Scala analysis: xen15-chalmers-triadic-diamond-81-64
Triadic diamond for M=81/64, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 32/27 294.134997 Pythagorean minor third 2: 81/64 407.820003 Pythagorean major third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 128/81 792.179997 Pythagorean minor sixth 6: 27/16 905.865003 Pythagorean major sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 32/27 294.1350 Pythagorean minor third 1: 32/27 294.1350 Pythagorean minor third 2: 2187/2048 113.6850 apotome 3: 256/243 90.2250 limma, Pythagorean minor second 4: 9/8 203.9100 major whole tone 5: 256/243 90.2250 limma, Pythagorean minor second 6: 2187/2048 113.6850 apotome 7: 32/27 294.1350 Pythagorean minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 256/243 90.225 cents limma, Pythagorean minor second 1: 2 2187/2048 113.685 cents apotome 1: 1 9/8 203.910 cents major whole tone 1: 2 32/27 294.135 cents Pythagorean minor third 2: 2 9/8 203.910 cents major whole tone 2: 2 32/27 294.135 cents Pythagorean minor third 2: 2 81/64 407.820 cents Pythagorean major third 2: 1 1024/729 588.270 cents Pythagorean diminished fifth 3: 1 8192/6561 384.360 cents Pythagorean diminished fourth 3: 2 81/64 407.820 cents Pythagorean major third 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: 2 128/81 792.180 cents Pythagorean minor sixth 4: 1 6561/4096 815.640 cents Pythagorean augmented fifth 5: 1 729/512 611.730 cents Pythagorean tritone 5: 2 128/81 792.180 cents Pythagorean minor sixth 5: 2 27/16 905.865 cents Pythagorean major sixth 5: 2 16/9 996.090 cents Pythagorean minor seventh 6: 2 27/16 905.865 cents Pythagorean major sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 4096/2187 1086.315 cents Pythagorean diminished octave 6: 2 243/128 1109.775 cents Pythagorean major seventh 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 : 294.1 407.8 498.0 702.0 792.2 905.9 1200.0 294.1 : 113.7 203.9 407.8 498.0 611.7 905.9 1200.0 407.8 : 90.2 294.1 384.4 498.0 792.2 1086.3 1200.0 498.0 : 203.9 294.1 407.8 702.0 996.1 1109.8 1200.0 702.0 : 90.2 203.9 498.0 792.2 905.9 996.1 1200.0 792.2 : 113.7 407.8 702.0 815.6 905.9 1109.8 1200.0 905.9 : 294.1 588.3 702.0 792.2 996.1 1086.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.2250 .. 294.1350 cents 9/8, 203.9100 cents 256/243, 90.2250 cents 2: 203.9100 .. 588.2700 cents 8192/6561, 384.3600 cents 243/256,-90.2250 cents 3: 384.3600 .. 701.9550 cents 19683/16384, 317.5950 cents 8/9,-203.9100 cents 4: 498.0450 .. 815.6400 cents 19683/16384, 317.5950 cents 8/9,-203.9100 cents 5: 611.7300 .. 996.0900 cents 8192/6561, 384.3600 cents 8/9,-203.9100 cents 6: 905.8650 .. 1109.7750 cents 9/8, 203.9100 cents 243/256,-90.2250 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 256/243, 90.2250 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 32/27, 294.1350 cents Average / Smallest step : 1.900012 Largest / Average step : 1.715787 Largest / Smallest step : 3.260017 Median interval of one step : 2187/2048, 113.6850 cents, amount: 2 Least squares average step : 165.77014 cents, oct.: 1160.39100 cents Scale is not proper Scale is a mode of a 665-tone equal temperament with octave 2/1 degrees: 163 226 276 389 439 502 665 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: 9 = 2 more = 