Scala analysis: China_Flute_91
91 (Flute), China
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 285.000 cents 285.000000 2: 440.000 cents 440.000000 3: 555.000 cents 555.000000 4: 673.000 cents 673.000000 5: 797.000 cents 797.000000 6: 943.000 cents 943.000000 7: 1120.000 cents 1120.000000 8: 1320.000 cents 1320.000000
SHOW/INTERVAL
0: 200.0000 cents 200.0000 1: 285.0000 cents 285.0000 2: 155.0000 cents 155.0000 3: 115.0000 cents 115.0000 4: 118.0000 cents 118.0000 5: 124.0000 cents 124.0000 6: 146.0000 cents 146.0000 7: 177.0000 cents 177.0000 8: 200.0000 cents 200.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 115.00000 cents 1: 1 118.00000 cents 1: 1 124.00000 cents 1: 1 146.00000 cents 1: 1 155.00000 cents 1: 1 177.00000 cents 1: 1 200.00000 cents 1: 1 285.00000 cents 2: 1 233.00000 cents 2: 1 242.00000 cents 2: 2 270.00000 cents 2: 1 323.00000 cents 2: 1 377.00000 cents 2: 1 440.00000 cents 2: 1 485.00000 cents 3: 1 357.00000 cents 3: 2 388.00000 cents 3: 1 447.00000 cents 3: 1 523.00000 cents 3: 1 555.00000 cents 3: 1 640.00000 cents 3: 1 662.00000 cents 4: 1 503.00000 cents 4: 1 512.00000 cents 4: 1 565.00000 cents 4: 1 647.00000 cents 4: 1 673.00000 cents 4: 1 755.00000 cents 4: 1 808.00000 cents 4: 1 817.00000 cents 5: 1 658.00000 cents 5: 1 680.00000 cents 5: 1 765.00000 cents 5: 1 797.00000 cents 5: 1 873.00000 cents 5: 2 932.00000 cents 5: 1 963.00000 cents 6: 1 835.00000 cents 6: 1 880.00000 cents 6: 1 943.00000 cents 6: 1 997.00000 cents 6: 2 1050.00000 cents 6: 1 1078.00000 cents 6: 1 1087.00000 cents 7: 1 1035.00000 cents 7: 1 1120.00000 cents 7: 1 1143.00000 cents 7: 1 1165.00000 cents 7: 1 1174.00000 cents 7: 1 1196.00000 cents 7: 1 1202.00000 cents 7: 1 1205.00000 cents Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 7.42857 = 52/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 285.0 440.0 555.0 673.0 797.0 943.0 1120.0 1320.0 285.0 : 155.0 270.0 388.0 512.0 658.0 835.0 1035.0 1320.0 440.0 : 115.0 233.0 357.0 503.0 680.0 880.0 1165.0 1320.0 555.0 : 118.0 242.0 388.0 565.0 765.0 1050.0 1205.0 1320.0 673.0 : 124.0 270.0 447.0 647.0 932.0 1087.0 1202.0 1320.0 797.0 : 146.0 323.0 523.0 808.0 963.0 1078.0 1196.0 1320.0 943.0 : 177.0 377.0 662.0 817.0 932.0 1050.0 1174.0 1320.0 1120.0: 200.0 485.0 640.0 755.0 873.0 997.0 1143.0 1320.0 1320.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 115.0000 .. 285.0000 cents 170.00000 cents 115.00000 cents 2: 233.0000 .. 485.0000 cents 252.00000 cents -52.00000 cents 3: 357.0000 .. 662.0000 cents 305.00000 cents -128.00000 cents 4: 503.0000 .. 817.0000 cents 314.00000 cents -159.00000 cents 5: 658.0000 .. 963.0000 cents 305.00000 cents -159.00000 cents 6: 835.0000 .. 1087.0000 cents 252.00000 cents -128.00000 cents 7: 1035.0000 .. 1205.0000 cents 170.00000 cents -52.00000 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 115.00000 cents, class 1 Average step (divided formal octave): 165.0000 cents Largest one step interval : 285.00000 cents Average / Smallest step : 1.434783 Largest / Average step : 1.727273 Largest / Smallest step : 2.478261 Median interval of one step : 150.50000 cents, amount: 0 Least squares average step : 164.53431 cents, oct.: 1316.27451 cents Scale is not proper Scale is a mode of a 1320-tone equal temperament with octave 1320.000 cents degrees: 285 440 555 673 797 943 1120 1320 Least number of segments generator : 661 of 661.