Scala analysis: xen10-chalmers-tritriadic-19-7-21
Tritriadic scale built from 19:7:21
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 21/19 173.267891 2: 441/361 346.535782 3: 4/3 498.044999 perfect fourth 4: 28/19 671.312890 5: 588/361 844.580782 6: 38/21 1026.732109 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 21/19 173.2679 1: 21/19 173.2679 2: 21/19 173.2679 3: 1444/1323 151.5092 4: 21/19 173.2679 5: 21/19 173.2679 6: 6859/6174 182.1513 7: 21/19 173.2679
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 1444/1323 151.509 cents 1: 5 21/19 173.268 cents 1: 1 6859/6174 182.151 cents 2: 2 76/63 324.777 cents 2: 3 441/361 346.536 cents 2: 2 361/294 355.419 cents 3: 3 4/3 498.045 cents perfect fourth 3: 1 9261/6859 519.804 cents 3: 3 19/14 528.687 cents 4: 3 28/19 671.313 cents 4: 1 13718/9261 680.196 cents 4: 3 3/2 701.955 cents perfect fifth 5: 2 588/361 844.581 cents 5: 3 722/441 853.464 cents 5: 2 63/38 875.223 cents 6: 1 12348/6859 1017.849 cents 6: 5 38/21 1026.732 cents 6: 1 1323/722 1048.491 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 : 173.3 346.5 498.0 671.3 844.6 1026.7 1200.0 173.3 : 173.3 324.8 498.0 671.3 853.5 1026.7 1200.0 346.5 : 151.5 324.8 498.0 680.2 853.5 1026.7 1200.0 498.0 : 173.3 346.5 528.7 702.0 875.2 1048.5 1200.0 671.3 : 173.3 355.4 528.7 702.0 875.2 1026.7 1200.0 844.6 : 182.2 355.4 528.7 702.0 853.5 1026.7 1200.0 1026.7: 173.3 346.5 519.8 671.3 844.6 1017.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 151.5092 .. 182.1513 cents 57/56, 30.6421 cents 1444/1323, 151.5092 cents 2: 324.7771 .. 355.4192 cents 57/56, 30.6421 cents 392/361, 142.6258 cents 3: 498.0450 .. 528.6871 cents 57/56, 30.6421 cents 392/361, 142.6258 cents 4: 671.3129 .. 701.9550 cents 57/56, 30.6421 cents 392/361, 142.6258 cents 5: 844.5808 .. 875.2229 cents 57/56, 30.6421 cents 392/361, 142.6258 cents 6: 1017.8487 .. 1048.4908 cents 57/56, 30.6421 cents 392/361, 142.6258 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 1444/1323, 151.5092 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 6859/6174, 182.1513 cents Average / Smallest step : 1.131473 Largest / Average step : 1.062549 Largest / Smallest step : 1.202246 Median interval of one step : 21/19, 173.2679 cents, amount: 5 Most common interval of one step : 21/19, 173.2679 cents, amount: 5 Least squares average step : 170.20730 cents, oct.: 1191.45113 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: AABAACA Step pattern size order : MMSMMLM Scale is a Constant Structure, by a margin of 142.62578 cents Scale diversity : 1.159124 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.846789 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 : 130321/129654, 8.8834 cents Most common intervals : 21/19, 173.2679 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 498.045 1026.732 cents Most common triad is 0.0 173.268 1026.732 cents, amount: 3 Number of recognisable fifths : 3, average 701.9550 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 19 21 Formal octave complements present : 3 = 42.8571% Scale is n-1 differentially coherent in interval classes 3 and 4 combined Limited transpositions with margin 30.6421 cents: 1 2 6 Limited inverse transpositions with margin 30.6421 cents: 3 4 5 -- Rational properties -- Prime limit : 19 Odd number limit : 9261 (O: 9261 U: 9261) Highest odd numerator or denominator: 441 Scale harmonicity : 0.006985 Average absolute harmonicity : 0.185603 Specific harmonicity : 0.038223 Fundamental : 1/7581, -12.8882 octaves, 0.0345 Hz. Guide tone : 33516, 15.0326 octaves, 8768642.447 Hz. Exponens Consonantiae : 2.540848E+08, 27.92073 octaves Euler's gradus suavitatis : 81 Sum of Mann's harmonic distance : 953.5, average 136.21429 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.60226, average 1.37175 Sum of Tenney's harmonic distance : 20.13793, average 2.87685 Vogel's harmonic complexity : 41.42857 Wille's k value : 4630 Wilson's harmonic complexity : 87 Rectangular lattice diameter : 9 Triangular lattice diameter : 6 Lattice compactness : 75.20963, average 2.68606 Lattice compactness (without 2's) : 63.54627, average 2.26951 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 1.14286 8 1 3: -1 .. 