Scala analysis: xen18-erlich-blacksmith-10
5L 5s MOS for Blacksmith, L=155.35, s=83.83
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 83.830 cents 83.830000 2: 239.180 cents 239.180000 3: 323.010 cents 323.010000 4: 478.360 cents 478.360000 5: 562.190 cents 562.190000 6: 717.540 cents 717.540000 7: 801.370 cents 801.370000 8: 956.720 cents 956.720000 9: 1040.550 cents 1040.550000 10: 1195.900 cents 1195.900000
SHOW/INTERVAL
0: 155.3500 cents 155.3500 1: 83.8300 cents 83.8300 2: 155.3500 cents 155.3500 3: 83.8300 cents 83.8300 4: 155.3500 cents 155.3500 5: 83.8300 cents 83.8300 6: 155.3500 cents 155.3500 7: 83.8300 cents 83.8300 8: 155.3500 cents 155.3500 9: 83.8300 cents 83.8300 10: 155.3500 cents 155.3500
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 83.83000 cents 1: 5 155.35000 cents 2: 10 239.18000 cents 3: 5 323.01000 cents 3: 5 394.53000 cents 4: 10 478.36000 cents 5: 5 562.19000 cents 5: 5 633.71000 cents 6: 10 717.54000 cents 7: 5 801.37000 cents 7: 5 872.89000 cents 8: 10 956.72000 cents 9: 5 1040.55000 cents 9: 5 1112.07000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.55556 = 14/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 83.8 239.2 323.0 478.4 562.2 717.5 801.4 956.7 1040.5 1195.9 83.8 : 155.3 239.2 394.5 478.4 633.7 717.5 872.9 956.7 1112.1 1195.9 239.2 : 83.8 239.2 323.0 478.4 562.2 717.5 801.4 956.7 1040.5 1195.9 323.0 : 155.3 239.2 394.5 478.4 633.7 717.5 872.9 956.7 1112.1 1195.9 478.4 : 83.8 239.2 323.0 478.4 562.2 717.5 801.4 956.7 1040.5 1195.9 562.2 : 155.3 239.2 394.5 478.4 633.7 717.5 872.9 956.7 1112.1 1195.9 717.5 : 83.8 239.2 323.0 478.4 562.2 717.5 801.4 956.7 1040.5 1195.9 801.4 : 155.3 239.2 394.5 478.4 633.7 717.5 872.9 956.7 1112.1 1195.9 956.7 : 83.8 239.2 323.0 478.4 562.2 717.5 801.4 956.7 1040.5 1195.9 1040.5: 155.4 239.2 394.5 478.4 633.7 717.5 872.9 956.7 1112.1 1195.9 1195.9
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 83.8300 .. 155.3500 cents 71.52000 cents 83.83000 cents 2: 239.1800 .. 239.1800 cents 1/1, 0.0000 cents 83.83000 cents 3: 323.0100 .. 394.5300 cents 71.52000 cents 83.83000 cents 4: 478.3600 .. 478.3600 cents 1/1, 0.0000 cents 83.83000 cents 5: 562.1900 .. 633.7100 cents 71.52000 cents 83.83000 cents 6: 717.5400 .. 717.5400 cents 1/1, 0.0000 cents 83.83000 cents 7: 801.3700 .. 872.8900 cents 71.52000 cents 83.83000 cents 8: 956.7200 .. 956.7200 cents 1/1, 0.0000 cents 83.83000 cents 9: 1040.5500 .. 1112.0700 cents 71.52000 cents 83.83000 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 83.83000 cents, class 1 Average step (divided formal octave): 119.5900 cents Largest one step interval : 155.35000 cents Average / Smallest step : 1.426578 Largest / Average step : 1.299022 Largest / Smallest step : 1.853155 Median interval of one step : 119.59000 cents, amount: 0 Least squares average step : 117.26792 cents, oct.: 1172.67922 cents Scale is strictly proper Scale has 5 repeating blocks of 2 notes Blocks have Myhill's property chromas: 71.52000 cents and 12.31000 cents, ratio: 5.809911 generator: 1 of 83.83000 cents ET pair of linear temperament : 85&100 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1070-tone equal temperament with octave 1195.900 cents degrees: 75 214 289 428 503 642 717 856 931 1070 Least number of segments generator : 537 of 600.185 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 567 of 633.715 cents and inv. generated superset size: 858 = 848 more = 8580.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABABABAB Step pattern size order : SLSLSLSLSL Scale is a Constant Structure, by a margin of 83.83000 cents Scale diversity : 1.176835 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.700978 Rothenberg efficiency (ambiguous key): 1.000000 redundancy: 0.000000 Efficiency x scale size : 10.000000 Number of different interval sizes : 14 = 1.55556 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.55556 = 14/9 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 71.52000 cents Scale is a chain of 5 triads 0.0 801.370 956.720 cents Most common triad is 0.0 239.180 478.360 cents, amount: 10 Number of recognisable fifths : 10, average 717.5400 cents Number of appreciable fifths : 0 Number of recognisable fourths : 0 Scale contains two identical disjunct pentachords Best major thirds form a closed circle Formal octave complements present : 5 = 50.0000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 2 4 6 8 Limited inverse transpositions : 1 3 5 7 9 Inversional symmetry on intervals : 0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 -- Rational properties --
FIT/MODE
10: 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 25.2861 c. M:-35.7600 c. 14: 1 2 1 2 1 1 1 2 1 2 P D3 SD: 24.1870 c. M:-35.7600 c. 15: 1 2 1 2 1 2 1 2 1 2 SP B ME SD: 2.9015 c. M: 4.1033 c. Blackwood Decatonic 55: 4 7 4 7 4 7 4 7 4 7 SP B DE SD: 2.2235 c. M:-3.1445 c. Blackwood-10 70: 5 9 5 9 5 9 5 9 5 9 SP B DE SD: 1.1253 c. M:-1.5914 c. 85: 6 11 6 11 6 11 6 11 6 11 SP B DE SD: 0.4147 c. M:-0.5865 c. 100: 7 13 7 13 7 13 7 13 7 13 SP B DE SD: 0.0827 c. M: 0.1170 c. Blackwood-10 285: 20 37 20 37 20 37 20 37 20 37 SP B DE SD: 0.0656 c. M:-0.0928 c. 385: 27 50 27 50 27 50 27 50 27 50 SP B DE SD: 0.0271 c. M:-0.0383 c. 485: 34 63 34 63 34 63 34 63 34 63 SP B DE SD: 0.0044 c. M:-0.0063 c. 1070: 75 139 75 139 75 139 75 139 75 139 SP B DE SD: 0.0037 c. M: 0.0052 c. 1555: 109 202 109 202 109 202 109 202 109 202 SP B DE SD: 0.0012 c. M: 0.0016 c. 2040: 143 265 143 265 143 265 143 265 143 265 SP B DE SD: 0.0002 c. M:-0.0002 c.
