Scala analysis: squares8
Squares[8] in 31et
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 77.419 cents 77.419355 2: 154.839 cents 154.838710 3: 425.806 cents 425.806452 4: 503.226 cents 503.225806 5: 580.645 cents 580.645161 6: 851.613 cents 851.612903 7: 929.032 cents 929.032258 8: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 270.9677 cents 270.9677 1: 77.4194 cents 77.4194 2: 77.4194 cents 77.4194 3: 270.9677 cents 270.9677 4: 77.4194 cents 77.4194 5: 77.4194 cents 77.4194 6: 270.9677 cents 270.9677 7: 77.4194 cents 77.4194 8: 270.9677 cents 270.9677
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 77.41935 cents 1: 3 270.96774 cents 2: 2 154.83871 cents 2: 6 348.38710 cents 3: 7 425.80645 cents 3: 1 619.35484 cents 4: 4 503.22581 cents 4: 4 696.77419 cents 5: 1 580.64516 cents 5: 7 774.19355 cents 6: 6 851.61290 cents 6: 2 1045.16129 cents 7: 3 929.03226 cents 7: 5 1122.58065 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 77.4 154.8 425.8 503.2 580.6 851.6 929.0 1200.0 77.4 : 77.4 348.4 425.8 503.2 774.2 851.6 1122.6 1200.0 154.8 : 271.0 348.4 425.8 696.8 774.2 1045.2 1122.6 1200.0 425.8 : 77.4 154.8 425.8 503.2 774.2 851.6 929.0 1200.0 503.2 : 77.4 348.4 425.8 696.8 774.2 851.6 1122.6 1200.0 580.6 : 271.0 348.4 619.4 696.8 774.2 1045.2 1122.6 1200.0 851.6 : 77.4 348.4 425.8 503.2 774.2 851.6 929.0 1200.0 929.0 : 271.0 348.4 425.8 696.8 774.2 851.6 1122.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 77.4194 .. 270.9677 cents 193.54839 cents 77.41935 cents 2: 154.8387 .. 348.3871 cents 193.54839 cents -116.12903 cents 3: 425.8065 .. 619.3548 cents 193.54839 cents 77.41935 cents 4: 503.2258 .. 696.7742 cents 193.54839 cents -116.12903 cents 5: 580.6452 .. 774.1935 cents 193.54839 cents -116.12903 cents 6: 851.6129 .. 1045.1613 cents 193.54839 cents 77.41935 cents 7: 929.0323 .. 1122.5806 cents 193.54839 cents -116.12903 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 77.41935 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 270.96774 cents Average / Smallest step : 1.937500 Largest / Average step : 1.806452 Largest / Smallest step : 3.500000 Median interval of one step : 77.41935 cents, amount: 5 Most common interval of one step : 77.41935 cents, amount: 5 Least squares average step : 136.24288 cents, oct.: 1089.94307 cents Scale is not proper Scale has Myhill's property chromas: 193.54839 cents and 116.12903 cents, ratio: 1.666667 generators: 3 of 425.80645 cents and 774.19355 cents ET pair of linear temperament : 14&17 Scale is distributional even Scale is a mode of a 31-tone equal temperament with octave 1200.000 cents degrees: 2 4 11 13 15 22 24 31 generators: 11 and 20 Number of contiguous 1-step segments: 0 Step pattern alph. order: AABAABAB Step pattern size order : SSLSSLSL Interval vector is [ 0 5 0 2 0 0 3 0 6 0 7 0 4 0 1 ] Scale is a Constant Structure, by a margin of 38.70968 cents Scale diversity : 1.280768 Lumma stability : 0.258065 Lumma impropriety factor : 0.354839 Rothenberg efficiency : 0.750000 redundancy: 0.250000 Efficiency x scale size : 6.000000 Number of different interval sizes : 14 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 38.70968 cents Most common intervals : 425.80645 cents & inv., amount: 7 Scale is a chain of 4 triads 0.0 77.419 774.194 cents Most common triad is 0.0 425.806 774.194 cents, amount: 6 Number of recognisable fifths : 4, average 696.7742 cents Formal octave complements present : 1 = 12.5000% Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 6-7 -- Rational properties --
FIT/MODE
8: 1 0 2 0 1 2 0 2 N D3 SD: 39.1607 c. M:-72.5806 c. 9: 0 1 2 1 0 2 1 2 N D3 SD: 40.2329 c. M: 77.4194 c. 10: 1 0 3 0 1 2 1 2 N SD: 31.5668 c. M:-54.1935 c. 13: 1 0 3 1 1 3 1 3 N SD: 35.8095 c. M: 62.5310 c. 14: 1 1 3 1 1 3 1 3 N M DE SD: 11.5667 c. M:-19.3548 c. Triolic Diatonic 17: 1 1 4 1 1 4 1 4 N M DE SD: 9.5255 c. M: 15.9393 c. 31: 2 2 7 2 2 7 2 7 N M DE SD: 0.0000 c. M:-0.0000 c.
