Scala analysis: China_Yang-chin
Yang-chin (Yangqin), China
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 169.000 cents 169.000000 2: 274.000 cents 274.000000 3: 491.000 cents 491.000000 4: 661.000 cents 661.000000 5: 878.000 cents 878.000000 6: 996.000 cents 996.000000 7: 1198.000 cents 1198.000000
SHOW/INTERVAL
0: 202.0000 cents 202.0000 1: 169.0000 cents 169.0000 2: 105.0000 cents 105.0000 3: 217.0000 cents 217.0000 4: 170.0000 cents 170.0000 5: 217.0000 cents 217.0000 6: 118.0000 cents 118.0000 7: 202.0000 cents 202.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 105.00000 cents 1: 1 118.00000 cents 1: 1 169.00000 cents 1: 1 170.00000 cents 1: 1 202.00000 cents 1: 2 217.00000 cents 2: 1 274.00000 cents 2: 1 320.00000 cents 2: 1 322.00000 cents 2: 1 335.00000 cents 2: 1 371.00000 cents 2: 2 387.00000 cents 3: 1 476.00000 cents 3: 1 489.00000 cents 3: 1 491.00000 cents 3: 1 492.00000 cents 3: 1 505.00000 cents 3: 1 537.00000 cents 3: 1 604.00000 cents 4: 1 594.00000 cents 4: 1 661.00000 cents 4: 1 693.00000 cents 4: 1 706.00000 cents 4: 1 707.00000 cents 4: 1 709.00000 cents 4: 1 722.00000 cents 5: 2 811.00000 cents 5: 1 827.00000 cents 5: 1 863.00000 cents 5: 1 876.00000 cents 5: 1 878.00000 cents 5: 1 924.00000 cents 6: 2 981.00000 cents 6: 1 996.00000 cents 6: 1 1028.00000 cents 6: 1 1029.00000 cents 6: 1 1080.00000 cents 6: 1 1093.00000 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 6.33333 = 19/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 169.0 274.0 491.0 661.0 878.0 996.0 1198.0 169.0 : 105.0 322.0 492.0 709.0 827.0 1029.0 1198.0 274.0 : 217.0 387.0 604.0 722.0 924.0 1093.0 1198.0 491.0 : 170.0 387.0 505.0 707.0 876.0 981.0 1198.0 661.0 : 217.0 335.0 537.0 706.0 811.0 1028.0 1198.0 878.0 : 118.0 320.0 489.0 594.0 811.0 981.0 1198.0 996.0 : 202.0 371.0 476.0 693.0 863.0 1080.0 1198.0 1198.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 105.0000 .. 217.0000 cents 112.00000 cents 105.00000 cents 2: 274.0000 .. 387.0000 cents 113.00000 cents 57.00000 cents 3: 476.0000 .. 604.0000 cents 128.00000 cents 89.00000 cents 4: 594.0000 .. 722.0000 cents 128.00000 cents -10.00000 cents 5: 811.0000 .. 924.0000 cents 113.00000 cents 89.00000 cents 6: 981.0000 .. 1093.0000 cents 112.00000 cents 57.00000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 105.00000 cents, class 1 Average step (divided formal octave): 171.1429 cents Largest one step interval : 217.00000 cents Average / Smallest step : 1.629932 Largest / Average step : 1.267947 Largest / Smallest step : 2.066667 Median interval of one step : 170.00000 cents, amount: 1 Most common interval of one step : 217.00000 cents, amount: 2 Least squares average step : 168.47143 cents, oct.: 1179.30000 cents Scale is not proper Scale is a mode of a 1198-tone equal temperament with octave 1198.000 cents degrees: 169 274 491 661 878 996 1198 Least number of segments generator : 601 of 601.