Scala analysis: septicyc
septicyclic 1029/1024-tempered scale, 252 et
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 152.381 cents 152.380952 2: 233.333 cents 233.333333 3: 385.714 cents 385.714286 4: 466.667 cents 466.666667 5: 500.000 cents 500.000000 6: 700.000 cents 700.000000 7: 733.333 cents 733.333333 8: 885.714 cents 885.714286 9: 966.667 cents 966.666667 10: 1119.048 cents 1119.047619 11: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 80.9524 cents 80.9524 1: 152.3810 cents 152.3810 2: 80.9524 cents 80.9524 3: 152.3810 cents 152.3810 4: 80.9524 cents 80.9524 5: 33.3333 cents 33.3333 6: 200.0000 cents 200.0000 7: 33.3333 cents 33.3333 8: 152.3810 cents 152.3810 9: 80.9524 cents 80.9524 10: 152.3810 cents 152.3810 11: 80.9524 cents 80.9524
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 33.33333 cents 1: 4 80.95238 cents 1: 4 152.38095 cents 1: 1 200.00000 cents 2: 1 114.28571 cents 2: 1 185.71429 cents 2: 9 233.33333 cents 3: 3 266.66667 cents 3: 4 314.28571 cents 3: 4 385.71429 cents 4: 2 347.61905 cents 4: 2 419.04762 cents 4: 7 466.66667 cents 5: 5 500.00000 cents 5: 3 547.61905 cents 5: 3 619.04762 cents 6: 3 580.95238 cents 6: 3 652.38095 cents 6: 5 700.00000 cents 7: 7 733.33333 cents 7: 2 780.95238 cents 7: 2 852.38095 cents 8: 4 814.28571 cents 8: 4 885.71429 cents 8: 3 933.33333 cents 9: 9 966.66667 cents 9: 1 1014.28571 cents 9: 1 1085.71429 cents 10: 1 1000.00000 cents 10: 4 1047.61905 cents 10: 4 1119.04762 cents 10: 2 1166.66667 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.20000 = 16/5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 0.0 : 152.4 233.3 385.7 466.7 500.0 700.0 733.3 885.7 966.7 1119.0 1200.0 152.4 : 81.0 233.3 314.3 347.6 547.6 581.0 733.3 814.3 966.7 1047.6 1200.0 233.3 : 152.4 233.3 266.7 466.7 500.0 652.4 733.3 885.7 966.7 1119.0 1200.0 385.7 : 81.0 114.3 314.3 347.6 500.0 581.0 733.3 814.3 966.7 1047.6 1200.0 466.7 : 33.3 233.3 266.7 419.0 500.0 652.4 733.3 885.7 966.7 1119.0 1200.0 500.0 : 200.0 233.3 385.7 466.7 619.0 700.0 852.4 933.3 1085.7 1166.7 1200.0 700.0 : 33.3 185.7 266.7 419.0 500.0 652.4 733.3 885.7 966.7 1000.0 1200.0 733.3 : 152.4 233.3 385.7 466.7 619.0 700.0 852.4 933.3 966.7 1166.7 1200.0 885.7 : 81.0 233.3 314.3 466.7 547.6 700.0 781.0 814.3 1014.3 1047.6 1200.0 966.7 : 152.4 233.3 385.7 466.7 619.0 700.0 733.3 933.3 966.7 1119.0 1200.0 1119.0: 81.0 233.3 314.3 466.7 547.6 581.0 781.0 814.3 966.7 1047.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.3333 .. 200.0000 cents 166.66667 cents 33.33333 cents 2: 114.2857 .. 233.3333 cents 119.04762 cents -85.71429 cents 3: 266.6667 .. 385.7143 cents 119.04762 cents 33.33333 cents 4: 347.6190 .. 466.6667 cents 119.04762 cents -38.09524 cents 5: 500.0000 .. 619.0476 cents 119.04762 cents 33.33333 cents 6: 580.9524 .. 