Scala analysis: xen09-chalmers-tritriadic-38-48-47
Tritriadic scale built from 38:48:47
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 48/47 36.448379 2: 47/38 367.993606 3: 24/19 404.441985 smaller undevicesimal major third 4: 2209/1444 735.987212 5: 564/361 772.435591 6: 76/47 832.006394 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 47/38 367.9936 1: 48/47 36.4484 2: 2209/1824 331.5452 3: 48/47 36.4484 4: 2209/1824 331.5452 5: 48/47 36.4484 6: 6859/6627 59.5708 7: 47/38 367.9936
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 48/47 36.448 cents 1: 1 6859/6627 59.571 cents 1: 2 2209/1824 331.545 cents 1: 1 47/38 367.994 cents 2: 1 109744/103823 96.019 cents 2: 4 47/38 367.994 cents 2: 1 24/19 404.442 cents smaller undevicesimal major third 2: 1 361/282 427.564 cents 3: 2 24/19 404.442 cents smaller undevicesimal major third 3: 1 361/282 427.564 cents 3: 2 2888/2209 464.013 cents 3: 1 103823/69312 699.539 cents 3: 1 2209/1444 735.987 cents 4: 1 2888/2209 464.013 cents 4: 1 138624/103823 500.461 cents 4: 2 2209/1444 735.987 cents 4: 1 564/361 772.436 cents 4: 2 19/12 795.558 cents undevicesimal minor sixth 5: 1 564/361 772.436 cents 5: 1 19/12 795.558 cents undevicesimal minor sixth 5: 4 76/47 832.006 cents 5: 1 103823/54872 1103.981 cents 6: 1 76/47 832.006 cents 6: 2 3648/2209 868.455 cents 6: 1 13254/6859 1140.429 cents 6: 3 47/24 1163.552 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 36.4 368.0 404.4 736.0 772.4 832.0 1200.0 36.4 : 331.5 368.0 699.5 736.0 795.6 1163.6 1200.0 368.0 : 36.4 368.0 404.4 464.0 832.0 868.5 1200.0 404.4 : 331.5 368.0 427.6 795.6 832.0 1163.6 1200.0 736.0 : 36.4 96.0 464.0 500.5 832.0 868.5 1200.0 772.4 : 59.6 427.6 464.0 795.6 832.0 1163.6 1200.0 832.0 : 368.0 404.4 736.0 772.4 1104.0 1140.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 36.4484 .. 367.9936 cents 2209/1824, 331.5452 cents 48/47, 36.4484 cents 2: 96.0192 .. 427.5644 cents 2209/1824, 331.5452 cents 4170272/4879681,-271.9744 cents 3: 404.4420 .. 735.9872 cents 2209/1824, 331.5452 cents 6768/6859,-23.1224 cents 4: 464.0128 .. 795.5580 cents 2209/1824, 331.5452 cents 4170272/4879681,-271.9744 cents 5: 772.4356 .. 1103.9808 cents 2209/1824, 331.5452 cents 6768/6859,-23.1224 cents 6: 832.0064 .. 1163.5516 cents 2209/1824, 331.5452 cents 4170272/4879681,-271.9744 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 48/47, 36.4484 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 47/38, 367.9936 cents Average / Smallest step : 4.703325 Largest / Average step : 2.146629 Largest / Smallest step : 10.096296 Median interval of one step : 6859/6627, 59.5708 cents, amount: 1 Most common interval of one step : 48/47, 36.4484 cents, amount: 3 Least squares average step : 158.45662 cents, oct.: 1109.19634 cents Scale is not proper Scale is a mode of a 1712-tone equal temperament with octave 2/1 degrees: 52 525 577 1050 1102 1187 1712 Least number of segments generator : 857 of 600.701 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1637 of 1147.430 cents and inv. generated superset size: 114 = 107 more = 1628.571% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABACD Step pattern size order : ACACABD