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 721 of 721.000 cents and inv. generated superset size: 486 = 478 more = 6075.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDEFGH Step pattern size order : HEABCDFG Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 4.00000 cents Scale diversity : 1.322505 Lumma stability : 0.174242 Lumma impropriety factor : 0.510606 Rothenberg efficiency : 0.267857 redundancy: 0.732143 Efficiency x scale size : 2.142857 Number of different interval sizes : 52 = 7.42857 / class Number of one step interval sizes : 8 Highest interval variety : 8 Mean interval variety : 7.42857 = 52/7 Median interval variety : 7 Lowest interval variety : 7 Smallest interval difference : 3.00000 cents Number of recognisable fifths : 0 Number of recognisable fourths : 3, average 500.0000 cents Number of appreciable fourths : 1, average 503.0000 cents Formal octave complements present : 1 = 12.5000% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
8: 2 1 0 1 1 1 1 1 N T3 SD: 40.3686 c. M: 60.0000 c. 10: 2 1 1 1 1 1 1 2 N D3 I SD: 31.1388 c. M: 64.0000 c. 12: 3 1 1 1 1 2 1 2 N SD: 26.3557 c. M:-47.0000 c. 14: 3 2 1 1 1 2 2 2 N SD: 20.0975 c. M: 42.7143 c. 15: 3 2 1 2 1 2 2 2 N SD: 20.4848 c. M:-31.0000 c. 18: 4 2 2 1 2 2 2 3 N SD: 15.1717 c. M:-31.6667 c. 21: 5 2 2 2 2 2 3 3 N SD: 15.2004 c. M:-29.2857 c. 24: 5 3 2 2 2 3 3 4 N SD: 13.6336 c. M: 27.0000 c. 26: 6 3 2 2 3 3 3 4 N SD: 13.9783 c. M:-21.6154 c. 27: 6 3 2 3 2 3 4 4 N SD: 10.8067 c. M: 17.2222 c. 28: 6 3 3 2 3 3 4 4 N SD: 9.2572 c. M: 15.7143 c. 31: 7 3 3 3 3 3 4 5 N SD: 9.9562 c. M: 14.1935 c. 33: 7 4 3 3 3 4 4 5 N SD: 7.0445 c. M:-17.0000 c. 38: 8 5 3 3 4 4 5 6 N SD: 7.5411 c. M: 13.0000 c. 41: 9 5 3 4 4 4 6 6 N SD: 7.0921 c. M:-10.7317 c. 45: 10 5 4 4 4 5 6 7 N SD: 4.3285 c. M:-8.3333 c. 55: 12 6 5 5 5 6 8 8 N SD: 5.2559 c. M: 8.0000 c. 59: 13 7 5 5 6 6 8 9 N SD: 4.9463 c. M:-8.4237 c. 60: 13 7 5 6 5 7 8 9 N SD: 4.2573 c. M:-9.0000 c. 64: 14 7 6 6 6 7 8 10 N SD: 5.5846 c. M:-7.6250 c. 66: 14 8 6 6 6 7 9 10 N SD: 3.8243 c. M:-7.0000 c. 71: 15 9 6 6 7 8 9 11 N SD: 4.3327 c. M:-6.1972 c. 73: 16 8 7 6 7 8 10 11 N SD: 3.7408 c. M: 6.0274 c. 74: 16 9 6 7 7 8 10 11 N SD: 3.8022 c. M:-5.9459 c. 78: 17 9 7 7 7 9 10 12 N SD: 2.9308 c. M:-4.6923 c. 88: 19 10 8 8 8 10 12 13 N SD: 2.7839 c. M:-5.0000 c. 98: 21 12 8 9 9 11 13 15 N SD: 2.2930 c. M:-4.4898 c. 112: 24 13 10 10 11 12 15 17 N SD: 2.3024 c. M:-4.4286 c. 119: 26 14 10 11 11 13 16 18 N SD: 2.2779 c. M:-3.6975 c. 126: 27 15 11 11 12 14 17 19 N SD: 1.2550 c. M: 2.5238 c. 147: 32 17 13 13 14 16 20 22 N SD: 1.5622 c. M:-2.4490 c. 157: 34 18 14 14 15 17 21 24 N SD: 1.4457 c. M: 2.8025 c. 171: 37 20 15 15 16 19 23 26 N SD: 1.0441 c. M: 1.9123 c. 204: 44 24 18 18 19 23 27 31 N SD: 0.9191 c. M:-1.7059 c. 245: 53 29 21 22 23 27 33 37 N SD: 0.7374 c. M:-1.7959 c. 283: 61 33 25 25 27 31 38 43 N SD: 0.8494 c. M: 1.5548 c. 286: 62 33 25 26 27 31 39 43 N SD: 1.2442 c. M: 1.5385 c. 288: 62 34 25 26 27 32 38 44 N SD: 0.8529 c. M: 1.6667 c. 298: 64 35 26 27 28 33 40 45 N SD: 0.9385 c. M: 1.5101 c. 302: 65 36 26 27 28 34 40 46 N SD: 0.9715 c. M: 1.5033 c. 312: 67 