Scala analysis: O3-rast_moha_Cup
Mode of Rast + Mohajira (Dudon) with near-pure 59/48 and 12:11 steps
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 207.422 cents 207.421880 2: 357.422 cents 357.421870 3: 495.703 cents 495.703120 4: 703.125 cents 703.125000 5: 854.297 cents 854.296870 6: 1061.719 cents 1061.718750 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 138.2813 cents 138.2813 1: 207.4219 cents 207.4219 2: 150.0000 cents 150.0000 3: 138.2813 cents 138.2813 4: 207.4219 cents 207.4219 5: 151.1719 cents 151.1719 6: 207.4219 cents 207.4219 7: 138.2813 cents 138.2813
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 138.28125 cents 1: 1 149.99999 cents 1: 1 151.17187 cents 1: 3 207.42188 cents 2: 1 288.28124 cents 2: 3 345.70313 cents 2: 1 357.42187 cents 2: 2 358.59375 cents 3: 3 495.70312 cents 3: 2 496.87500 cents 3: 1 553.12501 cents 3: 1 566.01563 cents 4: 1 633.98437 cents 4: 1 646.87499 cents 4: 2 703.12500 cents 4: 3 704.29688 cents 5: 2 841.40625 cents 5: 1 842.57813 cents 5: 3 854.29687 cents 5: 1 911.71876 cents 6: 3 992.57812 cents 6: 1 1048.82813 cents 6: 1 1050.00001 cents 6: 2 1061.71875 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 207.4 357.4 495.7 703.1 854.3 1061.7 1200.0 207.4 : 150.0 288.3 495.7 646.9 854.3 992.6 1200.0 357.4 : 138.3 345.7 496.9 704.3 842.6 1050.0 1200.0 495.7 : 207.4 358.6 566.0 704.3 911.7 1061.7 1200.0 703.1 : 151.2 358.6 496.9 704.3 854.3 992.6 1200.0 854.3 : 207.4 345.7 553.1 703.1 841.4 1048.8 1200.0 1061.7: 138.3 345.7 495.7 634.0 841.4 992.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 138.2813 .. 207.4219 cents 69.14063 cents 138.28125 cents 2: 288.2812 .. 358.5938 cents 70.31251 cents 80.85936 cents 3: 495.7031 .. 566.0156 cents 70.31251 cents 137.10937 cents 4: 633.9844 .. 704.2969 cents 70.31251 cents 67.96874 cents 5: 841.4063 .. 911.7188 cents 70.31251 cents 137.10937 cents 6: 992.5781 .. 1061.7188 cents 69.14063 cents 80.85936 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 138.28125 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 207.42188 cents Average / Smallest step : 1.239709 Largest / Average step : 1.209961 Largest / Smallest step : 1.500000 Median interval of one step : 151.17187 cents, amount: 1 Most common interval of one step : 207.42188 cents, amount: 3 Least squares average step : 173.31194 cents, oct.: 1213.18359 cents Scale is strictly proper Scale is a mode of a 1024-tone equal temperament with octave 2/1 degrees: 177 305 423 600 729 906 1024 Least number of segments generator : 513 of 601.172 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 831 of 973.828 cents and inv. generated superset size: 129 = 122 more = 1842.857% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCADAC Step pattern size order : DBADCDA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 67.96874 cents Scale diversity : 1.304801 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.650391 Rothenberg efficiency : 0.412245 redundancy: 0.587755 Efficiency x scale size : 2.885714 Number of different interval sizes : 24 = 4.00000 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 4.00000 = 4 