128.571% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDCBA Step pattern size order : DBACABD Scale is not a Constant Structure Scale diversity : 1.368436 Lumma stability : 0.150375 Lumma impropriety factor : 0.509775 Rothenberg efficiency : 0.521088 redundancy: 0.478912 Efficiency x scale size : 3.647619 Number of different interval sizes : 16 = 2.66667 / 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 81 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 : 6561 (O: 6561 U: 6561) Highest odd numerator or denominator: 81 Scale harmonicity : 0.029126 Average absolute harmonicity : 0.251981 Specific harmonicity : 0.163543 Fundamental : 1/5184, -12.3399 octaves, 0.0505 Hz. Guide tone : 10368, 13.3399 octaves, 2712533.861 Hz. Exponens Consonantiae : 5.374771E+07, 25.67970 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 235.5, average 33.64286 Mersenne's string divisions : 1614559485 Sum of van Prooijen's expressibility: 7.63394, average 1.09056 Sum of Tenney's harmonic distance : 15.46072, average 2.20867 Vogel's harmonic complexity : 18.57143 Wille's k value : 3280 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 8 Triangular lattice diameter : 8 Lattice compactness : 172.90785, average 6.17528 Lattice compactness (without 2's) : 92.00000, average 3.28571 Number of different primes : 2 Prime exponents' range, average, count, tones@limit: 2: -6 .. 7 0.57143 26 1 3: -4 .. 4 0.00000 16 6 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 16 / 7 = 2.28571
FIT/MODE
7: 2 0 1 1 1 0 2 N T3 I SD: 44.2647 c. M: 64.9629 c. 8: 2 1 0 2 0 1 2 N I SD: 34.3173 c. M:-48.0450 c. 9: 2 1 1 1 1 1 2 N D3 I SD: 24.2660 c. M:-35.2883 c. 12: 3 1 1 2 1 1 3 N I SD: 5.3284 c. M:-7.8200 c. Mela Yagapriya, Raga Kalahamsa 29: 7 3 2 5 2 3 7 N I SD: 4.0700 c. M:-5.9731 c. 41: 10 4 3 7 3 4 10 N I SD: 1.3192 c. M:-1.9361 c. 53: 13 5 4 9 4 5 13 N I SD: 0.1859 c. M:-0.2728 c. 200: 49 19 15 34 15 19 49 N I SD: 0.1226 c. M:-0.1800 c. 253: 62 24 19 43 19 24 62 N I SD: 0.0580 c. M:-0.0851 c. 306: 75 29 23 52 23 29 75 N I SD: 0.0158 c. M:-0.0231 c. 359: 88 34 27 61 27 34 88 N I SD: 0.0140 c. M:-0.0206 c. 665: 163 63 50 113 50 63 163 N I SD: 0.0003 c. M:-0.0005 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: 7.1688 cents 4 x 5 x 6 x 7:8 S SD: 16.6332 cents 5:6 x 7 x 8 x 10 S SD: 22.4440 cents 6:7 x 8:9 x 10:12 S SD: 6.9451 cents 7:8:9 x x 11:12:14 SD: 14.8924 cents 9:11 x 12 x 14:15:18 SD: 12.7183 cents 10:12 x 13:15:16:17:20 SD: 9.1431 cents 11:13:14:15 x 17:19:22 SD: 11.4792 cents 12:14:15:16:18:19:20:24 S SD: 5.8550 cents 16:19:20:21:24:25:27:32 SD: 5.7135 cents 22:26:28:29:33:35:37:44 SD: 3.7231 cents 26:31:33:35:39:41:44:52 SD: 3.0097 cents 38:45:48:51:57:60:64:76 SD: 1.7829 cents 48:57:61:64:72:76:81:96 SD: 1.2237 cents 60:71:76:80:90:95:101:120 SD: 0.8931 cents 86:102:109:115:129:136:145:172 SD: 0.8667 cents 102:121:129:136:153:161:172:204 SD: 0.4439 cents 150:178:190:200:225:237:253:300 SD: 0.3915 cents 162:192:205:216:243:256:273:324 SD: 0.3416 cents 222:263:281:296:333:351:375:444 SD: 0.2999 cents 276:327:349:368:414:436:466:552 SD: 0.2841 cents 282:334:357:376:423:446:476:564 SD: 0.2788 cents 298:353:377:397:447:471:503:596 SD: 0.2761 cents 324:384:410:432:486:512:547:648 SD: 0.1192 cents 384:455:486:512:576:607:648:768 SD: 0.0967 cents 486:576:615:648:729:768:820:972 SD: 0.0533 cents