Scala analysis: xen12-chalmers-tritriadic-dm-17-27-5
Tritriadic D->M scale built from 17:27:5
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 729/680 120.460882 2: 20/17 281.358304 septendecimal augmented second 3: 27/20 519.551289 acute fourth 4: 40/27 680.448711 grave fifth 5: 27/17 800.909593 septendecimal minor sixth 6: 800/459 961.807016 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 459/400 238.1930 1: 729/680 120.4609 2: 800/729 160.8974 grave whole tone 3: 459/400 238.1930 4: 800/729 160.8974 grave whole tone 5: 729/680 120.4609 6: 800/729 160.8974 grave whole tone 7: 459/400 238.1930
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 729/680 120.461 cents 1: 3 800/729 160.897 cents grave whole tone 1: 2 459/400 238.193 cents 2: 3 20/17 281.358 cents septendecimal augmented second 2: 1 19683/16000 358.654 cents 2: 3 34/27 399.090 cents septendecimal major third 3: 1 16000/12393 442.256 cents 3: 5 27/20 519.551 cents acute fourth 3: 1 27200/19683 559.988 cents 4: 1 19683/13600 640.012 cents 4: 5 40/27 680.449 cents grave fifth 4: 1 12393/8000 757.744 cents 5: 3 27/17 800.910 cents septendecimal minor sixth 5: 1 32000/19683 841.346 cents 5: 3 17/10 918.642 cents septendecimal diminished seventh 6: 2 800/459 961.807 cents 6: 3 729/400 1039.103 cents acute minor seventh 6: 2 1360/729 1079.539 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 120.5 281.4 519.6 680.4 800.9 961.8 1200.0 120.5 : 160.9 399.1 560.0 680.4 841.3 1079.5 1200.0 281.4 : 238.2 399.1 519.6 680.4 918.6 1039.1 1200.0 519.6 : 160.9 281.4 442.3 680.4 800.9 961.8 1200.0 680.4 : 120.5 281.4 519.6 640.0 800.9 1039.1 1200.0 800.9 : 160.9 399.1 519.6 680.4 918.6 1079.5 1200.0 961.8 : 238.2 358.7 519.6 757.7 918.6 1039.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 120.4609 .. 238.1930 cents 289/270, 117.7321 cents 729/680, 120.4609 cents 2: 281.3583 .. 399.0904 cents 289/270, 117.7321 cents 8000/7803, 43.1653 cents 3: 442.2557 .. 559.9878 cents 289/270, 117.7321 cents 8000/7803, 43.1653 cents 4: 640.0122 .. 757.7443 cents 289/270, 117.7321 cents 387420489/369920000, 80.0243 cents 5: 800.9096 .. 918.6417 cents 289/270, 117.7321 cents 8000/7803, 43.1653 cents 6: 961.8070 .. 1079.5391 cents 289/270, 117.7321 cents 8000/7803, 43.1653 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 729/680, 120.4609 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 459/400, 238.1930 cents Average / Smallest step : 1.423106 Largest / Average step : 1.389459 Largest / Smallest step : 1.977347 Median interval of one step : 800/729, 160.8974 cents, amount: 3 Most common interval of one step : 800/729, 160.8974 cents, amount: 3 Least squares average step : 165.27869 cents, oct.: 1156.95081 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCBABC Step pattern size order : SMLMSML Scale is a Constant Structure, by a margin of 43.16532 cents Scale diversity : 1.433252 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.411339 Rothenberg efficiency : 0.544218 redundancy: 0.455782 Efficiency x scale size : 3.809524 Number of different interval sizes : 18 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 544000/531441, 40.4365 cents Most common intervals : 27/20, 519.5513 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 399.090 680.449 cents Most common triad is 0.0 519.551 680.449 cents, amount: 3 Number of recognisable fifths : 0 Scale contains two identical disjunct tetrachords Best fifths form a closed circle Scale contains a complete diamond : 5 27 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 17 Odd number limit : 19683 (O: 19683 U: 19683) Highest odd numerator or denominator: 729 Scale harmonicity : 0.012297 Average absolute harmonicity : 0.172362 Specific harmonicity : 0.060406 Fundamental : 1/18360, -14.1643 octaves, 0.0142 Hz. Guide tone : 583200, 19.1536 octaves, 152580029.684 Hz. Exponens Consonantiae : 1.070755E+10, 33.31791 octaves Euler's gradus suavitatis : 55 Sum of Mann's harmonic distance : 1433.0, average 204.71429 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 11.04908, average 1.57844 Sum of Tenney's harmonic distance : 22.52028, average 3.21718 Vogel's harmonic complexity : 29.14286 Wille's k value : 9841 Wilson's harmonic complexity : 59 Rectangular lattice diameter : 13 Triangular lattice diameter : 9 Lattice compactness : 147.50107, average 5.26790 Lattice compactness (without 2's) : 114.67657, average 4.09559 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 5 0.85714 16 1 3: -3 .. 