Scala analysis: xen15-chalmers-triadic-diamond-40-33
Triadic diamond for M=40/33, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 40/33 333.040771 2: 99/80 368.914230 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 160/99 831.085770 6: 33/20 866.959229 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 40/33 333.0408 1: 40/33 333.0408 2: 3267/3200 35.8735 3: 320/297 129.1308 4: 9/8 203.9100 major whole tone 5: 320/297 129.1308 6: 3267/3200 35.8735 7: 40/33 333.0408
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 3267/3200 35.873 cents 1: 2 320/297 129.131 cents 1: 1 9/8 203.910 cents major whole tone 1: 2 40/33 333.041 cents 2: 2 11/10 165.004 cents Ptolemy's second, 4/5-tone 2: 2 40/33 333.041 cents 2: 2 99/80 368.914 cents 2: 1 1600/1089 666.082 cents 3: 2 99/80 368.914 cents 3: 1 12800/9801 462.172 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 9801/6400 737.828 cents 4: 2 160/99 831.086 cents 5: 1 1089/800 533.918 cents 5: 2 160/99 831.086 cents 5: 2 33/20 866.959 cents 5: 2 20/11 1034.996 cents large minor seventh 6: 2 33/20 866.959 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 297/160 1070.869 cents 6: 2 6400/3267 1164.127 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 : 333.0 368.9 498.0 702.0 831.1 867.0 1200.0 333.0 : 35.9 165.0 368.9 498.0 533.9 867.0 1200.0 368.9 : 129.1 333.0 462.2 498.0 831.1 1164.1 1200.0 498.0 : 203.9 333.0 368.9 702.0 1035.0 1070.9 1200.0 702.0 : 129.1 165.0 498.0 831.1 867.0 996.1 1200.0 831.1 : 35.9 368.9 702.0 737.8 867.0 1070.9 1200.0 867.0 : 333.0 666.1 702.0 831.1 1035.0 1164.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 35.8735 .. 333.0408 cents 128000/107811, 297.1673 cents 3267/3200, 35.8735 cents 2: 165.0042 .. 666.0815 cents 16000/11979, 501.0773 cents 363/400,-168.0365 cents 3: 368.9142 .. 701.9550 cents 40/33, 333.0408 cents 107811/128000,-297.1673 cents 4: 498.0450 .. 831.0858 cents 40/33, 333.0408 cents 8/9,-203.9100 cents 5: 533.9185 .. 1034.9958 cents 16000/11979, 501.0773 cents 107811/128000,-297.1673 cents 6: 866.9592 .. 1164.1265 cents 128000/107811, 297.1673 cents 363/400,-168.0365 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 3267/3200, 35.8735 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 40/33, 333.0408 cents Average / Smallest step : 4.778702 Largest / Average step : 1.942738 Largest / Smallest step : 9.283765 Median interval of one step : 320/297, 129.1308 cents, amount: 2 Least squares average step : 165.21435 cents, oct.: 1156.50042 cents Scale is not proper Step pattern alph. order: ABCDCBA Step pattern size order : DABCBAD Scale is not a Constant Structure Scale diversity : 1.363030 Lumma stability : 0.059789 Lumma impropriety factor : 0.665204 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 : 3267/3200, 35.8735 cents Number of recognisable fifths : 4, average 701.9550 cents Scale is a complete diamond : 5 33 99 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 : 11 Odd number limit : 9801 (O: 9801 U: 9801) Highest odd numerator or denominator: 99 Scale harmonicity : 0.014528 Average absolute harmonicity : 0.230341 Specific harmonicity : 0.079473 Fundamental : 1/7920, -12.9513 octaves, 0.0330 Hz. Guide tone : 15840, 13.9513 octaves, 4144148.954 Hz. Exponens Consonantiae : 1.254528E+08, 26.90257 octaves Euler's gradus suavitatis : 46 Sum of Mann's harmonic distance : 289.5, average 41.35714 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 7.98254, average 1.14036 Sum of Tenney's harmonic distance : 16.19696, average 2.31385 Vogel's harmonic complexity : 26.57143 Wille's k value : 4900 Wilson's harmonic complexity : 44 Rectangular lattice diameter : 8 Triangular lattice diameter : 6 Lattice compactness : 115.17655, average 4.11345 Lattice compactness (without 2's) : 59.16021, average 2.11286 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 5 0.57143 18 1 3: -2 .. 