Scala analysis: Vietnam_Sa_Mac

Sa Mac (Dan Tranh), Vietnam

Generated by Scala: https://www.huygens-fokker.org/scala/

SHOW
  0:          1/1               0.000000 unison, perfect prime
  1:        338.000 cents     338.000000
  2:        504.000 cents     504.000000
  3:        699.000 cents     699.000000
  4:       1026.000 cents    1026.000000
  5:       1200.000 cents    1200.000000
SHOW/INTERVAL
  0:        174.0000 cents    174.0000
  1:        338.0000 cents    338.0000
  2:        166.0000 cents    166.0000
  3:        195.0000 cents    195.0000
  4:        327.0000 cents    327.0000
  5:        174.0000 cents    174.0000
SHOW INTERVALS
Interval class, Number of incidences, Size:
  1:   1 166.00000 cents
  1:   1 174.00000 cents
  1:   1 195.00000 cents
  1:   1 327.00000 cents
  1:   1 338.00000 cents
  2:   1 361.00000 cents
  2:   1 501.00000 cents
  2:   1 504.00000 cents
  2:   1 512.00000 cents
  2:   1 522.00000 cents
  3:   1 678.00000 cents
  3:   1 688.00000 cents
  3:   1 696.00000 cents
  3:   1 699.00000 cents
  3:   1 839.00000 cents
  4:   1 862.00000 cents
  4:   1 873.00000 cents
  4:   1 1005.00000 cents
  4:   1 1026.00000 cents
  4:   1 1034.00000 cents
Highest number of different intervals for one interval class: 5
Average number of different intervals per interval class: 5.00000 = 5
SHOW/LINE/CENTS INTERVALS
         1     2     3     4      5     
 0.0   : 338.0 504.0 699.0 1026.0 1200.0
 338.0 : 166.0 361.0 688.0 862.0  1200.0
 504.0 : 195.0 522.0 696.0 1034.0 1200.0
 699.0 : 327.0 501.0 839.0 1005.0 1200.0
 1026.0: 174.0 512.0 678.0 873.0  1200.0
 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class:
  1:  166.0000  .. 338.0000 cents      172.00000 cents                    166.00000 cents
  2:  361.0000  .. 522.0000 cents      161.00000 cents                    23.00000 cents
  3:  678.0000  .. 839.0000 cents      161.00000 cents                    156.00000 cents
  4:  862.0000  .. 1034.0000 cents     172.00000 cents                    23.00000 cents
SHOW DATA
Number of notes                     : 5
-- Interval properties --
Smallest interval                   : 166.00000 cents, class 1
Average step (divided formal octave): 240.0000 cents
Largest one step interval           : 338.00000 cents
Average / Smallest step             : 1.445783
Largest / Average step              : 1.408333
Largest / Smallest step             : 2.036145
Median interval of one step         : 195.00000 cents, amount: 1
Least squares average step          : 246.30909 cents, oct.:  1231.54545 cents
Scale is strictly proper
Scale is a mode of a 1200-tone equal temperament with octave  1200.000 cents
  degrees: 338 504 699 1026 1200
Least number of segments generator  : 601 of 601.000 cents and inv.
  number of contiguous generator circle segments: 1
Shortest superset generator         : 857 of 857.000 cents and inv.
  generated superset size: 166 = 161 more = 3320.000%
Number of contiguous 1-step segments: 0
Step pattern alph. order: ABCDE
Step pattern size order : EACDB
Scale is sum-free (all different intervals)
Scale is a Constant Structure, by a margin of 23.00000 cents
Scale diversity                     : 1.380338
Rothenberg stability                : 1.000000 = 1
Lumma stability                     : 0.445000
Rothenberg efficiency               : 0.400000   redundancy: 0.600000
Efficiency x scale size             : 2.000000
Number of different interval sizes  : 20 = 5.00000 / class
Number of one step interval sizes   : 5
Highest interval variety            : 5
Mean interval variety               : 5.00000 = 5
Median interval variety             : 5
Lowest interval variety             : 5
Smallest interval difference        : 3.00000 cents
Number of recognisable fifths       : 3, average 694.3333 cents
Number of appreciable fifths        : 2, average 697.5000 cents
Best fifths form a closed circle
Formal octave complements present   : 1 = 20.0000%
Limited inverse transpositions with margin 172.0000 cents:
 4
-- Rational properties --
FIT/MODE
  5:  1 1 1 1 1  SP B ME I SD: 54.7302 c. M: 98.0000 c. 
