Scala analysis: zenop
Lesfip scale derived from Zen, using J O'S "good" intervals, 256/255
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 116.567 cents 116.566760 2: 204.622 cents 204.622470 3: 266.883 cents 266.882630 4: 435.275 cents 435.275080 5: 497.535 cents 497.535240 6: 585.591 cents 585.590960 7: 702.158 cents 702.157710 8: 761.026 cents 761.026300 9: 885.226 cents 885.225780 10: 1016.932 cents 1016.931930 11: 1141.131 cents 1141.131410 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 58.8686 cents 58.8686 1: 116.5668 cents 116.5668 2: 88.0557 cents 88.0557 3: 62.2602 cents 62.2602 4: 168.3925 cents 168.3925 5: 62.2602 cents 62.2602 6: 88.0557 cents 88.0557 7: 116.5667 cents 116.5667 8: 58.8686 cents 58.8686 9: 124.1995 cents 124.1995 10: 131.7061 cents 131.7061 11: 124.1995 cents 124.1995 12: 58.8686 cents 58.8686
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 58.86859 cents 1: 2 62.26016 cents 1: 2 88.05571 cents 1: 2 116.56676 cents 1: 2 124.19948 cents 1: 1 131.70615 cents 1: 1 168.39245 cents 2: 2 150.31587 cents 2: 2 175.43534 cents 2: 2 183.06807 cents 2: 2 204.62247 cents 2: 2 230.65261 cents 2: 2 255.90563 cents 3: 2 263.49106 cents 3: 2 266.88263 cents 3: 1 292.91277 cents 3: 2 299.63482 cents 3: 2 314.77422 cents 3: 2 318.70832 cents 3: 1 380.10511 cents 4: 2 325.75122 cents 4: 2 380.96848 cents 4: 2 387.69054 cents 4: 2 431.34097 cents 4: 2 435.27508 cents 4: 2 438.97370 cents 5: 2 449.95070 cents 5: 1 469.02420 cents 5: 2 494.14367 cents 5: 2 497.53524 cents 5: 1 497.84229 cents 5: 2 519.39669 cents 5: 2 555.54045 cents 6: 2 556.40383 cents 6: 2 581.65685 cents 6: 2 585.59096 cents 6: 2 614.40904 cents 6: 2 618.34315 cents 6: 2 643.59617 cents 7: 2 644.45954 cents 7: 2 680.60331 cents 7: 1 702.15771 cents 7: 2 702.46476 cents 7: 2 705.85633 cents 7: 1 730.97580 cents 7: 2 750.04930 cents 8: 2 761.02630 cents 8: 2 764.72492 cents 8: 2 768.65902 cents 8: 2 812.30946 cents 8: 2 819.03152 cents 8: 2 874.24878 cents 9: 1 819.89489 cents 9: 2 881.29168 cents 9: 2 885.22578 cents 9: 2 900.36517 cents 9: 1 907.08723 cents 9: 2 933.11737 cents 9: 2 936.50894 cents 10: 2 944.09437 cents 10: 2 969.34739 cents 10: 2 995.37753 cents 10: 2 1016.93193 cents 10: 2 1024.56465 cents 10: 2 1049.68413 cents 11: 1 1031.60755 cents 11: 1 1068.29385 cents 11: 2 1075.80052 cents 11: 2 1083.43324 cents 11: 2 1111.94429 cents 11: 2 1137.73984 cents 11: 2 1141.13141 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 6.54545 = 72/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 116.6 204.6 266.9 435.3 497.5 585.6 702.2 761.0 885.2 1016.9 1141.1 1200.0 116.6 : 88.1 150.3 318.7 381.0 469.0 585.6 644.5 768.7 900.4 1024.6 1083.4 1200.0 204.6 : 62.3 230.7 292.9 381.0 497.5 556.4 680.6 812.3 936.5 995.4 1111.9 1200.0 266.9 : 168.4 230.7 318.7 435.3 494.1 618.3 750.0 874.2 933.1 1049.7 1137.7 1200.0 435.3 : 62.3 150.3 266.9 325.8 450.0 581.7 705.9 764.7 881.3 969.3 1031.6 1200.0 497.5 : 88.1 204.6 263.5 387.7 519.4 643.6 702.5 819.0 907.1 969.3 1137.7 1200.0 585.6 : 116.6 175.4 299.6 431.3 555.5 614.4 731.0 819.0 881.3 1049.7 1111.9 1200.0 702.2 : 58.9 183.1 314.8 439.0 497.8 614.4 702.5 764.7 933.1 995.4 1083.4 1200.0 761.0 : 124.2 255.9 380.1 439.0 555.5 643.6 705.9 874.2 936.5 1024.6 1141.1 1200.0 885.2 : 131.7 255.9 314.8 431.3 519.4 581.7 750.0 812.3 900.4 1016.9 1075.8 1200.0 1016.9: 124.2 183.1 299.6 387.7 450.0 618.3 680.6 768.7 885.2 944.1 1068.3 1200.0 1141.1: 58.9 175.4 263.5 325.8 494.1 556.4 644.5 761.0 819.9 944.1 1075.