10 8 10 9 9 10 8 10 SP D3 S SD: 1.0007 c. M: 2.6589 c. 122: 9 11 11 9 11 9 11 10 10 11 9 11 SP D3 S SD: 1.0375 c. M: 2.3012 c. 153: 11 14 14 11 14 11 14 13 12 14 11 14 SP SD: 0.9501 c. M: 1.9955 c. 165: 12 15 15 12 15 12 15 14 13 15 12 15 SP SD: 0.7014 c. M:-1.5445 c. 177: 13 16 16 13 16 13 16 15 14 16 13 16 SP SD: 0.7467 c. M:-1.3004 c. 275: 20 25 25 20 25 20 25 23 22 25 20 25 SP SD: 0.6568 c. M:-1.5445 c. 287: 21 26 26 21 26 21 26 24 23 26 21 26 SP SD: 0.6490 c. M:-1.3165 c. 380: 28 34 34 28 35 28 34 32 30 35 27 35 SP SD: 0.6537 c. M:-1.2788 c. 383: 28 35 34 28 35 28 35 32 30 35 28 35 SP SD: 0.6245 c. M:-1.2990 c. 395: 29 36 35 29 36 29 36 33 31 36 29 36 SP SD: 0.5954 c. M:-1.3784 c. 403: 30 36 36 30 37 29 36 34 32 37 29 37 SP SD: 0.7965 c. M:-1.2708 c. 404: 30 36 36 30 37 29 37 34 32 37 29 37 SP SD: 0.5740 c. M: 1.1287 c. 408: 30 37 36 30 38 29 37 35 32 37 30 37 SP SD: 0.8019 c. M: 1.0122 c. 409: 30 37 37 30 37 30 37 34 33 37 30 37 SP SD: 0.7254 c. M:-1.2245 c. 416: 31 37 37 31 38 30 38 35 33 38 30 38 SP SD: 0.5694 c. M:-1.1531 c. 459: 34 41 41 34 42 33 42 39 36 42 33 42 SP SD: 0.5594 c. M: 1.0122 c. 464: 34 42 42 34 42 34 42 39 37 42 34 42 SP SD: 0.6544 c. M:-1.2624 c. 466: 34 42 42 34 43 34 42 39 37 42 34 43 SP SD: 0.6315 c. M: 1.2158 c. 471: 35 42 42 35 43 34 43 40 37 43 34 43 SP SD: 0.5555 c. M:-0.9775 c. 478: 35 43 43 35 44 35 43 40 38 43 35 44 SP SD: 0.5635 c. M: 1.2589 c. 502: 37 45 45 37 46 37 45 42 40 46 36 46 SP SD: 0.5096 c. M:-1.1907 c. 514: 38 46 46 38 47 37 47 43 41 47 37 47 SP SD: 0.4539 c. M:-0.9586 c. 518: 38 47 46 38 48 37 47 44 41 47 38 47 SP SD: 0.5814 c. M:-0.8947 c. 521: 38 47 47 38 48 38 47 44 41 47 38 48 SP SD: 0.5132 c. M: 1.0131 c. 526: 39 47 47 39 48 38 48 44 42 48 38 48 SP SD: 0.4449 c. M:-0.8698 c. 533: 39 48 48 39 49 39 48 45 42 48 39 49 SP SD: 0.4503 c. M: 1.0563 c. 545: 40 49 49 40 50 40 49 46 43 49 40 50 SP SD: 0.4324 c. M: 1.0976 c. 557: 41 50 50 41 51 41 50 47 44 51 40 51 SP SD: 0.4346 c. M:-1.0577 c. 568: 42 51 51 42 52 41 51 48 45 52 41 52 SP SD: 0.5287 c. M: 0.8619 c. 569: 42 51 51 42 52 41 52 48 45 52 41 52 SP SD: 0.3909 c. M:-0.9339 c. 581: 43 52 52 43 53 42 53 49 46 53 42 53 SP SD: 0.3848 c. M:-0.8541 c. 593: 44 53 53 44 54 43 54 50 47 54 43 54 SP SD: 0.4209 c. M:-0.7774 c. 631: 46 57 57 46 58 46 57 53 50 57 46 58 SP SD: 0.4143 c. M: 0.7898 c. 643: 47 58 58 47 59 47 58 54 51 58 47 59 SP SD: 0.3562 c. M: 0.7552 c. 655: 48 59 59 48 60 48 59 55 52 59 48 60 SP SD: 0.3358 c. M: 0.7951 c. 674: 50 60 61 49 62 49 61 57 53 61 49 62 SP SD: 0.4239 c. M:-0.7508 c. 676: 50 60 61 50 62 49 61 57 54 61 49 62 SP SD: 0.3901 c. M: 0.8237 c. 679: 