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1063 of 1063.000 cents and inv. generated superset size: 287 = 280 more = 4100.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDCEF Step pattern size order : CAFDFBE Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 10.00000 cents Scale diversity : 1.559445 Lumma stability : 0.419032 Lumma impropriety factor : 0.008347 Rothenberg efficiency : 0.312925 redundancy: 0.687075 Efficiency x scale size : 2.190476 Number of different interval sizes : 38 = 6.33333 / class Number of one step interval sizes : 6 Highest interval variety : 7 Mean interval variety : 6.33333 = 19/3 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 1.00000 cents Number of recognisable fifths : 4, average 703.7500 cents Number of recognisable fourths : 4, average 494.2500 cents Best fifths 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% -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 32.0156 c. M:-68.2857 c. Lebeng 8: 1 1 1 1 2 1 1 P M ME S SD: 37.3367 c. M: 62.0000 c. 10: 1 1 2 1 2 1 2 P M ME S SD: 38.8281 c. M: 62.0000 c. 11: 1 1 2 2 2 1 2 N D3 SD: 38.1442 c. M: 60.0909 c. 12: 2 1 2 2 2 1 2 P M ME I SD: 22.4068 c. M:-37.8333 c. G.Phrygian, M.Dorian, M.Hypomixolydian, Kafi That, Mela Kharaharapriya, Raga Bageshri, Bhimpalasi, Huseni, Kanara, Kapi, Nayaki Kanada, Ritigaula, Sriraga, Mischung 5, Gregorian nr.8, Eskimo Heptatonic, Yu: China, Hyojo, Oshikicho, Banshikicho: Japan, Nam: Vietnam 14: 2 1 3 2 2 2 2 P T3 SD: 20.0387 c. M:-30.8571 c. 17: 2 2 3 2 3 2 3 SP M ME S SD: 19.6626 c. M: 32.3529 c. Safi al-Din's maqam Higazi 18: 2 2 3 3 3 2 3 P D3 SD: 17.6009 c. M: 35.8889 c. 20: 3 2 3 3 4 2 3 P T3 SD: 16.1508 c. M:-25.5000 c. 22: 3 2 4 3 4 2 4 P T3 SD: 7.4449 c. M: 15.8182 c. 29: 4 3 5 4 5 3 5 SP T3 SD: 7.5333 c. M:-15.1724 c. 31: 4 3 6 4 6 3 5 N SD: 8.9478 c. M: 14.4194 c. 34: 5 3 6 5 6 3 6 P T3 SD: 6.4091 c. M: 9.4118 c. 42: 6 4 7 6 8 4 7 P SD: 5.8177 c. M:-11.2381 c. 49: 7 4 9 7 9 5 8 N SD: 3.3976 c. M:-6.4082 c. 71: 10 6 13 10 13 7 12 N SD: 2.0125 c. M: 4.0282 c. 78: 11 7 14 11 14 8 13 P SD: 1.6259 c. M: 2.5385 c. 105: 15 9 19 15 19 10 18 N SD: 1.5580 c. M: 3.3714 c. 149: 21 13 27 21 27 15 25 N SD: 1.0129 c. M: 1.6980 c. 161: 23 14 29 23 29 16 27 N SD: 1.1397 c. M:-2.1429 c. 183: 26 16 33 26 33 18 31 N SD: 0.7450 c. M:-1.2077 c. 232: 33 20 42 33 42 23 39 N SD: 0.6175 c. M:-1.4052 c. 254: 36 22 46 36 46 25 43 N SD: 0.6221 c. M: 0.8110 c. 297: 42 26 54 42 54 29 50 N SD: 0.7222 c. M:-1.3401 c. 310: 44 27 56 44 56 31 52 N SD: 0.6499 c. M:-1.0452 c. 319: 45 28 58 45 58 31 54 N SD: 0.5619 c. M:-0.9687 c. 368: 52 32 67 52 67 36 62 N SD: 0.4906 c. M:-0.9674 c. 381: 54 33 69 54 69 38 64 N SD: 0.6131 c. M:-0.7953 c. 390: 55 34 71 55 71 38 66 N SD: 0.5015 c. M: 0.7385 c. 397: 56 35 72 56 72 39 