Scala analysis: China_Flute_90
90 (Flute), China
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 264.000 cents 264.000000 2: 430.000 cents 430.000000 3: 607.000 cents 607.000000 4: 763.000 cents 763.000000 5: 910.000 cents 910.000000 6: 1145.000 cents 1145.000000 7: 1462.000 cents 1462.000000
SHOW/INTERVAL
0: 317.0000 cents 317.0000 1: 264.0000 cents 264.0000 2: 166.0000 cents 166.0000 3: 177.0000 cents 177.0000 4: 156.0000 cents 156.0000 5: 147.0000 cents 147.0000 6: 235.0000 cents 235.0000 7: 317.0000 cents 317.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 147.00000 cents 1: 1 156.00000 cents 1: 1 166.00000 cents 1: 1 177.00000 cents 1: 1 235.00000 cents 1: 1 264.00000 cents 1: 1 317.00000 cents 2: 1 303.00000 cents 2: 1 333.00000 cents 2: 1 343.00000 cents 2: 1 382.00000 cents 2: 1 430.00000 cents 2: 1 552.00000 cents 2: 1 581.00000 cents 3: 1 480.00000 cents 3: 1 499.00000 cents 3: 1 538.00000 cents 3: 1 607.00000 cents 3: 1 699.00000 cents 3: 1 747.00000 cents 3: 1 816.00000 cents 4: 1 646.00000 cents 4: 1 715.00000 cents 4: 1 763.00000 cents 4: 1 855.00000 cents 4: 1 924.00000 cents 4: 1 963.00000 cents 4: 1 982.00000 cents 5: 1 881.00000 cents 5: 1 910.00000 cents 5: 1 1032.00000 cents 5: 1 1080.00000 cents 5: 1 1119.00000 cents 5: 1 1129.00000 cents 5: 1 1159.00000 cents 6: 1 1145.00000 cents 6: 1 1198.00000 cents 6: 1 1227.00000 cents 6: 1 1285.00000 cents 6: 1 1296.00000 cents 6: 1 1306.00000 cents 6: 1 1315.00000 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 : 264.0 430.0 607.0 763.0 910.0 1145.0 1462.0 264.0 : 166.0 343.0 499.0 646.0 881.0 1198.0 1462.0 430.0 : 177.0 333.0 480.0 715.0 1032.0 1296.0 1462.0 607.0 : 156.0 303.0 538.0 855.0 1119.0 1285.0 1462.0 763.0 : 147.0 382.0 699.0 963.0 1129.0 1306.0 1462.0 910.0 : 235.0 552.0 816.0 982.0 1159.0 1315.0 1462.0 1145.0: 317.0 581.0 747.0 924.0 1080.0 1227.0 1462.0 1462.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 147.0000 .. 317.0000 cents 170.00000 cents 147.00000 cents 2: 303.0000 .. 581.0000 cents 278.00000 cents -14.00000 cents 3: 480.0000 .. 816.0000 cents 336.00000 cents -101.00000 cents 4: 646.0000 .. 982.0000 cents 336.00000 cents -170.00000 cents 5: 881.0000 .. 1159.0000 cents 278.00000 cents -101.00000 cents 6: 1145.0000 .. 1315.0000 cents 170.00000 cents -14.00000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 147.00000 cents, class 1 Average step (divided formal octave): 208.8571 cents Largest one step interval : 317.00000 cents Average / Smallest step : 1.420797 Largest / Average step : 1.517784 Largest / Smallest step : 2.156463 Median interval of one step : 177.00000 cents, amount: 1 Least squares average step : 197.50714 cents, oct.: 1382.55000 cents Scale is not proper Scale is a mode of a 1462-tone equal temperament with octave 1462.000 cents degrees: 264 430 607 763 910 1145 1462 Least number of segments generator : 733 of 733.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 753 of 753.000 cents and inv. generated superset size: 334 = 327 more = 4771.429% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDEFG Step pattern size order : FCDBAEG Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 14.00000 cents Scale diversity : 1.040606 Lumma stability : 0.201094 Lumma impropriety factor : 0.273598 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 : 9.00000 cents Number of recognisable fifths : 2, average 707.0000 cents Number of appreciable fifths : 1, average 699.0000 cents Number of recognisable fourths : 2, average 489.5000 cents Number of appreciable fourths : 1, average 499.0000 cents Formal octave complements present : 1 = 14.2857% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
