Scala analysis: China_Flute_02
Flute 2 (Flute), China
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 177.000 cents 177.000000 2: 337.000 cents 337.000000 3: 495.000 cents 495.000000 4: 656.000 cents 656.000000 5: 845.000 cents 845.000000 6: 971.000 cents 971.000000 7: 1180.000 cents 1180.000000
SHOW/INTERVAL
0: 209.0000 cents 209.0000 1: 177.0000 cents 177.0000 2: 160.0000 cents 160.0000 3: 158.0000 cents 158.0000 4: 161.0000 cents 161.0000 5: 189.0000 cents 189.0000 6: 126.0000 cents 126.0000 7: 209.0000 cents 209.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 126.00000 cents 1: 1 158.00000 cents 1: 1 160.00000 cents 1: 1 161.00000 cents 1: 1 177.00000 cents 1: 1 189.00000 cents 1: 1 209.00000 cents 2: 1 315.00000 cents 2: 1 318.00000 cents 2: 1 319.00000 cents 2: 1 335.00000 cents 2: 1 337.00000 cents 2: 1 350.00000 cents 2: 1 386.00000 cents 3: 1 476.00000 cents 3: 1 479.00000 cents 3: 1 495.00000 cents 3: 1 508.00000 cents 3: 1 512.00000 cents 3: 1 524.00000 cents 3: 1 546.00000 cents 4: 1 634.00000 cents 4: 1 656.00000 cents 4: 1 668.00000 cents 4: 1 672.00000 cents 4: 1 685.00000 cents 4: 1 701.00000 cents 4: 1 704.00000 cents 5: 1 794.00000 cents 5: 1 830.00000 cents 5: 1 843.00000 cents 5: 1 845.00000 cents 5: 1 861.00000 cents 5: 1 862.00000 cents 5: 1 865.00000 cents 6: 1 971.00000 cents 6: 1 991.00000 cents 6: 1 1003.00000 cents 6: 1 1019.00000 cents 6: 1 1020.00000 cents 6: 1 1022.00000 cents 6: 1 1054.00000 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 : 177.0 337.0 495.0 656.0 845.0 971.0 1180.0 177.0 : 160.0 318.0 479.0 668.0 794.0 1003.0 1180.0 337.0 : 158.0 319.0 508.0 634.0 843.0 1020.0 1180.0 495.0 : 161.0 350.0 476.0 685.0 862.0 1022.0 1180.0 656.0 : 189.0 315.0 524.0 701.0 861.0 1019.0 1180.0 845.0 : 126.0 335.0 512.0 672.0 830.0 991.0 1180.0 971.0 : 209.0 386.0 546.0 704.0 865.0 1054.0 1180.0 1180.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 126.0000 .. 209.0000 cents 83.00000 cents 126.00000 cents 2: 315.0000 .. 386.0000 cents 71.00000 cents 106.00000 cents 3: 476.0000 .. 546.0000 cents 70.00000 cents 90.00000 cents 4: 634.0000 .. 704.0000 cents 70.00000 cents 88.00000 cents 5: 794.0000 .. 865.0000 cents 71.00000 cents 90.00000 cents 6: 971.0000 .. 1054.0000 cents 83.00000 cents 106.00000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 126.00000 cents, class 1 Average step (divided formal octave): 168.5714 cents Largest one step interval : 209.00000 cents Average / Smallest step : 1.337868 Largest / Average step : 1.239831 Largest / Smallest step : 1.658730 Median interval of one step : 161.00000 cents, amount: 1 Least squares average step : 166.22143 cents, oct.: 1163.55000 cents Scale is strictly proper Scale is a mode of a 1180-tone equal temperament with octave 1180.000 cents degrees: 177 337 495 656 845 971 1180 Least number of segments generator : 591 of 591.