Scala analysis: China_Flute_03
Flute 3 (Flute), China
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 151.000 cents 151.000000 2: 303.000 cents 303.000000 3: 451.000 cents 451.000000 4: 628.000 cents 628.000000 5: 826.000 cents 826.000000 6: 986.000 cents 986.000000 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 214.0000 cents 214.0000 1: 151.0000 cents 151.0000 2: 152.0000 cents 152.0000 3: 148.0000 cents 148.0000 4: 177.0000 cents 177.0000 5: 198.0000 cents 198.0000 6: 160.0000 cents 160.0000 7: 214.0000 cents 214.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 148.00000 cents 1: 1 151.00000 cents 1: 1 152.00000 cents 1: 1 160.00000 cents 1: 1 177.00000 cents 1: 1 198.00000 cents 1: 1 214.00000 cents 2: 1 300.00000 cents 2: 1 303.00000 cents 2: 1 325.00000 cents 2: 1 358.00000 cents 2: 1 365.00000 cents 2: 1 374.00000 cents 2: 1 375.00000 cents 3: 1 451.00000 cents 3: 1 477.00000 cents 3: 1 517.00000 cents 3: 1 523.00000 cents 3: 1 525.00000 cents 3: 1 535.00000 cents 3: 1 572.00000 cents 4: 1 628.00000 cents 4: 1 665.00000 cents 4: 1 675.00000 cents 4: 1 677.00000 cents 4: 1 683.00000 cents 4: 1 723.00000 cents 4: 1 749.00000 cents 5: 1 825.00000 cents 5: 1 826.00000 cents 5: 1 835.00000 cents 5: 1 842.00000 cents 5: 1 875.00000 cents 5: 1 897.00000 cents 5: 1 900.00000 cents 6: 1 986.00000 cents 6: 1 1002.00000 cents 6: 1 1023.00000 cents 6: 1 1040.00000 cents 6: 1 1048.00000 cents 6: 1 1049.00000 cents 6: 1 1052.00000 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 7.00000 = 7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 151.0 303.0 451.0 628.0 826.0 986.0 1200.0 151.0 : 152.0 300.0 477.0 675.0 835.0 1049.0 1200.0 303.0 : 148.0 325.0 523.0 683.0 897.0 1048.0 1200.0 451.0 : 177.0 375.0 535.0 749.0 900.0 1052.0 1200.0 628.0 : 198.0 358.0 572.0 723.0 875.0 1023.0 1200.0 826.0 : 160.0 374.0 525.0 677.0 825.0 1002.0 1200.0 986.0 : 214.0 365.0 517.0 665.0 842.0 1040.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 148.0000 .. 214.0000 cents 66.00000 cents 148.00000 cents 2: 300.0000 .. 375.0000 cents 75.00000 cents 86.00000 cents 3: 451.0000 .. 572.0000 cents 121.00000 cents 76.00000 cents 4: 628.0000 .. 749.0000 cents 121.00000 cents 56.00000 cents 5: 825.0000 .. 900.0000 cents 75.00000 cents 76.00000 cents 6: 986.0000 .. 1052.0000 cents 66.00000 cents 86.00000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 148.00000 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 214.00000 cents Average / Smallest step : 1.158301 Largest / Average step : 1.248333 Largest / Smallest step : 1.445946 Median interval of one step : 160.00000 cents, amount: 1 Least squares average step : 164.77143 cents, oct.: 1153.40000 cents Scale is strictly proper Scale is a mode of a 1200-tone equal temperament with octave 1200.000 cents degrees: 151 303 451 628 826 986 1200 Least number of segments generator : 601 of 601.