7: 1 1 1 0 1 1 2 N T3 SD: 73.5738 c. M: 136.4286 c. 8: 1 1 1 1 1 1 2 P M ME S SD: 50.1479 c. M: 81.2500 c. 9: 2 1 1 1 1 1 2 N D3 I SD: 47.0431 c. M:-64.6667 c. 10: 2 1 1 1 1 2 2 N S SD: 24.1376 c. M: 32.8000 c. 16: 3 2 2 1 2 3 3 N SD: 26.0919 c. M:-42.8750 c. 17: 3 2 2 2 2 2 4 N SD: 17.7563 c. M:-36.0000 c. 21: 4 2 3 2 2 3 5 N SD: 15.7792 c. M: 31.0952 c. 23: 4 3 3 2 2 4 5 N SD: 14.8503 c. M:-28.6522 c. 24: 4 3 3 3 2 4 5 N SD: 14.3198 c. M:-28.9167 c. 27: 5 3 3 3 3 4 6 N SD: 7.3873 c. M: 11.3704 c. 38: 7 4 5 4 4 6 8 N SD: 8.0482 c. M:-13.3684 c. 48: 9 5 6 5 5 8 10 N SD: 6.4439 c. M:-12.4167 c. 50: 9 6 6 5 5 8 11 N SD: 4.8704 c. M:-8.6000 c. 55: 10 6 7 6 5 9 12 N SD: 4.6149 c. M:-7.8727 c. 61: 11 7 7 7 6 10 13 N SD: 3.9440 c. M: 7.8197 c. 74: 13 9 9 8 7 12 16 N SD: 4.8014 c. M:-7.5135 c. 75: 14 8 9 8 8 12 16 N SD: 4.7800 c. M:-8.9067 c. 77: 14 9 9 8 8 12 17 N SD: 3.7078 c. M:-6.7013 c. 79: 14 9 10 8 8 13 17 N SD: 3.6000 c. M: 4.9114 c. 82: 15 9 10 9 8 13 18 N SD: 2.5685 c. M: 3.9268 c. 106: 19 12 13 11 11 17 23 N SD: 2.0478 c. M: 4.4151 c. 111: 20 13 13 12 11 18 24 N SD: 1.9376 c. M:-4.6486 c. 140: 25 16 17 15 14 23 30 N SD: 2.0741 c. M:-3.7143 c. 149: 27 17 18 16 15 24 32 N SD: 1.9498 c. M:-3.0134 c. 157: 28 18 19 17 16 25 34 N SD: 1.8307 c. M: 3.2611 c. 161: 29 18 20 17 16 26 35 N SD: 1.5643 c. M: 3.2050 c. 167: 30 19 20 18 17 27 36 N SD: 1.5590 c. M: 2.9401 c. 188: 34 21 23 20 19 30 41 N SD: 1.1821 c. M: 2.2872 c. 193: 35 22 23 21 19 31 42 N SD: 1.3146 c. M:-2.0881 c. 207: 37 24 25 22 21 33 45 N SD: 1.1926 c. M: 2.6763 c. 217: 39 25 26 23 22 35 47 N SD: 0.9661 c. M: 1.6820 c. 255: 46 29 31 27 26 41 55 N SD: 0.9384 c. M:-1.6667 c. 272: 49 31 33 29 27 44 59 N SD: 0.6814 c. M: 1.6250 c. 299: 54 34 36 32 30 48 65 N SD: 0.4726 c. M: 0.8261 c. 448: 81 51 54 48 45 72 97 N SD: 0.4696 c. M:-0.7679 c. 527: 95 60 64 56 53 85 114 N SD: 0.3907 c. M:-0.7419 c. 554: 100 63 67 59 56 89 120 N SD: 0.2543 c. M:-0.4513 c. 609: 110 69 74 65 61 98 132 N SD: 0.2455 c. M:-0.4089 c. 636: 115 72 77 68 64 102 138 N SD: 0.2196 c. M:-0.3553 c. 826: 149 94 100 88 83 133 179 N SD: 0.1691 c. M: 0.2736 c. 908: 164 103 110 97 91 146 197 N SD: 0.1551 c. M: 0.2753 c. 1163: 210 132 141 124 117 187 252 N SD: 0.1215 c. M:-0.2124 c. 1462: 264 166 177 156 147 235 317 N SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x x 2 x S SD: 55.0000 cents 2 x x x 3 x 4:5 S SD: 49.6716 cents 3 x 4 x x 5:6:7 S SD: 22.8259 cents 4 x 5 x 6:7:8:9 S SD: 24.8957 cents 5:6 x 7:8 x 10:12 S SD: 21.6684 cents 6:7:8 x 9:10:12:14 S SD: 18.3114 cents 7:8:9:10:11:12:14:16 S SD: 11.1607 cents 11:13:14:16:17:19:21:26 SD: 10.4190 cents 12:14:15:17:19:20:23:28 SD: 9.0609 cents 13:15:17:18:20:22:25:30 SD: 9.0563 cents 14:16:18:20:22:24:27:33 SD: 7.4169 cents 17:20:22:24:26:29:33:40 SD: 6.4220 cents 18:21:23:26:28:30:35:42 SD: 5.7868 cents 22:26:28:31:34:37:43:51 SD: 5.3970 cents 24:28:31:34:37:41:47:56 SD: 4.6096 cents 29:34:37:41:45:49:56:67 SD: 3.0190 cents 31:36:40:44:48:52:60:72 SD: 2.9079 cents 36:42:46:51:56:61:70:84 SD: 1.6354 cents 43:50:55:61:67:73:83:100 SD: 1.6354 cents 61:71:78:87:95:103:118:142 SD: 1.5142 cents 67:78:86:95:104:113:130:156 SD: 0.9961 cents 85:99:109:121:132:144:165:198 SD: 0.9279 cents 103:120:132:146:160:174:200:240 SD: 0.8534 cents 110:128:141:156:171:186:213:256 SD: 0.4390 cents 159:185:204:226:247:269:308:370 SD: 0.4246 cents 181:211:232:257:281:306:351:421 SD: 0.4125 cents 188:219:241:267:292:318:364:437 SD: 0.3184 cents 195:227:250:277:303:330:378:454 SD: 0.2834 cents 224:261:287:318:348:379:434:521 SD: 0.2102 cents 334:389:428:474:519:565:647:777 SD: 0.1801 cents 383:446:491:544:595:648:742:891 SD: 0.1250 cents 493:574:632:700:766:834:955:1147 SD: 0.1077 cents