Scale is not a Constant Structure Scale diversity : 1.102070 Lumma stability : 0.060747 Lumma impropriety factor : 0.718473 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 : 4 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 6859/6768, 23.1224 cents Most common intervals : 47/38, 367.9936 cents & inv., amount: 5 Most common triad is 0.0 367.994 832.006 cents, amount: 3 Number of recognisable fifths : 1, average 699.5388 cents Scale contains a complete diamond : 19 47 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 47 Odd number limit : 103823 (O: 103823 U: 103823) Highest odd numerator or denominator: 2209 Scale harmonicity : 0.009010 Fundamental : 1/67868, -16.0504 octaves, 0.0039 Hz. Guide tone : 2014608, 20.9421 octaves, 527072956.860 Hz. Exponens Consonantiae : 1.367274E+11, 36.99251 octaves Euler's gradus suavitatis : 201 Sum of Mann's harmonic distance : 2463.5, average 351.92857 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 12.19675, average 1.74239 Sum of Tenney's harmonic distance : 24.93068, average 3.56153 Vogel's harmonic complexity : 89.42857 Wille's k value : 51911 Wilson's harmonic complexity : 201 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 85.33167, average 3.04756 Lattice compactness (without 2's) : 42.59183, average 1.52114 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 4 1.28571 15 1 3: 0 .. 1 0.42857 3 19: -2 .. 1 -0.71429 7 1 47: -1 .. 2 0.28571 6 5 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 16 / 7 = 2.28571 Scale is weakly epimorphic with val: <7 10 27 42| Scale is weakly epimorphic with val: <7 10 28 41| Scale is weakly epimorphic with val: <7 10 29 40| Scale is weakly epimorphic with val: <7 10 30 39| Scale is weakly epimorphic with val: <7 10 32 37| Scale is weakly epimorphic with val: <7 10 33 36| Scale is weakly epimorphic with val: <7 11 27 37| Scale is weakly epimorphic with val: <7 11 28 36| Scale is weakly epimorphic with val: <7 11 29 42| Scale is weakly epimorphic with val: <7 11 30 41| Scale is weakly epimorphic with val: <7 11 31 40| Scale is weakly epimorphic with val: <7 11 33 38| Scale is weakly epimorphic with val: <7 12 27 39| Scale is weakly epimorphic with val: <7 12 28 38| Scale is weakly epimorphic with val: <7 12 29 37| Scale is weakly epimorphic with val: <7 12 30 36| Scale is weakly epimorphic with val: <7 12 31 42| Scale is weakly epimorphic with val: <7 12 32 41|
FIT/MODE
7: 0 2 0 2 0 1 2 N T3 SD: 48.4515 c. M: 86.7213 c. 8: 0 2 1 2 0 1 2 N T3 SD: 43.6708 c. M: 67.9936 c. 9: 0 3 0 3 0 0 3 N M DE S SD: 34.3396 c. M:-64.0128 c. 10: 0 3 0 3 0 1 3 N T3 SD: 30.3231 c. M: 52.4356 c. 11: 0 3 1 3 0 1 3 N T3 SD: 30.4860 c. M: 40.7209 c. 13: 0 4 0 4 0 1 4 N T3 SD: 23.0891 c. M: 36.4484 c. 16: 0 5 0 5 0 1 5 N T3 SD: 20.6785 c. M: 36.4484 c. 17: 1 4 1 4 1 1 5 N SD: 20.3736 c. M:-34.1399 c. 20: 1 5 1 5 1 1 6 N SD: 13.2952 c. M:-23.5516 c. 23: 1 6 1 6 1 1 7 N SD: 8.9818 c. M:-15.7255 c. 26: 1 7 1 7 1 1 8 N SD: 7.2847 c. M:-12.1798 c. 33: 1 9 1 9 1 2 10 N SD: 5.4913 c. M: 8.7992 c. 36: 1 10 1 10 1 2 11 N SD: 3.2355 c. M: 5.7689 c. 39: 1 11 1 11 1 2 12 N SD: 3.1946 c. M: 5.6791 c. 59: 2 16 2 16 2 3 18 N SD: 2.5363 c. M:-4.2296 c. 62: 2 17 2 17 2 