37 27 28 29 35 42 47 N SD: 0.9492 c. M: 1.6154 c. 316: 68 37 28 28 30 35 42 48 N SD: 0.8264 c. M: 1.3924 c. 318: 69 37 28 28 30 35 43 48 N SD: 0.7840 c. M:-1.4151 c. 323: 70 38 28 29 30 36 43 49 N SD: 0.8972 c. M:-1.3622 c. 328: 71 38 29 29 31 36 44 50 N SD: 0.9024 c. M: 1.3415 c. 330: 71 39 29 29 31 37 44 50 N SD: 0.7906 c. M: 1.0000 c. 333: 72 39 29 30 31 37 45 50 N SD: 0.7429 c. M:-1.8018 c. 343: 74 40 30 31 32 38 46 52 N SD: 0.5899 c. M: 1.2828 c. 371: 80 44 32 33 35 41 50 56 N SD: 0.5512 c. M:-1.1860 c. 381: 82 45 33 34 36 42 51 58 N SD: 0.6475 c. M: 0.9449 c. 402: 87 47 35 36 38 44 54 61 N SD: 0.4700 c. M:-0.9104 c. 469: 101 55 41 42 44 52 63 71 N SD: 0.5154 c. M: 0.9382 c. 487: 105 57 43 43 46 54 65 74 N SD: 0.5528 c. M: 0.9035 c. 490: 106 57 43 44 46 54 66 74 N SD: 0.4913 c. M: 0.8980 c. 500: 108 59 43 45 47 55 67 76 N SD: 0.4934 c. M:-0.8800 c. 504: 109 59 44 45 47 56 68 76 N SD: 0.4842 c. M:-0.9524 c. 514: 111 60 45 46 48 57 69 78 N SD: 0.4997 c. M: 0.8911 c. 528: 114 62 46 47 50 58 71 80 N SD: 0.3062 c. M: 0.5000 c. 588: 127 69 51 53 55 65 79 89 N SD: 0.2638 c. M: 0.5102 c. 606: 131 71 53 54 57 67 81 92 N SD: 0.2647 c. M:-0.4455 c. 714: 154 84 62 64 67 79 96 108 N SD: 0.2246 c. M: 0.3782 c. 732: 158 86 64 65 69 81 98 111 N SD: 0.2119 c. M:-0.4098 c. 792: 171 93 69 71 74 88 106 120 N SD: 0.2041 c. M: 0.3333 c. 1065: 230 125 93 95 100 118 143 161 N SD: 0.2020 c. M:-0.4507 c. 1075: 232 126 94 96 101 119 144 163 N SD: 0.1681 c. M: 0.4093 c. 1116: 241 131 97 100 105 123 150 169 N SD: 0.1680 c. M: 0.3118 c. 1149: 248 135 100 103 108 127 154 174 N SD: 0.1554 c. M:-0.2846 c. 1194: 258 140 104 107 112 132 160 181 N SD: 0.1324 c. M:-0.2663 c. 1320: 285 155 115 118 124 146 177 200 N SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x x x 2 x S SD: 80.0000 cents 2 x x x 3 x x 4 x S SD: 42.5394 cents 3 x x 4 x x 5:6 x S SD: 38.1265 cents 4 x 5 x 6 x 7:8:9 S SD: 26.7047 cents 5:6 x 7 x 8:9:10:11 S SD: 21.0583 cents 6:7 x 8:9 x 10:11:13 SD: 19.1371 cents 7:8:9 x 10:11:12:13:15 SD: 13.2818 cents 9:11 x 12:13:14:16:17:19 SD: 16.5161 cents 10:12:13:14:15:16:17:19:21 SD: 8.7928 cents 11:13:14:15:16:17:19:21:24 SD: 8.1683 cents 15:18:19:21:22:24:26:29:32 SD: 7.5284 cents 17:20:22:23:25:27:29:32:36 SD: 6.2557 cents 21:25:27:29:31:33:36:40:45 SD: 3.1921 cents 32:38:41:44:47:51:55:61:69 SD: 3.0293 cents 34:40:44:47:50:54:59:65:73 SD: 2.0373 cents 51:60:66:70:75:81:88:97:109 SD: 1.8555 cents 55:65:71:76:81:87:95:105:118 SD: 1.0911 cents 84:99:108:116:124:133:145:160:180 SD: 1.0251 cents 90:106:116:124:133:143:155:172:193 SD: 0.7924 cents 101:119:130:139:149:160:174:193:216 SD: 0.7279 cents 111:131:143:153:164:176:191:212:238 SD: 0.6387 cents 135:159:174:186:199:214:233:258:289 SD: 0.4918 cents 145:171:187:200:214:230:250:277:311 SD: 0.3647 cents 217:256:280:299:320:344:374:414:465 SD: 0.3339 cents 246:290:317:339:363:390:424:470:527 SD: 0.2487 cents 286:337:369:394:422:453:493:546:613 SD: 0.2353 cents 301:355:388:415:444:477:519:575:645 SD: 0.1911 cents 402:474:518:554:593:637:693:768:862 SD: 0.1844 cents 431:508:556:594:636:683:743:823:924 SD: 0.1558 cents 453:534:584:624:668:718:781:865:971 SD: 0.1211 cents 508:599:655:700:749:805:876:970:1089 SD: 0.1211 cents 587:692:757:809:866:930:1012:1121:1258 SD: 0.0910 cents