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 58.8686 .. 168.3925 cents 109.52386 cents 58.86859 cents 2: 150.3159 .. 255.9056 cents 105.58976 cents -18.07658 cents 3: 263.4911 .. 380.1051 cents 116.61405 cents 7.58543 cents 4: 325.7512 .. 438.9737 cents 113.22248 cents -54.35389 cents 5: 449.9507 .. 555.5404 cents 105.58975 cents 10.97700 cents 6: 556.4038 .. 643.5962 cents 87.19234 cents 0.86338 cents 7: 644.4595 .. 750.0493 cents 105.58976 cents 0.86337 cents 8: 761.0263 .. 874.2488 cents 113.22248 cents 10.97700 cents 9: 819.8949 .. 936.5089 cents 116.61405 cents -54.35389 cents 10: 944.0944 .. 1049.6841 cents 105.58976 cents 7.58543 cents 11: 1031.6075 .. 1141.1314 cents 109.52386 cents -18.07658 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 58.86859 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 168.39245 cents Average / Smallest step : 1.698699 Largest / Average step : 1.683925 Largest / Smallest step : 2.860480 Median interval of one step : 102.31124 cents, amount: 0 Least squares average step : 100.24753 cents, oct.: 1202.97033 cents Scale is not proper Step pattern alph. order: ABCDCBAEFGFE Step pattern size order : DCBGBCDAEFEA Scale is a Constant Structure, by a margin of 0.86337 cents Scale diversity : 1.493132 Lumma stability : 0.130491 Lumma impropriety factor : 0.120717 Rothenberg efficiency : 0.242424 redundancy: 0.757576 Efficiency x scale size : 2.909091 Number of different interval sizes : 72 = 6.54545 / class Number of one step interval sizes : 7 Highest interval variety : 7 Mean interval variety : 6.54545 = 72/11 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 0.30705 cents Number of recognisable fifths : 5, average 703.7600 cents Best fifths form a closed circle Formal octave complements present : 1 = 8.3333% Limited inverse transpositions : 7 Inversional symmetry on intervals : 3-4 9-10 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 23.4005 c. M: 41.1314 c. Twelve-tone Chromatic (1/11-comma) 14: 1 1 1 2 1 1 1 1 1 2 1 1 P B ME SD: 19.8014 c. M: 33.1939 c. 17: 2 1 1 2 1 1 2 1 2 1 2 1 P D3 SD: 17.6687 c. M:-32.4213 c. 19: 2 1 1 3 1 1 2 1 2 2 2 1 N D3 SD: 9.3725 c. M: 17.1699 c. 24: 2 2 1 4 1 2 2 1 3 2 3 1 N SD: 11.9764 c. M: 16.9319 c. 27: 3 2 1 4 1 2 3 1 3 3 3 1 N SD: 9.8757 c. M:-17.5998 c. 31: 3 2 2 4 2 2 3 2 3 3 3 2 P D3 SD: 8.9829 c. M: 18.5508 c. 34: 3 3 2 4 2 3 3 2 3 4 3 2 P T3 SD: 10.0137 c. M:-15.4703 c. 36: 4 2 2 5 2 3 3 2 4 4 3 2 N SD: 9.5941 c. M:-16.7666 c. 39: 4 3 2 5 2 3 4 2 4 4 4 2 N SD: 6.2264 c. M:-10.7621 c. 41: 4 3 2 6 2 3 4 2 4 5 4 2 N SD: 3.3390 c. M:-7.4583 c. 60: 6 4 3 9 3 4 6 3 6 7 6 3 N SD: 3.9147 c. M: 6.8826 c. 72: 7 5 4 10 4 5 7 4 7 8 7 4 N SD: 3.3825 c. M: 7.7981 c. 80: 8 6 4 11 4 6 8 4 8 9 8 4 N SD: 2.7672 c. M:-5.3775 c. 94: 9 7 5 13 5 