3 19 N SD: 1.3428 c. M:-2.2613 c. 98: 3 27 3 27 3 5 30 N SD: 0.7305 c. M: 1.2933 c. 101: 3 28 3 28 3 5 31 N SD: 0.4678 c. M: 0.8048 c. 163: 5 45 5 45 5 8 50 N SD: 0.3249 c. M:-0.5705 c. 199: 6 55 6 55 6 10 61 N SD: 0.3218 c. M: 0.5763 c. 261: 8 72 8 72 8 13 80 N SD: 0.2154 c. M: 0.3550 c. 264: 8 73 8 73 8 13 81 N SD: 0.2123 c. M:-0.3764 c. 362: 11 100 11 100 11 18 111 N SD: 0.0429 c. M: 0.0756 c. 988: 30 273 30 273 30 49 303 N SD: 0.0253 c. M:-0.0452 c. 1350: 41 373 41 373 41 67 414 N SD: 0.0070 c. M:-0.0128 c. 1712: 52 473 52 473 52 85 525 N SD: 0.0036 c. M: 0.0059 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: 17.0161 cents 3 x x 4 x x 5:6 S SD: 35.7496 cents 4 x x 5:6 x x 8 S SD: 12.8531 cents 5 x 6 x x x 8:10 S SD: 18.4884 cents 6 x 7:8:9 x 10:12 S SD: 30.2564 cents 7 x x 9 x 11 x 14 SD: 10.7500 cents 8 x x 10:12 x 13:16 SD: 9.8724 cents 9:10:11 x x 14:15:18 SD: 31.3203 cents 10:11:12:13:15 x 16:20 SD: 25.4069 cents 11:12 x 14:17 x 18:22 SD: 23.6179 cents 12:13 x 15:18:19 x 24 SD: 22.3167 cents 13:14:16 x 20 x 21:26 SD: 18.5560 cents 14:15:17:18:21:22:23:28 SD: 14.8837 cents 15:16 x 19:23 x 24:30 SD: 15.5465 cents 16:17 x 20:24:25:26:32 SD: 13.1790 cents 17:18:21 x 26:27 x 34 SD: 13.7443 cents 18:19:22:23 x 28:29:36 SD: 10.7807 cents 19:20 x 24:29:30:31:38 SD: 9.6213 cents 20:21 x 25 x 31:32:40 SD: 11.2395 cents 21:22:26:27:32:33:34:42 SD: 7.8733 cents 22:23:27:28:34 x 36:44 SD: 8.7046 cents 23:24:28:29:35:36:37:46 SD: 6.8846 cents 24:25 x 30:37 x 39:48 SD: 8.3717 cents 25:26:31:32:38:39:40:50 SD: 6.3888 cents 26:27:32:33:40:41:42:52 SD: 5.2185 cents 28:29 x 35:43:44:45:56 SD: 5.7201 cents 29:30:36:37:44:45:47:58 SD: 4.9331 cents 30:31:37:38:46:47:49:60 SD: 4.0438 cents 32:33 x 40:49:50:52:64 SD: 4.3688 cents 34:35:42:43:52:53:55:68 SD: 2.0878 cents 36:37 x 45:55:56:58:72 SD: 3.9129 cents 37:38:46:47:57:58:60:74 SD: 3.1100 cents 38:39:47:48:58:59:61:76 SD: 2.7247 cents 39:40:48:49:60:61:63:78 SD: 2.5397 cents 41:42:51:52:63:64:66:82 SD: 2.4591 cents 42:43:52:53:64:66:68:84 SD: 1.8955 cents 60:61:74:76:92:94:97:120 SD: 1.7376 cents 76:78:94:96:116:119:123:152 SD: 1.4634 cents 80:82:99:101:122:125:129:160 SD: 1.3867 cents 83:85:103:105:127:130:134:166 SD: 1.3510 cents 84:86:104:106:129:131:136:168 SD: 1.3072 cents 87:89:108:110:133:136:141:174 SD: 1.1875 cents 89:91:110:112:136:139:144:178 SD: 1.0389 cents 92:94:114:116:141:144:149:184 SD: 0.9959 cents 94:96:116:119:144:147:152:188 SD: 0.8886 cents 102:104:126:129:156:159:165:204 SD: 0.8199 cents 130:133:161:164:199:203:210:260 SD: 0.7065 cents 140:143:173:177:214:219:226:280 SD: 0.6407 cents 144:147:178:182:220:225:233:288 SD: 0.4288 cents 185:189:229:234:283:289:299:370 SD: 0.4172 cents 190:194:235:240:291:297:307:380 SD: 0.3747 cents 194:198:240:245:297:303:314:388 SD: 0.3554 cents 228:233:282:288:349:356:369:456 SD: 0.3383 cents 240:245:297:303:367:375:388:480 SD: 0.2427 cents 274:280:339:346:419:428:443:548 SD: 0.2152 cents 334:341:413:422:511:522:540:668 SD: 0.1531 cents 464:474:574:586:710:725:750:928 SD: 0.1514 cents 468:478:579:591:716:731:757:936 SD: 0.1378 cents 562:574:695:710:860:878:909:1124 SD: 0.1140 cents 566:578:700:715:866:884:915:1132 SD: 0.1129 cents