  7:  2 1 1 2 1   P M ME S SD: 7.9058 c. M: 13.2857 c.  Thai mode 6
 22:  6 3 4 6 3  SP   T3   SD: 9.9567 c. M: 13.0909 c. 
 26:  7 4 4 7 4  SP M DE S SD: 8.8747 c. M: 14.9231 c. 
 29:  8 4 5 8 4  SP   T3   SD: 6.2568 c. M:-8.4828 c. 
 33:  9 5 5 9 5  SP M DE S SD: 7.3154 c. M: 10.7273 c. 
 36:  10 5 6 10 5  SP   T3   SD: 4.3025 c. M:-7.3333 c. 
 43:  12 6 7 12 6  SP   T3   SD: 3.3847 c. M:-6.5581 c. 
 50:  14 7 8 14 7  SP   T3   SD: 3.1305 c. M:-6.0000 c. 
 57:  16 8 9 16 8  SP   T3   SD: 3.2322 c. M:-5.5789 c. 
 60:  17 8 10 16 9  SP        SD: 3.3764 c. M: 6.0000 c. 
 64:  18 9 10 18 9  SP   T3   SD: 3.4767 c. M: 5.2500 c. 
 67:  19 9 11 18 10  SP        SD: 2.7520 c. M: 5.1045 c. 
 74:  21 10 12 20 11  SP        SD: 2.4579 c. M: 4.3784 c. 
 81:  23 11 13 22 12  SP        SD: 2.4158 c. M: 3.7778 c. 
 88:  25 12 14 24 13  SP        SD: 2.5315 c. M: 3.5455 c. 
 96:  27 13 16 26 14  SP        SD: 1.9105 c. M: 4.0000 c. 
 103: 29 14 17 28 15  SP        SD: 1.3977 c. M: 3.0291 c. 
 110: 31 15 18 30 16  SP        SD: 1.0733 c. M: 2.1818 c. 
 117: 33 16 19 32 17  SP        SD: 0.9849 c. M: 1.5641 c. 
 160: 45 22 26 44 23  SP        SD: 1.1832 c. M:-1.5000 c. 
 202: 57 28 33 55 29  SP        SD: 1.2813 c. M:-1.9901 c. 
 209: 59 29 34 57 30  SP        SD: 1.2182 c. M:-1.7512 c. 
 213: 60 29 35 58 31  SP        SD: 1.2086 c. M: 2.5915 c. 
 214: 60 30 35 58 31  SP        SD: 1.1516 c. M:-1.9346 c. 
 221: 62 31 36 60 32  SP        SD: 0.9943 c. M:-1.4525 c. 
 228: 64 32 37 62 33  SP        SD: 0.8984 c. M:-1.2632 c. 
 235: 66 33 38 64 34  SP        SD: 0.8696 c. M:-1.5319 c. 
 269: 76 37 44 73 39  SP        SD: 0.7692 c. M:-1.3717 c. 
 276: 78 38 45 75 40  SP        SD: 0.6937 c. M:-1.1304 c. 
 283: 80 39 46 77 41  SP        SD: 0.6764 c. M:-1.2226 c. 
 288: 81 40 47 78 42  SP        SD: 0.6749 c. M: 1.0000 c. 
 295: 83 41 48 80 43  SP        SD: 0.5620 c. M: 0.9153 c. 
