Scala analysis: prelude_in_shur
Tuning set for _Prelude in Shur for Erv Wilson_ (10)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 138.281 cents 138.281260 2: 264.844 cents 264.843760 3: 472.266 cents 472.265620 4: 495.703 cents 495.703130 5: 633.984 cents 633.984380 6: 703.125 cents 703.125000 7: 760.547 cents 760.546880 8: 841.406 cents 841.406250 9: 967.969 cents 967.968760 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 232.0312 cents 232.0312 1: 138.2813 cents 138.2813 2: 126.5625 cents 126.5625 3: 207.4219 cents 207.4219 4: 23.4375 cents 23.4375 5: 138.2812 cents 138.2812 6: 69.1406 cents 69.1406 7: 57.4219 cents 57.4219 8: 80.8594 cents 80.8594 9: 126.5625 cents 126.5625 10: 232.0312 cents 232.0312
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 23.43751 cents 1: 1 57.42188 cents 1: 1 69.14062 cents 1: 1 80.85937 cents 1: 2 126.56250 cents 1: 2 138.28126 cents 1: 1 207.42186 cents 1: 1 232.03124 cents 2: 1 126.56250 cents 2: 1 138.28125 cents 2: 1 161.71876 cents 2: 2 207.42187 cents 2: 1 230.85937 cents 2: 1 264.84376 cents 2: 1 333.98436 cents 2: 1 358.59375 cents 2: 1 370.31250 cents 3: 1 207.42187 cents 3: 1 230.85938 cents 3: 2 264.84375 cents 3: 1 357.42187 cents 3: 1 369.14062 cents 3: 1 439.45312 cents 3: 1 472.26562 cents 3: 2 496.87501 cents 4: 1 288.28126 cents 4: 1 333.98438 cents 4: 1 345.70312 cents 4: 1 438.28124 cents 4: 2 495.70313 cents 4: 1 496.87500 cents 4: 1 577.73438 cents 4: 1 623.43751 cents 4: 1 704.29686 cents 5: 1 369.14063 cents 5: 1 472.26563 cents 5: 1 495.70312 cents 5: 1 564.84374 cents 5: 1 566.01562 cents 5: 1 633.98438 cents 5: 1 635.15626 cents 5: 1 704.29688 cents 5: 1 727.73437 cents 5: 1 830.85937 cents 6: 1 495.70314 cents 6: 1 576.56249 cents 6: 1 622.26562 cents 6: 1 703.12500 cents 6: 2 704.29687 cents 6: 1 761.71876 cents 6: 1 854.29688 cents 6: 1 866.01562 cents 6: 1 911.71874 cents 7: 2 703.12499 cents 7: 1 727.73438 cents 7: 1 760.54688 cents 7: 1 830.85938 cents 7: 1 842.57813 cents 7: 2 935.15625 cents 7: 1 969.14062 cents 7: 1 992.57813 cents 8: 1 829.68750 cents 8: 1 841.40625 cents 8: 1 866.01564 cents 8: 1 935.15624 cents 8: 1 969.14063 cents 8: 2 992.57813 cents 8: 1 1038.28124 cents 8: 1 1061.71875 cents 8: 1 1073.43750 cents 9: 1 967.96876 cents 9: 1 992.57814 cents 9: 2 1061.71874 cents 9: 2 1073.43750 cents 9: 1 1119.14063 cents 9: 1 1130.85938 cents 9: 1 1142.57812 cents 9: 1 1176.56249 cents Highest number of different intervals for one interval class: 10 Average number of different intervals per interval class: 8.66667 = 26/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 138.3 