50 61 61 50 62 49 62 57 54 61 50 62 SP SD: 0.3468 c. M: 0.8706 c. 688: 51 61 62 51 63 50 62 58 55 62 50 63 SP SD: 0.4150 c. M: 0.7412 c. 691: 51 62 62 51 63 50 63 58 55 63 50 63 SP SD: 0.3417 c. M:-0.8302 c. 698: 51 63 63 51 64 51 63 59 55 63 51 64 SP SD: 0.3426 c. M: 0.6402 c. 703: 52 63 63 52 64 51 64 59 56 64 51 64 SP SD: 0.3656 c. M:-0.7659 c. 710: 52 64 64 52 65 52 64 60 56 64 52 65 SP SD: 0.3251 c. M: 0.6790 c. 746: 55 67 67 55 68 54 68 63 59 68 54 68 SP SD: 0.3562 c. M:-0.8209 c. 753: 55 68 68 55 69 55 68 63 60 68 55 69 SP SD: 0.3552 c. M: 0.6206 c. 758: 56 68 68 56 69 55 69 64 60 69 55 69 SP SD: 0.3757 c. M:-0.7614 c. 761: 56 68 69 56 69 56 69 64 60 69 55 70 SP SD: 0.4138 c. M: 0.6061 c. 762: 56 68 69 56 70 55 69 64 61 69 55 70 SP SD: 0.3894 c. M: 0.8144 c. 765: 56 69 69 56 70 56 69 64 61 69 56 70 SP SD: 0.3344 c. M: 0.5911 c. 796: 59 71 72 58 73 58 72 67 63 72 58 73 SP SD: 0.3185 c. M:-0.6747 c. 808: 59 73 73 59 74 59 73 68 64 73 59 74 SP SD: 0.3010 c. M: 0.6462 c. 816: 60 73 74 60 74 60 74 68 65 74 59 75 SP SD: 0.3995 c. M: 0.5191 c. 817: 60 74 73 60 75 59 74 69 65 74 59 75 SP SD: 0.3225 c. M:-0.7276 c. 820: 60 74 74 60 75 60 74 69 65 74 60 75 SP SD: 0.2814 c. M:-0.5086 c. 841: 62 75 76 62 77 61 76 71 67 76 61 77 SP SD: 0.2799 c. M: 0.6084 c. 870: 64 78 78 64 80 63 79 73 69 79 63 80 SP SD: 0.3178 c. M: 0.5698 c. 882: 65 79 79 65 81 64 80 74 70 80 64 81 SP SD: 0.2750 c. M: 0.5086 c. 894: 66 80 80 66 82 65 81 75 71 81 65 82 SP SD: 0.2575 c. M: 0.5543 c. 925: 68 83 83 68 85 67 84 78 73 84 67 85 SP SD: 0.2537 c. M: 0.4953 c. 937: 69 84 84 69 86 68 85 79 74 85 68 86 SP SD: 0.2070 c. M: 0.3881 c. 949: 70 85 85 70 87 69 86 80 75 86 69 87 SP SD: 0.1885 c. M: 0.4327 c. 1035: 76 93 93 76 95 75 94 87 82 94 75 95 SP SD: 0.1944 c. M: 0.3699 c. 1047: 77 94 94 77 96 76 95 88 83 95 76 96 SP SD: 0.1385 c. M: 0.2537 c. 1059: 78 95 95 78 97 77 96 89 84 96 77 97 SP SD: 0.1092 c. M: 0.2273 c. 1114: 82 100 100 82 102 81 101 94 88 101 81 102 SP SD: 0.0985 c. M:-0.2594 c. 1212: 89 109 109 89 111 88 110 102 96 110 88 111 SP SD: 0.0825 c. M: 0.1512 c. 1224: 90 110 110 90 112 89 111 103 97 111 89 112 SP SD: 0.0189 c. M: 0.0347 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: 1.9550 cents 3 x x x x 4 x x x 5 x x 6 S SD: 3.5097 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 8.7069 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 4.9519 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.3805 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 11.0713 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.3285 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.4337 