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 717 of 717.000 cents and inv. generated superset size: 285 = 278 more = 4071.429% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDEFG Step pattern size order : ECBDFAG Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 88.00000 cents Scale diversity : 1.449891 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.620339 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 : 2, average 702.5000 cents Number of recognisable fourths : 3, average 505.0000 cents Number of appreciable fourths : 2, average 501.5000 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% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 83.0000 cents: 4 -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 17.5633 c. M:-40.4286 c. Lebeng 16: 2 3 2 2 2 2 3 P D3 S SD: 22.9255 c. M: 33.7500 c. 17: 2 3 2 2 3 2 3 SP M ME S SD: 19.8821 c. M: 38.1765 c. 18: 3 2 3 2 3 2 3 SP M ME I SD: 14.8481 c. M:-29.4444 c. 21: 3 3 3 3 3 2 4 SP T3 SD: 10.5102 c. M:-18.2857 c. 22: 3 3 3 3 4 2 4 SP D3 S SD: 11.9367 c. M: 16.0909 c. 24: 4 3 3 3 4 3 4 SP D3 SD: 11.7640 c. M:-19.6667 c. 27: 4 4 3 4 4 3 5 SP T3 SD: 9.8011 c. M: 14.6296 c. 28: 4 4 4 4 4 3 5 SP T3 SD: 8.6829 c. M:-18.2857 c. 29: 4 4 4 4 5 3 5 SP D3 S SD: 8.6626 c. M: 14.2414 c. 34: 5 5 4 5 5 4 6 SP T3 SD: 7.1113 c. M: 12.0588 c. 38: 6 5 5 5 6 4 7 SP SD: 5.8508 c. M:-9.3158 c. 45: 7 6 6 6 7 5 8 SP SD: 3.8538 c. M:-6.5556 c. 52: 8 7 7 7 8 6 9 SP SD: 3.8915 c. M: 5.3846 c. 60: 9 8 8 8 10 6 11 SP SD: 4.1652 c. M: 7.3333 c. 67: 10 9 9 9 11 7 12 SP SD: 2.2204 c. M: 4.3582 c. 74: 11 10 10 10 12 8 13 SP SD: 1.4826 c. M: 2.2162 c. 119: 18 16 16 16 19 13 21 SP SD: 1.2211 c. M: 2.1429 c. 162: 24 22 22 22 26 17 29 SP SD: 1.4052 c. M: 2.2346 c. 165: 25 22 22 23 26 18 29 SP SD: 1.4119 c. M:-1.9394 c. 169: 25 23 23 23 27 18 30 SP SD: 1.2130 c. M: 2.4438 c. 186: 28 25 25 25 30 20 33 SP SD: 1.1474 c. M: 2.5591 c. 193: 29 26 26 26 31 21 34 SP SD: 0.9862 c. M: 1.8031 c. 207: 31 28 28 28 33 22 37 SP SD: 1.0043 c. M: 1.9179 c. 214: 32 29 29 29 34 23 38 SP SD: 0.7982 c. M: 1.3551 c. 281: 42 38 38 38 45 30 50 SP SD: 0.7955 c. M: 1.0569 c. 288: 43 39 39 39 46 31 51 SP SD: 0.7026 c. M: 1.0278 c. 293: 44 40 39 40 47 31 52 SP SD: 0.6279 c. M:-1.2935 c. 295: 44 40 40 40 47 32 52 SP SD: 0.8452 c. M: 1.0000 c. 300: 45 41 40 41 48 32 53 SP SD: 0.7015 c. M:-1.2667 c. 327: 49 44 44 45 52 35 58 SP SD: 0.6984 c. M: 1.4037 