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: 60.6549 cents 3 x x x 4 x 5 x 6 S SD: 11.0510 cents 4 x x 5 x 6 x 7:8 S SD: 33.4097 cents 5 x x 6 x 7:8:9:10 S SD: 29.2724 cents 6 x 7 x 8 x 10 x 12 S SD: 29.2087 cents 7 x 8:9 x 10:11:12:14 S SD: 18.3068 cents 8 x 9:10 x 11:13:14:16 SD: 13.4724 cents 9 x 10 x 12:13:15 x 18 SD: 14.1306 cents 10 x 11:13 x 14:16:17:20 SD: 8.2667 cents 11 x 12:14:15 x 18:19:22 SD: 6.4966 cents 12 x 13:15:16:17:20:21:24 SD: 10.1083 cents 13 x 14:17 x 18:21:22:26 SD: 9.5496 cents 14 x 15:18:19:20:23:24:28 SD: 8.3578 cents 15:16 x 19:20:21:25:26:30 SD: 7.9459 cents 17:18:19:22:23:24:28:29:34 SD: 7.0155 cents 18:19:20:23:24:25:29:31:36 SD: 5.6074 cents 20:21:22:26:27:28:33:34:40 SD: 4.9584 cents 21:22:23:27:28:29:34:36:42 SD: 3.8078 cents 33:35:36:42:44:46:54:56:66 SD: 3.8028 cents 35:37:38:45:47:49:57:60:70 SD: 3.3510 cents 39:41:43:50:52:55:64:67:78 SD: 3.1550 cents 41:43:45:52:55:57:67:70:82 SD: 2.5465 cents 42:44:46:54:56:59:69:72:84 SD: 2.0458 cents 60:63:66:77:80:84:98:103:120 SD: 2.0440 cents 61:64:67:78:82:85:100:104:122 SD: 1.9978 cents 62:65:68:79:83:87:101:106:124 SD: 1.6237 cents 63:66:69:81:84:88:103:108:126 SD: 1.5361 cents 65:68:71:83:87:91:106:111:130 SD: 0.8655 cents 86:90:94:110:115:120:141:147:172 SD: 0.7635 cents 107:112:117:137:143:150:175:183:214 SD: 0.6347 cents 128:134:140:164:171:179:209:219:256 SD: 0.6344 cents 148:155:162:189:198:207:242:253:296 SD: 0.5094 cents 151:158:165:193:202:211:247:258:302 SD: 0.3720 cents 244:255:267:312:326:341:399:417:488 SD: 0.3551 cents 258:270:282:330:345:361:422:441:516 SD: 0.2582 cents 266:278:291:340:356:372:435:455:532 SD: 0.2534 cents 329:344:360:421:440:460:538:563:658 SD: 0.2357 cents 352:368:385:450:471:492:576:602:704 SD: 0.2311 cents 373:390:408:477:499:522:610:638:746 SD: 0.1826 cents 394:412:431:504:527:551:644:674:788 SD: 0.1657 cents 459:480:502:587:614:642:751:785:918 SD: 0.1194 cents 480:502:525:614:642:671:785:821:960 SD: 0.1185 cents 524:548:573:670:701:733:857:896:1048 SD: 0.1089 cents 545:570:596:697:729:762:891:932:1090 SD: 0.1083 cents