Scala analysis: xen15-chalmers-triadic-diamond-8192-6561
Triadic diamond for M=8192/6561, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 19683/16384 317.595008 Pythagorean augmented second 2: 8192/6561 384.359993 Pythagorean diminished fourth 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 6561/4096 815.640007 Pythagorean augmented fifth 6: 32768/19683 882.404992 Pythagorean diminished seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 19683/16384 317.5950 Pythagorean augmented second 1: 19683/16384 317.5950 Pythagorean augmented second 2: 134217728/129140163 66.7650 Pythagorean double diminished third 3: 2187/2048 113.6850 apotome 4: 9/8 203.9100 major whole tone 5: 2187/2048 113.6850 apotome 6: 134217728/129140163 66.7650 Pythagorean double diminished third 7: 19683/16384 317.5950 Pythagorean augmented second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 134217728/129140163 66.765 cents Pythagorean double diminished third 1: 2 2187/2048 113.685 cents apotome 1: 1 9/8 203.910 cents major whole tone 1: 2 19683/16384 317.595 cents Pythagorean augmented second 2: 2 65536/59049 180.450 cents Pythagorean diminished third 2: 2 19683/16384 317.595 cents Pythagorean augmented second 2: 2 8192/6561 384.360 cents Pythagorean diminished fourth 2: 1 387420489/268435456 635.190 cents Pythagorean double augmented third 3: 2 8192/6561 384.360 cents Pythagorean diminished fourth 3: 1 43046721/33554432 431.280 cents Pythagorean double augmented second 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 67108864/43046721 768.720 cents Pythagorean double diminished seventh 4: 2 6561/4096 815.640 cents Pythagorean augmented fifth 5: 1 536870912/387420489 564.810 cents Pythagorean double diminished sixth 5: 2 6561/4096 815.640 cents Pythagorean augmented fifth 5: 2 32768/19683 882.405 cents Pythagorean diminished seventh 5: 2 59049/32768 1019.550 cents Pythagorean augmented sixth 6: 2 32768/19683 882.405 cents Pythagorean diminished seventh 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 4096/2187 1086.315 cents Pythagorean diminished octave 6: 2 129140163/67108864 1133.235 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 : 317.6 384.4 498.0 702.0 815.6 882.4 1200.0 317.6 : 66.8 180.4 384.4 498.0 564.8 882.4 1200.0 384.4 : 113.7 317.6 431.3 498.0 815.6 1133.2 1200.0 498.0 : 203.9 317.6 384.4 702.0 1019.6 1086.3 1200.0 702.0 : 113.7 180.4 498.0 815.6 882.4 996.1 1200.0 815.6 : 66.8 384.4 702.0 768.7 882.4 1086.3 1200.0 882.4 : 317.6 635.2 702.0 815.6 1019.6 1133.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 66.7650 .. 317.5950 cents 250.83002 cents 134217728/129140163, 66.7650 cents 2: 180.4500 .. 635.1900 cents 454.74002 cents 1073741824/1162261467,-137.1450 cents 3: 384.3600 .. 701.9550 cents 19683/16384, 317.5950 cents -250.83002 cents 4: 498.0450 .. 815.6400 cents 19683/16384, 317.5950 cents 8/9,-203.9100 cents 5: 564.8100 .. 1019.5500 cents 454.74002 cents -250.83002 cents 6: 882.4050 .. 1133.2350 cents 250.83002 cents 1073741824/1162261467,-137.1450 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 134217728/129140163, 66.7650 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 19683/16384, 317.5950 cents Average / Smallest step : 2.567642 Largest / Average step : 1.852638 Largest / Smallest step : 4.756910 Median interval of one step : 2187/2048, 113.6850 cents, amount: 2 Least squares average step : 165.43500 cents, oct.: 1158.04500 cents Scale is not proper Scale is a mode of a 665-tone equal temperament with octave 2/1 degrees: 176 213 276 389 452 489 665 Least number of segments generator : 333 of 600.902 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 389 of 701.955 cents and inv. generated superset size: 19 = 12 more = 