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1033 of 1033.000 cents and inv. generated superset size: 359 = 352 more = 5128.571% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDEFG Step pattern size order : BCAEFDG Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 56.00000 cents Scale diversity : 1.445783 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.563333 Rothenberg efficiency : 0.285714 redundancy: 0.714286 Efficiency x scale size : 2.000000 Number of different interval sizes : 42 = 7.00000 / class Number of one step interval sizes : 7 Highest interval variety : 7 Mean interval variety : 7.00000 = 7 Median interval variety : 7 Lowest interval variety : 7 Smallest interval difference : 1.00000 cents Number of recognisable fifths : 0 Best fifths form a closed circle Best minor thirds form a closed circle Formal octave complements present : 1 = 14.2857% Limited inverse transpositions with margin 95.0000 cents: 4 -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 41.6175 c. M:-63.2857 c. Lebeng 8: 1 1 1 1 2 1 1 P M ME S SD: 38.4838 c. M:-74.0000 c. 10: 1 2 1 1 2 1 2 P M ME S SD: 30.9539 c. M:-57.0000 c. 11: 1 2 1 2 2 1 2 P M ME S SD: 27.9422 c. M:-46.7273 c. 13: 2 1 2 2 2 2 2 SP M ME S SD: 21.1688 c. M:-33.6154 c. Tamashian 15: 2 2 2 2 2 2 3 SP M ME S SD: 19.6651 c. M:-29.0000 c. 16: 2 2 2 2 3 2 3 P D3 S SD: 11.4455 c. M: 28.0000 c. 17: 2 2 2 3 3 2 3 P D3 SD: 15.9424 c. M: 27.4706 c. 19: 2 3 2 3 3 3 3 SP D3 S SD: 14.5937 c. M: 24.6842 c. 23: 3 3 3 3 4 3 4 SP D3 S SD: 9.1414 c. M:-18.5652 c. 29: 4 3 4 4 5 4 5 SP SD: 8.5579 c. M:-14.5172 c. 32: 4 4 4 5 5 4 6 SP SD: 5.6474 c. M: 11.0000 c. 40: 5 5 5 6 7 5 7 SP SD: 5.6946 c. M:-14.0000 c. 46: 6 6 5 7 8 6 8 SP SD: 6.5123 c. M:-10.0435 c. 48: 6 6 6 7 8 6 9 SP SD: 4.5040 c. M: 11.0000 c. 51: 6 7 6 8 8 7 9 SP SD: 5.1360 c. M: 9.8235 c. 55: 7 7 7 8 9 7 10 SP SD: 3.9637 c. M:-7.1818 c. 63: 8 8 8 9 10 9 11 SP SD: 3.9901 c. M: 6.9524 c. 67: 8 9 8 10 11 9 12 SP SD: 3.3563 c. M: 7.7164 c. 71: 9 9 9 10 12 9 13 SP SD: 3.2874 c. M: 5.7183 c. 74: 9 10 9 11 12 10 13 SP SD: 3.6221 c. M:-5.1081 c. 78: 10 10 9 12 13 10 14 SP SD: 3.5038 c. M: 4.8462 c. 79: 10 10 10 11 13 11 14 SP SD: 3.4954 c. M: 5.7468 c. 80: 10 10 10 12 13 11 14 SP SD: 2.1381 c. M:-4.0000 c. 96: 12 12 12 14 16 13 17 SP SD: 1.8225 c. M: 3.0000 c. 119: 15 15 15 17 20 16 21 SP SD: 1.7569 c. M: 2.7899 c. 128: 16 16 16 19 21 17 23 SP SD: 1.4470 c. M: 3.0000 c. 151: 19 19 19 22 25 20 27 SP SD: 0.8901 c. M:-1.9801 c. 189: 24 24 23 28 31 25 34 SP SD: 