Scala analysis: supermagic7
A distributionally even scale in supermagic temperament, abababc
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 59.110 cents 59.110000 2: 321.680 cents 321.680000 3: 380.790 cents 380.790000 4: 643.360 cents 643.360000 5: 702.470 cents 702.470000 6: 965.040 cents 965.040000 7: 1201.030 cents 1201.030000
SHOW/INTERVAL
0: 235.9900 cents 235.9900 1: 59.1100 cents 59.1100 2: 262.5700 cents 262.5700 3: 59.1100 cents 59.1100 4: 262.5700 cents 262.5700 5: 59.1100 cents 59.1100 6: 262.5700 cents 262.5700 7: 235.9900 cents 235.9900
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 59.11000 cents 1: 1 235.99000 cents 1: 3 262.57000 cents 2: 1 295.10000 cents 2: 5 321.68000 cents 2: 1 498.56000 cents 3: 2 380.79000 cents 3: 3 557.67000 cents 3: 2 584.25000 cents 4: 2 616.78000 cents 4: 3 643.36000 cents 4: 2 820.24000 cents 5: 1 702.47000 cents 5: 5 879.35000 cents 5: 1 905.93000 cents 6: 3 938.46000 cents 6: 1 965.04000 cents 6: 3 1141.92000 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 0.0 : 59.1 321.7 380.8 643.4 702.5 965.0 1201.0 59.1 : 262.6 321.7 584.3 643.4 905.9 1141.9 1201.0 321.7 : 59.1 321.7 380.8 643.4 879.4 938.5 1201.0 380.8 : 262.6 321.7 584.3 820.2 879.4 1141.9 1201.0 643.4 : 59.1 321.7 557.7 616.8 879.3 938.5 1201.0 702.5 : 262.6 498.6 557.7 820.2 879.3 1141.9 1201.0 965.0 : 236.0 295.1 557.7 616.8 879.4 938.5 1201.0 1201.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 59.1100 .. 262.5700 cents 203.46000 cents 59.11000 cents 2: 295.1000 .. 498.5600 cents 203.46000 cents 32.53000 cents 3: 380.7900 .. 584.2500 cents 203.46000 cents -117.77000 cents 4: 616.7800 .. 820.2400 cents 203.46000 cents 32.53000 cents 5: 702.4700 .. 905.9300 cents 203.46000 cents -117.77000 cents 6: 938.4600 .. 1141.9200 cents 203.46000 cents 32.53000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 59.11000 cents, class 1 Average step (divided formal octave): 171.5757 cents Largest one step interval : 262.57000 cents Average / Smallest step : 2.902651 Largest / Average step : 1.530345 Largest / Smallest step : 4.442057 Median interval of one step : 235.99000 cents, amount: 1 Least squares average step : 158.05771 cents, oct.: 1106.40400 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABABABC Step pattern size order : SLSLSLM Scale is a Constant Structure, by a margin of 32.53000 cents Scale diversity : 1.282979 Lumma stability : 0.179687 Lumma impropriety factor : 0.196115 Rothenberg efficiency : 0.544218 redundancy: 0.455782 Efficiency x scale size : 3.809524 Number of different interval sizes : 18 = 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 : 26.58000 cents Most common intervals : 321.68000 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 59.110 321.680 cents Most common triad is 0.0 321.680 879.350 cents, amount: 3 Number of recognisable fifths : 1, average 702.4700 cents Number of recognisable fourths : 1, average 498.5600 cents Formal octave complements present : 1 = 14.2857% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 203.4600 cents: 5 -- Rational properties --
FIT/MODE
