Scala analysis: xen15-chalmers-triadic-diamond-32-25
Triadic diamond for M=32/25, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 75/64 274.582429 classic augmented second 2: 32/25 427.372572 classic diminished fourth 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 25/16 772.627428 classic augmented fifth 6: 128/75 925.417571 diminished seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 75/64 274.5824 classic augmented second 1: 75/64 274.5824 classic augmented second 2: 2048/1875 152.7901 double diminished third 3: 25/24 70.6724 classic chromatic semitone, minor chroma 4: 9/8 203.9100 major whole tone 5: 25/24 70.6724 classic chromatic semitone, minor chroma 6: 2048/1875 152.7901 double diminished third 7: 75/64 274.5824 classic augmented second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 2 2048/1875 152.790 cents double diminished third 1: 1 9/8 203.910 cents major whole tone 1: 2 75/64 274.582 cents classic augmented second 2: 2 256/225 223.463 cents Neapolitan diminished third 2: 2 75/64 274.582 cents classic augmented second 2: 2 32/25 427.373 cents classic diminished fourth 2: 1 5625/4096 549.165 cents double augmented third 3: 1 625/512 345.255 cents classic neutral third 3: 2 32/25 427.373 cents classic diminished 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 25/16 772.627 cents classic augmented fifth 4: 1 1024/625 854.745 cents two (classic diminished fourth) 5: 1 8192/5625 650.835 cents double diminished sixth 5: 2 25/16 772.627 cents classic augmented fifth 5: 2 128/75 925.418 cents diminished seventh 5: 2 225/128 976.537 cents augmented sixth 6: 2 128/75 925.418 cents diminished seventh 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 1875/1024 1047.210 cents double augmented sixth 6: 2 48/25 1129.328 cents classic diminished octave 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 : 274.6 427.4 498.0 702.0 772.6 925.4 1200.0 274.6 : 152.8 223.5 427.4 498.0 650.8 925.4 1200.0 427.4 : 70.7 274.6 345.3 498.0 772.6 1047.2 1200.0 498.0 : 203.9 274.6 427.4 702.0 976.5 1129.3 1200.0 702.0 : 70.7 223.5 498.0 772.6 925.4 996.1 1200.0 772.6 : 152.8 427.4 702.0 854.7 925.4 1129.3 1200.0 925.4 : 274.6 549.2 702.0 772.6 976.5 1047.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 274.5824 cents 9/8, 203.9100 cents 25/24, 70.6724 cents 2: 223.4626 .. 549.1649 cents 1265625/1048576, 325.7023 cents 16384/16875,-51.1199 cents 3: 345.2549 .. 701.9550 cents 768/625, 356.7001 cents 8/9,-203.9100 cents 4: 498.0450 .. 854.7451 cents 768/625, 356.7001 cents 8/9,-203.9100 cents 5: 650.8351 .. 976.5374 cents 1265625/1048576, 325.7023 cents 8/9,-203.9100 cents 6: 925.4176 .. 1129.3276 cents 9/8, 203.9100 cents 16384/16875,-51.1199 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 25/24, 70.6724 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 75/64, 274.5824 cents Average / Smallest step : 2.425678 Largest / Average step : 1.601731 Largest / Smallest step : 3.885284 Median interval of one step : 2048/1875, 152.7901 cents, amount: 2 Least squares average step : 166.04947 cents, oct.: 1162.34626 cents Scale is not proper Step pattern alph. order: ABCDCBA Step pattern size order : DBACABD Scale is not a Constant Structure Scale diversity : 1.461989 Lumma stability : 0.117787 Lumma impropriety factor : 0.509775 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 : 2048/2025, 19.5526 cents Number of recognisable fifths : 4, average 701.9550 cents Scale is a complete diamond : 1 3 75 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 : 5 Odd number limit : 5625 (O: 5625 U: 5625) Highest odd numerator or denominator: 75 Scale harmonicity : 0.022762 Average absolute harmonicity : 0.241973 Specific harmonicity : 0.123743 Fundamental : 1/4800, -12.2288 octaves, 0.0545 Hz. Guide tone : 9600, 13.2288 octaves, 2511605.427 Hz. Exponens Consonantiae : 4.608000E+07, 25.45764 