2 0.28571 6 1 7: -1 .. 2 0.71429 7 19: -2 .. 1 -0.71429 7 5 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 20 / 7 = 2.85714 Scale is weakly epimorphic with val: <7 10 18 29| Scale is weakly epimorphic with val: <7 10 19 30| Scale is weakly epimorphic with val: <7 10 20 31| Scale is weakly epimorphic with val: <7 10 21 32| Scale is weakly epimorphic with val: <7 10 22 33| Scale is JI-epimorphic with val: <7 11 18 28| Scale is JI-epimorphic with val: <7 11 19 29| Scale is JI-epimorphic with val: <7 11 20 30| = patent Scale is JI-epimorphic with val: <7 11 21 31| Scale is JI-epimorphic with val: <7 11 22 32| Scale is weakly epimorphic with val: <7 12 18 27| Scale is weakly epimorphic with val: <7 12 19 28| Scale is weakly epimorphic with val: <7 12 20 29| Scale is weakly epimorphic with val: <7 12 21 30| Scale is weakly epimorphic with val: <7 12 22 31|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 9.6308 c. M:-16.2407 c. Lebeng 27: 4 4 3 4 4 4 4 SP M ME S SD: 5.7006 c. M: 9.1561 c. 34: 5 5 4 5 5 5 5 SP M ME S SD: 3.4565 c. M:-6.4054 c. 41: 6 6 5 6 6 6 6 SP M ME S SD: 2.7834 c. M:-4.6837 c. 48: 7 7 6 7 7 7 7 SP M ME S SD: 3.0422 c. M:-5.4192 c. 70: 10 10 9 10 10 11 10 SP T3 SD: 2.6622 c. M: 4.5808 c. 77: 11 11 10 11 11 12 11 SP T3 SD: 2.1133 c. M: 3.6786 c. 84: 12 12 11 12 12 13 12 SP T3 SD: 1.9678 c. M: 3.6786 c. 97: 14 14 12 14 14 15 14 SP T3 SD: 2.1432 c. M: 3.3437 c. 104: 15 15 13 15 15 16 15 SP T3 SD: 1.3783 c. M: 2.2731 c. 111: 16 16 14 16 16 17 16 SP T3 SD: 0.7519 c. M: 1.3375 c. 118: 17 17 15 17 17 18 17 SP T3 SD: 0.4214 c. M: 0.7731 c. 159: 23 23 20 23 23 24 23 SP T3 SD: 0.4224 c. M:-0.7022 c. 263: 38 38 33 38 38 40 38 SP T3 SD: 0.4060 c. M: 0.7066 c. 270: 39 39 34 39 39 41 39 SP T3 SD: 0.1495 c. M: 0.2672 c. 277: 40 40 35 40 40 42 40 SP T3 SD: 0.1110 c. M:-0.1846 c. 547: 79 79 69 79 79 83 79 SP T3 SD: 0.0450 c. M:-0.0821 c. 665: 96 96 84 96 96 101 96 SP T3 SD: 0.0436 c. M: 0.0696 c. 942: 136 136 119 136 136 143 136 SP T3 SD: 0.0264 c. M:-0.0442 c. 1212: 175 175 153 175 175 184 175 SP T3 SD: 0.0169 c. M: 0.0263 c. 1489: 215 215 188 215 215 226 215 SP T3 SD: 0.0073 c. M:-0.0129 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: 15.3211 cents 3 x x 4 x 5 x 6 S SD: 13.2593 cents 4 x 5 x 6 x 7:8 S SD: 19.1611 cents 5 x 6:7 x 8:9:10 S SD: 19.1072 cents 6 x 7:8:9:10:11:12 S SD: 16.1416 cents 7:8 x 9:10:11:13:14 SD: 21.1421 cents 8:9:10:11:12:13:14:16 S SD: 14.0464 cents 9:10:11:12:13:15:16:18 SD: 8.8170 cents 17:19:21:23:25:28:31:34 SD: 6.3027 cents 18:20:22:24:27:29:33:36 SD: 6.2156 cents 19:21:23:25:28:31:34:38 SD: 4.8559 cents 21:23:26:28:31:34:38:42 SD: 4.2965 cents 27:30:33:36:40:44:49:54 SD: 1.9898 cents 48:53:59:64:71:78:87:96 SD: 1.9319 cents 57:63:70:76:84:93:103:114 SD: 1.4133 cents 67:74:82:89:99:109:121:134 SD: 1.3617 cents 68:75:83:91:100:111:123:136 SD: 1.3059 cents 78:86:95:104:115:127:141:156 SD: 0.9998 cents 95:105:116:127:140:155:172:190 SD: 0.7940 cents 105:116:128:140:155:171:190:210 SD: 0.6778 cents 135:149:165:180:199:220:244:270 SD: 0.4910 cents 162:179:198:216:239:264:293:324 SD: 0.3537 cents 258:285:315:344:380:420:467:516 SD: 0.2842 cents 285:315:348:380:420:464:516:570 SD: 0.2096 cents 294:325:359:392:433:479:532:588 SD: 0.1993 cents 321:355:392:428:473:523:581:642 SD: 0.1962 cents 342:378:418:456:504:557:619:684 SD: 0.1390 cents 420:464:513:560:619:684:760:840 SD: 0.1250 cents 447:494:546:596:659:728:809:894 SD: 0.1173 cents 456:504:557:608:672:743:825:912 SD: 0.1003 cents