Scala analysis: magic10
Magic[10] in 41-et tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 263.415 cents 263.414634 2: 321.951 cents 321.951220 3: 380.488 cents 380.487805 4: 439.024 cents 439.024390 5: 702.439 cents 702.439024 6: 760.976 cents 760.975610 7: 819.512 cents 819.512195 8: 1082.927 cents 1082.926829 9: 1141.463 cents 1141.463415 10: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 58.5366 cents 58.5366 1: 263.4146 cents 263.4146 2: 58.5366 cents 58.5366 3: 58.5366 cents 58.5366 4: 58.5366 cents 58.5366 5: 263.4146 cents 263.4146 6: 58.5366 cents 58.5366 7: 58.5366 cents 58.5366 8: 263.4146 cents 263.4146 9: 58.5366 cents 58.5366 10: 58.5366 cents 58.5366
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 58.53659 cents 1: 3 263.41463 cents 2: 4 117.07317 cents 2: 6 321.95122 cents 3: 1 175.60976 cents 3: 9 380.48781 cents 4: 8 439.02439 cents 4: 2 643.90244 cents 5: 5 497.56098 cents 5: 5 702.43902 cents 6: 2 556.09756 cents 6: 8 760.97561 cents 7: 9 819.51220 cents 7: 1 1024.39024 cents 8: 6 878.04878 cents 8: 4 1082.92683 cents 9: 3 936.58537 cents 9: 7 1141.46341 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 9 10 0.0 : 263.4 322.0 380.5 439.0 702.4 761.0 819.5 1082.9 1141.5 1200.0 263.4 : 58.5 117.1 175.6 439.0 497.6 556.1 819.5 878.0 936.6 1200.0 322.0 : 58.5 117.1 380.5 439.0 497.6 761.0 819.5 878.0 1141.5 1200.0 380.5 : 58.5 322.0 380.5 439.0 702.4 761.0 819.5 1082.9 1141.5 1200.0 439.0 : 263.4 322.0 380.5 643.9 702.4 761.0 1024.4 1082.9 1141.5 1200.0 702.4 : 58.5 117.1 380.5 439.0 497.6 761.0 819.5 878.0 936.6 1200.0 761.0 : 58.5 322.0 380.5 439.0 702.4 761.0 819.5 878.0 1141.5 1200.0 819.5 : 263.4 322.0 380.5 643.9 702.4 761.0 819.5 1082.9 1141.5 1200.0 1082.9: 58.5 117.1 380.5 439.0 497.6 556.1 819.5 878.0 936.6 1200.0 1141.5: 58.5 322.0 380.5 439.0 497.6 761.0 819.5 878.0 1141.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 58.5366 .. 263.4146 cents 204.87805 cents 58.53659 cents 2: 117.0732 .. 321.9512 cents 204.87805 cents -146.34146 cents 3: 175.6098 .. 380.4878 cents 204.87805 cents -146.34146 cents 4: 439.0244 .. 643.9024 cents 204.87805 cents 58.53659 cents 5: 497.5610 .. 702.4390 cents 204.87805 cents -146.34146 cents 6: 556.0976 .. 760.9756 cents 204.87805 cents -146.34146 cents 7: 819.5122 .. 1024.3902 cents 204.87805 cents 58.53659 cents 8: 878.0488 .. 1082.9268 cents 204.87805 cents -146.34146 cents 9: 936.5854 .. 1141.4634 cents 204.87805 cents -146.34146 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 58.53658 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 263.41463 cents Average / Smallest step : 2.050000 Largest / Average step : 2.195122 Largest / Smallest step : 4.500000 Median interval of one step : 58.53659 cents, amount: 7 Most common interval of one step : 58.53659 cents, amount: 7 Least squares average step : 126.11973 cents, oct.: 1261.19734 cents Scale is not proper Scale has Myhill's property chromas: 204.87805 cents and 146.34146 cents, ratio: 1.400000 generators: 3 of 380.48781 cents and 7 of 819.51219 cents ET pair of linear temperament : 19&22 Scale is distributional even Scale is a mode of a 41-tone equal temperament with octave 1200.000 cents degrees: 9 11 13 15 24 26 28 37 39 41 generators: 13 and 28 Number of contiguous 1-step segments: 0 Scale is fully connected major-minor triadic in 41-tone equal temperament Step pattern alph. order: ABBBABBABB Step pattern size order : LSSSLSSLSS Interval vector is [ 0 7 0 4 0 1 0 0 3 0 6 0 9 0 8 0 5 0 2 0 ] Scale is a Constant Structure, by a margin of 58.53658 cents Scale diversity : 1.266526 Lumma stability : 0.195122 Lumma impropriety factor : 0.512195 Rothenberg efficiency : 0.733333 redundancy: 0.266667 Efficiency x scale size : 7.333333 Number of different interval sizes : 18 = 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 : 58.53658 cents Most common intervals : 380.48781 cents & inv., amount: 9 Scale is a chain of 5 triads 0.0 497.561 819.512 cents Most common triad is 0.0 380.488 819.512 cents, amount: 8 Number of recognisable fifths : 5, average 702.4390 cents Formal octave complements present : 5 = 50.0000% Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 7-8 -- Rational properties --