264.8 472.3 495.7 634.0 703.1 760.5 841.4 968.0 1200.0 138.3 : 126.6 334.0 357.4 495.7 564.8 622.3 703.1 829.7 1061.7 1200.0 264.8 : 207.4 230.9 369.1 438.3 495.7 576.6 703.1 935.2 1073.4 1200.0 472.3 : 23.4 161.7 230.9 288.3 369.1 495.7 727.7 866.0 992.6 1200.0 495.7 : 138.3 207.4 264.8 345.7 472.3 704.3 842.6 969.1 1176.6 1200.0 634.0 : 69.1 126.6 207.4 334.0 566.0 704.3 830.9 1038.3 1061.7 1200.0 703.1 : 57.4 138.3 264.8 496.9 635.2 761.7 969.1 992.6 1130.9 1200.0 760.5 : 80.9 207.4 439.5 577.7 704.3 911.7 935.2 1073.4 1142.6 1200.0 841.4 : 126.6 358.6 496.9 623.4 830.9 854.3 992.6 1061.7 1119.1 1200.0 968.0 : 232.0 370.3 496.9 704.3 727.7 866.0 935.2 992.6 1073.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 23.4375 .. 232.0312 cents 208.59373 cents 23.43751 cents 2: 126.5625 .. 370.3125 cents 243.75000 cents -105.46874 cents 3: 207.4219 .. 496.8750 cents 289.45314 cents -162.89063 cents 4: 288.2813 .. 704.2969 cents 416.01560 cents -208.59375 cents 5: 369.1406 .. 830.8594 cents 461.71874 cents -335.15623 cents 6: 495.7031 .. 911.7187 cents 416.01560 cents -335.15623 cents 7: 703.1250 .. 992.5781 cents 289.45314 cents -208.59375 cents 8: 829.6875 .. 1073.4375 cents 243.75000 cents -162.89063 cents 9: 967.9688 .. 1176.5625 cents 208.59373 cents -105.46874 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 23.43751 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 232.03124 cents Average / Smallest step : 5.119998 Largest / Average step : 1.933594 Largest / Smallest step : 9.899995 Median interval of one step : 126.56250 cents, amount: 2 Least squares average step : 114.86506 cents, oct.: 1148.65057 cents Scale is not proper Scale is a mode of a 1024-tone equal temperament with octave 2/1 degrees: 118 226 403 423 541 600 649 718 826 1024 Least number of segments generator : 513 of 601.172 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 663 of 776.953 cents and inv. generated superset size: 269 = 259 more = 2690.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDAEFGBH Step pattern size order : FEGAFCBDEH Scale is not a Constant Structure Scale diversity : 1.486803 Lumma stability : 0.039063 Lumma impropriety factor : 0.789062 Rothenberg efficiency : 0.279127 redundancy: 0.720873 Efficiency x scale size : 2.791270 Number of different interval sizes : 54 = 6.00000 / class Number of one step interval sizes : 8 Highest interval variety : 10 Mean interval variety : 8.66667 = 26/3 Median interval variety : 8 Lowest interval variety : 8 Smallest interval difference : 1.17186 cents Most common triad is 0.0 207.422 704.297 cents, amount: 3 Number of recognisable fifths : 7, average 703.7946 cents Formal octave complements present : 1 = 10.0000% -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
