Scala analysis: xen18-erlich-blackwood-10
5L 5s MOS for Blackwood, L=158.78, s=80.09
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 80.090 cents 80.090000 2: 238.870 cents 238.870000 3: 318.960 cents 318.960000 4: 477.740 cents 477.740000 5: 557.830 cents 557.830000 6: 716.610 cents 716.610000 7: 796.700 cents 796.700000 8: 955.480 cents 955.480000 9: 1035.570 cents 1035.570000 10: 1194.350 cents 1194.350000
SHOW/INTERVAL
0: 158.7800 cents 158.7800 1: 80.0900 cents 80.0900 2: 158.7800 cents 158.7800 3: 80.0900 cents 80.0900 4: 158.7800 cents 158.7800 5: 80.0900 cents 80.0900 6: 158.7800 cents 158.7800 7: 80.0900 cents 80.0900 8: 158.7800 cents 158.7800 9: 80.0900 cents 80.0900 10: 158.7800 cents 158.7800
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 80.09000 cents 1: 5 158.78000 cents 2: 10 238.87000 cents 3: 5 318.96000 cents 3: 5 397.65000 cents 4: 10 477.74000 cents 5: 5 557.83000 cents 5: 5 636.52000 cents 6: 10 716.61000 cents 7: 5 796.70000 cents 7: 5 875.39000 cents 8: 10 955.48000 cents 9: 5 1035.57000 cents 9: 5 1114.26000 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 : 80.1 238.9 319.0 477.7 557.8 716.6 796.7 955.5 1035.6 1194.3 80.1 : 158.8 238.9 397.6 477.7 636.5 716.6 875.4 955.5 1114.3 1194.3 238.9 : 80.1 238.9 319.0 477.7 557.8 716.6 796.7 955.5 1035.6 1194.3 319.0 : 158.8 238.9 397.6 477.7 636.5 716.6 875.4 955.5 1114.3 1194.3 477.7 : 80.1 238.9 319.0 477.7 557.8 716.6 796.7 955.5 1035.6 1194.3 557.8 : 158.8 238.9 397.6 477.7 636.5 716.6 875.4 955.5 1114.3 1194.3 716.6 : 80.1 238.9 319.0 477.7 557.8 716.6 796.7 955.5 1035.6 1194.3 796.7 : 158.8 238.9 397.6 477.7 636.5 716.6 875.4 955.5 1114.3 1194.3 955.5 : 80.1 238.9 319.0 477.7 557.8 716.6 796.7 955.5 1035.6 1194.3 1035.6: 158.8 238.9 397.6 477.7 636.5 716.6 875.4 955.5 1114.3 1194.3 1194.3
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.0900 .. 158.7800 cents 78.69000 cents 80.09000 cents 2: 238.8700 .. 238.8700 cents 1/1, 0.0000 cents 80.09000 cents 3: 318.9600 .. 397.6500 cents 78.69000 cents 80.09000 cents 4: 477.7400 .. 477.7400 cents 1/1, 0.0000 cents 80.09000 cents 5: 557.8300 .. 636.5200 cents 78.69000 cents 80.09000 cents 6: 716.6100 .. 716.6100 cents 1/1, 0.0000 cents 80.09000 cents 7: 796.7000 .. 875.3900 cents 78.69000 cents 80.09000 cents 8: 955.4800 .. 955.4800 cents 1/1, 0.0000 cents 80.09000 cents 9: 1035.5700 .. 1114.2600 cents 78.69000 cents 80.09000 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 80.09000 cents, class 1 Average step (divided formal octave): 119.4350 cents Largest one step interval : 158.78000 cents Average / Smallest step : 1.491260 Largest / Average step : 1.329426 Largest / Smallest step : 1.982520 Median interval of one step : 119.43500 cents, amount: 0 Least squares average step : 116.88013 cents, oct.: 1168.80130 cents Scale is strictly proper Scale has 5 repeating blocks of 2 notes Blocks have Myhill's property chromas: 78.69000 cents and 1.40000 cents, ratio: 56.207143 generator: 1 of 80.09000 cents ET pair of linear temperament : 