Scala analysis: mir8
tet3a in 72-et
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 116.667 cents 116.666667 2: 316.667 cents 316.666667 3: 433.333 cents 433.333333 4: 583.333 cents 583.333333 5: 700.000 cents 700.000000 6: 816.667 cents 816.666667 7: 933.333 cents 933.333333 8: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 266.6667 cents 266.6667 1: 116.6667 cents 116.6667 2: 200.0000 cents 200.0000 3: 116.6667 cents 116.6667 4: 150.0000 cents 150.0000 5: 116.6667 cents 116.6667 6: 116.6667 cents 116.6667 7: 116.6667 cents 116.6667 8: 266.6667 cents 266.6667
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 116.66667 cents 1: 1 150.00000 cents 1: 1 200.00000 cents 1: 1 266.66667 cents 2: 2 233.33333 cents 2: 2 266.66667 cents 2: 2 316.66667 cents 2: 2 383.33333 cents 3: 1 350.00000 cents 3: 2 383.33333 cents 3: 1 433.33333 cents 3: 1 466.66667 cents 3: 2 500.00000 cents 3: 1 583.33333 cents 4: 2 500.00000 cents 4: 2 583.33333 cents 4: 2 616.66667 cents 4: 2 700.00000 cents 5: 1 616.66667 cents 5: 2 700.00000 cents 5: 1 733.33333 cents 5: 1 766.66667 cents 5: 2 816.66667 cents 5: 1 850.00000 cents 6: 2 816.66667 cents 6: 2 883.33333 cents 6: 2 933.33333 cents 6: 2 966.66667 cents 7: 1 933.33333 cents 7: 1 1000.00000 cents 7: 1 1050.00000 cents 7: 5 1083.33333 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.57143 = 32/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 116.7 316.7 433.3 583.3 700.0 816.7 933.3 1200.0 116.7 : 200.0 316.7 466.7 583.3 700.0 816.7 1083.3 1200.0 316.7 : 116.7 266.7 383.3 500.0 616.7 883.3 1000.0 1200.0 433.3 : 150.0 266.7 383.3 500.0 766.7 883.3 1083.3 1200.0 583.3 : 116.7 233.3 350.0 616.7 733.3 933.3 1050.0 1200.0 700.0 : 116.7 233.3 500.0 616.7 816.7 933.3 1083.3 1200.0 816.7 : 116.7 383.3 500.0 700.0 816.7 966.7 1083.3 1200.0 933.3 : 266.7 383.3 583.3 700.0 850.0 966.7 1083.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 116.6667 .. 266.6667 cents 150.00000 cents 116.66667 cents 2: 233.3333 .. 383.3333 cents 150.00000 cents -33.33333 cents 3: 350.0000 .. 583.3333 cents 233.33333 cents -33.33333 cents 4: 500.0000 .. 700.0000 cents 200.00000 cents -83.33333 cents 5: 616.6667 .. 850.0000 cents 233.33333 cents -83.33333 cents 6: 816.6667 .. 966.6667 cents 150.00000 cents -33.33333 cents 7: 933.3333 .. 1083.3333 cents 150.00000 cents -33.33333 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 116.66667 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 266.66667 cents Average / Smallest step : 1.285714 Largest / Average step : 1.777778 Largest / Smallest step : 2.285714 Median interval of one step : 116.66667 cents, amount: 5 Most common interval of one step : 116.66667 cents, amount: 5 Least squares average step : 141.74837 cents, oct.: 1133.98693 cents Scale is not proper Scale is a mode of a 72-tone equal temperament with octave 1200.000 cents degrees: 7 19 26 35 42 49 56 72 Least number of segments generator : 37 of 616.667 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 65 of 1083.333 cents and inv. generated superset size: 15 = 7 more = 187.500% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABACAAAD Step pattern size order : ACABAAAD Interval vector is [ 0 0 0 0 0 0 5 0 1 0 0 1 0 2 0 3 0 0 2 0 1 0 4 0 0 1 0 1 0 4 0 0 0 0 3 0 ] Scale is not a Constant Structure Scale diversity : 1.435476 Lumma stability : 0.194444 Lumma impropriety factor : 0.250000 Rothenberg efficiency : 0.444643 redundancy: 0.555357 Efficiency x scale size : 3.557143 Number of different interval sizes : 24 = 3.42857 / class Number of one step interval sizes : 4 Highest interval variety : 6 Mean interval variety : 4.57143 = 32/7 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 33.33333 cents Most common intervals : 116.66667 cents & inv., amount: 5 Number of recognisable fifths : 4, average 700.0000 cents Formal octave complements present : 1 = 12.5000% -- Rational properties --
FIT/MODE
8: 1 1 1 1 1 0 1 2 N T3 SD: 35.3553 c. M: 66.6667 c. 9: 1 1 1 1 1 1 1 2 P M ME SD: 31.1805 c. M: 50.0000 c. 10: 1 2 1 1 1 1 1 2 N D3 SD: 27.3861 c. M:-46.6667 c. 12: 1 2 1 2 1 1 1 3 N SD: 20.4124 c. M: 33.3333 c. 19: 2 3 2 2 2 2 2 4 N SD: 8.9241 c. M: 14.9123 c. 22: 2 4 2 3 2 2 2 5 N SD: 8.5038 c. M:-16.6667 c. 31: 3 5 3 4 3 3 3 7 N SD: 4.4171 c. M: 7.5269 c. 41: 4 7 4 5 4 4 4 9 N SD: 3.3398 c. M:-5.6911 c. 53: 5 9 5 7 5 5 5 12 N SD: 3.1992 c. M:-5.3459 c. 72: 7 12 7 9 7 7 7 16 N SD: 0.0000 c. M:-0.0000 c. Three Tetrads
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x x 4 S SD: 0.9775 cents 3 x x 4 x x x 5:6 S SD: 27.0516 cents 4 x x 5 x 6 x 7:8 S SD: 14.7360 cents 5 x 6 x 7 x 8:9:10 S SD: 16.8652 cents 6 x 7:8 x 9 x 10:12 S SD: 19.0468 cents 7 x 8:9:10 x 11:12:14 S SD: 16.3695 cents 8:9 x 10:11:12:13:14:16 S SD: 16.0866 cents 9:10:11:12:13 x 14:15:18 S SD: 18.8278 cents 10:11:12:13:14:15:16:17:20 SD: 6.8497 cents 14:15:17:18:20:21:22:24:28 SD: 6.5286 cents 15:16:18:19:21:22:24:26:30 SD: 6.0451 cents 18:19:22:23:25:27:29:31:36 SD: 5.4723 cents 20:21:24:26:28:30:32:34:40 SD: 5.1585 cents 24:26:29:31:34:36:38:41:48 SD: 4.9527 cents 25:27:30:32:35:37:40:43:50 SD: 3.5457 cents 28:30:34:36:39:42:45:48:56 SD: 2.8214 cents 40:43:48:51:56:60:64:69:80 SD: 2.3767 cents 42:45:50:54:59:63:67:72:84 SD: 2.2573 cents 45:48:54:58:63:67:72:77:90 SD: 1.7767 cents 56:60:67:72:78:84:90:96:112 SD: 1.6246 cents 60:64:72:77:84:90:96:103:120 SD: 0.8455 cents 70:75:84:90:98:105:112:120:140 SD: 0.6280 cents 130:139:156:167:182:195:208:223:260 SD: 0.4989 cents 144:154:173:185:202:216:231:247:288 SD: 0.4826 cents 169:181:203:217:237:253:271:290:338 SD: 0.4789 cents 189:202:227:243:265:283:303:324:378 SD: 0.4003 cents 214:229:257:275:300:321:343:367:428 SD: 0.3417 cents 229:245:275:294:321:343:367:393:458 SD: 0.2980 cents 259:277:311:333:363:388:415:444:518 SD: 0.2715 cents 299:320:359:384:419:448:479:513:598 SD: 0.2386 cents 414:443:497:532:580:620:664:710:828 SD: 0.2368 cents 429:459:515:551:601:643:688:736:858 SD: 0.2214 cents 444:475:533:570:622:665:712:761:888 SD: 0.1982 cents 474:507:569:609:664:710:760:813:948 SD: 0.1634 cents 504:539:605:647:706:755:808:864:1008 SD: 0.1595 cents 514:550:617:660:720:770:824:881:1028 SD: 0.1386 cents 544:582:653:699:762:815:872:933:1088 SD: 0.1368 cents 574:614:689:737:804:860:920:984:1148 SD: 0.1030 cents