Scala analysis: China_Flute_89
89 (Flute), China
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 250.000 cents 250.000000 2: 428.000 cents 428.000000 3: 580.000 cents 580.000000 4: 780.000 cents 780.000000 5: 980.000 cents 980.000000 6: 1180.000 cents 1180.000000 7: 1380.000 cents 1380.000000 8: 1680.000 cents 1680.000000
SHOW/INTERVAL
0: 300.0000 cents 300.0000 1: 250.0000 cents 250.0000 2: 178.0000 cents 178.0000 3: 152.0000 cents 152.0000 4: 200.0000 cents 200.0000 5: 200.0000 cents 200.0000 6: 200.0000 cents 200.0000 7: 200.0000 cents 200.0000 8: 300.0000 cents 300.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 152.00000 cents 1: 1 178.00000 cents 1: 4 200.00000 cents 1: 1 250.00000 cents 1: 1 300.00000 cents 2: 1 330.00000 cents 2: 1 352.00000 cents 2: 3 400.00000 cents 2: 1 428.00000 cents 2: 1 500.00000 cents 2: 1 550.00000 cents 3: 1 530.00000 cents 3: 1 552.00000 cents 3: 1 580.00000 cents 3: 2 600.00000 cents 3: 1 700.00000 cents 3: 1 728.00000 cents 3: 1 750.00000 cents 4: 1 730.00000 cents 4: 1 752.00000 cents 4: 1 780.00000 cents 4: 1 800.00000 cents 4: 1 880.00000 cents 4: 1 900.00000 cents 4: 1 928.00000 cents 4: 1 950.00000 cents 5: 1 930.00000 cents 5: 1 952.00000 cents 5: 1 980.00000 cents 5: 2 1080.00000 cents 5: 1 1100.00000 cents 5: 1 1128.00000 cents 5: 1 1150.00000 cents 6: 1 1130.00000 cents 6: 1 1180.00000 cents 6: 1 1252.00000 cents 6: 3 1280.00000 cents 6: 1 1328.00000 cents 6: 1 1350.00000 cents 7: 1 1380.00000 cents 7: 1 1430.00000 cents 7: 4 1480.00000 cents 7: 1 1502.00000 cents 7: 1 1528.00000 cents Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 6.28571 = 44/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 250.0 428.0 580.0 780.0 980.0 1180.0 1380.0 1680.0 250.0 : 178.0 330.0 530.0 730.0 930.0 1130.0 1430.0 1680.0 428.0 : 152.0 352.0 552.0 752.0 952.0 1252.0 1502.0 1680.0 580.0 : 200.0 400.0 600.0 800.0 1100.0 1350.0 1528.0 1680.0 780.0 : 200.0 400.0 600.0 900.0 1150.0 1328.0 1480.0 1680.0 980.0 : 200.0 400.0 700.0 950.0 1128.0 1280.0 1480.0 1680.0 1180.0: 200.0 500.0 750.0 928.0 1080.0 1280.0 1480.0 1680.0 1380.0: 300.0 550.0 728.0 880.0 1080.0 1280.0 1480.0 1680.0 1680.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 152.0000 .. 300.0000 cents 148.00000 cents 152.00000 cents 2: 330.0000 .. 550.0000 cents 220.00000 cents 30.00000 cents 3: 530.0000 .. 750.0000 cents 220.00000 cents -20.00000 cents 4: 730.0000 .. 950.0000 cents 220.00000 cents -20.00000 cents 5: 930.0000 .. 1150.0000 cents 220.00000 cents -20.00000 cents 6: 1130.0000 .. 1350.0000 cents 220.00000 cents -20.00000 cents 7: 1380.0000 .. 