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