Scala analysis: xen15-chalmers-triadic-diamond-56-45
Triadic diamond for M=56/45, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 135/112 323.352810 septimal wide minor third 2: 56/45 378.602191 septimal narrow major third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 45/28 821.397809 septimale wide minor sixth 6: 224/135 876.647190 narrow septimal major sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 135/112 323.3528 septimal wide minor third 1: 135/112 323.3528 septimal wide minor third 2: 6272/6075 55.2494 3: 15/14 119.4428 major diatonic semitone 4: 9/8 203.9100 major whole tone 5: 15/14 119.4428 major diatonic semitone 6: 6272/6075 55.2494 7: 135/112 323.3528 septimal wide minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 6272/6075 55.249 cents 1: 2 15/14 119.443 cents major diatonic semitone 1: 1 9/8 203.910 cents major whole tone 1: 2 135/112 323.353 cents septimal wide minor third 2: 2 448/405 174.692 cents 2: 2 135/112 323.353 cents septimal wide minor third 2: 2 56/45 378.602 cents septimal narrow major third 2: 1 18225/12544 646.706 cents two (septimal wide minor third) 3: 2 56/45 378.602 cents septimal narrow major third 3: 1 2025/1568 442.796 cents 3: 2 4/3 498.045 cents perfect fourth 3: 2 3/2 701.955 cents perfect fifth 4: 2 4/3 498.045 cents perfect fourth 4: 2 3/2 701.955 cents perfect fifth 4: 1 3136/2025 757.204 cents two (septimal narrow major third) 4: 2 45/28 821.398 cents septimale wide minor sixth 5: 1 25088/18225 553.294 cents 5: 2 45/28 821.398 cents septimale wide minor sixth 5: 2 224/135 876.647 cents narrow septimal major sixth 5: 2 405/224 1025.308 cents 6: 2 224/135 876.647 cents narrow septimal major sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 28/15 1080.557 cents grave major seventh 6: 2 6075/3136 1144.751 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 323.4 378.6 498.0 702.0 821.4 876.6 1200.0 323.4 : 55.2 174.7 378.6 498.0 553.3 876.6 1200.0 378.6 : 119.4 323.4 442.8 498.0 821.4 1144.8 1200.0 498.0 : 203.9 323.4 378.6 702.0 1025.3 1080.6 1200.0 702.0 : 119.4 174.7 498.0 821.4 876.6 996.1 1200.0 821.4 : 55.2 378.6 702.0 757.2 876.6 1080.6 1200.0 876.6 : 323.4 646.7 702.0 821.4 1025.3 1144.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 55.2494 .. 323.3528 cents 820125/702464, 268.1034 cents 6272/6075, 55.2494 cents 2: 174.6922 .. 646.7056 cents 7381125/5619712, 472.0134 cents 50176/54675,-148.6606 cents 3: 378.6022 .. 701.9550 cents 135/112, 323.3528 cents 702464/820125,-268.1034 cents 4: 498.0450 .. 821.3978 cents 135/112, 323.3528 cents 8/9,-203.9100 cents 5: 553.2944 .. 1025.3078 cents 7381125/5619712, 472.0134 cents 702464/820125,-268.1034 cents 6: 876.6472 .. 1144.7506 cents 820125/702464, 268.1034 cents 50176/54675,-148.6606 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 6272/6075, 55.2494 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 135/112, 323.3528 cents Average / Smallest step : 3.102814 Largest / Average step : 1.886225 Largest / Smallest step : 5.852605 Median interval of one step : 15/14, 119.4428 cents, amount: 2 Least squares average step : 165.35275 cents, oct.: 1157.46922 cents Scale is not proper Step pattern alph. order: ABCDCBA Step pattern size order : DABCBAD Scale is not a Constant Structure Scale diversity : 1.448345 Lumma stability : 0.092082 Lumma impropriety factor : 0.616764 Rothenberg efficiency : 0.506122 redundancy: 0.493878 Efficiency x scale size : 3.542857 Number of different interval sizes : 18 = 3.00000 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 4.00000 = 4 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 3645/3584, 29.2178 cents Number of recognisable fifths : 4, average 701.9550 cents Scale is a complete diamond : 7 45 135 Formal octave complements present : 7 = 100.0000% Scale is differentially coherent in interval classes 3 and 4 combined Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 3-4 -- Rational properties -- Prime limit : 7 Odd number limit : 18225 (O: 18225 U: 18225) Highest odd numerator or denominator: 135 Scale harmonicity : 0.017132 Average absolute