2 0.00000 8 2 5: -1 .. 1 0.00000 4 11: -1 .. 1 0.00000 4 4 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 15 24| Scale is weakly epimorphic with val: <7 10 15 25| Scale is weakly epimorphic with val: <7 10 16 25| Scale is weakly epimorphic with val: <7 10 16 26| Scale is weakly epimorphic with val: <7 10 17 26| Scale is weakly epimorphic with val: <7 11 15 26| Scale is weakly epimorphic with val: <7 11 17 22| Scale is weakly epimorphic with val: <7 11 18 22| Scale is weakly epimorphic with val: <7 11 18 23| Scale is weakly epimorphic with val: <7 12 15 23| Scale is weakly epimorphic with val: <7 12 16 24| Scale is weakly epimorphic with val: <7 12 17 22| Scale is weakly epimorphic with val: <7 12 17 25| Scale is weakly epimorphic with val: <7 12 18 23| Scale is weakly epimorphic with val: <7 12 18 26|
FIT/MODE
7: 2 0 1 1 1 0 2 N T3 I SD: 17.2303 c. M: 26.0571 c. 17: 5 0 2 3 2 0 5 N I SD: 13.8005 c. M:-19.9004 c. 19: 5 1 2 3 2 1 5 N I SD: 11.3436 c. M: 17.2513 c. 22: 6 1 2 4 2 1 6 N I SD: 8.4634 c. M:-12.9040 c. 26: 7 1 3 4 3 1 7 N I SD: 7.4152 c. M:-9.9638 c. 29: 8 1 3 5 3 1 8 N I SD: 2.2992 c. M:-3.4996 c. 36: 10 1 4 6 4 1 10 N I SD: 1.5999 c. M: 2.2476 c. 65: 18 2 7 11 7 2 18 N I SD: 0.4814 c. M:-0.7331 c. 205: 57 6 22 35 22 6 57 N I SD: 0.4255 c. M:-0.6178 c. 234: 65 7 25 40 25 7 65 N I SD: 0.3989 c. M:-0.6091 c. 241: 67 7 26 41 26 7 67 N I SD: 0.3929 c. M:-0.5692 c. 270: 75 8 29 46 29 8 75 N I SD: 0.2122 c. M:-0.2926 c. 335: 93 10 36 57 36 10 93 N I SD: 0.0903 c. M:-0.1346 c. 400: 111 12 43 68 43 12 111 N I SD: 0.0562 c. M: 0.0858 c. 771: 214 23 83 131 83 23 214 N I SD: 0.0293 c. M: 0.0426 c. 836: 232 25 90 142 90 25 232 N I SD: 0.0273 c. M:-0.0411 c. 1171: 325 35 126 199 126 35 325 N I SD: 0.0065 c. M: 0.0091 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: 5.7998 cents 4 x 5 x 6 x 7:8 S SD: 25.8355 cents 5:6 x 7 x 8 x 10 S SD: 21.9946 cents 6:7 x 8:9 x 10:12 S SD: 13.6838 cents 7:8 x 9 x 11:12:14 SD: 29.0384 cents 8 x 10:11:12:13 x 16 SD: 11.3664 cents 9:11 x 12:14 x 15:18 SD: 13.3764 cents 10:12 x 13:15:16:17:20 SD: 12.0159 cents 11:13:14:15:17 x 18:22 SD: 15.5221 cents 12 x 15:16:18:19:20:24 S SD: 7.2028 cents 13 x 16:17:20:21 x 26 SD: 11.2091 cents 14:17 x 19:21 x 23:28 SD: 6.3400 cents 16:19:20:21:24:26 x 32 SD: 8.1606 cents 17 x 21:23:26:27:28:34 SD: 8.6580 cents 18:22 x 24:27:29:30:36 SD: 3.8677 cents 19:23:24:25:29:31 x 38 SD: 9.0829 cents 20:24:25:27:30:32:33:40 SD: 5.2891 cents 22 x 27:29:33 x 36:44 SD: 5.6721 cents 23:28 x 31:35:37:38:46 SD: 5.5194 cents 24:29:30:32:36:39:40:48 SD: 3.8439 cents 26 x 32:35:39:42:43:52 SD: 3.2513 cents 27:33 x 36:41:44:45:54 SD: 5.6931 cents 28:34:35:37:42:45:46:56 SD: 3.7894 cents 31 x 38:41:47:50:51:62 SD: 4.8522 cents 32:39:40:43:48:52:53:64 SD: 3.7942 cents 33:40:41:44:50:53:54:66 SD: 3.7094 cents 34:41:42:45:51:55:56:68 SD: 2.3241 cents 42:51:52:56:63:68:69:84 SD: 1.2469 cents 72:87:89:96:108:116:119:144 SD: 1.2036 cents 80:97:99:107:120:129:132:160 SD: 0.9571 cents 84:102:104:112:126:136:139:168 SD: 0.9547 cents 114:138:141:152:171:184:188:228 SD: 0.4967 cents 156:189:193:208:234:252:257:312 SD: 0.4247 cents 180:218:223:240:270:291:297:360 SD: 0.3542 cents 198:240:245:264:297:320:327:396 SD: 0.2284 cents 240:291:297:320:360:388:396:480 SD: 0.1093 cents 354:429:438:472:531:572:584:708 SD: 0.0953 cents 552:669:683:736:828:892:911:1104 SD: 0.0807 cents 594:720:735:792:891:960:980:1188 SD: 0.0357 cents