octaves Euler's gradus suavitatis : 34 Sum of Mann's harmonic distance : 227.5, average 32.50000 Mersenne's string divisions : 329715645 Sum of van Prooijen's expressibility: 7.50025, average 1.07146 Sum of Tenney's harmonic distance : 15.32702, average 2.18957 Vogel's harmonic complexity : 19.57143 Wille's k value : 2812 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 6 Triangular lattice diameter : 6 Lattice compactness : 158.71776, average 5.66849 Lattice compactness (without 2's) : 60.26375, average 2.15228 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -6 .. 7 0.57143 26 1 3: -1 .. 1 0.00000 4 2 5: -2 .. 2 0.00000 8 4 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 12 / 7 = 1.71429 Scale is weakly epimorphic with val: <7 10 17| Scale is weakly epimorphic with val: <7 11 15| Scale is weakly epimorphic with val: <7 11 18| Scale is weakly epimorphic with val: <7 12 17|
FIT/MODE
7: 1 1 1 1 0 1 2 N T3 SD: 66.0372 c. M: 103.1539 c. 8: 2 1 0 2 0 1 2 N I SD: 31.4705 c. M:-48.0450 c. 9: 2 1 1 1 1 1 2 N D3 I SD: 24.2439 c. M:-35.2883 c. 12: 3 1 1 2 1 1 3 N I SD: 19.9938 c. M: 27.3726 c. Mela Yagapriya, Raga Kalahamsa 14: 3 2 1 2 1 2 3 N G I SD: 12.7541 c. M: 17.4396 c. 17: 4 2 1 3 1 2 4 N I SD: 5.0871 c. M: 7.7705 c. 31: 7 4 2 5 2 4 7 N I SD: 3.4789 c. M: 5.1808 c. 48: 11 6 3 8 3 6 11 N I SD: 1.6584 c. M: 2.3726 c. 70: 16 9 4 12 4 9 16 N I SD: 0.8175 c. M: 1.1989 c. 118: 27 15 7 20 7 15 27 N I SD: 0.1943 c. M:-0.2601 c. 188: 43 24 11 32 11 24 43 N I SD: 0.1892 c. M: 0.2870 c. 306: 70 39 18 52 18 39 70 N I SD: 0.0572 c. M:-0.0784 c. 424: 97 54 25 72 25 54 97 N I SD: 0.0471 c. M:-0.0682 c. 730: 167 93 43 124 43 93 167 N I SD: 0.0408 c. M: 0.0619 c. 1053: 241 134 62 179 62 134 241 N I SD: 0.0407 c. M: 0.0614 c. 1154: 264 147 68 196 68 147 264 N I SD: 0.0412 c. M: 0.0590 c. 1171: 268 149 69 199 69 149 268 N I SD: 0.0383 c. M: 0.0546 c. 1359: 311 173 80 231 80 173 311 N I SD: 0.0238 c. M:-0.0318 c. 1477: 338 188 87 251 87 188 338 N I SD: 0.0190 c. M: 0.0283 c. 1665: 381 212 98 283 98 212 381 N I SD: 0.0177 c. M: 0.0270 c. 1783: 408 227 105 303 105 227 408 N I SD: 0.0074 c. M: 0.0110 c. 2089: 478 266 123 355 123 266 478 N I SD: 0.0063 c. M: 0.0089 c. 2207: 505 281 130 375 130 281 505 N I SD: 0.0046 c. M:-0.0067 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: 13.6863 cents 4 x 5 x 6 x 7:8 S SD: 14.9376 cents 5:6 x 7 x 8:9:10 S SD: 27.5705 cents 6:7 x 8:9 x 10:12 S SD: 8.3554 cents 7:8:9 x x 11:12:14 SD: 9.1663 cents 9:11 x 12 x 14:15:18 SD: 16.7915 cents 10:12:13 x 15:16:17:20 SD: 10.7213 cents 11:13:14:15 x 17:19:22 SD: 8.5265 cents 13:15 x 17 x 20:22:26 SD: 10.5546 cents 14:16:18:19:21:22:24:28 SD: 7.8759 cents 15:18:19:20 x 23:26:30 SD: 10.2728 cents 16:19:20:21:24:25:27:32 SD: 8.2527 cents 17:20:22:23:26:27:29:34 SD: 7.7932 cents 18:21:23:24:27:28:31:36 SD: 2.7654 cents 36:42:46:48:54:56:61:72 SD: 2.4024 cents 42:49:54:56:63:66:72:84 SD: 2.3721 cents 46:54:59:61:69:72:79:92 SD: 2.1999 cents 48:56:61:64:72:75:82:96 SD: 2.1051 cents 54:63:69:72:81:84:92:108 SD: 1.6723 cents 64:75:82:85:96:100:109:128 SD: 1.1222 cents 82:96:105:109:123:128:140:164 SD: 0.8394 cents 110:129:141:147:165:172:188:220 SD: 0.7914 cents 122:143:156:163:183:191:208:244 SD: 0.7900 cents 126:148:161:168:189:197:215:252 SD: 0.7363 cents 132:155:169:176:198:206:225:264 SD: 0.6612 cents 140:164:179:187:210:219:239:280 SD: 0.6037 cents 146:171:187:195:219:228:249:292 SD: 0.5202 cents 150:176:192:200:225:234:256:300 SD: 0.5014 cents 174:204:223:232:261:272:297:348 SD: 0.3514 cents 192:225:246:256:288:300:328:384 SD: 0.3414 cents 204:239:261:272:306:319:348:408 SD: 0.2601 cents 222:260:284:296:333:347:379:444 SD: 0.2357 cents 354:415:453:472:531:553:604:708 SD: 0.1428 cents 396:464:507:528:594:619:676:792 SD: 0.1340 cents 528:619:676:704:792:825:901:1056 SD: 0.1204 cents 546:640:699:728:819:853:932:1092 SD: 0.0926 cents