271.429% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDCBA Step pattern size order : DABCBAD Scale is not a Constant Structure Scale diversity : 1.452487 Lumma stability : 0.111275 Lumma impropriety factor : 0.587975 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 : 531441/524288, 23.4600 cents Number of recognisable fifths : 4, average 701.9550 cents Scale is a complete diamond : 1 3 19683 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 : 3 Odd number limit : 387420489 (O: 387420489 U: 387420489) Highest odd numerator or denominator: 19683 Scale harmonicity : 0.012987 Average absolute harmonicity : 0.228299 Specific harmonicity : 0.070848 Fundamental : 1/322486272, -28.2647 octaves, 0.0000 Hz. Guide tone : 644972544, 29.2647 octaves, 168741306427.624 Hz. Exponens Consonantiae : 2.079948E+17, 57.52933 octaves Euler's gradus suavitatis : 66 Sum of Mann's harmonic distance : 56971.5, average 8138.78571 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 17.17637, average 2.45377 Sum of Tenney's harmonic distance : 34.63610, average 4.94801 Vogel's harmonic complexity : 41.57143 Wille's k value : 193710244 Wilson's harmonic complexity : 54 Rectangular lattice diameter : 18 Triangular lattice diameter : 18 Lattice compactness : 399.27769, average 14.25992 Lattice compactness (without 2's) : 212.00000, average 7.57143 Number of different primes : 2 Prime exponents' range, average, count, tones@limit: 2: -14 .. 15 0.57143 58 1 3: -9 .. 9 0.00000 36 6 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 36 / 7 = 5.14286
FIT/MODE
7: 2 0 1 1 1 0 2 N T3 I SD: 27.3831 c. M: 41.5029 c. 12: 3 1 1 2 1 1 3 N I SD: 12.6267 c. M:-17.5950 c. Mela Yagapriya, Raga Kalahamsa 19: 5 1 2 3 2 1 5 N I SD: 4.9181 c. M:-7.2182 c. 34: 9 2 3 6 3 2 9 N I SD: 2.9493 c. M:-3.9274 c. 53: 14 3 5 9 5 3 14 N I SD: 0.4405 c. M: 0.6139 c. 200: 53 11 19 34 19 11 53 N I SD: 0.2906 c. M:-0.4050 c. 253: 67 14 24 43 24 14 67 N I SD: 0.1375 c. M:-0.1916 c. 306: 81 17 29 52 29 17 81 N I SD: 0.0374 c. M:-0.0521 c. 359: 95 20 34 61 34 20 95 N I SD: 0.0332 c. M:-0.0463 c. 665: 176 37 63 113 63 37 176 N I SD: 0.0007 c. M:-0.0010 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: 0.6512 cents 4 x 5 x 6 x 7:8 S SD: 21.6107 cents 5:6 x 7 x 8 x 10 S SD: 21.1281 cents 6:7 x 8:9 x 10:12 S SD: 10.1523 cents 7:8:9 x x 11:12:14 SD: 23.4207 cents 8 x 10:11:12:13 x 16 SD: 11.7664 cents 9:11 x 12 x 14:15:18 SD: 11.7738 cents 10:12 x 13:15:16:17:20 SD: 9.4896 cents 11:13:14:15:17 x 18:22 SD: 13.9225 cents 12:14:15:16:18:19:20:24 S SD: 7.8035 cents 13 x 16:17:20:21:22:26 SD: 11.4139 cents 14:17 x 19:21:22:23:28 SD: 8.9880 cents 15:18:19:20:23:24:25:30 SD: 6.5130 cents 18:22 x 24:27:29:30:36 SD: 5.2524 cents 20:24:25:27:30:32:33:40 SD: 3.8134 cents 24:29:30:32:36:38:40:48 SD: 3.2308 cents 30:36:37:40:45:48:50:60 SD: 3.0789 cents 36:43:45:48:54:58:60:72 SD: 2.0599 cents 45:54:56:60:68:72:75:90 SD: 2.0596 cents 48:58:60:64:72:77:80:96 SD: 1.5298 cents 60:72:75:80:90:96:100:120 S SD: 0.5582 cents 144:173:180:192:216:231:240:288 SD: 0.5371 cents 168:202:210:224:252:269:280:336 SD: 0.4576 cents 194:233:242:259:291:311:323:388 SD: 0.4465 cents 198:238:247:264:297:317:330:396 SD: 0.4008 cents 218:262:272:291:327:349:363:436 SD: 0.3773 cents 234:281:292:312:351:375:390:468 SD: 0.3506 cents 254:305:317:339:381:407:423:508 SD: 0.3155 cents 274:329:342:365:411:439:456:548 SD: 0.2908 cents 294:353:367:392:441:471:489:588 SD: 0.2740 cents 318:382:397:424:477:509:529:636 SD: 0.2643 cents 322:387:402:429:483:516:536:644 SD: 0.2458 cents 334:401:417:445:501:535:556:668 SD: 0.2432 cents 342:411:427:456:513:548:569:684 SD: 0.1942 cents 382:459:477:509:573:612:636:764 SD: 0.1759 cents 402:483:502:536:603:644:669:804 SD: 0.1041 cents 462:555:577:616:693:740:769:924 SD: 0.0792 cents