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.0103 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 11.0696 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 7.4579 cents 13:14:15 x 16:17:18:19:21:22:23:24:26 SD: 9.7131 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 7.6509 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 4.7929 cents 20:21:22:24:25:27:28:30:32:34:36:38:40 SD: 4.5595 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 4.2249 cents 24:25:27:29:30:32:34:36:38:40:43:45:48 SD: 3.0535 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.2642 cents 41:43:46:49:51:55:58:61:65:69:73:77:82 SD: 2.0674 cents 42:44:47:50:53:56:59:63:67:70:75:79:84 SD: 1.6822 cents 56:59:63:67:70:75:79:84:89:94:100:105:112 SD: 1.2770 cents 59:62:66:70:74:79:83:88:94:99:105:111:118 SD: 1.2343 cents 74:78:83:88:93:99:104:111:117:124:132:139:148 SD: 0.8303 cents 98:103:110:117:123:131:138:147:155:164:175:184:196 SD: 0.8020 cents 99:104:111:118:124:132:139:148:157:166:177:186:198 SD: 0.6042 cents 131:138:147:156:164:175:184:196:208:220:234:246:262 SD: 0.5619 cents 157:165:176:187:197:210:221:235:249:263:280:295:314 SD: 0.4215 cents 173:182:194:206:217:231:243:259:274:290:309:325:346 SD: 0.4050 cents 193:203:216:230:242:258:271:289:306:323:344:362:386 SD: 0.3876 cents 208:219:233:248:261:278:292:311:330:349:371:390:416 SD: 0.3459 cents 232:244:260:277:291:310:326:347:368:389:414:435:464 SD: 0.3445 cents 235:247:263:280:295:314:330:352:373:394:419:441:470 SD: 0.3424 cents 244:257:273:291:306:326:343:365:387:409:435:458:488 SD: 0.2832 cents 286:301:320:341:359:382:402:428:454:479:510:537:572 SD: 0.2781 cents 291:306:326:347:365:389:409:436:462:488:519:546:582 SD: 0.2767 cents 292:307:327:348:366:390:410:437:463:489:521:548:584 SD: 0.2763 cents 302:318:338:360:379:404:424:452:479:506:539:567:604 SD: 0.2748 cents 303:319:339:361:380:405:426:453:481:508:541:569:606 SD: 0.2657 cents 306:322:343:365:384:409:430:458:485:513:546:574:612 SD: 0.2603 cents 308:324:345:367:386:412:433:461:489:516:550:578:616 SD: 0.2491 cents 324:341:363:386:406:433:455:485:514:543:578:608:648 SD: 0.2176 cents 343:361:384:409:430:458:482:513:544:575:612:644:686 SD: 0.2016 cents 365:384:409:435:458:488:513:546:579:612:651:685:730 SD: 0.1892 cents 401:422:449:478:503:536:564:600:636:672:716:753:802 SD: 0.1529 cents 417:439:467:497:523:557:586:624:662:699:744:783:834 SD: 0.1504 cents 491:517:550:585:616:656:690:735:779:823:876:922:982 SD: 0.1468 cents 515:542:577:614:646:688:724:771:817:863:919:967:1030 SD: 0.1223 cents 594:625:665:708:745:794:835:889:942:996:1060:1115:1188 SD: 0.1118 cents