Scala analysis: propsep
proper septicyclic 1029/1024-tempered scale in 252 et
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 38.095 cents 38.095238 2: 152.381 cents 152.380952 3: 304.762 cents 304.761905 4: 385.714 cents 385.714286 5: 538.095 cents 538.095238 6: 619.048 cents 619.047619 7: 700.000 cents 700.000000 8: 852.381 cents 852.380952 9: 933.333 cents 933.333333 10: 1085.714 cents 1085.714286 11: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 114.2857 cents 114.2857 1: 38.0952 cents 38.0952 2: 114.2857 cents 114.2857 3: 152.3810 cents 152.3810 4: 80.9524 cents 80.9524 5: 152.3810 cents 152.3810 6: 80.9524 cents 80.9524 7: 80.9524 cents 80.9524 8: 152.3810 cents 152.3810 9: 80.9524 cents 80.9524 10: 152.3810 cents 152.3810 11: 114.2857 cents 114.2857
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 38.09524 cents 1: 4 80.95238 cents 1: 2 114.28571 cents 1: 4 152.38095 cents 2: 2 152.38095 cents 2: 1 161.90476 cents 2: 6 233.33333 cents 2: 2 266.66667 cents 3: 1 266.66667 cents 3: 2 304.76191 cents 3: 4 314.28571 cents 3: 2 347.61905 cents 3: 2 385.71429 cents 4: 2 385.71429 cents 4: 2 395.23810 cents 4: 2 419.04762 cents 4: 3 466.66667 cents 4: 2 500.00000 cents 5: 2 500.00000 cents 5: 2 538.09524 cents 5: 4 547.61905 cents 5: 1 571.42857 cents 5: 2 580.95238 cents 6: 2 619.04762 cents 6: 1 628.57143 cents 6: 4 652.38095 cents 6: 2 661.90476 cents 6: 2 700.00000 cents 7: 2 700.00000 cents 7: 3 733.33333 cents 7: 2 780.95238 cents 7: 2 804.76190 cents 7: 2 814.28571 cents 8: 2 814.28571 cents 8: 2 852.38095 cents 8: 4 885.71429 cents 8: 2 895.23810 cents 8: 1 933.33333 cents 9: 2 933.33333 cents 9: 6 966.66667 cents 9: 1 1038.09524 cents 9: 2 1047.61905 cents 10: 4 1047.61905 cents 10: 2 1085.71429 cents 10: 4 1119.04762 cents 10: 1 1161.90476 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.60000 = 23/5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 0.0 : 38.1 152.4 304.8 385.7 538.1 619.0 700.0 852.4 933.3 1085.7 1200.0 38.1 : 114.3 266.7 347.6 500.0 581.0 661.9 814.3 895.2 1047.6 1161.9 1200.0 152.4 : 152.4 233.3 385.7 466.7 547.6 700.0 781.0 933.3 1047.6 1085.7 1200.0 304.8 : 81.0 233.3 314.3 395.2 547.6 628.6 781.0 895.2 933.3 1047.6 1200.0 385.7 : 152.4 233.3 314.3 466.7 547.6 700.0 814.3 852.4 966.7 1119.0 1200.0 538.1 : 81.0 161.9 314.3 395.2 547.6 661.9 700.0 814.3 966.7 1047.6 1200.0 619.0 : 81.0 233.3 314.3 466.7 581.0 619.0 733.3 885.7 966.7 1119.0 1200.0 700.0 : 152.4 233.3 385.7 500.0 538.1 652.4 804.8 885.7 1038.1 1119.0 1200.0 852.4 : 81.0 233.3 347.6 385.7 500.0 652.4 733.3 885.7 966.7 1047.6 1200.0 933.3 : 152.4 266.7 304.8 419.0 571.4 652.4 804.8 885.7 966.7 1119.0 1200.0 1085.7: 114.3 152.4 266.7 419.0 500.0 652.4 733.3 814.3 966.7 1047.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.0952 .. 152.3810 cents 114.28572 cents 38.09524 cents 2: 152.3810 .. 