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 4.1000 cents 2 x x x x x 3 x x x 4 S SD: 8.0576 cents 3 x x x 4 x x x 5 x 6 S SD: 25.0343 cents 4 x x 5 x x 6 x 7 x 8 S SD: 16.6088 cents 5 x x 6 x 7 x 8 x 9:10 S SD: 6.8196 cents 6 x 7 x 8 x 9 x 10:11:12 S SD: 13.6705 cents 7 x 8 x 9:10 x 11:12:13:14 S SD: 11.8622 cents 8 x 9:10 x 11:12:13:14:15:16 S SD: 12.2386 cents 9 x 10:11:12 x x 14:16 x 18 S SD: 14.0456 cents 10 x 11:12:13:14:15:16:17:18:20 S SD: 10.5061 cents 11:12 x 13 x 15:17 x 19:20:22 SD: 12.5390 cents 12:13:14 x 16:17:18:19:21:22:24 SD: 8.8431 cents 13:14:15:16:17:18:20:21:23:24:26 SD: 8.1383 cents 15:16:17:18:20:21:23:24:26:27:30 SD: 5.7959 cents 17:18 x 20:22:24:26:27:30:31:34 SD: 8.0498 cents 18:19:21:22:24:25:27:29:31:33:36 SD: 5.5304 cents 19:20:22:23:25:26:29:30:33:35:38 SD: 3.6192 cents 29:30:33:35:38:40:44:46:50:53:58 SD: 3.5447 cents 34:36:39:41:45:47:51:54:59:62:68 SD: 2.3441 cents 39:41:45:47:51:54:59:62:68:71:78 SD: 1.8427 cents 53:56:61:64:70:73:80:84:92:97:106 SD: 1.8136 cents 54:57:62:65:71:75:82:86:94:98:108 SD: 1.7755 cents 59:62:68:71:78:82:89:94:103:108:118 SD: 1.7706 cents 60:63:69:72:79:83:91:95:104:109:120 SD: 1.4107 cents 68:71:78:82:90:94:103:108:118:124:136 SD: 1.2735 cents 78:82:90:94:103:108:118:124:136:142:156 SD: 1.2417 cents 81:85:93:98:107:112:123:129:141:148:162 SD: 1.2060 cents 88:92:101:106:116:122:133:140:153:161:176 SD: 1.0816 cents 97:102:111:117:128:134:147:154:169:177:194 SD: 0.9979 cents 102:107:117:123:134:141:154:162:177:186:204 SD: 0.9230 cents 107:112:123:129:141:148:162:170:186:195:213 SD: 0.6872 cents 122:128:140:147:161:169:185:194:212:223:243 SD: 0.6657 cents 136:143:156:164:179:188:206:216:236:248:271 SD: 0.6088 cents 141:148:162:170:186:195:213:224:245:257:281 SD: 0.4603 cents 175:184:201:211:231:242:265:278:304:319:349 SD: 0.4404 cents 195:205:224:235:257:270:295:310:339:356:389 SD: 0.3859 cents 224:235:257:270:295:310:339:356:389:409:447 SD: 0.3244 cents 243:255:279:293:320:336:368:386:422:443:485 SD: 0.3034 cents 263:276:302:317:347:364:398:418:457:480:525 SD: 0.2239 cents 365:383:419:440:481:505:552:580:634:666:728 SD: 0.2145 cents 386:405:443:465:509:534:584:613:671:704:770 SD: 0.1759 cents 399:419:458:481:526:552:604:634:693:728:796 SD: 0.1646 cents 459:482:527:553:605:635:695:729:798:837:916 SD: 0.1608 cents 487:511:559:587:642:674:737:774:846:888:972 SD: 0.1552 cents 506:531:581:610:667:700:766:804:879:923:1010 SD: 0.1292 cents 600:630:689:723:791:830:908:953:1043:1094:1197 SD: 0.1282 cents