Scala analysis: bug
"Bug I" well-temperament
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 92.578 cents 92.578120 2: 194.531 cents 194.531250 3: 296.484 cents 296.484380 4: 389.062 cents 389.062500 5: 498.047 cents 498.046880 6: 592.969 cents 592.968750 7: 698.438 cents 698.437500 8: 794.531 cents 794.531250 9: 890.625 cents 890.625000 10: 996.094 cents 996.093750 11: 1091.016 cents 1091.015600 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 108.9844 cents 108.9844 1: 92.5781 cents 92.5781 2: 101.9531 cents 101.9531 3: 101.9531 cents 101.9531 4: 92.5781 cents 92.5781 5: 108.9844 cents 108.9844 6: 94.9219 cents 94.9219 7: 105.4688 cents 105.4688 8: 96.0937 cents 96.0937 9: 96.0937 cents 96.0937 10: 105.4688 cents 105.4688 11: 94.9218 cents 94.9218 12: 108.9844 cents 108.9844
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 92.57812 cents 1: 2 94.92187 cents 1: 2 96.09375 cents 1: 2 101.95313 cents 1: 2 105.46875 cents 1: 2 108.98438 cents 2: 1 192.18750 cents 2: 2 194.53125 cents 2: 2 200.39062 cents 2: 4 201.56250 cents 2: 3 203.90626 cents 3: 6 296.48438 cents 3: 2 297.65625 cents 3: 2 303.51563 cents 3: 2 309.37500 cents 4: 1 389.06250 cents 4: 2 392.57812 cents 4: 2 398.43750 cents 4: 2 401.95312 cents 4: 1 403.12500 cents 4: 4 405.46876 cents 5: 6 498.04688 cents 5: 2 500.39063 cents 5: 2 501.56250 cents 5: 2 503.90625 cents 6: 3 592.96875 cents 6: 2 594.14062 cents 6: 2 600.00000 cents 6: 2 605.85938 cents 6: 3 607.03125 cents 7: 2 696.09375 cents 7: 2 698.43750 cents 7: 2 699.60937 cents 7: 6 701.95313 cents 8: 4 794.53125 cents 8: 1 796.87500 cents 8: 2 798.04688 cents 8: 2 801.56250 cents 8: 2 807.42188 cents 8: 1 810.93750 cents 9: 2 890.62500 cents 9: 2 896.48435 cents 9: 2 902.34375 cents 9: 6 903.51563 cents 10: 3 996.09375 cents 10: 4 998.43748 cents 10: 2 999.60938 cents 10: 2 1005.46875 cents 10: 1 1007.81250 cents 11: 2 1091.01560 cents 11: 2 1094.53125 cents 11: 2 1098.04687 cents 11: 2 1103.90625 cents 11: 2 1105.07813 cents 11: 2 1107.42188 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.00000 = 5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 92.6 194.5 296.5 389.1 498.0 593.0 698.4 794.5 890.6 996.1 1091.0 1200.0 92.6 : 102.0 203.9 296.5 405.5 500.4 605.9 702.0 798.0 903.5 998.4 1107.4 1200.0 194.5 : 102.0 194.5 303.5 398.4 503.9 600.0 696.1 801.6 896.5 1005.5 1098.0 1200.0 296.5 : 92.6 201.6 296.5 402.0 498.0 594.1 699.6 794.5 903.5 996.1 1098.0 1200.0 389.1 : 109.0 203.9 309.4 405.5 501.6 607.0 702.0 810.9 903.5 1005.5 1107.4 1200.0 498.0 : 94.9 200.4 296.5 392.6 498.0 593.0 702.0 794.5 896.5 998.4 1091.0 1200.0 593.0 : 105.5 201.6 297.7 403.1 498.0 607.0 699.6 801.6 903.5 996.1 1105.1 1200.0 698.4 : 96.1 192.2 297.7 392.6 501.6 594.1 696.1 798.0 890.6 999.6 1094.5 1200.0 794.5 : 96.1 201.6 296.5 405.5 498.0 600.0 702.0 794.5 903.5 998.4 1103.9 1200.0 890.6 : 105.5 200.4 309.4 402.0 503.9 605.9 698.4 807.4 902.3 1007.8 1103.9 1200.0 996.1 : 94.9 203.9 296.5 398.4 500.4 593.0 702.0 796.9 902.3 998.4 1094.5 1200.0 1091.0: 109.0 201.6 303.5 405.5 498.0 607.0 702.0 807.4 903.5 999.6 1105.