harmonicity : 0.233880 Specific harmonicity : 0.094146 Fundamental : 1/15120, -13.8842 octaves, 0.0173 Hz. Guide tone : 30240, 14.8842 octaves, 7911557.095 Hz. Exponens Consonantiae : 4.572288E+08, 28.76834 octaves Euler's gradus suavitatis : 42 Sum of Mann's harmonic distance : 397.5, average 56.78571 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 8.52134, average 1.21733 Sum of Tenney's harmonic distance : 17.32027, average 2.47432 Vogel's harmonic complexity : 25.57143 Wille's k value : 9112 Wilson's harmonic complexity : 42 Rectangular lattice diameter : 10 Triangular lattice diameter : 8 Lattice compactness : 125.96740, average 4.49884 Lattice compactness (without 2's) : 77.56742, average 2.77027 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 5 0.57143 18 1 3: -3 .. 3 0.00000 12 2 5: -1 .. 1 0.00000 4 7: -1 .. 1 0.00000 4 4 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 20 / 7 = 2.85714 Scale is weakly epimorphic with val: <7 10 15 22| Scale is weakly epimorphic with val: <7 10 17 18| Scale is weakly epimorphic with val: <7 10 18 18| Scale is weakly epimorphic with val: <7 10 18 19| Scale is weakly epimorphic with val: <7 11 15 21| Scale is weakly epimorphic with val: <7 11 15 22| Scale is weakly epimorphic with val: <7 11 16 22| Scale is weakly epimorphic with val: <7 11 18 18| Scale is weakly epimorphic with val: <7 12 15 19| Scale is weakly epimorphic with val: <7 12 15 22| Scale is weakly epimorphic with val: <7 12 16 20| Scale is weakly epimorphic with val: <7 12 17 21| Scale is weakly epimorphic with val: <7 12 18 18| Scale is weakly epimorphic with val: <7 12 18 22|
FIT/MODE
7: 2 0 1 1 1 0 2 N T3 I SD: 23.4331 c. M: 35.7450 c. 12: 3 1 1 2 1 1 3 N I SD: 16.9625 c. M:-23.3528 c. Mela Yagapriya, Raga Kalahamsa 15: 4 1 1 3 1 1 4 N I SD: 15.0687 c. M: 21.3978 c. 19: 5 1 2 3 2 1 5 N I SD: 5.5914 c. M: 7.5633 c. 22: 6 1 2 4 2 1 6 N I SD: 4.6791 c. M:-7.1359 c. 41: 11 2 4 7 4 2 11 N I SD: 1.2822 c. M: 1.8856 c. 89: 24 4 9 15 9 4 24 N I SD: 0.7375 c. M: 1.0741 c. 111: 30 5 11 19 11 5 30 N I SD: 0.6661 c. M:-0.9715 c. 130: 35 6 13 22 13 6 35 N I SD: 0.2774 c. M:-0.4165 c. 241: 65 11 24 41 24 11 65 N I SD: 0.1968 c. M:-0.2986 c. 282: 76 13 28 48 28 13 76 N I SD: 0.1161 c. M:-0.1727 c. 371: 100 17 37 63 37 17 100 N I SD: 0.1089 c. M: 0.1655 c. 412: 111 19 41 70 41 19 111 N I SD: 0.0353 c. M: 0.0518 c. 1065: 287 49 106 181 106 49 287 N I SD: 0.0181 c. M:-0.0275 c. 1477: 398 68 147 251 147 68 398 N I SD: 0.0056 c. M: 0.0084 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: 0.0000 cents 3 x x 4 x x 5:6 S SD: 2.5705 cents 4 x 5 x 6 x 7:8 S SD: 23.1252 cents 5:6 x 7 x 8 x 10 S SD: 21.2921 cents 6:7 x 8:9 x 10:12 S SD: 11.4012 cents 7:8:9 x x 11:12:14 SD: 25.6055 cents 8 x 10:11:12:13 x 16 SD: 11.4253 cents 9:11 x 12 x 14:15:18 SD: 12.3747 cents 10:12 x 13:15:16:17:20 SD: 10.2789 cents 11:13:14:15:17 x 18:22 SD: 14.3786 cents 12:14:15:16:18:19:20:24 S SD: 9.0089 cents 13 x 16:17:20:21:22:26 SD: 11.3791 cents 14:17 x 19:21 x 23:28 SD: 7.4779 cents 15:18:19:20:23:24:25:30 SD: 7.2354 cents 18:22 x 24:27:29:30:36 SD: 4.2699 cents 20:24:25:27:30:32:33:40 SD: 3.8724 cents 22 x 27:29:33:35:37:44 SD: 7.1212 cents 23:28:29:31:35:37:38:46 SD: 6.1273 cents 24:29:30:32:36:39:40:48 SD: 3.2043 cents 30:36:37:40:45:48:50:60 SD: 2.9259 cents 36:43:45:48:54:58:60:72 SD: 2.8033 cents 38:46:47:51:57:61:63:76 SD: 2.4844 cents 44:53:55:59:66:71:73:88 SD: 2.0494 cents 48:58:60:64:72:77:80:96 SD: 1.7348 cents 54:65:67:72:81:87:90:108 SD: 1.4981 cents 74:89:92:99:111:119:123:148 SD: 1.1221 cents 78:94:97:104:117:125:129:156 SD: 1.0872 cents 82:99:102:109:123:132:136:164 SD: 0.9573 cents 94:113:117:125:141:151:156:188 SD: 0.9445 cents 102:123:127:136:153:164:169:204 SD: 0.4097 cents 156:188:194:208:234:251:259:312 SD: 0.3640 cents 234:282:291:312:351:376:388:468 SD: 0.2493 cents 258:311:321:344:387:415:428:516 SD: 0.2254 cents 282:340:351:376:423:453:468:564 SD: 0.1494 cents 384:463:478:512:576:617:637:768 SD: 0.1323 cents 438:528:545:584:657:704:727:876 SD: 0.0954 cents 540:651:672:720:810:868:896:1080 SD: 0.0576 cents