1528.0000 cents 148.00000 cents 30.00000 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 152.00000 cents, class 1 Average step (divided formal octave): 210.0000 cents Largest one step interval : 300.00000 cents Average / Smallest step : 1.381579 Largest / Average step : 1.428571 Largest / Smallest step : 1.973684 Median interval of one step : 200.00000 cents, amount: 4 Most common interval of one step : 200.00000 cents, amount: 4 Least squares average step : 201.20588 cents, oct.: 1609.64706 cents Scale is not proper Scale is a mode of a 840-tone equal temperament with octave 1680.000 cents degrees: 125 214 290 390 490 590 690 840 Least number of segments generator : 421 of 842.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 677 of 1354.000 cents and inv. generated superset size: 136 = 128 more = 1700.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDDDDE Step pattern size order : DBACCCCE Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 2.00000 cents Scale diversity : 0.624764 Lumma stability : 0.216667 Lumma impropriety factor : 0.047619 Rothenberg efficiency : 0.309375 redundancy: 0.690625 Efficiency x scale size : 2.475000 Number of different interval sizes : 44 = 6.28571 / class Number of one step interval sizes : 5 Highest interval variety : 8 Mean interval variety : 6.28571 = 44/7 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 2.00000 cents Most common intervals : 200.00000 cents & inv., amount: 4 Most common triad is 0.0 200.000 1480.000 cents, amount: 3 Number of recognisable fifths : 1, average 700.0000 cents Number of recognisable fourths : 1, average 500.0000 cents Formal octave complements present : 1 = 12.5000% 2/1 octave complements present : 0 = 0.0000% -- Rational properties --
FIT/MODE
8: 1 1 1 1 1 1 1 1 SP B ME I SD: 58.2709 c. M:-90.0000 c. 9: 1 1 1 1 1 1 1 2 P M ME SD: 49.5810 c. M: 73.3333 c. 11: 2 1 1 1 1 2 1 2 N SD: 37.1440 c. M: 63.6364 c. 12: 2 1 1 2 1 1 2 2 N D3 SD: 33.4739 c. M:-60.0000 c. 15: 2 2 1 2 2 2 1 3 P D3 SD: 28.0089 c. M:-52.0000 c. 16: 2 2 1 2 2 2 2 3 P T3 SD: 33.1455 c. M: 55.0000 c. 17: 3 1 2 2 2 2 2 3 N SD: 21.2828 c. M:-46.4706 c. 19: 3 2 2 2 2 2 3 3 N SD: 23.4279 c. M:-38.9474 c. 20: 3 2 2 2 3 2 2 4 N SD: 18.7216 c. M: 36.0000 c. 21: 3 2 2 3 2 3 2 4 P SD: 18.9868 c. M: 28.0000 c. 23: 3 3 2 3 2 3 3 4 P SD: 18.5191 c. M: 30.8696 c. 24: 4 2 2 3 3 3 3 4 N SD: 15.6684 c. M:-30.0000 c. 26: 4 3 2 3 3 3 3 5 N SD: 14.2348 c. M:-24.3077 c. 28: 4 3 3 3 3 4 3 5 P SD: 13.0576 c. M:-20.0000 c. 33: 5 3 3 4 4 4 4 6 N SD: 13.1929 c. M: 20.7273 c. 34: 5 4 3 4 4 4 4 6 P SD: 9.2345 c. M:-16.7059 c. 38: 6 4 3 5 4 5 4 7 N SD: 11.4030 c. M:-15.7895 c. 39: 6 4 3 5 5 4 5 7 N SD: 10.6378 c. M: 20.0000 c. 40: 6 4 4 5 4 5 5 7 N SD: 9.3808 c. M:-18.0000 c. 41: 6 4 4 5 5 5 5 7 P SD: 8.9881 c. M: 18.2439 c. 43: 6 5 4 5 5 5 5 8 P SD: 8.0253 c. M: 15.5814 c. 46: 7 5 4 5 6 5 6 8 N SD: 8.3093 c. M: 13.0435 c. 47: 7 5 4 6 5 6 6 8 N SD: 8.1104 c. M: 14.8936 c. 50: 7 6 4 6 6 6 6 9 P SD: 7.7369 c. M: 14.8000 c. 51: 8 5 5 6 6 6 6 9 N SD: 8.4968 