Scala analysis: mecaa
{225/224, 441/440} tempering of decad, 72-et version
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 83.333 cents 83.333333 2: 266.667 cents 266.666667 3: 383.333 cents 383.333333 4: 500.000 cents 500.000000 5: 583.333 cents 583.333333 6: 700.000 cents 700.000000 7: 883.333 cents 883.333333 8: 966.667 cents 966.666667 9: 1083.333 cents 1083.333333 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 116.6667 cents 116.6667 1: 83.3333 cents 83.3333 2: 183.3333 cents 183.3333 3: 116.6667 cents 116.6667 4: 116.6667 cents 116.6667 5: 83.3333 cents 83.3333 6: 116.6667 cents 116.6667 7: 183.3333 cents 183.3333 8: 83.3333 cents 83.3333 9: 116.6667 cents 116.6667 10: 116.6667 cents 116.6667
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 83.33333 cents 1: 5 116.66667 cents 1: 2 183.33333 cents 2: 4 200.00000 cents 2: 2 233.33333 cents 2: 2 266.66667 cents 2: 2 300.00000 cents 3: 4 316.66667 cents 3: 5 383.33333 cents 3: 1 416.66667 cents 4: 1 400.00000 cents 4: 1 433.33333 cents 4: 1 466.66667 cents 4: 7 500.00000 cents 5: 5 583.33333 cents 5: 5 616.66667 cents 6: 7 700.00000 cents 6: 1 733.33333 cents 6: 1 766.66667 cents 6: 1 800.00000 cents 7: 1 783.33333 cents 7: 5 816.66667 cents 7: 4 883.33333 cents 8: 2 900.00000 cents 8: 2 933.33333 cents 8: 2 966.66667 cents 8: 4 1000.00000 cents 9: 2 1016.66667 cents 9: 5 1083.33333 cents 9: 3 1116.66667 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.33333 = 10/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 83.3 266.7 383.3 500.0 583.3 700.0 883.3 966.7 1083.3 1200.0 83.3 : 183.3 300.0 416.7 500.0 616.7 800.0 883.3 1000.0 1116.7 1200.0 266.7 : 116.7 233.3 316.7 433.3 616.7 700.0 816.7 933.3 1016.7 1200.0 383.3 : 116.7 200.0 316.7 500.0 583.3 700.0 816.7 900.0 1083.3 1200.0 500.0 : 83.3 200.0 383.3 466.7 583.3 700.0 783.3 966.7 1083.3 1200.0 583.3 : 116.7 300.0 383.3 500.0 616.7 700.0 883.3 1000.0 1116.7 1200.0 700.0 : 183.3 266.7 383.3 500.0 583.3 766.7 883.3 1000.0 1083.3 1200.0 883.3 : 83.3 200.0 316.7 400.0 583.3 700.0 816.7 900.0 1016.7 1200.0 966.7 : 116.7 233.3 316.7 500.0 616.7 733.3 816.7 933.3 1116.7 1200.0 1083.3: 116.7 200.0 383.3 500.0 616.7 700.0 816.7 1000.0 1083.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 83.3333 .. 183.3333 cents 100.00000 cents 83.33333 cents 2: 200.0000 .. 300.0000 cents 100.00000 cents 16.66667 cents 3: 316.6667 .. 416.6667 cents 100.00000 cents 16.66667 cents 4: 400.0000 .. 500.0000 cents 100.00000 cents -16.66667 cents 5: 583.3333 .. 616.6667 cents 33.33333 cents 83.33333 cents 6: 700.0000 .. 800.0000 cents 100.00000 cents 83.33333 cents 7: 783.3333 .. 883.3333 cents 100.00000 cents -16.66667 cents 8: 900.0000 .. 1000.0000 cents 100.00000 cents 16.66667 cents 9: 1016.6667 .. 1116.6667 cents 100.00000 cents 16.66667 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 83.33333 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 183.33333 cents Average / Smallest step : 1.440000 Largest / Average step : 1.527778 Largest / Smallest step : 2.200000 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 : 120.90909 cents, oct.: 1209.09091 cents Scale is not proper Scale is a mode of a 72-tone equal temperament with octave 2/1 degrees: 5 16 23 30 35 42 53 58 65 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: 