266.6667 cents 114.28572 cents -0.00000 cents 3: 266.6667 .. 385.7143 cents 119.04762 cents -0.00000 cents 4: 385.7143 .. 500.0000 cents 114.28571 cents 1/1, 0.0000 cents 5: 500.0000 .. 580.9524 cents 80.95238 cents 1/1, 0.0000 cents 6: 619.0476 .. 700.0000 cents 80.95238 cents 38.09524 cents 7: 700.0000 .. 814.2857 cents 114.28571 cents 1/1, 0.0000 cents 8: 814.2857 .. 933.3333 cents 119.04762 cents 1/1, 0.0000 cents 9: 933.3333 .. 1047.6190 cents 114.28571 cents -0.00000 cents 10: 1047.6190 .. 1161.9048 cents 114.28572 cents -0.00000 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 38.09524 cents, class 1 Average step (divided formal octave): 109.0909 cents Largest one step interval : 152.38095 cents Average / Smallest step : 2.863636 Largest / Average step : 1.396825 Largest / Smallest step : 4.000000 Median interval of one step : 114.28571 cents, amount: 2 Least squares average step : 105.49595 cents, oct.: 1160.45549 cents Scale is proper Scale is a mode of a 252-tone equal temperament with octave 1200.000 cents degrees: 8 32 64 81 113 130 147 179 196 228 252 Least number of segments generator : 131 of 623.810 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 187 of 890.476 cents and inv. generated superset size: 61 = 50 more = 554.545% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDCDDCDCB Step pattern size order : ACDBDBBDBDC Scale is not a Constant Structure Scale diversity : 1.432189 Rothenberg stability : 0.690909 = 38/55 Lumma stability : 0.095238 Rothenberg efficiency : 0.342700 redundancy: 0.657300 Efficiency x scale size : 3.769697 Number of different interval sizes : 38 = 3.80000 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 4.60000 = 23/5 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 9.52381 cents Number of recognisable fifths : 4, average 700.0000 cents Best minor thirds form a closed circle Formal octave complements present : 1 = 9.0909% Limited inverse transpositions : 1 Inversional symmetry on degrees : 6 Inversional symmetry on intervals : 0-1 -- Rational properties --
FIT/MODE
11: 0 1 1 1 1 1 1 1 1 1 2 N T3 SD: 70.3312 c. M: 103.8961 c. 12: 0 1 2 1 1 1 1 1 1 2 1 N D3 S SD: 30.5923 c. M: 52.3810 c. 16: 0 2 2 1 2 1 1 2 1 2 2 P D3 S SD: 23.1399 c. M: 38.0952 c. 21: 1 2 2 2 2 2 1 3 1 3 2 P D3 SD: 15.1947 c. M: 23.8095 c. 22: 1 2 3 1 3 1 2 3 1 3 2 P T3 SD: 13.1305 c. M:-22.5108 c. 23: 1 2 3 1 3 2 1 3 2 3 2 N SD: 13.2658 c. M: 21.7391 c. 24: 1 2 3 2 3 1 2 3 2 3 2 P SD: 11.1446 c. M: 19.0476 c. 27: 1 2 4 2 3 2 2 3 2 3 3 N SD: 10.5724 c. M: 19.0476 c. 29: 1 3 3 2 4 2 2 4 2 3 3 P S SD: 10.9271 c. M:-18.3908 c. 31: 1 3 4 2 4 2 2 4 2 4 3 P S SD: 2.7006 c. M:-4.9155 c. 72: 2 7 9 5 9 5 5 9 5 9 7 P S SD: 2.9599 c. M: 4.7619 c. 87: 3 8 11 6 11 6 6 11 6 11 8 P S SD: 2.5630 c. M:-4.5977 c. 94: 3 9 12 6 12 6 7 12 6 12 9 P SD: 2.5139 c. M: 6.2817 c. 103: 3 10 