Scala analysis: magic7
Magic[7] in 41-et tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 321.951 cents 321.951220 2: 380.488 cents 380.487805 3: 702.439 cents 702.439024 4: 760.976 cents 760.975610 5: 819.512 cents 819.512195 6: 1141.463 cents 1141.463415 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 58.5366 cents 58.5366 1: 321.9512 cents 321.9512 2: 58.5366 cents 58.5366 3: 321.9512 cents 321.9512 4: 58.5366 cents 58.5366 5: 58.5366 cents 58.5366 6: 321.9512 cents 321.9512 7: 58.5366 cents 58.5366
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 58.53658 cents 1: 3 321.95122 cents 2: 1 117.07317 cents 2: 6 380.48781 cents 3: 5 439.02439 cents 3: 2 702.43902 cents 4: 2 497.56098 cents 4: 5 760.97561 cents 5: 6 819.51220 cents 5: 1 1082.92683 cents 6: 3 878.04878 cents 6: 4 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 0.0 : 322.0 380.5 702.4 761.0 819.5 1141.5 1200.0 322.0 : 58.5 380.5 439.0 497.6 819.5 878.0 1200.0 380.5 : 322.0 380.5 439.0 761.0 819.5 1141.5 1200.0 702.4 : 58.5 117.1 439.0 497.6 819.5 878.0 1200.0 761.0 : 58.5 380.5 439.0 761.0 819.5 1141.5 1200.0 819.5 : 322.0 380.5 702.4 761.0 1082.9 1141.5 1200.0 1141.5: 58.5 380.5 439.0 761.0 819.5 878.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 58.5366 .. 321.9512 cents 263.41464 cents 58.53658 cents 2: 117.0732 .. 380.4878 cents 263.41463 cents -204.87805 cents 3: 439.0244 .. 702.4390 cents 263.41463 cents 58.53658 cents 4: 497.5610 .. 760.9756 cents 263.41463 cents -204.87805 cents 5: 819.5122 .. 1082.9268 cents 263.41463 cents 58.53659 cents 6: 878.0488 .. 1141.4634 cents 263.41463 cents -204.87805 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 58.53658 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 321.95122 cents Average / Smallest step : 2.928571 Largest / Average step : 1.878049 Largest / Smallest step : 5.500000 Median interval of one step : 58.53658 cents, amount: 4 Most common interval of one step : 58.53658 cents, amount: 4 Least squares average step : 182.71777 cents, oct.: 1279.02439 cents Scale is not proper Scale has Myhill's property chromas: 263.41464 cents and 204.87805 cents, ratio: 1.285714 generators: 2 of 380.48781 cents and 5 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: 11 13 24 26 28 39 41 generators: 13 and 28 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABBAB Step pattern size order : LSLSSLS Interval vector is [ 0 4 0 1 0 0 0 0 0 0 3 0 6 0 5 0 2 0 0 0 ] Scale is a Constant Structure, by a margin of 58.53658 cents Scale diversity : 1.128539 Lumma stability : 0.195122 Lumma impropriety factor : 0.512195 Rothenberg efficiency : 0.761905 redundancy: 0.238095 Efficiency x scale size : 5.333333 Number of different interval sizes : 12 = 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: 6 Scale is a chain of 3 triads 0.0 380.488 760.976 cents Most common triad is 0.0 380.488 819.512 cents, amount: 5 Number of recognisable fifths : 2, average 702.4390 cents Scale contains two identical disjunct "tetrachords" of 3 notes Formal octave complements present : 3 = 42.8571% Limited inverse transpositions : 1 Inversional symmetry on degrees : 4 Inversional symmetry on intervals : 0-1 -- Rational properties --