700.0000 cents 119.04762 cents -38.09524 cents 7: 733.3333 .. 852.3810 cents 119.04762 cents 33.33333 cents 8: 814.2857 .. 933.3333 cents 119.04762 cents -38.09524 cents 9: 966.6667 .. 1085.7143 cents 119.04762 cents 33.33333 cents 10: 1000.0000 .. 1166.6667 cents 166.66667 cents -85.71429 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 33.33333 cents, class 1 Average step (divided formal octave): 109.0909 cents Largest one step interval : 200.00000 cents Average / Smallest step : 3.272727 Largest / Average step : 1.833333 Largest / Smallest step : 6.000000 Median interval of one step : 80.95238 cents, amount: 4 Least squares average step : 109.98494 cents, oct.: 1209.83437 cents Scale is not proper Scale is a mode of a 252-tone equal temperament with octave 1200.000 cents degrees: 32 49 81 98 105 147 154 186 203 235 252 Least number of segments generator : 127 of 604.762 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 137 of 652.381 cents and inv. generated superset size: 49 = 38 more = 445.455% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABCDCABAB Step pattern size order : CBCBADACBCB Scale is a Constant Structure, by a margin of 14.28571 cents Scale diversity : 1.437930 Lumma stability : 0.166667 Lumma impropriety factor : 0.238095 Rothenberg efficiency : 0.512121 redundancy: 0.487879 Efficiency x scale size : 5.633333 Number of different interval sizes : 32 = 3.20000 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.20000 = 16/5 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 14.28571 cents Most common intervals : 233.33333 cents & inv., amount: 9 Most common triad is 0.0 233.333 966.667 cents, amount: 7 Number of recognisable fifths : 5, average 700.0000 cents Best minor thirds form a closed circle Formal octave complements present : 7 = 63.6364% -- Rational properties --
FIT/MODE
11: 1 1 1 1 0 2 0 2 1 1 1 N T3 SD: 42.5874 c. M: 78.7879 c. 12: 2 0 2 1 0 2 0 2 1 1 1 N T3 SD: 26.0820 c. M:-47.6190 c. 15: 2 1 2 1 0 3 0 2 1 2 1 N SD: 11.8327 c. M: 20.0000 c. 24: 3 2 3 1 1 4 1 3 1 3 2 N SD: 13.1002 c. M: 19.0476 c. 26: 3 2 3 2 1 4 1 3 2 3 2 N SD: 8.8203 c. M: 16.4835 c. 31: 4 2 4 2 1 5 1 4 2 4 2 N SD: 2.5945 c. M:-4.6083 c. 72: 9 5 9 5 2 12 2 9 5 9 5 N SD: 1.4358 c. M: 2.3810 c. 103: 13 7 13 7 3 17 3 13 7 13 7 N SD: 0.7251 c. M: 1.2483 c. 149: 19 10 19 10 4 25 4 19 10 19 10 N SD: 0.5013 c. M:-0.8629 c. 180: 23 12 23 12 5 30 5 23 12 23 12 N SD: 0.5743 c. M:-0.9524 c. 221: 28 15 28 15 6 37 6 28 15 28 15 N SD: 0.3639 c. M: 0.6464 c. 252: 32 17 32 17 7 42 7 32 17 32 17 N SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x 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 x 4 S SD: 0.9775 cents 3 x x x x 4 x x 5 x x 6 S SD: 0.7930 cents 4 x x 5 x x 6 x x 7 x 8 S SD: 0.7435 cents 5 x x 6 x 7 x x 8:9 x 10 S SD: 27.9287 cents 6 x 7 x x 8:9 x 