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