FIT/MODE
7: 2 0 2 0 1 2 0 N T3 SD: 42.4932 c. M: 75.2613 c. 10: 3 0 3 0 1 3 0 N T3 SD: 33.1687 c. M:-58.5366 c. 11: 3 0 3 1 0 3 1 N T3 SD: 39.3499 c. M: 55.8758 c. 12: 3 1 3 0 1 3 1 N T3 SD: 30.9065 c. M: 60.9756 c. 13: 3 1 3 1 1 3 1 N M DE S SD: 31.8397 c. M: 56.2852 c. 14: 4 0 4 1 0 4 1 N T3 SD: 27.4974 c. M: 48.0836 c. 15: 4 1 4 1 0 4 1 N T3 SD: 20.8985 c. M:-39.0244 c. 16: 4 1 4 1 1 4 1 N M DE S SD: 15.5219 c. M: 27.4390 c. 19: 5 1 5 1 1 5 1 N M DE S SD: 4.3570 c. M: 7.7022 c. Oljare Augmented, Magic-7 22: 6 1 6 1 1 6 1 N M DE S SD: 3.7629 c. M:-6.6519 c. Magic-7 41: 11 2 11 2 2 11 2 N M DE S SD: 0.0000 c. M: 0.0000 c. Magic-7
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x x 4 S SD: 0.2420 cents 3 x 4 x x 5 x 6 S SD: 44.7521 cents 4 x 5:6 x x x 8 S SD: 1.9487 cents 5:6 x x x 8 x 10 S SD: 2.8627 cents 6:7 x 9 x 10 x 12 SD: 21.2708 cents 7:8:9 x 11 x x 14 SD: 27.0234 cents 8 x 10:12 x 13:15:16 SD: 11.4987 cents 9:11 x x 14 x 17:18 SD: 11.9822 cents 10:12 x 15 x 16:19:20 SD: 6.2926 cents 11:13:14 x 17:18:21:22 SD: 10.6388 cents 12:14:15:18 x 19:23:24 SD: 10.3698 cents 13 x 16 x 20:21:25:26 SD: 5.9175 cents 14:17 x 21:22 x 27:28 SD: 5.2299 cents 15:18:19 x 23:24:29:30 SD: 6.1020 cents 16:19:20:24:25:26:31:32 SD: 4.9930 cents 17:20:21 x 26:27:33:34 SD: 8.9770 cents 18:22 x 27:28:29:35:36 SD: 4.7054 cents 19:23:24 x 29:31:37:38 SD: 8.2071 cents 20:24:25:30:31:32:39:40 SD: 2.5922 cents 22 x 27:33:34:35:43:44 SD: 6.0650 cents 24:29:30:36:37:39:46:48 SD: 4.2175 cents 25:30:31:38:39:40:48:50 SD: 4.2113 cents 28:34:35:42:43:45:54:56 SD: 3.4777 cents 33:40:41:50:51:53:64:66 SD: 3.2365 cents 34:41:42:51:53:55:66:68 SD: 3.1864 cents 36:43:45:54:56:58:70:72 SD: 2.8165 cents 38:46:47:57:59:61:73:76 SD: 2.7090 cents 40:48:50:60:62:64:77:80 SD: 1.8696 cents 44:53:55:66:68:71:85:88 SD: 1.8570 cents 54:65:67:81:84:87:104:108 SD: 1.7525 cents 58:70:72:87:90:93:112:116 SD: 1.1119 cents 74:89:92:111:115:119:143:148 SD: 0.8250 cents 78:94:97:117:121:125:151:156 SD: 0.7203 cents 94:113:117:141:146:151:182:188 SD: 0.6655 cents 118:142:147:177:183:189:228:236 SD: 0.6591 cents 122:147:152:183:189:196:236:244 SD: 0.5180 cents 152:183:189:228:236:244:294:304 SD: 0.5043 cents 170:205:212:255:264:273:329:340 SD: 0.4914 cents 180:217:224:270:279:289:348:360 SD: 0.4901 cents 190:229:237:285:295:305:367:380 SD: 0.4528 cents 192:231:239:288:298:308:371:384 SD: 0.4142 cents 196:236:244:294:304:315:379:392 SD: 0.3729 cents 216:260:269:324:335:347:418:432 SD: 0.3688 cents 236:284:294:354:366:379:456:472 SD: 0.3405 cents 244:294:304:366:379:392:472:488 SD: 0.3218 cents 264:318:329:396:410:424:510:528 SD: 0.3095 cents 268:323:334:402:416:430:518:536 SD: 0.2680 cents 284:342:354:426:441:456:549:568 SD: 0.2102 cents 342:412:426:513:531:549:661:684 SD: 0.1708 cents 362:436:451:543:562:581:700:724 SD: 0.1238 cents 484:583:603:726:751:777:936:968 SD: 0.1088 cents 558:672:695:837:866:896:1079:1116 SD: 0.1075 cents