c. M:-13.5294 c. 54: 8 6 5 6 6 7 6 10 N SD: 8.3448 c. M: 15.5556 c. 55: 8 6 5 7 6 7 6 10 P SD: 7.0397 c. M:-14.1818 c. 58: 9 6 5 7 7 7 7 10 N SD: 6.6042 c. M:-10.6897 c. 60: 9 6 6 7 7 7 7 11 N SD: 5.3385 c. M: 8.0000 c. 67: 10 7 6 8 8 8 8 12 N SD: 1.9023 c. M: 3.2836 c. 168: 25 18 15 20 20 20 20 30 N SD: 0.7071 c. M:-2.0000 c. 235: 35 25 21 28 28 28 28 42 N SD: 0.6109 c. M: 0.9362 c. 403: 60 43 36 48 48 48 48 72 N SD: 0.5724 c. M:-1.3797 c. 437: 65 46 40 52 52 52 52 78 N SD: 0.5278 c. M: 1.2723 c. 483: 72 51 44 57 58 57 58 86 N SD: 0.7071 c. M:-0.8696 c. 487: 72 52 44 58 58 58 58 87 N SD: 0.6294 c. M: 1.6222 c. 504: 75 53 46 60 60 60 60 90 N SD: 0.4714 c. M: 1.3333 c. 525: 78 56 47 63 62 63 62 94 N SD: 0.7071 c. M:-0.8000 c. 530: 79 56 48 63 63 63 63 95 N SD: 0.5573 c. M: 1.1321 c. 538: 80 57 49 64 64 64 64 96 N SD: 0.4538 c. M:-0.8178 c. 605: 90 64 55 72 72 72 72 108 N SD: 0.2373 c. M: 0.3636 c. 672: 100 71 61 80 80 80 80 120 N SD: 0.1768 c. M: 0.5000 c. 773: 115 82 70 92 92 92 92 138 N SD: 0.1649 c. M:-0.2846 c. 840: 125 89 76 100 100 100 100 150 N SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x x x x 2 x 3 S SD: 111.4271 cents 2 x x x 3 x 4 x 5 S SD: 41.1881 cents 3 x 4 x x 5:6:7:8 S SD: 29.8836 cents 4 x 5 x 6:7:8:9:11 SD: 19.7284 cents 5:6 x 7:8:9:10:11:13 SD: 12.8992 cents 6:7:8 x 9:11:12:13:16 SD: 19.4491 cents 7:8:9:10:11:12:14:16:18 S SD: 11.8909 cents 10:12:13:14:16:18:20:22:26 SD: 11.7529 cents 11:13:14:15:17:19:22:24:29 SD: 10.1579 cents 12:14:15:17:19:21:24:27:32 SD: 8.1160 cents 13:15:17:18:20:23:26:29:34 SD: 7.4616 cents 14:16:18:20:22:25:28:31:37 SD: 6.6184 cents 17:20:22:24:27:30:34:38:45 SD: 6.4264 cents 18:21:23:25:28:32:36:40:48 SD: 5.0667 cents 25:29:32:35:39:44:49:55:66 SD: 3.0852 cents 32:37:41:45:50:56:63:71:84 SD: 2.5755 cents 33:38:42:46:52:58:65:73:87 SD: 2.1973 cents 45:52:58:63:71:79:89:100:119 SD: 2.0776 cents 46:53:59:64:72:81:91:102:121 SD: 1.5496 cents 58:67:74:81:91:102:115:129:153 SD: 1.1856 cents 78:90:100:109:122:137:154:173:206 SD: 1.0681 cents 83:96:106:116:130:146:164:184:219 SD: 0.8299 cents 96:111:123:134:151:169:190:213:253 SD: 0.7603 cents 118:136:151:165:185:208:233:262:311 SD: 0.7267 cents 121:140:155:169:190:213:239:269:319 SD: 0.6491 cents 128:148:164:179:201:225:253:284:338 SD: 0.5336 cents 160:185:205:224:251:282:316:355:422 SD: 0.4844 cents 168:194:215:235:264:296:332:373:443 SD: 0.4417 cents 181:209:232:253:284:319:358:402:478 SD: 0.3849 cents 206:238:264:288:323:363:407:457:544 SD: 0.3424 cents 214:247:274:299:336:377:423:475:565 SD: 0.3037 cents 218:252:279:305:342:384:431:484:575 SD: 0.2847 cents 264:305:338:369:414:465:522:586:697 SD: 0.1820 cents 360:416:461:503:565:634:712:799:950 SD: 0.1581 cents 432:499:553:604:678:761:854:959:1140 SD: 0.1245 cents 520:601:666:727:816:916:1028:1154:1372 SD: 0.1096 cents