Scala analysis: xen15-chalmers-triadic-diamond-8-7
Triadic diamond for M=8/7, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 8/7 231.174094 septimal whole tone 2: 21/16 470.780907 narrow fourth 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 32/21 729.219093 wide fifth 6: 7/4 968.825906 harmonic seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 8/7 231.1741 septimal whole tone 2: 147/128 239.6068 3: 64/63 27.2641 septimal comma, Archytas' comma 4: 9/8 203.9100 major whole tone 5: 64/63 27.2641 septimal comma, Archytas' comma 6: 147/128 239.6068 7: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 64/63 27.264 cents septimal comma, Archytas' comma 1: 1 9/8 203.910 cents major whole tone 1: 2 8/7 231.174 cents septimal whole tone 1: 2 147/128 239.607 cents 2: 2 8/7 231.174 cents septimal whole tone 2: 2 7/6 266.871 cents septimal minor third 2: 1 64/49 462.348 cents 2 septatones or septatonic major third 2: 2 21/16 470.781 cents narrow fourth 3: 1 512/441 258.438 cents 3: 2 21/16 470.781 cents narrow fourth 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: 2 32/21 729.219 cents wide fifth 4: 1 441/256 941.562 cents two (narrow fourth) 5: 2 32/21 729.219 cents wide fifth 5: 1 49/32 737.652 cents 5: 2 12/7 933.129 cents septimal major sixth 5: 2 7/4 968.826 cents harmonic seventh 6: 2 256/147 960.393 cents 6: 2 7/4 968.826 cents harmonic seventh 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 63/32 1172.736 cents octave - septimal comma 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 : 231.2 470.8 498.0 702.0 729.2 968.8 1200.0 231.2 : 239.6 266.9 470.8 498.0 737.7 968.8 1200.0 470.8 : 27.3 231.2 258.4 498.0 729.2 960.4 1200.0 498.0 : 203.9 231.2 470.8 702.0 933.1 1172.7 1200.0 702.0 : 27.3 266.9 498.0 729.2 968.8 996.1 1200.0 729.2 : 239.6 470.8 702.0 941.6 968.8 1172.7 1200.0 968.8 : 231.2 462.3 702.0 729.2 933.1 960.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 27.2641 .. 239.6068 cents 9261/8192, 212.3427 cents 64/63, 27.2641 cents 2: 231.1741 .. 470.7809 cents 147/128, 239.6068 cents 1024/1029,-8.4327 cents 3: 258.4382 .. 701.9550 cents 1323/1024, 443.5168 cents 8192/9261,-212.3427 cents 4: 498.0450 .. 941.5618 cents 1323/1024, 443.5168 cents 8/9,-203.9100 cents 5: 729.2191 .. 968.8259 cents 147/128, 239.6068 cents 8192/9261,-212.3427 cents 6: 960.3932 .. 1172.7359 cents 9261/8192, 212.3427 cents 1024/1029,-8.4327 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 64/63, 27.2641 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 147/128, 239.6068 cents Average / Smallest step : 6.287705 Largest / Average step : 1.397706 Largest / Smallest step : 8.788366 Median interval of one step : 8/7, 231.1741 cents, amount: 2 Least squares average step : 166.66958 cents, oct.: 1166.68709 cents Scale is not proper Step pattern alph. order: ABCDCBA Step pattern size order : CDABADC Scale is not a Constant Structure Scale diversity : 1.051756 Lumma stability : 0.045440 Lumma impropriety factor : 0.537884 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 : 1029/1024, 8.4327 cents Number of recognisable fifths : 4, average 701.9550 cents Scale is a complete diamond : 1 3 21 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 7 = 100.0000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Scale is differentially coherent in interval classes 2 and 3 combined 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 : 441 (O: 441 U: 441) Highest odd numerator or denominator: 21 Scale harmonicity : 0.028649 Average absolute harmonicity : 0.251195 Specific harmonicity : 0.156533 Fundamental : 1/336, -8.3923 octaves, 0.7786 Hz. Guide tone : 672, 9.3923 octaves, 175812.380 Hz. Exponens Consonantiae : 2.257920E+05, 17.78463 octaves Euler's gradus suavitatis : 26 Sum of Mann's harmonic distance : 65.5, average 9.35714 Mersenne's string divisions : 2264955 Sum of van Prooijen's expressibility: 5.28888, average 0.75555 Sum of Tenney's harmonic distance : 10.70742, average 1.52963 Vogel's harmonic complexity : 14.57143 Wille's k value : 220 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 4 Triangular lattice diameter : 4 Lattice compactness : 106.64880, average 3.80889 Lattice compactness (without 2's) : 39.08641, average 1.39594 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 5 0.57143 18 1 3: -1 .. 