6 0.85714 18 5: -1 .. 2 0.28571 6 2 17: -1 .. 0 -0.57143 4 4 Average exponent except 2's : 4 / 7 = 0.57143 Average absolute exponent except 2's: 28 / 7 = 4.00000 Scale is weakly epimorphic with val: <7 10 15 26| Scale is weakly epimorphic with val: <7 10 17 27| Scale is weakly epimorphic with val: <7 10 18 31| Scale is weakly epimorphic with val: <7 11 15 31| Scale is JI-epimorphic with val: <7 11 16 28| Scale is weakly epimorphic with val: <7 11 17 32| Scale is weakly epimorphic with val: <7 11 18 29| Scale is weakly epimorphic with val: <7 12 16 26| Scale is weakly epimorphic with val: <7 12 17 30| Scale is weakly epimorphic with val: <7 12 18 27|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 44.8090 c. M:-66.7644 c. Lebeng 9: 1 1 2 1 1 1 2 P M ME S SD: 14.9905 c. M: 28.4737 c. Pseudo Pelog, Pelogic-7, Antiionian 16: 2 2 3 2 2 2 3 SP M ME S SD: 17.0455 c. M:-29.5391 c. Pseudo Pelog, Pelogic-7, Antiionian 19: 2 2 4 3 2 2 4 P SD: 16.3970 c. M: 28.7267 c. 20: 2 3 4 2 2 3 4 P SD: 15.2339 c. M: 20.9096 c. 21: 2 3 4 3 2 3 4 SP T3 SD: 5.4243 c. M:-9.6216 c. 30: 3 4 6 4 3 4 6 SP T3 SD: 0.9675 c. M: 1.8070 c. 111: 11 15 22 15 11 15 22 SP T3 SD: 0.7753 c. M: 1.5420 c. 141: 14 19 28 19 14 19 28 SP T3 SD: 0.6698 c. M: 1.3119 c. 171: 17 23 34 23 17 23 34 SP T3 SD: 0.6438 c. M: 1.1626 c. 201: 20 27 40 27 20 27 40 SP T3 SD: 0.6487 c. M: 1.0579 c. 231: 23 31 46 31 23 31 46 SP T3 SD: 0.6646 c. M: 0.9804 c. 247: 25 33 49 33 25 33 49 SP T3 SD: 0.5154 c. M:-0.9966 c. 261: 26 35 52 35 26 35 52 SP T3 SD: 0.6835 c. M: 0.9207 c. 268: 27 36 53 36 27 36 53 SP T3 SD: 0.5184 c. M:-0.8796 c. 277: 28 37 55 37 28 37 55 SP T3 SD: 0.4197 c. M:-0.8388 c. 298: 30 40 59 40 30 40 59 SP T3 SD: 0.3711 c. M:-0.6091 c. 307: 31 41 61 41 31 41 61 SP T3 SD: 0.3643 c. M:-0.7118 c. 328: 33 44 65 44 33 44 65 SP T3 SD: 0.2521 c. M:-0.3881 c. 358: 36 48 71 48 36 48 71 SP T3 SD: 0.1564 c. M:-0.2095 c. 388: 39 52 77 52 39 52 77 SP T3 SD: 0.0860 c. M:-0.1577 c. 418: 42 56 83 56 42 56 83 SP T3 SD: 0.0668 c. M:-0.1133 c. 806: 81 108 160 108 81 108 160 SP T3 SD: 0.0674 c. M:-0.1347 c. 887: 89 119 176 119 89 119 176 SP T3 SD: 0.0489 c. M:-0.0870 c. 917: 92 123 182 123 92 123 182 SP T3 SD: 0.0351 c. M: 0.0683 c. 1275: 128 171 253 171 128 171 253 SP T3 SD: 0.0389 c. M:-0.0753 c. 1305: 131 175 259 175 131 175 259 SP T3 SD: 0.0161 c. M:-0.0321 c. 1335: 134 179 265 179 134 179 265 SP T3 SD: 0.0079 c. M: 0.0114 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 10.7531 cents 3 x x 4 x x 5:6 S SD: 26.7930 cents 4 x 5 x 6 x 7:8 S SD: 26.8415 cents 5 x 6:7 x 8:9:10 S SD: 18.3468 cents 6 x 7:8:9 x 10:12 S SD: 16.8916 cents 7 x 8:9:10:11:12:14 S SD: 20.2614 cents 8 x 9:11:12:13:14:16 SD: 15.8891 cents 10:11:12:14:15:16:17:20 SD: 14.0062 cents 11:12:13:15:16:17:19:22 SD: 9.8587 cents 12:13:14:16:18:19:21:24 SD: 5.6077 cents 17:18:20:23:25:27:30:34 SD: 4.7434 cents 27:29:32:36:40:43:47:54 SD: 3.6798 cents 29:31:34:39:43:46:51:58 SD: 2.6846 cents 39:42:46:53:58:62:68:78 SD: 2.3033 cents 46:49:54:62:68:73:80:92 SD: 1.8907 cents 56:60:66:76:83:89:98:112 SD: 1.7215 cents 58:62:68:78:86:92:101:116 SD: 1.5281 cents 68:73:80:92:101:108:119:136 SD: 1.3469 cents 83:89:98:112:123:132:145:166 SD: 1.1220 cents 85:91:100:115:126:135:148:170 SD: 0.6981 cents 97:104:114:131:144:154:169:194 SD: 0.5929 cents 152:163:179:205:225:241:265:304 SD: 0.5895 cents 166:178:195:224:246:264:289:332 SD: 0.5883 cents 168:180:198:227:249:267:293:336 SD: 0.5726 cents 180:193:212:243:267:286:314:360 SD: 0.4790 cents 194:208:228:262:287:308:338:388 SD: 0.4638 cents 197:211:232:266:292:313:343:394 SD: 0.4556 cents 209:224:246:282:310:332:364:418 SD: 0.3984 cents 226:242:266:305:335:359:394:452 SD: 0.3574 cents 237:254:279:320:351:376:413:474 SD: 0.3361 cents 249:267:293:336:369:395:434:498 SD: 0.3313 cents 260:279:306:351:385:413:453:520 SD: 0.2951 cents 277:297:326:374:410:440:483:554 SD: 0.2699 cents 289:310:340:390:428:459:504:578 SD: 0.2388 cents 318:341:374:429:471:505:554:636 SD: 0.2373 cents 345:370:406:466:511:548:601:690 SD: 0.2259 cents 357:383:420:482:529:567:622:714 SD: 0.2067 cents 374:401:440:505:554:594:652:748 SD: 0.0872 cents