10 x 11:12 S SD: 12.8994 cents 7 x 8 x 9 x x 11 x 12:13:14 SD: 13.7286 cents 8 x 9:10 x 11:12 x 13:14:15:16 S SD: 10.0757 cents 9:10 x 11 x 12:13:14:15:16:17:18 S SD: 10.2914 cents 10:11 x x 13 x 15 x 17 x 19:20 SD: 6.3772 cents 11:12:13:14 x 15:16:17:18:19:21:22 SD: 10.0317 cents 12:13:14:15 x 16:18 x 20:21:23:24 SD: 4.1318 cents 13:14:15:16:17 x 19:20:22:23:25:26 SD: 6.8776 cents 14:15:16 x 18:19:21 x 23:24:27:28 SD: 7.8976 cents 15:16:17:19 x 20:22:23:25:26:29:30 SD: 6.7837 cents 16:17:18:20:21 x 24 x 27:28:31:32 SD: 7.2198 cents 17:19 x 21:22:23:25:26:28:30:32:34 SD: 7.3118 cents 18:20:21:22 x 24:27 x 30:31:34:36 SD: 7.4365 cents 19:21:22:24:25 x 28:29:32:33:36:38 SD: 5.1598 cents 20:22:23:25:26:27:30:31:33:35:38:40 SD: 3.8973 cents 21:23:24:26 x 28:31:32:35:37:40:42 SD: 3.4302 cents 22:24:25:27:29 x 33:34:37:38:42:44 SD: 4.7891 cents 23:25:26:29:30:31:34:35:38:40:44:46 SD: 4.0906 cents 24:26:27:30:31:32:36:37:40:42:46:48 SD: 4.0019 cents 25:27:29:31:33 x 37:38:42:44:48:50 SD: 4.7180 cents 26:28:30:32:34:35:39:40:43:45:50:52 SD: 4.5715 cents 27:29:31:34:35:36:40:41:45:47:52:54 SD: 4.1870 cents 28:31:32:35:37 x 42:43:47:49:53:56 SD: 3.5311 cents 30:33:34:37:39:40:45:46:50:52:57:60 SD: 3.4344 cents 31:34:35:39 x 41:46:47:52:54:59:62 SD: 3.9867 cents 32:35:37:40:42:43:48:49:53:56:61:64 SD: 2.3405 cents 34:37:39:42 x 45:51:52:57:59:65:68 SD: 3.0256 cents 35:38:40:44:46:47:52:53:58:61:67:70 SD: 2.8441 cents 36:39:41:45:47:48:54:55:60:63:69:72 SD: 1.7028 cents 48:52:55:60:63:64:72:73:80:84:92:96 SD: 1.6681 cents 55:60:63:69:72:73:82:84:92:96:105:110 SD: 1.4488 cents 64:70:73:80:84:85:96:98:107:112:122:128 SD: 1.2198 cents 68:74:78:85:89:91:102:104:113:119:130:136 SD: 1.0639 cents 84:92:96:105:110:112:126:128:140:147:160:168 SD: 0.7853 cents 96:105:110:120:126:128:144:147:160:168:183:192 SD: 0.7489 cents 119:130:136:149:156:159:178:182:198:208:227:238 SD: 0.6862 cents 120:131:137:150:157:160:180:183:200:210:229:240 SD: 0.5760 cents 132:144:151:165:173:176:198:202:220:231:252:264 SD: 0.5073 cents 152:166:174:190:199:203:228:232:254:266:290:304 SD: 0.4307 cents 165:180:189:206:216:220:247:252:275:288:315:330 SD: 0.4296 cents 195:213:223:244:255:260:292:298:325:341:372:390 SD: 0.4159 cents 207:226:237:259:271:276:310:316:345:362:395:414 SD: 0.3485 cents 229:250:262:286:300:306:343:350:382:400:437:458 SD: 0.2569 cents 305:333:349:381:399:407:457:466:509:533:582:610 SD: 0.1921 cents 317:346:363:396:415:423:475:484:529:554:605:634 SD: 0.1861 cents 349:381:399:436:457:466:523:533:582:610:666:698 SD: 0.1684 cents 424:463:485:530:555:566:635:648:707:741:809:848 SD: 0.1642 cents 436:476:499:545:571:582:653:666:727:762:832:872 SD: 0.1180 cents 576:629:659:720:754:769:863:880:961:1007:1099:1152 SD: 0.1165 cents 588:642:673:735:770:785:881:898:981:1028:1122:1176 SD: 0.1054 cents