c. 360: 54 49 48 49 58 38 64 SP SD: 0.4816 c. M: 0.7778 c. 367: 55 50 49 50 59 39 65 SP SD: 0.3369 c. M:-0.6131 c. 441: 66 60 59 60 71 47 78 SP SD: 0.3270 c. M:-0.5329 c. 486: 73 66 65 66 78 52 86 SP SD: 0.3007 c. M:-0.4897 c. 581: 87 79 78 79 93 62 103 SP SD: 0.2605 c. M:-0.5594 c. 599: 90 81 80 82 96 64 106 SP SD: 0.2527 c. M: 0.5426 c. 648: 97 88 87 88 104 69 115 SP SD: 0.2962 c. M: 0.4444 c. 655: 98 89 88 89 105 70 116 SP SD: 0.2562 c. M: 0.4504 c. 687: 103 93 92 94 110 73 122 SP SD: 0.2822 c. M: 0.5488 c. 694: 104 94 93 95 111 74 123 SP SD: 0.2105 c. M: 0.3429 c. 739: 111 100 99 101 118 79 131 SP SD: 0.1952 c. M: 0.3180 c. 806: 121 109 108 110 129 86 143 SP SD: 0.2175 c. M: 0.3548 c. 813: 122 110 109 111 130 87 144 SP SD: 0.1521 c. M: 0.2768 c. 1061: 159 144 142 145 170 113 188 SP SD: 0.1370 c. M:-0.2403 c. 1106: 166 150 148 151 177 118 196 SP SD: 0.0992 c. M:-0.1483 c. 1180: 177 160 158 161 189 126 209 SP SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 20.0000 cents 2 x x x 3 x x 4 S SD: 25.0592 cents 3 x x 4 x 5 x 6 S SD: 14.7512 cents 4 x 5 x 6 x 7:8 S SD: 17.5863 cents 5 x 6 x 7:8:9:10 S SD: 19.3994 cents 6 x 7:8:9:10:11:12 S SD: 20.5001 cents 7:8 x 9:10:11:12:14 S SD: 19.5430 cents 8:9:10:11:12:13:14:16 S SD: 13.4501 cents 9:10:11:12:13:15:16:18 SD: 7.9553 cents 17:19:21:23:25:28:30:34 SD: 7.7181 cents 18:20:22:24:26:29:32:36 SD: 6.2690 cents 19:21:23:25:28:31:33:38 SD: 5.1930 cents 24:27:29:32:35:39:42:47 SD: 4.7907 cents 27:30:33:36:39:44:47:53 SD: 4.0519 cents 28:31:34:37:41:46:49:55 SD: 3.2386 cents 36:40:44:48:53:59:63:71 SD: 3.0619 cents 37:41:45:49:54:60:65:73 SD: 1.9159 cents 46:51:56:61:67:75:81:91 SD: 1.7883 cents 57:63:69:76:83:93:100:113 SD: 1.5976 cents 73:81:89:97:107:119:128:144 SD: 1.4833 cents 76:84:92:101:111:124:133:150 SD: 1.2749 cents 84:93:102:112:123:137:147:166 SD: 0.8727 cents 102:113:124:136:149:166:179:202 SD: 0.7811 cents 121:134:147:161:177:197:212:239 SD: 0.4638 cents 130:144:158:173:190:212:228:257 SD: 0.3770 cents 251:278:305:334:367:409:440:496 SD: 0.3061 cents 269:298:327:358:393:438:471:532 SD: 0.2916 cents 278:308:338:370:406:453:487:550 SD: 0.2775 cents 308:341:374:410:450:502:540:609 SD: 0.2559 cents 326:361:396:434:476:531:571:645 SD: 0.2555 cents 335:371:407:446:489:546:587:662 SD: 0.2401 cents 354:392:430:471:517:577:620:700 SD: 0.2083 cents 399:442:485:531:583:650:699:789 SD: 0.1720 cents 447:495:543:595:653:728:783:884 SD: 0.1540 cents 456:505:554:607:666:743:799:902 SD: 0.1460 cents 493:546:599:656:720:803:864:975 SD: 0.1441 cents 558:618:678:743:815:909:978:1103 SD: 0.1409 cents 577:639:701:768:843:940:1011:1141 SD: 0.0881 cents