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 92.5781 .. 108.9844 cents 16.40626 cents 92.57812 cents 2: 192.1875 .. 203.9063 cents 11.71876 cents 83.20312 cents 3: 296.4844 .. 309.3750 cents 12.89062 cents 92.57812 cents 4: 389.0625 .. 405.4688 cents 16.40626 cents 79.68750 cents 5: 498.0469 .. 503.9063 cents 5.85937 cents 92.57812 cents 6: 592.9687 .. 607.0313 cents 14.06250 cents 89.06250 cents 7: 696.0937 .. 701.9531 cents 5.85938 cents 89.06250 cents 8: 794.5312 .. 810.9375 cents 16.40625 cents 92.57812 cents 9: 890.6250 .. 903.5156 cents 12.89063 cents 79.68750 cents 10: 996.0938 .. 1007.8125 cents 11.71875 cents 92.57812 cents 11: 1091.0156 .. 1107.4219 cents 16.40628 cents 83.20310 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 92.57812 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 108.98438 cents Average / Smallest step : 1.080169 Largest / Average step : 1.089844 Largest / Smallest step : 1.177215 Median interval of one step : 99.02344 cents, amount: 0 Least squares average step : 99.38221 cents, oct.: 1192.58653 cents Scale is strictly proper Scale is a mode of a 1024-tone equal temperament with octave 2/1 degrees: 79 166 253 332 425 506 596 678 760 850 931 1024 Least number of segments generator : 513 of 601.172 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 659 of 772.266 cents and inv. generated superset size: 643 = 631 more = 5358.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBACDEFFEDC Step pattern size order : ADDAFBECCEBF Scale is a Constant Structure, by a margin of 79.68750 cents Scale diversity : 1.096446 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.882812 Rothenberg efficiency : 0.282011 redundancy: 0.717989 Efficiency x scale size : 3.384127 Number of different interval sizes : 55 = 5.00000 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 5.00000 = 5 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 1.17187 cents Number of recognisable fifths : 12, average 700.0000 cents Scale is a well-temperament. It has 4 different sizes of fifth Scale has monotonic third-sizes over circle of fifths Best fifths form a closed circle Formal octave complements present : 1 = 8.3333% Limited transpositions with margin 16.4063 cents: 1 2 3 4 5 6 7 8 9 10 11 Limited inverse transpositions : 4 Inversional symmetry on degrees : 2 8 -- 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: 6.3669 c. M:-10.9375 c. Twelve-tone Chromatic (1/11-comma) 53: 4 4 5 4 5 4 5 4 4 5 4 5 SP M ME SD: 5.1299 c. M: 13.3992 c. 55: 4 5 5 4 5 4 5 4 5 5 4 5 SP M ME SD: 5.0776 c. M: 9.0767 c. Meantone Chromatic (3/17-comma) 62: 5 5 5 5 6 5 5 5 5 5 5 6 SP D3 S SD: 4.7652 c. M: 8.9970 c. 63: 5 5 6 4 6 5 6 5 5 5 5 6 SP D3 SD: 5.1862 c. M:-8.2775 c. 65: 5 6 5 5 