7 9 5 9 11 9 5 N SD: 2.8234 c. M: 4.9612 c. 96: 9 7 5 14 5 7 9 5 10 10 10 5 N SD: 3.1173 c. M: 4.6225 c. 99: 10 7 5 14 5 7 10 5 10 11 10 5 N SD: 2.0763 c. M:-4.6454 c. 104: 10 8 5 15 5 8 10 5 11 11 11 5 N SD: 2.0561 c. M:-3.2358 c. 123: 12 9 6 18 6 9 12 6 13 13 13 6 N SD: 1.7931 c. M:-3.7493 c. 125: 12 9 7 17 7 9 12 6 13 14 13 6 N SD: 1.8947 c. M: 3.2751 c. 145: 14 11 7 21 7 11 14 7 15 16 15 7 N SD: 1.5755 c. M:-3.3456 c. 156: 15 12 8 22 8 11 15 8 16 17 16 8 N SD: 2.0068 c. M:-3.1865 c. 157: 15 12 8 22 8 12 15 8 16 17 16 8 N SD: 1.7255 c. M:-3.3049 c. 164: 16 12 8 23 9 12 16 8 17 18 17 8 N SD: 1.4537 c. M: 3.5678 c. 172: 17 12 9 24 9 13 17 8 18 19 18 8 N SD: 1.9204 c. M:-3.0546 c. 176: 17 13 9 25 9 13 17 9 18 19 18 9 N SD: 1.2449 c. M:-2.6101 c. 183: 18 13 10 25 10 13 18 9 19 20 19 9 N SD: 1.2703 c. M: 2.4882 c. 184: 18 13 10 26 9 14 18 9 19 20 19 9 N SD: 1.5076 c. M: 2.4486 c. 188: 18 14 10 26 10 14 18 9 20 20 20 9 N SD: 1.3238 c. M: 2.0383 c. 203: 20 15 10 29 10 15 20 10 21 22 21 10 N SD: 1.3153 c. M:-2.2741 c. 205: 20 15 11 28 11 15 20 10 21 23 21 10 N SD: 1.1184 c. M:-2.3857 c. 217: 21 16 11 31 11 16 21 11 22 24 22 11 N SD: 1.0805 c. M:-2.1073 c. 224: 22 16 12 31 12 16 22 11 23 25 23 11 N SD: 0.9804 c. M: 1.6624 c. 229: 22 17 12 32 12 17 22 11 24 25 24 11 N SD: 0.7609 c. M:-1.3086 c. 248: 24 18 13 35 13 18 24 12 26 27 26 12 N SD: 0.7619 c. M: 1.3967 c. 270: 26 20 14 38 14 20 26 13 28 30 28 13 N SD: 0.7053 c. M:-1.0908 c. 287: 28 21 15 40 15 21 28 14 30 31 30 14 N SD: 0.5387 c. M:-1.1854 c. 309: 30 23 16 43 16 23 30 15 32 34 32 15 N SD: 0.6387 c. M:-1.2028 c. 328: 32 24 17 46 17 24 32 16 34 36 34 16 N SD: 0.2326 c. M:-0.5064 c. 629: 61 46 33 88 33 46 61 31 65 69 65 31 N SD: 0.2414 c. M: 0.4889 c. 670: 65 49 35 94 35 49 65 33 69 74 69 33 N SD: 0.2590 c. M: 0.4497 c. 733: 71 54 38 103 38 54 71 36 76 80 76 36 N SD: 0.2554 c. M:-0.4936 c. 752: 73 55 39 106 39 55 73 37 78 82 78 37 N SD: 0.2830 c. M: 0.4426 c. 774: 75 57 40 109 40 57 75 38 80 85 80 38 N SD: 0.2232 c. M:-0.4556 c. 899: 87 66 47 126 47 66 87 44 93 99 93 44 N SD: 0.2582 c. M: 0.4377 c. 904: 88 66 47 127 47 66 88 44 94 99 94 44 N SD: 0.2320 c. M:-0.4615 c. 916: 89 67 48 128 48 67 89 45 95 100 95 45 N SD: 0.2348 c. M:-0.3663 c. 938: 91 69 49 131 49 69 91 46 97 103 97 46 N SD: 0.2192 c. M:-0.4948 c. 957: 93 70 50 134 50 70 93 47 99 105 99 47 N SD: 0.1342 c. M:-0.2704 c. 1102: 107 81 57 155 57 81 107 54 114 121 114 54 N SD: 0.1498 c. M:-0.2966 c. 1227: 119 90 64 172 64 90 119 60 127 135 127 60 N SD: 0.1668 c. M:-0.2643 c. 1285: 125 94 67 180 67 94 125 63 133 141 133 63 N SD: 0.1143 c. M:-0.2080 c. 1430: 139 105 74 201 74 105 139 70 148 157 148 70 N SD: 0.1332 c. M:-0.2494 c. 1555: 151 114 81 218 81 114 151 76 161 171 161 76 N SD: 0.1311 c. M:-0.2191 c. 1613: 157 118 84 226 84 118 157 79 167 177 167 79 N SD: 0.1213 c. M:-0.2342 c. 1731: 168 127 90 243 90 127 168 85 179 190 179 85 N SD: 0.1135 c. M:-0.2117 c. 1758: 171 129 91 247 91 129 171 86 182 193 182 86 N SD: 0.1358 c. M:-0.2314 c. 1830: 178 134 95 257 95 134 178 90 189 201 189 90 N SD: 0.1318 c. M:-0.2852 c. 1834: 178 135 95 257 95 135 178 90 190 201 190 90 N SD: 0.1207 c. M: 