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 1.17188 cents Most common triad is 0.0 495.703 854.297 cents, amount: 2 Number of recognisable fifths : 5, average 703.8281 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 1 = 14.2857% Limited inverse transpositions with margin 70.3125 cents: 4 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 21.5901 c. M: 35.9933 c. Lebeng 10: 2 1 1 2 1 2 1 P M ME S SD: 17.4763 c. M:-32.5781 c. Sethares Neutral, Beatles-7, Dichotic-7 16: 3 2 2 2 2 3 2 P D3 S SD: 21.5901 c. M:-29.2969 c. 17: 3 2 2 3 2 3 2 SP M ME S SD: 3.9610 c. M: 7.2380 c. Beatles-7, Dichotic-7 41: 7 5 5 7 5 7 5 SP M DE S SD: 4.5397 c. M: 8.0602 c. Beatles-7, Dichotic-7 53: 9 7 6 9 7 9 6 SP T3 SD: 3.5252 c. M:-6.0805 c. 58: 10 7 7 10 7 10 7 SP M DE S SD: 4.0120 c. M: 6.5463 c. Beatles-7, Dichotic-7 63: 11 8 7 11 8 11 7 SP T3 SD: 2.9275 c. M:-4.9479 c. 70: 12 9 8 12 9 12 8 SP T3 SD: 1.7363 c. M:-2.8460 c. 80: 14 10 9 14 10 14 9 SP T3 SD: 2.0201 c. M:-3.2813 c. 87: 15 11 10 15 11 15 10 SP T3 SD: 0.6997 c. M:-1.1988 c. 104: 18 13 12 18 13 18 12 SP T3 SD: 0.3973 c. M:-0.7212 c. 191: 33 24 22 33 24 33 22 SP T3 SD: 0.4153 c. M:-0.6933 c. 295: 51 37 34 51 37 51 34 SP T3 SD: 0.3759 c. M:-0.6038 c. 399: 69 50 46 69 50 69 46 SP T3 SD: 0.3693 c. M:-0.6344 c. 486: 84 61 56 84 61 84 56 SP T3 SD: 0.3875 c. M:-0.6028 c. 503: 87 63 58 87 63 87 58 SP T3 SD: 0.3695 c. M:-0.6523 c. 521: 90 65 60 90 66 90 60 SP SD: 0.3567 c. M: 0.6298 c. 538: 93 67 62 93 68 93 62 SP SD: 0.3500 c. M: 0.5445 c. 591: 102 74 68 102 75 102 68 SP SD: 0.3468 c. M: 0.5869 c. 601: 104 75 69 104 76 104 69 SP SD: 0.3295 c. M: 0.5284 c. 608: 105 76 70 105 77 105 70 SP SD: 0.2719 c. M: 0.4934 c. 625: 108 78 72 108 79 108 72 SP SD: 0.2358 c. M: 0.4050 c. 642: 111 80 74 111 81 111 74 SP SD: 0.2471 c. M: 0.4125 c. 695: 120 87 80 120 88 120 80 SP SD: 0.2387 c. M: 0.3912 c. 712: 123 89 82 123 90 123 82 SP SD: 0.1741 c. M: 0.3160 c. 729: 126 91 84 126 92 126 84 SP SD: 0.1521 c. M: 0.2443 c. 816: 141 102 94 141 103 141 94 SP SD: 0.1013 c. M: 0.1838 c. 833: 144 104 96 144 105 144 96 SP SD: 0.0952 c. M: 0.1590 c. 920: 159 115 106 159 116 159 106 SP SD: 0.0449 c. M: 0.0815 c. 1024: 177 128 118 177 129 177 118 SP SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 0.5850 cents 3 x x 4 x 5 x 6 S SD: 10.0510 cents 4 x 5 x 6 x 7:8 S SD: 24.3223 cents 5 x 6:7 x 8:9:10 S SD: 22.6958 cents 6:7 x 8:9:10:11:12 S SD: 11.3007 cents 7:8 x 9 x 11:13:14 SD: 19.4879 cents 8:9:10:11:12:13:15:16 SD: 9.9344 cents 14:16:17:19:21:23:26:28 SD: 6.7507 cents 18:20:22:24:27:29:33:36 SD: 5.8994 cents 22:25:27:29:33:36:41:44 SD: 3.9552 cents 30:34:37:40:45:49:55:60 SD: 2.4804 cents 39:44:48:52:59:64:72:78 SD: 2.0510 cents 48:54:59:64:72:79:89:96 SD: 1.6891 cents 64:72:79:85:96:105:118:128 SD: 1.4164 cents 70:79:86:93:105:115:129:140 SD: 1.0992 cents 78:88:96:104:117:128:144:156 SD: 0.6927 cents 118:133:145:157:177:193:218:236 SD: 0.4719 cents 157:177:193:209:236:257:290:314 SD: 0.4052 cents 196:221:241:261:294:321:362:392 SD: 0.2000 cents 353:398:434:470:530:578:652:706 SD: 0.1440 cents 431:486:530:574:647:706:796:862 SD: 0.1304 cents 519:585:638:691:779:850:958:1038 SD: 0.0944 cents