6 5 6 5 5 6 5 6 SP M ME SD: 3.0977 c. M:-8.5457 c. 66: 5 6 5 5 6 6 5 6 5 6 5 6 SP D3 SD: 5.1525 c. M: 7.5284 c. 67: 5 6 6 5 6 5 6 5 6 6 5 6 SP M ME SD: 4.4266 c. M:-7.9932 c. Meantone Chromatic (4/25-comma) 74: 6 6 6 6 7 6 6 6 6 6 6 7 SP D3 S SD: 3.9327 c. M:-7.0313 c. 77: 6 6 7 6 7 6 7 6 6 7 6 7 SP M ME SD: 2.4862 c. M: 7.5183 c. 81: 6 7 7 6 8 6 7 7 6 7 7 7 SP D3 SD: 3.4427 c. M:-5.6568 c. 89: 7 7 8 7 8 7 8 7 7 8 7 8 SP M ME SD: 2.1178 c. M: 5.7672 c. 98: 8 8 8 8 9 7 9 8 8 8 8 9 SP D3 SD: 3.1734 c. M:-5.3811 c. 101: 8 8 9 8 9 8 9 8 8 9 8 9 SP M ME SD: 2.1253 c. M: 4.4322 c. 113: 9 9 10 9 10 9 10 9 9 10 9 10 SP M ME SD: 2.3128 c. M:-3.8579 c. 129: 10 11 11 10 12 10 11 10 11 11 10 12 SP SD: 2.1890 c. M:-4.2787 c. 130: 10 11 11 10 12 10 12 10 10 12 10 12 SP D3 S SD: 1.8839 c. M: 4.4712 c. 135: 10 12 11 11 12 11 12 10 11 12 11 12 SP SD: 2.4195 c. M:-3.7847 c. 139: 11 12 11 11 13 11 12 11 11 12 11 13 SP SD: 2.4096 c. M:-4.0299 c. 141: 11 12 12 11 13 11 12 11 12 12 11 13 SP SD: 2.1623 c. M:-4.0808 c. 142: 11 12 12 11 13 11 13 11 11 13 11 13 SP D3 S SD: 1.4375 c. M: 3.3011 c. 154: 12 13 13 12 14 12 14 12 12 14 12 14 SP D3 S SD: 1.2154 c. M:-2.8612 c. 166: 13 14 14 13 15 13 15 13 13 15 13 15 SP D3 S SD: 1.2059 c. M:-2.7673 c. 178: 14 15 15 14 16 14 16 14 14 16 14 16 SP D3 S SD: 1.3388 c. M:-2.6861 c. 186: 14 16 16 14 17 15 16 15 15 16 15 17 SP S SD: 1.3766 c. M: 2.5454 c. 190: 15 16 16 15 17 15 17 15 15 17 15 17 SP D3 S SD: 1.5360 c. M:-2.6151 c. 198: 15 17 17 15 18 16 17 16 16 17 16 18 SP S SD: 1.0845 c. M: 2.1544 c. 210: 16 18 18 16 19 17 18 17 17 18 17 19 SP S SD: 0.9323 c. M: 1.8080 c. 222: 17 19 19 17 20 18 19 18 18 19 18 20 SP S SD: 0.9256 c. M:-1.6258 c. 272: 21 23 23 21 25 21 24 22 22 24 21 25 SP S SD: 0.9188 c. M: 1.7923 c. 275: 21 23 24 21 25 22 24 22 22 24 22 25 SP SD: 0.9232 c. M: 2.5312 c. 284: 22 24 24 22 26 22 25 23 23 25 22 26 SP S SD: 0.7907 c. M: 1.4195 c. 287: 22 25 24 22 26 23 25 23 23 25 23 26 SP SD: 0.7277 c. M:-1.9844 c. 296: 23 25 25 23 27 23 26 24 24 26 23 27 SP S SD: 0.7559 c. M:-1.2669 c. 299: 23 25 26 23 27 24 26 24 24 26 24 27 SP SD: 0.7223 c. M: 1.8891 c. 328: 25 28 28 25 30 26 29 26 26 29 26 30 SP S SD: 0.8253 c. M: 1.6006 c. 340: 26 29 29 26 31 27 30 27 27 30 27 31 SP S SD: 0.5980 c. M: 1.2132 c. 352: 27 30 30 27 32 28 31 28 28 31 28 32 SP S SD: 0.4126 c. M: 0.8523 c. 364: 28 31 31 28 33 29 32 29 29 32 29 33 SP S SD: 0.3074 c. M: 0.5151 c. 376: 29 32 32 29 34 30 33 30 30 33 30 34 SP S SD: 0.3323 c. M:-0.6483 c. 624: 48 53 53 48 57 49 55 50 50 55 49 57 SP S SD: 0.3821 c. M: 0.6611 c. 636: 49 54 54 49 58 50 56 51 51 56 50 58 SP S SD: 0.2741 c. M: 0.5159 c. 648: 50 55 55 50 59 51 57 52 52 57 51 59 SP S SD: 0.1928 c. M: 0.3762 c. 660: 51 56 56 51 60 52 58 53 53 58 52 60 SP S SD: 0.1695 c. M:-0.2841 c. 1000: 77 85 85 77 91 79 88 80 80 88 79 91 SP S SD: 0.1528 c. M: 0.2625 c. 1012: 78 86 86 78 92 80 89 81 81 89 80 92 SP S SD: 0.0755 c. M: 0.1297 