1 0.00000 4 2 7: -1 .. 1 0.00000 4 4 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 8 / 7 = 1.14286 Scale is weakly epimorphic with val: <7 10 19| Scale is weakly epimorphic with val: <7 10 20| Scale is weakly epimorphic with val: <7 11 22| Scale is weakly epimorphic with val: <7 12 20|
FIT/MODE
7: 1 2 0 1 0 2 1 N T3 I SD: 40.4473 c. M:-59.7455 c. 10: 2 2 0 2 0 2 2 N D3 I SD: 11.8142 c. M:-18.0450 c. 15: 3 3 0 3 0 3 3 N D3 I SD: 11.8142 c. M:-18.0450 c. 21: 4 4 1 3 1 4 4 N G I SD: 11.4209 c. M:-16.2407 c. 26: 5 5 1 4 1 5 5 N G I SD: 7.1446 c. M:-9.6473 c. 31: 6 6 1 5 1 6 6 N G I SD: 4.3838 c. M:-6.2648 c. 36: 7 7 1 6 1 7 7 N G I SD: 2.6945 c. M: 4.1142 c. 41: 8 8 1 7 1 8 8 N G I SD: 2.0880 c. M:-2.9722 c. 84: 16 17 2 14 2 17 16 N I SD: 1.7740 c. M:-2.6027 c. 89: 17 18 2 15 2 18 17 N I SD: 1.2884 c. M:-1.9606 c. 94: 18 19 2 16 2 19 18 N I SD: 1.1193 c. M:-1.5595 c. 125: 24 25 3 21 3 25 24 N I SD: 0.7706 c. M:-1.1550 c. 130: 25 26 3 22 3 26 25 N I SD: 0.3106 c. M:-0.4165 c. 135: 26 27 3 23 3 27 26 N I SD: 0.2295 c. M:-0.3302 c. 265: 51 53 6 45 6 53 51 N I SD: 0.1552 c. M:-0.2307 c. 306: 59 61 7 52 7 61 59 N I SD: 0.1479 c. M:-0.1985 c. 436: 84 87 10 74 10 87 84 N I SD: 0.0986 c. M:-0.1387 c. 441: 85 88 10 75 10 88 85 N I SD: 0.0801 c. M:-0.1184 c. 571: 110 114 13 97 13 114 110 N I SD: 0.0213 c. M:-0.0286 c. 1277: 246 255 29 217 29 255 246 N I SD: 0.0068 c. M:-0.0100 c. 1848: 356 369 42 314 42 369 356 N I SD: 0.0047 c. M:-0.0069 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: 28.1557 cents 4 x 5 x 6 x 7:8 S SD: 21.1168 cents 5:6 x 7 x 8:9:10 S SD: 30.8433 cents 6:7 x 8:9 x 11:12 SD: 17.6187 cents 7:8:9 x x 11:12:14 SD: 14.6786 cents 8:9 x 11:12 x 14:16 SD: 11.9689 cents 9:10 x 12 x 14:16:18 S SD: 13.2607 cents 10:11:13 x 15 x 18:20 SD: 16.7708 cents 11:13:14:15 x 17:19:22 SD: 15.6598 cents 12:14 x 16:18 x 21:24 S SD: 7.1394 cents 13:15:17 x x 20:23:26 SD: 6.1556 cents 14:16:18:19:21 x 25:28 SD: 9.7703 cents 15:17 x 20 x 23:26:30 SD: 4.9018 cents 16:18:21 x 24 x 28:32 S SD: 5.4528 cents 17:19:22:23 x 26:30:34 SD: 9.0929 cents 18:21 x 24:27 x 32:36 SD: 8.9835 cents 19:22:25 x x 29:33:38 SD: 5.3282 cents 20:23:26:27:30 x 35:40 SD: 4.8686 cents 21:24 x 28 x 32:37:42 SD: 2.3474 cents 22:25:29 x 33:34:39:44 SD: 5.8891 cents 23:26:30:31 x 35:40:46 SD: 5.1276 cents 24:27 x 32:36:37:42:48 SD: 5.6523 cents 25:29:33 x x 38:44:50 SD: 5.9255 cents 26:30:34:35:39:40:46:52 SD: 4.9934 cents 27:31:35:36 x 41:47:54 SD: 4.2396 cents 28:32:37 x 42:43:49:56 SD: 2.9781 cents 29:33:38:39 x 44:51:58 SD: 3.3877 cents 31:35:41 x x 47:54:62 SD: 5.5132 cents 32:37:42:43:48:49:56:64 SD: 3.6685 cents 33:38:43:44 x 50:58:66 SD: 3.6557 cents 34:39 x 45:51:52:60:68 SD: 3.5506 cents 35:40:46:47 x 53:61:70 SD: 3.0061 cents 36:41:47:48:54:55:63:72 SD: 1.6956 cents 37:42 x 49 x 56:65:74 SD: 4.2792 cents 38:43:50:51:57:58:67:76 SD: 3.5534 cents 39:45:51:52 x 59:68:78 SD: 3.7719 cents 40:46 x 53:60:61:70:80 SD: 2.5603 cents 41:47:54:55 x 62:72:82 SD: 3.2766 cents 42:48:55:56:63:64:74:84 SD: 1.7682 cents 48:55:63:64:72:73:84:96 SD: 0.8047 cents 84:96:110:112:126:128:147:168 SD: 0.5615 cents 132:151:173:176:198:201:231:264 SD: 0.4618 cents 176:201:231:235:264:268:308:352 SD: 0.4301 cents 204:233:268:272:306:311:357:408 SD: 0.2986 cents 252:288:331:336:378:384:441:504 SD: 0.1869 cents 288:329:378:384:432:439:504:576 SD: 0.1342 cents 336:384:441:448:504:512:588:672 SD: 0.0000 cents