10: 1 1 2 0 1 1 0 1 1 2 N SD: 20.9930 c. M: 40.5469 c. 15: 2 1 3 0 2 1 1 1 1 3 N SD: 21.9677 c. M:-39.4531 c. 17: 2 2 3 0 2 1 1 1 2 3 N G SD: 12.2497 c. M:-21.8520 c. 26: 3 3 4 1 3 1 1 2 3 5 N SD: 11.2799 c. M: 22.0853 c. 27: 3 3 5 0 3 2 1 2 3 5 N SD: 8.2647 c. M:-16.6233 c. 31: 4 3 5 1 3 2 2 2 3 6 N SD: 9.8646 c. M:-16.5574 c. 32: 4 3 6 0 4 2 1 2 4 6 N SD: 9.8605 c. M: 16.4063 c. 33: 4 3 6 1 3 2 2 2 4 6 N SD: 9.8117 c. M: 15.8026 c. 36: 4 4 6 1 4 2 2 2 4 7 N SD: 4.3832 c. M: 8.0729 c. 46: 5 5 8 1 5 3 2 3 5 9 N SD: 4.6494 c. M: 7.8974 c. 51: 6 5 9 1 6 3 2 4 5 10 N SD: 3.9964 c. M: 7.6057 c. 58: 7 6 10 1 7 3 3 4 6 11 N SD: 4.6898 c. M:-7.3949 c. 60: 7 6 11 1 7 3 3 4 6 12 N SD: 4.6522 c. M: 7.9688 c. 63: 7 7 11 1 7 4 3 4 7 12 N SD: 3.1652 c. M: 5.4130 c. 68: 8 7 12 1 8 4 3 5 7 13 N SD: 2.8231 c. M:-5.6526 c. 77: 9 8 13 2 9 4 4 5 8 15 N SD: 2.7567 c. M:-4.9767 c. 87: 10 9 15 2 10 5 4 6 9 17 N SD: 1.7178 c. M: 3.3001 c. 104: 12 11 18 2 12 6 5 7 11 20 N SD: 0.7412 c. M:-1.2620 c. 191: 22 20 33 4 22 11 9 13 20 37 N SD: 0.6012 c. M: 1.0614 c. 295: 34 31 51 6 34 17 14 20 31 57 N SD: 0.4277 c. M:-0.6276 c. 399: 46 42 69 8 46 23 19 27 42 77 N SD: 0.4379 c. M:-0.6990 c. 445: 51 47 77 9 51 26 21 30 47 86 N SD: 0.4287 c. M: 0.7532 c. 475: 55 50 82 9 55 27 23 32 50 92 N SD: 0.4241 c. M: 0.8092 c. 503: 58 53 87 10 58 29 24 34 53 97 N SD: 0.4748 c. M:-0.7409 c. 511: 59 54 88 10 59 29 25 34 54 99 N SD: 0.4683 c. M: 0.9724 c. 513: 59 54 89 10 59 30 24 35 54 99 N SD: 0.4665 c. M:-0.9686 c. 521: 60 55 90 10 60 30 25 35 55 101 N SD: 0.4584 c. M: 0.7153 c. 538: 62 57 93 10 62 31 26 36 57 104 N SD: 0.4249 c. M:-0.5968 c. 549: 63 58 95 11 63 32 26 37 58 106 N SD: 0.3669 c. M:-0.7001 c. 579: 67 61 100 11 67 33 28 39 61 112 N SD: 0.3295 c. M:-0.5788 c. 625: 72 66 108 12 72 36 30 42 66 121 N SD: 0.2796 c. M: 0.4463 c. 666: 77 70 115 13 77 38 32 45 70 129 N SD: 0.2698 c. M:-0.4575 c. 693: 80 73 120 13 80 40 33 47 73 134 N SD: 0.2680 c. M: 0.4650 c. 729: 84 77 126 14 84 42 35 49 77 141 N SD: 0.1731 c. M: 0.2540 c. 816: 94 86 141 16 94 47 39 55 86 158 N SD: 0.1889 c. M: 0.3217 c. 833: 96 88 144 16 96 48 40 56 88 161 N SD: 0.1378 c. M:-0.2434 c. 920: 106 97 159 18 106 53 44 62 97 178 N SD: 0.0838 c. M: 0.1427 c. 1024: 118 108 177 20 118 59 49 69 108 198 N SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x x x 4 S SD: 0.5850 cents 3 x x x 4 x x x 5 x 6 S SD: 14.3388 cents 4 x x 5 x x 6 x x 7:8 S SD: 21.4910 cents 5 x 6 x x 7 x x 8:9:10 S SD: 18.3968 cents 