850&3415 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 850-tone equal temperament with octave 1194.350 cents degrees: 57 170 227 340 397 510 567 680 737 850 Least number of segments generator : 427 of 599.985 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 453 of 636.518 cents and inv. generated superset size: 682 = 672 more = 6820.000% 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 80.09000 cents Scale diversity : 1.180049 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.670574 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 : 78.69000 cents Scale is a chain of 5 triads 0.0 796.700 955.480 cents Most common triad is 0.0 238.870 477.740 cents, amount: 10 Number of recognisable fifths : 10, average 716.6100 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: 27.8211 c. M:-39.3450 c. 14: 1 2 1 2 1 1 1 2 1 2 P D3 SD: 24.4103 c. M:-39.3450 c. 15: 1 2 1 2 1 2 1 2 1 2 SP B ME SD: 0.3300 c. M: 0.4667 c. Blackwood Decatonic 430: 29 57 29 57 29 57 29 57 29 57 SP B DE SD: 0.3247 c. M:-0.4592 c. 445: 30 59 30 59 30 59 30 59 30 59 SP B DE SD: 0.3026 c. M:-0.4280 c. 460: 31 61 31 61 31 61 31 61 31 61 SP B DE SD: 0.2820 c. M:-0.3988 c. 475: 32 63 32 63 32 63 32 63 32 63 SP B DE SD: 0.2627 c. M:-0.3715 c. 490: 33 65 33 65 33 65 33 65 33 65 SP B DE SD: 0.2445 c. M:-0.3458 c. 505: 34 67 34 67 34 67 34 67 34 67 SP B DE SD: 0.2275 c. M:-0.3217 c. 520: 35 69 35 69 35 69 35 69 35 69 SP B DE SD: 0.2114 c. M:-0.2989 c. 535: 36 71 36 71 36 71 36 71 36 71 SP B DE SD: 0.1962 c. M:-0.2775 c. 550: 37 73 37 73 37 73 37 73 37 73 SP B DE SD: 0.1819 c. M:-0.2572 c. 565: 38 75 38 75 38 75 38 75 38 75 SP B DE SD: 0.1683 c. M:-0.2380 c. 580: 39 77 39 77 39 77 39 77 39 77 SP B DE SD: 0.1554 c. M:-0.2197 c. 595: 40 79 40 79 40 79 40 79 40 79 SP B DE SD: 0.1431 c. M:-0.2024 c. 610: 41 81 41 81 41 81 41 81 41 81 SP B DE SD: 0.1315 c. M:-0.1860 c. 625: 42 83 42 83 42 83 42 83 42 83 SP B DE SD: 0.1204 c. M:-0.1703 c. 640: 43 85 43 85 43 85 43 85 43 85 SP B DE SD: 0.1099 c. M:-0.1554 c. 655: 44 87 44 87 44 87 44 87 44 87 SP B DE SD: 0.0998 c. M:-0.1411 c. 670: 45 89 45 89 45 89 45 89 45 89 SP B DE SD: 0.0902 c. M:-0.1275 c. 685: 46 91 46 91 46 91 46 91 46 91 SP B DE SD: 0.0810 c. M:-0.1145 c. 700: 47 93 47 93 47 93 47 93 47 93 SP B DE SD: 0.0722 c. M:-0.1021 c. 715: 48 95 48 95 48 95 48 95 48 95 SP B DE SD: 0.0637 c. M:-0.0901 c. 730: 49 97 49 97 49 97 49 97 49 97 SP B DE SD: 0.0556 c. M:-0.0787 c. 745: 50 99 50 99 50 99 50 99 50 99 SP B DE SD: 0.0479 c. M:-0.0677 c. 760: 51 101 51 101 51 101 51 101 51 101 SP B DE SD: 0.0404 c. M:-0.0572 c. 775: 52 103 52 103 52 103 52 103 52 103 SP B DE SD: 0.0333 c. M:-0.0470 c. 790: 53 105 53 105 53 105 53 105 53 105 SP B DE SD: 0.0264 c. M:-0.0373 c. 805: 54 107 54 107 54 107 54 107 54 107 SP B DE SD: 0.0197 c. M:-0.0279 c. 820: 55 109 55 109 55 109 55 109 55 109 SP B DE SD: 0.0133 c. M:-0.0188 c. 835: 56 111 56 111 56 111 56 111 56 111 SP B DE SD: 0.0072 c. M:-0.0101 c. 850: 57 113 57 113 57 113 57 113 57 113 SP B DE SD: 0.0012 c. M:-0.0017 c.
