Scala analysis: supermagic11
A distributionally even scale in supermagic temperament, abacbabcabc
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 85.700 cents 85.700000 2: 144.810 cents 144.810000 3: 321.690 cents 321.690000 4: 380.800 cents 380.800000 5: 466.500 cents 466.500000 6: 643.380 cents 643.380000 7: 702.490 cents 702.490000 8: 788.190 cents 788.190000 9: 965.070 cents 965.070000 10: 1024.180 cents 1024.180000 11: 1201.060 cents 1201.060000
SHOW/INTERVAL
0: 176.8800 cents 176.8800 1: 85.7000 cents 85.7000 2: 59.1100 cents 59.1100 3: 176.8800 cents 176.8800 4: 59.1100 cents 59.1100 5: 85.7000 cents 85.7000 6: 176.8800 cents 176.8800 7: 59.1100 cents 59.1100 8: 85.7000 cents 85.7000 9: 176.8800 cents 176.8800 10: 59.1100 cents 59.1100 11: 176.8800 cents 176.8800
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 59.11000 cents 1: 3 85.70000 cents 1: 4 176.88000 cents 2: 3 144.81000 cents 2: 5 235.99000 cents 2: 3 262.58000 cents 3: 1 295.10000 cents 3: 9 321.69000 cents 3: 1 412.87000 cents 4: 5 380.80000 cents 4: 1 407.39000 cents 4: 5 498.57000 cents 5: 2 466.50000 cents 5: 7 557.68000 cents 5: 2 584.27000 cents 6: 2 616.79000 cents 6: 7 643.38000 cents 6: 2 734.56000 cents 7: 5 702.49000 cents 7: 1 793.67000 cents 7: 5 820.26000 cents 8: 1 788.19000 cents 8: 9 879.37000 cents 8: 1 905.96000 cents 9: 3 938.48000 cents 9: 5 965.07000 cents 9: 3 1056.25000 cents 10: 4 1024.18000 cents 10: 3 1115.36000 cents 10: 4 1141.95000 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 0.0 : 85.7 144.8 321.7 380.8 466.5 643.4 702.5 788.2 965.1 1024.2 1201.1 85.7 : 59.1 236.0 295.1 380.8 557.7 616.8 702.5 879.4 938.5 1115.4 1201.1 144.8 : 176.9 236.0 321.7 498.6 557.7 643.4 820.3 879.4 1056.3 1142.0 1201.1 321.7 : 59.1 144.8 321.7 380.8 466.5 643.4 702.5 879.4 965.1 1024.2 1201.1 380.8 : 85.7 262.6 321.7 407.4 584.3 643.4 820.3 906.0 965.1 1141.9 1201.1 466.5 : 176.9 236.0 321.7 498.6 557.7 734.6 820.3 879.4 1056.3 1115.4 1201.1 643.4 : 59.1 144.8 321.7 380.8 557.7 643.4 702.5 879.4 938.5 1024.2 1201.1 702.5 : 85.7 262.6 321.7 498.6 584.3 643.4 820.3 879.4 965.1 1142.0 1201.1 788.2 : 176.9 236.0 412.9 498.6 557.7 734.6 793.7 879.4 1056.3 1115.4 1201.1 965.1 : 59.1 236.0 321.7 380.8 557.7 616.8 702.5 879.4 938.5 1024.2 1201.1 1024.2: 176.9 262.6 321.7 498.6 557.7 643.4 820.3 879.4 965.1 1141.9 1201.1 1201.1