0.2615 c. 1853: 180 136 96 260 96 136 180 91 192 203 192 91 N SD: 0.1133 c. M: 0.2023 c. 1875: 182 138 97 263 97 138 182 92 194 206 194 92 N SD: 0.1051 c. M: 0.2552 c. 1894: 184 139 98 266 98 139 184 93 196 208 196 93 N SD: 0.1037 c. M: 0.1752 c. 2059: 200 151 107 289 107 151 200 101 213 226 213 101 N SD: 0.0912 c. M:-0.1821 c. 2181: 212 160 113 306 113 160 212 107 226 239 226 107 N SD: 0.0950 c. M: 0.1714 c. 2203: 214 162 114 309 114 162 214 108 228 242 228 108 N SD: 0.0905 c. M: 0.2134 c. 2222: 216 163 115 312 115 163 216 109 230 244 230 109 N SD: 0.0879 c. M: 0.1724 c. 2299: 223 169 119 323 119 169 223 113 238 252 238 113 N SD: 0.0981 c. M: 0.1683 c. 2379: 231 175 123 334 123 175 231 117 246 261 246 117 N SD: 0.0960 c. M: 0.1834 c. 2387: 232 175 124 335 124 175 232 117 247 262 247 117 N SD: 0.0874 c. M:-0.1606 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: 0.1014 cents 3 x x x x 4 x x x 5 x x 6 S SD: 0.3353 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 17.1600 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 14.3672 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 5.4079 cents 7 x 8 x 9 x 10 x 11:12:13 x 14 S SD: 12.3534 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 12.9174 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 11.9872 cents 10 x 11:12:13 x 14:15:16:17:18:19:20 S SD: 9.5401 cents 11:12 x 13:14:15 x x 17:18:20:21:22 SD: 8.1981 cents 12:13 x 14:15:16:17:18:19:20:22:23:24 S SD: 6.8328 cents 13:14 x 15:17 x 18 x 20:22:23:25:26 SD: 6.7278 cents 14:15:16 x 18:19:20:21:22:23:25:27:28 SD: 5.7608 cents 15:16:17:18:19:20:21 x 23:25:27:29:30 SD: 5.5124 cents 16:17:18:19 x 21:22:24:25:27:29:31:32 SD: 5.5296 cents 17:18:19:20:22:23:24 x 26:28:31:33:34 SD: 5.2022 cents 18:19:20:21:23:24:25:27:28:30:32:35:36 SD: 3.7056 cents 19:20:21:22:24:25:27 x 29:32:34:37:38 SD: 6.6087 cents 20:21 x 23:26:27:28:30:31:33:36:39:40 SD: 5.0370 cents 24:26:27:28:31:32:34:36:37:40:43:46:48 SD: 2.9568 cents 30:32:34:35:39:40:42:45:47:50:54:58:60 SD: 2.3591 cents 40:43:45:47:51:53:56:60:62:67:72:77:80 SD: 2.1699 cents 42:45:47:49:54:56:59:63:65:70:76:81:84 SD: 1.3244 cents 60:64:68:70:77:80:84:90:93:100:108:116:120 SD: 1.1691 cents 70:75:79:82:90:93:98:105:109:117:126:135:140 SD: 1.1434 cents 72:77:81:84:93:96:101:108:112:120:130:139:144 SD: 0.9098 cents 90:96:101:105:116:120:126:135:140:150:162:174:180 SD: 0.7953 cents 102:109:115:119:131:136:143:153:158:170:184:197:204 SD: 0.5985 cents 144:154:162:168:185:192:202:216:223:240:259:278:288 SD: 0.4150 cents 168:180:189:196:216:224:236:252:261:280:302:325:336 SD: 0.4143 cents 174:186:196:203:224:232:244:261:270:290:313:336:348 SD: 0.2951 cents 216:231:243:252:278:288:303:324:335:360:389:418:432 SD: 0.2853 cents 246:263:277:287:316:328:345:369:382:410:443:476:492 SD: 0.2783 cents 270:289:304:315:347:360:379:405:419:450:486:522:540 SD: 0.2124 cents 288:308:324:336:370:384:404:432:447:480:518:557:576 SD: 0.1904 cents 360:385:405:420:463:480:505:540:559:600:648:696:720 SD: 0.1448 cents 462:494:520:539:594:616:648:693:717:770:831:893:924 SD: 0.1153 cents 574:614:646:670:738:765:805:861:891:957:1033:1110:1148 SD: 0.1003 cents