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 5.6500 cents 2 x x x x x 3 x x x 4 S SD: 7.8532 cents 3 x x x 4 x x x 5 x 6 S SD: 24.7262 cents 4 x x 5 x x 6 x 7 x 8 S SD: 17.6092 cents 5 x x 6 x 7 x 8 x 9:10 S SD: 7.1098 cents 6 x 7 x 8 x 9 x 10:11:12 S SD: 13.6336 cents 7 x 8 x 9:10 x 11:12:13:14 S SD: 12.3525 cents 8 x 9:10 x 11:12:13:14:15:16 S SD: 13.0647 cents 9 x 10:11:12 x x 14 x 16:18 S SD: 13.9551 cents 10 x 11:12:13:14:15:16:17:18:20 S SD: 10.4499 cents 11:12 x 13 x 15:17 x 19:20:22 SD: 12.6066 cents 12:13:14 x 16:17:18:19:21:22:24 SD: 9.4760 cents 13:14:15:16:17:18:20:21:23:24:26 SD: 8.9279 cents 14:15:16:17:18:19:21:22:24:25:28 SD: 8.0801 cents 15:16:17:18:20:21:23:24:26:27:30 SD: 6.1049 cents 16:17:18:19:21:22:24:25:28:29:32 SD: 5.8579 cents 17:18 x 20:22:23:26:27:30:31:34 SD: 7.9734 cents 18:19:21:22:24:25:27:29:31:33:36 SD: 6.1554 cents 19:20:22:23:25:26:29:30:33:35:38 SD: 3.8174 cents 26:27:30:31:34:36:39:41:45:47:52 SD: 3.4238 cents 29:30:33:35:38:40:44:46:50:53:58 SD: 3.3401 cents 34:36:39:41:45:47:51:54:59:62:68 SD: 2.7103 cents 39:41:45:47:51:54:59:62:68:71:78 SD: 2.1521 cents 41:43:47:49:54:57:62:65:71:75:82 SD: 2.0833 cents 45:47:52:54:59:62:68:71:78:82:90 SD: 1.8974 cents 60:63:69:72:79:83:91:95:104:109:120 SD: 1.1188 cents 82:86:94:99:108:113:124:130:142:149:163 SD: 1.1115 cents 84:88:96:101:111:116:127:133:146:153:167 SD: 1.0773 cents 88:92:101:106:116:121:133:139:153:160:175 SD: 1.0765 cents 89:93:102:107:117:123:135:141:155:162:177 SD: 1.0598 cents 94:98:108:113:124:130:142:149:163:171:187 SD: 1.0327 cents 100:105:115:120:132:138:151:158:174:182:199 SD: 1.0165 cents 103:108:118:124:136:142:156:163:179:187:205 SD: 0.8006 cents 123:129:141:148:162:170:186:195:214:224:245 SD: 0.6268 cents 129:135:148:155:170:178:195:204:224:235:257 SD: 0.5045 cents 148:155:170:178:195:204:224:234:257:269:295 SD: 0.4671 cents 189:198:217:227:249:261:286:299:328:344:377 SD: 0.3945 cents 236:247:271:284:311:326:357:374:410:429:470 SD: 0.3296 cents 258:270:296:310:340:356:390:409:448:469:514 SD: 0.2978 cents 271:284:311:326:357:374:410:429:471:493:540 SD: 0.2751 cents 277:290:318:333:365:382:419:439:481:504:552 SD: 0.1904 cents 337:353:387:405:444:465:510:534:585:613:672 SD: 0.1609 cents 460:482:528:553:606:635:696:729:799:837:917 SD: 0.1441 cents 513:537:589:617:676:708:776:813:891:933:1023 SD: 0.1410 cents 573:600:658:689:755:791:867:908:995:1042:1142 SD: 0.1083 cents 589:617:676:708:776:813:891:933:1023:1071:1174 SD: 0.1004 cents