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 59.1100 .. 176.8800 cents 117.77000 cents 59.11000 cents 2: 144.8100 .. 262.5800 cents 117.77000 cents -32.07000 cents 3: 295.1000 .. 412.8700 cents 117.77000 cents 32.52000 cents 4: 380.8000 .. 498.5700 cents 117.77000 cents -32.07000 cents 5: 466.5000 .. 584.2700 cents 117.77000 cents -32.07000 cents 6: 616.7900 .. 734.5600 cents 117.77000 cents 32.52000 cents 7: 702.4900 .. 820.2600 cents 117.77000 cents -32.07000 cents 8: 788.1900 .. 905.9600 cents 117.77000 cents -32.07000 cents 9: 938.4800 .. 1056.2500 cents 117.77000 cents 32.52000 cents 10: 1024.1800 .. 1141.9500 cents 117.77000 cents -32.07000 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 59.11000 cents, class 1 Average step (divided formal octave): 109.1873 cents Largest one step interval : 176.88000 cents Average / Smallest step : 1.847188 Largest / Average step : 1.619969 Largest / Smallest step : 2.992387 Median interval of one step : 85.70000 cents, amount: 3 Least squares average step : 103.59370 cents, oct.: 1139.53065 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABCBACBACBC Step pattern size order : MSLSMLSMLSL Scale is a Constant Structure, by a margin of 5.48000 cents Scale diversity : 1.360591 Lumma stability : 0.179658 Lumma impropriety factor : 0.160208 Rothenberg efficiency : 0.513420 redundancy: 0.486580 Efficiency x scale size : 5.647619 Number of different interval sizes : 30 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 5.48000 cents Most common intervals : 321.69000 cents & inv., amount: 9 Scale is a chain of 5 triads 0.0 498.570 879.370 cents Most common triad is 0.0 321.690 879.370 cents, amount: 7 Number of recognisable fifths : 5, average 702.4900 cents Number of recognisable fourths : 5, average 498.5700 cents Formal octave complements present : 1 = 9.0909% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
11: 1 0 2 0 1 2 0 1 2 0 2 N T3 SD: 30.9814 c. M: 53.2382 c. 12: 1 0 2 1 1 1 1 1 2 0 2 N D3 SD: 27.0052 c. M: 44.7217 c. 13: 1 1 2 0 1 2 1 1 2 0 2 N D3 SD: 30.1423 c. M:-51.2115 c. 14: 1 0 2 1 1 2 1 1 2 1 2 N T3 SD: 34.7570 c. M: 64.3200 c. 15: 1 1 2 1 1 2 1 1 2 1 2 P M ME S SD: 12.1984 c. M:-19.5533 c. 25: 2 1 4 1 2 3 2 1 4 1 4 N SD: 12.9481 c. M: 19.5116 c. 26: 2 1 4 1 2 4 1 2 4 1 4 N T3 SD: 6.2675 c. M: 11.2431 c. 41: 3 2 6 2 3 6 2 3 6 2 6 N T3 SD: 1.5285 c. M:-2.7520 c. 142: 10 7 21 7 10 21 7 10 21 7 21 N T3 SD: 0.8725 c. M: 1.5803 c. 183: 13 9 27 9 13 27 9 13 27 9 27 N T3 SD: 0.3385 c. M: 0.6097 c. 224: 16 11 33 11 16 33 11 16 33 11 33 N T3 SD: 0.0599 c. M: 0.1069 c. 1501: 107 74 221 74 107 221 74 107 221 74 221 N T3 SD: 0.0483 c. M:-0.0825 c. 1542: 110 76 227 76 110 227 76 110 227 76 227 N T3 SD: 0.0511 c. M:-0.0809 c. 1725: 123 85 254 85 123 254 85 123 254 85 254 N T3 SD: 0.0344 c. M: 0.0592 c. 1766: 126 87 260 87 126 260 87 126 260 87 260 N T3 SD: 0.0390 c. M:-0.0571 c. 1949: 139 96 287 96 139 287 96 139 287 96 287 N T3 SD: 0.0238 c. M: 0.0421 c. 2173: 155 107 320 107 155 320 107 155 320 107 320 N T3 SD: 0.0155 c. M: 0.0284 c. 2397: 171 118 353 118 171 353 118 171 353 118 353 N T3 SD: 0.0090 c. M: 0.0174 c.