c. 1024: 79 87 87 79 93 81 90 82 82 90 81 93 SP S 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: 1.7588 cents 3 x x x x 4 x x x 5 x x 6 S SD: 2.0888 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 6.9077 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.2266 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 8.6016 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 11.4165 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.5782 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 7.7015 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.2825 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 11.0541 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.5197 cents 13:14 x 15:16:17:18:19:21:22:23:24:26 SD: 9.4821 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 7.8421 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 5.2517 cents 16:17:18:19:20:21:23:24:25:27:28:30:32 SD: 5.0794 cents 17:18:19:20:21:23:24:25:27:28:30:32:34 SD: 4.8238 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 4.2514 cents 24:25:27:28:30:32:34:36:38:40:43:45:48 SD: 3.5302 cents 27:28:30:32:34:36:38:40:43:45:48:51:54 SD: 3.4553 cents 31:33:35:37:39:41:44:46:49:52:55:58:62 SD: 3.0515 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.4375 cents 36:38:40:43:45:48:51:54:57:60:64:68:72 SD: 1.9245 cents 48:51:54:57:60:64:68:72:76:80:85:90:96 S SD: 1.7807 cents 52:55:58:62:65:69:73:78:82:87:92:98:104 SD: 1.6248 cents 57:60:64:68:71:76:80:85:90:95:101:107:114 SD: 1.6192 cents 58:61:65:69:73:77:82:87:92:97:103:109:116 SD: 1.3682 cents 59:62:66:70:74:79:83:88:93:99:105:111:118 SD: 1.2918 cents 68:72:76:81:85:91:96:102:108:114:121:128:136 SD: 1.2811 cents 74:78:83:88:93:99:104:111:117:124:132:139:148 SD: 1.1225 cents 75:79:84:89:94:100:106:112:119:125:133:141:150 SD: 1.0190 cents 76:80:85:90:95:101:107:114:120:127:135:143:152 SD: 0.8833 cents 91:96:102:108:114:121:128:136:144:152:162:171:182 SD: 0.6413 cents 108:114:121:128:135:144:152:162:171:181:192:203:216 SD: 0.5755 cents 144:152:161:171:180:192:203:216:228:241:256:270:288 SD: 0.4974 cents 159:168:178:189:199:212:224:238:252:266:283:299:318 SD: 0.4825 cents 167:176:187:198:209:223:235:250:264:279:297:314:334 SD: 0.4515 cents 177:187:198:210:222:236:249:265:280:296:315:332:354 SD: 0.4514 cents 183:193:205:217:229:244:258:274:290:306:325:344:366 SD: 0.3966 cents 199:210:223:236:249:265:280:298:315:333:354:374:398 SD: 0.3877 cents 203:214:227:241:254:271:286:304:321:340:361:381:406 SD: 0.3452 cents 235:248:263:279:294:313:331:352:372:393:418:441:470 SD: 0.2650 cents 294:310:329:349:368:392:414:440:465:492:523:552:588 SD: 0.1679 cents 453:478:507:538:567:604:638:678:717:758:805:851:906 SD: 0.1575 cents 455:480:509:540:570:607:641:681:720:761:809:854:910 SD: 0.1540 cents 477:503:534:566:597:636:672:714:755:798:848:896:954 SD: 0.1263 cents 531:560:594:630:665:708:748:795:840:888:944:997:1062 SD: 0.1073 cents