 302: 85 42 49 82 44  SP        SD: 0.5055 c. M: 0.8344 c. 
 319: 90 44 52 87 46  SP        SD: 0.5845 c. M:-0.9592 c. 
 326: 92 45 53 89 47  SP        SD: 0.5739 c. M:-0.9939 c. 
 331: 93 46 54 90 48  SP        SD: 0.4895 c. M: 0.8399 c. 
 338: 95 47 55 92 49  SP        SD: 0.3766 c. M: 0.7219 c. 
 345: 97 48 56 94 50  SP        SD: 0.3213 c. M: 0.6087 c. 
 352: 99 49 57 96 51  SP        SD: 0.3420 c. M:-0.5455 c. 
 412: 116 57 67 112 60  SP        SD: 0.3482 c. M: 0.7573 c. 
 419: 118 58 68 114 61  SP        SD: 0.3273 c. M: 0.7017 c. 
 448: 126 62 73 122 65  SP        SD: 0.3022 c. M: 0.5000 c. 
 455: 128 63 74 124 66  SP        SD: 0.2272 c. M: 0.4176 c. 
 462: 130 64 75 126 67  SP        SD: 0.2072 c. M: 0.3377 c. 
 731: 206 101 119 199 106  SP        SD: 0.1605 c. M:-0.3160 c. 
 738: 208 102 120 201 107  SP        SD: 0.1297 c. M:-0.2114 c. 
 855: 241 118 139 233 124  SP        SD: 0.1296 c. M:-0.2456 c. 
 1076: 303 149 175 293 156  SP        SD: 0.1272 c. M:-0.2565 c. 
 1083: 305 150 176 295 157  SP        SD: 0.1064 c. M:-0.1690 c. 
 1090: 307 151 177 297 158  SP        SD: 0.1083 c. M:-0.2202 c. 
 1186: 334 164 193 323 172  SP        SD: 0.0933 c. M:-0.1568 c. 
 1193: 336 165 194 325 173  SP        SD: 0.0464 c. M:-0.0780 c. 
 1200: 338 166 195 327 174  SP        SD: 0.0000 c. M:-0.0000 c. 
FIT/HARMONIC
 1 x x x x 2  S SD: 0.0000 cents
 2 x x 3 x 4  S SD: 1.4775 cents
 3 x 4 x 5:6  S SD: 47.2555 cents
 4:5 x 6:7:8  S SD: 18.7280 cents
 6:7:8:9:11:12    SD: 15.0325 cents
 7 x 9:10:13:14    SD: 29.0283 cents
 8:10:11:12:14:16  S SD: 17.7210 cents
 9:11:12:13:16:18    SD: 14.0145 cents
 10:12:13:15:18:20    SD: 11.0597 cents
 12:15:16:18:22:24    SD: 10.8152 cents
 14:17:19:21:25:28    SD: 6.6767 cents
 18:22:24:27:33:36    SD: 5.2097 cents
 24:29:32:36:43:48    SD: 4.1089 cents
 32:39:43:48:58:64    SD: 1.9813 cents
 42:51:56:63:76:84    SD: 1.3889 cents
 56:68:75:84:101:112    SD: 1.2655 cents
 74:90:99:111:134:148    SD: 0.7314 cents
 115:140:154:172:208:230    SD: 0.7272 cents
 121:147:162:181:219:242    SD: 0.5294 cents
 157:191:210:235:284:314    SD: 0.3241 cents
 195:237:261:292:353:390    SD: 0.3239 cents
 213:259:285:319:385:426    SD: 0.2661 cents
 251:305:336:376:454:502    SD: 0.2621 cents
 287:349:384:430:519:574    SD: 0.2376 cents
 320:389:428:479:579:640    SD: 0.2083 cents
 334:406:447:500:604:668    SD: 0.1609 cents
 376:457:503:563:680:752    SD: 0.0835 cents