1.1497 c. M: 1.8730 c. 218: 27 28 27 32 36 29 39 SP SD: 0.9736 c. M: 2.3761 c. 231: 29 29 29 34 38 31 41 SP SD: 0.8676 c. M: 1.7013 c. 237: 30 30 29 35 39 32 42 SP SD: 0.7435 c. M:-1.3418 c. 269: 34 34 33 40 44 36 48 SP SD: 0.5728 c. M:-0.9963 c. 285: 36 36 35 42 47 38 51 SP SD: 0.5437 c. M: 0.7368 c. 325: 41 41 40 48 54 43 58 SP SD: 0.5027 c. M:-1.0769 c. 365: 46 46 45 54 60 49 65 SP SD: 0.4491 c. M: 0.7945 c. 388: 49 49 48 57 64 52 69 SP SD: 0.3858 c. M:-0.5979 c. 420: 53 53 52 62 69 56 75 SP SD: 0.3541 c. M:-0.5714 c. 516: 65 65 64 76 85 69 92 SP SD: 0.3148 c. M: 0.6744 c. 590: 74 75 73 87 97 79 105 SP SD: 0.3772 c. M:-0.5254 c. 594: 75 75 73 88 98 79 106 SP SD: 0.3117 c. M:-0.5152 c. 606: 76 77 75 89 100 81 108 SP SD: 0.3056 c. M: 0.5050 c. 684: 86 87 84 101 113 91 122 SP SD: 0.2375 c. M:-0.5088 c. 705: 89 89 87 104 116 94 126 SP SD: 0.3138 c. M:-0.4894 c. 713: 90 90 88 105 118 95 127 SP SD: 0.2625 c. M:-0.4727 c. 745: 94 94 92 110 123 99 133 SP SD: 0.2340 c. M:-0.4094 c. 764: 96 97 94 113 126 102 136 SP SD: 0.2293 c. M:-0.3874 c. 780: 98 99 96 115 129 104 139 SP SD: 0.1907 c. M: 0.3077 c. 812: 102 103 100 120 134 108 145 SP SD: 0.1843 c. M: 0.2857 c. 915: 115 116 113 135 151 122 163 SP SD: 0.1693 c. M:-0.2295 c. 931: 117 118 115 137 154 124 166 SP SD: 0.1655 c. M: 0.2879 c. 1049: 132 133 129 155 173 140 187 SP SD: 0.1281 c. M: 0.2850 c. 1200: 151 152 148 177 198 160 214 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: 36.9775 cents 3 x x 4 x 5 x 6 S SD: 24.9866 cents 4 x x 5:6 x 7:8 S SD: 24.9357 cents 5 x 6 x 7:8:9:10 S SD: 11.6257 cents 6 x 7:8:9:10:11:12 S SD: 21.3493 cents 7 x 8:9:10:11:12:14 S SD: 16.8416 cents 8:9 x 10:12:13:14:16 S SD: 18.9730 cents 9:10:11:12:13:15:16:18 SD: 13.3656 cents 10:11:12:13:14:16:18:20 S SD: 8.5540 cents 16:17:19:21:23:26:28:32 SD: 7.8864 cents 20:22:24:26:29:32:35:40 SD: 4.6198 cents 21:23:25:27:30:34:37:42 SD: 3.2062 cents 36:39:43:47:52:58:64:72 SD: 3.0777 cents 41:45:49:53:59:66:72:82 SD: 2.5133 cents 43:47:51:56:62:69:76:86 SD: 1.9700 cents 57:62:68:74:82:92:101:114 SD: 1.1616 cents 64:70:76:83:92:103:113:128 SD: 1.0714 cents 78:85:93:101:112:126:138:156 SD: 0.9501 cents 98:107:117:127:141:158:173:196 SD: 0.7692 cents 121:132:144:157:174:195:214:242 SD: 0.3261 cents 219:239:261:284:315:353:387:438 SD: 0.2776 cents 309:337:368:401:444:498:546:618 SD: 0.1707 cents 430:469:512:558:618:693:760:860 SD: 0.1596 cents 450:491:536:584:647:725:795:900 SD: 0.1554 cents 460:502:548:597:661:741:813:920 SD: 0.1170 cents 517:564:616:671:743:833:914:1034 SD: 0.1143 cents 528:576:629:685:759:851:933:1056 SD: 0.1092 cents 538:587:641:698:773:867:951:1076 SD: 0.1027 cents 581:634:692:754:835:936:1027:1162 SD: 0.0918 cents