FIT/MODE
10: 2 1 0 1 2 0 1 2 1 0 N D3 SD: 31.5229 c. M:-58.5366 c. 11: 2 1 0 1 2 1 0 3 0 1 N SD: 35.9940 c. M: 55.8758 c. 12: 3 0 1 0 3 1 0 3 0 1 N D3 SD: 27.6483 c. M: 41.4634 c. 13: 3 1 0 1 3 0 1 3 0 1 N SD: 25.9547 c. M:-47.2795 c. 14: 3 1 0 1 3 1 1 3 0 1 N SD: 23.5134 c. M: 37.6307 c. 16: 3 1 1 1 3 1 1 3 1 1 N M DE SD: 20.8969 c. M: 38.4146 c. 17: 4 1 0 1 4 1 1 3 1 1 N SD: 20.1368 c. M:-30.9900 c. 18: 4 1 1 1 4 0 1 4 1 1 N SD: 19.2736 c. M:-30.8943 c. 19: 4 1 1 1 4 1 1 4 1 1 N M DE SD: 5.8658 c. M: 10.7831 c. Magic-10 22: 5 1 1 1 5 1 1 5 1 1 N M DE SD: 5.0659 c. M:-9.3126 c. Magic-10 41: 9 2 2 2 9 2 2 9 2 2 N M DE SD: 0.0000 c. M: 0.0000 c. Magic-10
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x x x x 4 S SD: 0.2420 cents 3 x x x 4 x x 5 x x 6 S SD: 29.2280 cents 4 x x 5 x 6 x x 7 x 8 S SD: 28.5626 cents 5 x 6 x x x x 8:9 x 10 S SD: 16.4732 cents 6:7 x x 8:9 x 10:11 x 12 S SD: 15.6589 cents 7:8 x x 9 x 11 x 13 x 14 SD: 8.1091 cents 8:9 x 10 x 12 x 13:15 x 16 SD: 10.6003 cents 9:10:11 x 12 x 14 x 17 x 18 SD: 17.5104 cents 10 x 12 x 13:15 x 16:19 x 20 SD: 5.5379 cents 11:13 x x 14 x 17:18 x 21:22 SD: 8.7567 cents 12:14 x 15 x 18 x 19:22:23:24 SD: 6.3500 cents 13:15 x 16:17 x 20:21:24:25:26 SD: 5.9011 cents 14:16:17 x 18:21:22 x 26:27:28 SD: 5.3979 cents 15:17:18:19 x x 23:24:28:29:30 SD: 7.4263 cents 16 x 19:20:21:24:25:26:30:31:32 SD: 5.2805 cents 17:20 x 21:22 x 26:27:32:33:34 SD: 5.2678 cents 18:21:22 x 23:27:28:29:34:35:36 SD: 4.0858 cents 19:22:23:24 x x 29:31:36:37:38 SD: 6.9237 cents 20:23:24:25:26:30:31:32:37:39:40 SD: 3.6613 cents 22:26 x 27:28:33:34:35:41:43:44 SD: 5.5327 cents 23:27:28:29:30:35:36:37:43:44:46 SD: 5.0829 cents 24:28:29:30:31:36:37:39:45:46:48 SD: 3.0471 cents 30:35:36:37:39:45:47:48:56:58:60 SD: 2.9832 cents 36:42:43:45:46:54:56:58:67:70:72 SD: 2.5928 cents 38:44:46:47:49:57:59:61:71:73:76 SD: 2.1301 cents 44:51:53:55:57:66:68:71:82:85:88 SD: 1.8447 cents 48:56:58:60:62:72:74:77:90:93:96 SD: 1.6493 cents 54:63:65:67:70:81:84:87:101:104:108 SD: 1.6390 cents 56:65:67:70:72:84:87:90:105:108:112 SD: 1.6281 cents 60:70:72:75:77:90:93:96:112:116:120 SD: 1.3480 cents 69:80:83:86:89:104:107:111:129:133:138 SD: 1.2917 cents 73:85:88:91:94:110:113:117:136:141:146 SD: 1.1201 cents 74:86:89:92:95:111:115:119:138:143:148 SD: 1.0148 cents 93:108:112:116:120:140:144:149:174:180:186 SD: 0.9857 cents 94:109:113:117:121:141:146:151:176:182:188 SD: 0.9167 cents 98:114:118:122:126:147:152:157:183:189:196 SD: 0.7551 cents 114:133:137:142:147:171:177:183:213:220:228 SD: 0.6302 cents 122:142:147:152:157:183:189:196:228:236:244 SD: 0.4384 cents 152:177:183:189:196:228:236:244:284:294:304 SD: 0.3781 cents 170:198:205:212:219:255:264:273:318:329:340 SD: 0.3745 cents 212:247:255:264:273:318:329:340:396:410:424 SD: 0.3629 cents 225:262:271:280:290:338:349:361:421:435:450 SD: 0.3629 cents 236:275:284:294:304:354:366:379:441:456:472 SD: 0.2878 cents 268:312:323:334:345:402:416:430:501:518:536 SD: 0.2608 cents 274:319:330:341:353:411:425:440:512:530:548 SD: 0.2391 cents 284:331:342:354:366:426:441:456:531:549:568 SD: 0.2308 cents 304:354:366:379:392:456:472:488:568:588:608 SD: 0.2223 cents 322:375:388:401:415:483:500:517:602:623:644 SD: 0.1937 cents 382:445:460:476:492:573:593:613:714:739:764 SD: 0.1904 cents 391:455:471:487:504:587:607:628:731:756:782 SD: 0.1837 cents 395:460:476:492:509:593:613:634:738:764:790 SD: 0.1810 cents 406:473:489:506:523:609:630:652:759:785:812 SD: 0.1621 cents 420:489:506:523:541:630:652:674:785:812:840 SD: 0.1540 cents 426:496:513:531:549:639:661:684:796:824:852 SD: 0.1515 cents 451:525:543:562:581:677:700:724:843:872:902 SD: 0.1262 cents 529:616:637:659:682:794:821:849:989:1023:1058 SD: 0.1254 cents 558:650:672:695:719:837:866:896:1043:1079:1116 SD: 0.1106 cents