25 = 15 more = 250.000% Number of contiguous 1-step segments: 0 Scale is fully connected major-minor triadic in 72-tone equal temperament Step pattern alph. order: ABCCACBACC Step pattern size order : SLMMSMLSMM Interval vector is [ 0 0 0 0 3 0 5 0 0 0 2 4 0 2 0 2 0 2 4 0 0 0 5 1 1 1 0 1 0 7 0 0 0 0 5 0 ] Scale is a Constant Structure, by a margin of 16.66667 cents Scale diversity : 1.360557 Lumma stability : 0.333333 Lumma impropriety factor : 0.027778 Rothenberg efficiency : 0.427778 redundancy: 0.572222 Efficiency x scale size : 4.277778 Number of different interval sizes : 30 = 3.33333 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.33333 = 10/3 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 16.66667 cents Most common intervals : 500.00000 cents & inv., amount: 7 Most common triad is 0.0 500.000 700.000 cents, amount: 4 Number of recognisable fifths : 7, average 700.0000 cents Formal octave complements present : 3 = 30.0000% -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
10: 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 23.6878 c. M: 43.3333 c. 12: 1 2 1 1 1 1 2 1 1 1 P B ME S SD: 19.0029 c. M:-33.3333 c. 19: 1 3 2 2 1 2 3 1 2 2 N D3 SD: 11.6933 c. M: 20.1754 c. 24: 2 3 3 2 2 2 4 1 3 2 P SD: 13.9443 c. M:-16.6667 c. 26: 2 4 2 3 2 2 4 2 2 3 P T3 SD: 11.4167 c. M: 21.7949 c. 27: 2 4 3 2 2 3 4 2 2 3 P SD: 10.0922 c. M:-16.6667 c. 29: 2 4 3 3 2 3 4 2 3 3 P D3 SD: 9.9161 c. M: 18.3908 c. 31: 2 5 3 3 2 3 5 2 3 3 N SD: 3.8206 c. M:-6.9892 c. 41: 3 6 4 4 3 4 6 3 4 4 P SD: 2.8888 c. M: 5.2846 c. 72: 5 11 7 7 5 7 11 5 7 7 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: 0.9775 cents 3 x x x 4 x x 5 x x 6 S SD: 0.7359 cents 4 x x 5 x x 6 x 7 x 8 S SD: 1.0418 cents 5 x 6 x x 7 x 8:9 x 10 S SD: 19.8431 cents 6 x 7 x 8 x 9:10 x 11:12 S SD: 5.6831 cents 7 x 8:9 x 10:11 x 12:13:14 S SD: 16.3940 cents 8 x 9:10 x 11:12:13:14:15:16 S SD: 10.3361 cents 9 x x 11:12:13 x 15:16:17:18 SD: 10.4141 cents 10:11:12 x 13:14:15:17 x 19:20 SD: 14.3574 cents 11:12:13:14:15 x 16:18:19:21:22 SD: 12.6072 cents 12:13:14:15:16:17:18:20:21:22:24 S SD: 6.7930 cents 16:17:19:20:21:22:24:27:28:30:32 SD: 6.2025 cents 17:18:20:21:23:24:25:28:30:32:34 SD: 5.7750 cents 18:19:21:22:24:25:27:30:31:34:36 SD: 5.0838 cents 20:21:23:25:27:28:30:33:35:37:40 SD: 4.0188 cents 24:25:28:30:32:34:36:40:42:45:48 SD: 2.4367 cents 36:38:42:45:48:50:54:60:63:67:72 SD: 2.0109 cents 48:50:56:60:64:67:72:80:84:90:96 SD: 1.5579 cents 60:63:70:75:80:84:90:100:105:112:120 S SD: 0.5652 cents 138:145:161:172:184:193:207:230:241:258:276 SD: 0.5218 cents 162:170:189:202:216:227:243:270:283:303:324 SD: 0.3489 cents 185:194:216:231:247:259:277:308:323:346:370 SD: 0.3386 cents 222:233:259:277:296:311:333:370:388:415:444 SD: 0.3012 cents 245:257:286:306:327:343:367:408:428:458:490 SD: 0.2465 cents 287:301:335:358:383:402:430:478:502:537:574 SD: 0.2442 cents 307:322:358:383:410:430:460:511:537:574:614 SD: 0.2277 cents 347:364:405:433:463:486:520:578:606:649:694 SD: 0.2018 cents 367:385:428:458:490:514:550:611:641:686:734 SD: 0.1777 cents 407:427:475:508:543:570:610:678:711:761:814 SD: 0.1694 cents 427:448:498:533:570:598:640:711:746:798:854 SD: 0.1542 cents 469:492:547:585:626:657:703:781:820:877:938 SD: 0.1417 cents 529:555:617:660:706:741:793:881:925:989:1058 SD: 0.1323 cents