6 x 7 x 8 x 9 x 10:11:12 S SD: 15.3486 cents 7 x 8:9 x 10 x 11 x 12:14 S SD: 11.1600 cents 8 x 9 x 11 x 12 x 13:14:16 SD: 13.7526 cents 9:10 x x 12:13 x 14:15:16:18 S SD: 9.7038 cents 10:11:12:13 x 14:15 x 16:17:20 SD: 12.1660 cents 11:12:13:14:15:16 x 17:18:19:22 SD: 8.8255 cents 12:13:14 x 16:17:18:19:20:21:24 S SD: 7.0645 cents 13:14:15:17 x 19 x 20:21:23:26 SD: 5.1782 cents 15:16:17 x 20:22 x 23:24:26:30 SD: 9.1099 cents 16:17:19:21 x 23:24:25:26:28:32 SD: 5.3995 cents 17:18:20:22:23:25 x 26:28:30:34 SD: 8.4266 cents 18:20:21 x 24:26:27:28:29:31:36 SD: 6.0370 cents 19:21:22:25 x 27 x 29:31:33:38 SD: 6.8565 cents 20:22:23:26:27:29:30:31:33:35:40 SD: 5.3636 cents 21:23:24 x 28:30:32:33:34:37:42 SD: 6.2398 cents 22:24:26:29 x 32:33:34:36:38:44 SD: 4.5088 cents 24:26:28 x 32:35:36:37:39:42:48 SD: 2.4986 cents 25:27:29:33 x 36:38:39:41:44:50 SD: 3.6282 cents 28:30:33:37 x 40:42:43:46:49:56 SD: 4.6652 cents 29:31:34:38:39:42:44:45:47:51:58 SD: 3.8248 cents 31:34:36 x 41:45:47:48:50:54:62 SD: 4.0393 cents 32:35:37:42:43:46:48:50:52:56:64 SD: 3.0003 cents 34:37:40 x 45:49:51:53:55:59:68 SD: 3.1027 cents 36:39:42:47:48:52:54:56:59:63:72 SD: 1.8537 cents 37:40:43 x 49:53:56:57:60:65:74 SD: 2.9357 cents 38:41:44:50:51:55:57:59:62:66:76 SD: 2.4280 cents 40:43:47 x 53:58:60:62:65:70:80 SD: 2.5860 cents 45:49:52:59:60:65:68:70:73:79:90 SD: 2.2963 cents 47:51:55:62:63:68:71:73:76:82:94 SD: 2.2617 cents 48:52:56:63:64:69:72:74:78:84:96 SD: 1.3110 cents 72:78:84:95:96:104:108:112:117:126:144 SD: 0.9855 cents 84:91:98:110:112:121:126:130:137:147:168 SD: 0.9772 cents 96:104:112:126:128:138:144:149:156:168:192 SD: 0.6900 cents 109:118:127:143:145:157:164:169:177:191:218 SD: 0.6824 cents 120:130:140:158:160:173:180:186:195:210:240 SD: 0.5692 cents 147:159:171:193:196:212:221:228:239:257:294 SD: 0.5489 cents 156:169:182:205:208:225:234:242:254:273:312 SD: 0.4330 cents 181:196:211:238:241:261:272:281:294:317:362 SD: 0.4017 cents 192:208:224:252:256:277:288:298:312:336:384 SD: 0.3913 cents 217:235:253:285:289:313:326:337:353:380:434 SD: 0.3254 cents 230:249:268:302:306:332:345:357:374:402:460 SD: 0.3008 cents 265:287:309:348:353:382:398:411:431:464:530 SD: 0.2836 cents 278:301:324:365:370:401:417:431:452:486:556 SD: 0.2492 cents 326:353:380:428:434:470:489:506:530:570:652 SD: 0.2034 cents 350:379:408:460:466:505:525:543:569:612:700 SD: 0.1910 cents 395:428:460:519:526:570:593:613:642:691:790 SD: 0.1791 cents 411:445:479:540:547:593:617:638:668:719:822 SD: 0.1661 cents 443:480:516:582:590:639:665:687:720:775:886 SD: 0.1583 cents 459:497:535:603:611:662:689:712:746:803:918 SD: 0.1205 cents