FIT/HARMONIC
1 x x x x x x x x x x 2 S SD: 1.0600 cents 2 x x x x x x 3 x x x 4 S SD: 0.5937 cents 3 x x x x 4 x x x 5 x 6 S SD: 28.8878 cents 4 x x x 5 x x 6 x 7 x 8 S SD: 1.6941 cents 5 x x 6 x x 7 x 8 x 9:10 S SD: 13.3207 cents 6 x x 7 x 8 x 9 x 10:11:12 S SD: 17.5990 cents 7 x 8 x x 9:10 x 11:12:13:14 S SD: 15.9260 cents 8 x 9 x 10 x x 12:13:14 x 16 S SD: 13.2056 cents 9 x 10:11 x 12:13 x 14 x 16:18 S SD: 9.5269 cents 10 x 11:12 x 13 x 15:16:17:18:20 SD: 7.3376 cents 11 x 12:13:14 x 16 x 17:19:20:22 SD: 8.0358 cents 12 x 13:14:15:16:17:18:19:21:22:24 SD: 8.0025 cents 13 x 14 x 16:17:19 x 21:23 x 26 SD: 8.0832 cents 14 x 15:17 x 18:20:21:22:24:25:28 SD: 7.0086 cents 15:16 x 18:19:20:22:23:24:26:27:30 S SD: 7.1912 cents 16:17 x 19:20:21:23:24:25:28:29:32 SD: 3.8975 cents 17:18 x 20:21:22:25:26:27:30:31:34 SD: 6.9751 cents 18:19:20:22 x 24:26:27:28:31:33:36 SD: 7.0204 cents 19:20:21:23:24:25:28:29:30:33:34:38 SD: 5.4274 cents 20:21:22:24:25:26:29:30:32:35:36:40 SD: 3.3231 cents 24:25:26:29:30:31:35:36:38:42:43:48 SD: 3.2249 cents 33:35:36:40:41:43:48:50:52:58:60:66 SD: 2.9808 cents 35:37:38:42:44:46:51:53:55:61:63:70 SD: 2.6407 cents 36:38:39:43:45:47:52:54:57:63:65:72 SD: 1.9734 cents 54:57:59:65:67:71:78:81:85:94:98:108 SD: 1.7844 cents 56:59:61:67:70:73:81:84:88:98:101:112 SD: 1.6316 cents 58:61:63:70:72:76:84:87:91:101:105:116 SD: 1.2035 cents 78:82:85:94:97:102:113:117:123:136:141:156 SD: 0.6150 cents 138:145:150:166:172:181:200:207:218:241:249:276 SD: 0.5242 cents 158:166:172:190:197:207:229:237:249:276:285:316 SD: 0.4526 cents 162:170:176:195:202:212:235:243:255:283:293:324 SD: 0.4307 cents 182:191:198:219:227:238:264:273:287:318:329:364 SD: 0.3871 cents 196:206:213:236:244:257:284:294:309:342:354:392 SD: 0.3576 cents 216:227:235:260:269:283:313:324:341:377:390:432 SD: 0.3482 cents 220:231:239:265:274:288:319:330:347:384:398:440 SD: 0.3082 cents 240:252:261:289:299:314:348:360:378:419:434:480 SD: 0.2866 cents 298:313:324:359:371:390:432:447:470:520:538:596 SD: 0.2767 cents 300:315:326:361:374:393:435:450:473:524:542:600 SD: 0.2463 cents 333:350:362:401:415:436:483:500:525:581:602:666 SD: 0.2241 cents 378:397:411:455:471:495:548:567:596:660:683:756 SD: 0.1553 cents 529:556:575:637:659:693:767:794:834:924:956:1059 SD: 0.1473 cents 549:577:597:661:684:719:796:824:866:959:992:1099 SD: 0.1400 cents 553:581:601:666:689:724:802:830:872:966:999:1107 SD: 0.1193 cents