13 7 13 7 7 13 7 13 10 P S SD: 1.7593 c. M: 3.1438 c. 118: 4 11 15 8 15 8 8 15 8 15 11 P S SD: 1.5688 c. M:-2.5827 c. 134: 4 13 17 9 17 9 9 17 9 17 13 P S SD: 1.3815 c. M: 2.2743 c. 149: 5 14 19 10 19 10 10 19 10 19 14 P S SD: 1.2161 c. M:-2.1732 c. 180: 6 17 23 12 23 12 12 23 12 23 17 P S SD: 1.1840 c. M:-1.9048 c. 190: 6 18 24 13 24 13 13 24 13 24 18 P S SD: 0.8813 c. M: 1.6040 c. 221: 7 21 28 15 28 15 15 28 15 28 21 P S SD: 0.3788 c. M: 0.6895 c. 252: 8 24 32 17 32 17 17 32 17 32 24 P S 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 x 3 x x x 4 S SD: 0.9775 cents 3 x x x x 4 x x 5 x x 6 S SD: 17.0835 cents 4 x x x 5 x x 6 x 7 x 8 S SD: 8.8879 cents 5 x x 6 x x 7 x 8 x 9:10 S SD: 17.4247 cents 6 x x 7 x 8 x 9:10 x 11:12 S SD: 12.2333 cents 7 x x 8:9 x 10 x 11:12:13:14 S SD: 16.2480 cents 8 x 9 x 10:11 x 12:13:14:15:16 S SD: 8.1404 cents 9 x 10 x 11:12:13 x 15 x 17:18 SD: 10.6322 cents 10 x 11:12:13 x 14:15:16:17:19:20 SD: 10.3466 cents 11 x 12:13:14:15:16 x 18:19:21:22 SD: 6.5166 cents 12 x 13:14:15:16:17:18:20:21:22:24 S SD: 8.4237 cents 13 x 14 x 16:18:19 x 21:22:24:26 SD: 8.7812 cents 14 x 15:17:18:19:20:21:23:24:26:28 SD: 6.9623 cents 15 x 16:18:19:20:21:22:25:26:28:30 SD: 8.9644 cents 16 x 17:19:20:22:23:24:26:27:30:32 SD: 5.8885 cents 17 x 19:20:21:23:24:25:28:29:32:34 SD: 6.7838 cents 20:21:22:24:25:27:29:30:33:34:37:40 SD: 5.9047 cents 21:22:23:25:26:29:30:31:34:36:39:42 SD: 5.5392 cents 22:23:24:26:27:30:31:33:36:38:41:44 SD: 5.4562 cents 24:25:26:29:30:33:34:36:39:41:45:48 SD: 4.4507 cents 25:26:27:30:31:34:36:37:41:43:47:50 SD: 4.3454 cents 28:29:31:33:35:38:40:42:46:48:52:56 SD: 3.8945 cents 30:31:33:36:37:41:43:45:49:51:56:60 SD: 3.4246 cents 31:32:34:37:39:42:44:46:51:53:58:62 SD: 3.1400 cents 32:33:35:38:40:44:46:48:52:55:60:64 SD: 2.4396 cents 41:42:45:49:51:56:59:61:67:70:77:82 SD: 2.0854 cents 42:43:46:50:52:57:60:63:69:72:79:84 SD: 2.0450 cents 44:45:48:52:55:60:63:66:72:75:82:88 SD: 1.8667 cents 52:53:57:62:65:71:74:78:85:89:97:104 SD: 1.2670 cents 77:79:84:92:96:105:110:115:126:132:144:154 SD: 0.9438 cents 88:90:96:105:110:120:126:132:144:151:165:176 SD: 0.4497 cents 140:143:153:167:175:191:200:210:229:240:262:280 SD: 0.3093 cents 217:222:237:259:271:296:310:325:355:372:406:434 SD: 0.2879 cents 228:233:249:272:285:311:326:342:373:391:427:456 SD: 0.2215 cents 305:312:333:364:381:416:436:457:499:523:571:610 SD: 0.1952 cents 368:376:402:439:460:502:526:551:602:631:689:736 SD: 0.1839 cents 437:447:477:521:546:596:625:655:715:749:818:874 SD: 0.1741 cents 445:455:486:531:556:607:636:667:728:763:833:890 SD: 0.1593 cents 456:466:498:544:570:622:652:683:746:782:854:912 SD: 0.1423 cents 500:511:546:596:625:682:715:749:818:857:936:1000 SD: 0.1276 cents 586:599:640:699:732:800:838:878:959:1005:1097:1172 SD: 0.1237 cents 588:601:642:701:735:802:841:881:962:1008:1101:1176 SD: 0.1149 cents