7: 0 2 0 2 0 2 1 N T3 SD: 40.7542 c. M:-64.4143 c. 9: 0 2 1 2 0 2 2 N T3 S SD: 37.1180 c. M: 59.1100 c. 10: 0 3 0 2 1 2 2 N SD: 32.9252 c. M: 59.1100 c. 11: 0 3 0 3 0 3 2 N T3 SD: 35.9649 c. M: 59.1100 c. 12: 1 2 1 2 1 3 2 N T3 SD: 28.3912 c. M: 42.8450 c. 15: 1 3 1 3 1 3 3 N M DE S SD: 12.9758 c. M:-20.9587 c. Kleismic-7, Triolic Diatonic 19: 1 4 1 4 1 4 4 N M DE S SD: 8.5537 c. M: 16.8584 c. Kleismic-7 26: 1 6 1 6 1 6 5 N T3 SD: 7.7829 c. M: 12.9165 c. 34: 2 7 2 7 2 7 7 N M DE S SD: 7.6322 c. M:-11.5388 c. Kleismic-7 37: 2 8 2 8 2 8 7 N T3 SD: 7.2258 c. M:-11.6559 c. 41: 2 9 2 9 2 9 8 N T3 SD: 0.8280 c. M:-1.6427 c. 142: 7 31 7 31 7 31 28 N T3 SD: 0.4363 c. M: 0.8328 c. 183: 9 40 9 40 9 40 36 N T3 SD: 0.1660 c. M: 0.2782 c. 224: 11 49 11 49 11 49 44 N T3 SD: 0.0789 c. M: 0.1308 c. 407: 20 89 20 89 20 89 80 N T3 SD: 0.0891 c. M: 0.1478 c. 631: 31 138 31 138 31 138 124 N T3 SD: 0.0766 c. M: 0.1244 c. 855: 42 187 42 187 42 187 168 N T3 SD: 0.0738 c. M: 0.1133 c. 1079: 53 236 53 236 53 236 212 N T3 SD: 0.0732 c. M: 0.1159 c. 1400: 69 306 69 306 69 306 275 N T3 SD: 0.0798 c. M:-0.1326 c. 1460: 72 319 72 319 72 319 287 N T3 SD: 0.0759 c. M:-0.1189 c. 1486: 73 325 73 325 73 325 292 N T3 SD: 0.0747 c. M: 0.1180 c. 1501: 74 328 74 328 74 328 295 N T3 SD: 0.0610 c. M:-0.1013 c. 1542: 76 337 76 337 76 337 303 N T3 SD: 0.0535 c. M:-0.0847 c. 1583: 78 346 78 346 78 346 311 N T3 SD: 0.0549 c. M:-0.0908 c. 1624: 80 355 80 355 80 355 319 N T3 SD: 0.0633 c. M:-0.1030 c. 1684: 83 368 83 368 83 368 331 N T3 SD: 0.0557 c. M:-0.0857 c. 1725: 85 377 85 377 85 377 339 N T3 SD: 0.0428 c. M:-0.0712 c. 1766: 87 386 87 386 87 386 347 N T3 SD: 0.0377 c. M:-0.0577 c. 1807: 89 395 89 395 89 395 355 N T3 SD: 0.0418 c. M:-0.0694 c. 1908: 94 417 94 417 94 417 375 N T3 SD: 0.0405 c. M: 0.0615 c. 1949: 96 426 96 426 96 426 383 N T3 SD: 0.0289 c. M:-0.0480 c. 1990: 98 435 98 435 98 435 391 N T3 SD: 0.0260 c. M:-0.0420 c. 2173: 107 475 107 475 107 475 427 N T3 SD: 0.0178 c. M:-0.0295 c. 2214: 109 484 109 484 109 484 435 N T3 SD: 0.0177 c. M:-0.0295 c. 2397: 118 524 118 524 118 524 471 N T3 SD: 0.0087 c. M:-0.0145 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 1.0300 cents 2 x x x x 3 x 4 S SD: 0.5758 cents 3 x x 4 x x 5:6 S SD: 47.4450 cents 4 x x 5 x 6:7:8 S SD: 1.6987 cents 5 x 6 x 7:8:9:10 S SD: 27.4745 cents 6 x 7 x x 9:10:12 SD: 24.3860 cents 7 x 8:9:10:11:12:14 S SD: 23.1129 cents 8 x x 10 x 12:14:16 S SD: 1.6987 cents 9:10:11 x 13:14:16:18 SD: 24.0216 cents 10:11:12 x x 15:17:20 SD: 23.1553 cents 11:12:13:14:16:17:19:22 SD: 16.7712 cents 12:13:14:15:17:18:21:24 SD: 14.9785 cents 13:14 x 16:19:20:23:26 SD: 14.7385 cents 14:15:17 x 20:21:24:28 SD: 12.4028 cents 15:16:18:19:22:23:26:30 SD: 10.6676 cents 16:17:19:20:23:24:28:32 SD: 7.7717 cents 18:19:22 x 26:27:31:36 SD: 8.2838 cents 19:20:23:24:28:29:33:38 SD: 8.1664 cents 20:21:24:25:29:30:35:40 SD: 3.8482 cents 24:25:29:30:35:36:42:48 SD: 2.5221 cents 52:54:63:65:75:78:91:104 SD: 2.4006 cents 53:55:64:66:77:80:93:106 SD: 2.2106 cents 54:56:65:67:78:81:94:108 SD: 1.7217 cents 58:60:70:72:84:87:101:116 SD: 1.3218 cents 78:81:94:97:113:117:136:156 SD: 1.1299 cents 82:85:99:102:119:123:143:164 SD: 0.9755 cents 113:117:136:141:164:170:197:226 SD: 0.9063 cents 114:118:137:142:165:171:199:228 SD: 0.7161 cents 118:122:142:147:171:177:206:236 SD: 0.3539 cents 142:147:171:177:206:213:248:284 SD: 0.2483 cents 260:269:313:324:377:390:454:520 SD: 0.1840 cents 402:416:484:501:583:603:702:804 SD: 0.1815 cents 460:476:554:573:667:690:803:921 SD: 0.1798 cents 520:538:626:648:754:780:908:1041 SD: 0.1428 cents