67 N SD: 0.4138 c. M:-0.8741 c. 446: 63 39 81 63 81 44 75 N SD: 0.3439 c. M:-0.5561 c. 468: 66 41 85 66 85 46 79 N SD: 0.2975 c. M: 0.5641 c. 547: 77 48 99 78 99 54 92 N SD: 0.3475 c. M:-0.5082 c. 551: 78 48 100 78 100 54 93 N SD: 0.3127 c. M:-0.5898 c. 569: 80 50 103 81 103 56 96 N SD: 0.2969 c. M: 0.5641 c. 622: 88 54 113 88 113 61 105 N SD: 0.3337 c. M: 0.5016 c. 629: 89 55 114 89 114 62 106 N SD: 0.2686 c. M:-0.5103 c. 647: 91 57 117 92 117 64 109 N SD: 0.2663 c. M: 0.5023 c. 651: 92 57 118 92 118 64 110 N SD: 0.2920 c. M: 0.4270 c. 652: 92 57 118 93 118 64 110 N SD: 0.2773 c. M:-0.4724 c. 700: 99 61 127 99 127 69 118 N SD: 0.2399 c. M:-0.4314 c. 730: 103 64 132 104 132 72 123 N SD: 0.1907 c. M:-0.3616 c. 752: 106 66 136 107 136 74 127 N SD: 0.2040 c. M: 0.3298 c. 879: 124 77 159 125 159 87 148 N SD: 0.2039 c. M: 0.3515 c. 913: 129 80 165 130 165 90 154 N SD: 0.2185 c. M:-0.3275 c. 944: 133 83 171 134 171 93 159 N SD: 0.1674 c. M:-0.2182 c. 966: 136 85 175 137 175 95 163 N SD: 0.1483 c. M: 0.3375 c. 1015: 143 89 184 144 184 100 171 N SD: 0.1343 c. M: 0.2177 c. 1120: 158 98 203 159 203 110 189 N SD: 0.1132 c. M:-0.1768 c. 1127: 159 99 204 160 204 111 190 N SD: 0.1268 c. M:-0.2538 c. 1198: 169 105 217 170 217 118 202 N SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 2.0000 cents 2 x x x 3 x x 4 S SD: 20.5019 cents 3 x x 4 x 5 x 6 S SD: 3.2329 cents 4 x x 5:6 x 7:8 S SD: 28.9169 cents 5 x 6 x 7:8:9:10 S SD: 22.3616 cents 6 x 7:8:9:10:11:12 S SD: 11.3893 cents 7 x 8:9:10:12 x 14 S SD: 19.8969 cents 8:9 x 11:12:13:14:16 SD: 15.5285 cents 9:10:11:12:13:15:16:18 SD: 11.3001 cents 11:12:13:15:16:18:20:22 SD: 10.1035 cents 12:13:14:16:18:20:21:24 S SD: 8.4352 cents 17:19:20:23:25:28:30:34 SD: 6.4882 cents 18:20:21:24:26:30:32:36 SD: 4.3308 cents 28:31:33:37:41:46:50:56 SD: 3.6216 cents 30:33:35:40:44:50:53:60 SD: 2.3944 cents 47:52:55:62:69:78:84:94 SD: 2.3745 cents 48:53:56:64:70:80:85:96 SD: 2.2909 cents 49:54:57:65:72:81:87:98 SD: 2.2580 cents 52:57:61:69:76:86:92:104 SD: 2.2398 cents 58:64:68:77:85:96:103:116 SD: 0.9406 cents 88:97:103:117:129:146:156:176 SD: 0.8809 cents 116:128:136:154:170:193:206:232 SD: 0.6868 cents 135:149:158:179:198:224:240:270 SD: 0.6824 cents 165:182:193:219:242:274:293:330 SD: 0.6387 cents 168:185:197:223:246:279:299:336 SD: 0.5807 cents 174:192:204:231:255:289:309:348 SD: 0.4926 cents 198:218:232:263:290:329:352:396 SD: 0.4841 cents 204:225:239:271:299:339:363:408 SD: 0.4531 cents 244:269:286:324:357:405:434:487 SD: 0.4400 cents 256:282:300:340:375:425:455:511 SD: 0.3191 cents 262:289:307:348:384:435:466:523 SD: 0.2971 cents 292:322:342:388:428:485:519:583 SD: 0.2705 cents 333:367:390:442:488:553:592:665 SD: 0.2050 cents 351:387:411:466:514:583:624:701 SD: 0.1808 cents 409:451:479:543:599:679:727:817 SD: 0.1332 cents 536:591:628:712:785:890:953:1071 SD: 0.1312 cents