Scala analysis: xen15-chalmers-triadic-reversed-diamond-32-25
Triadic reversed 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: 25/24 70.672427 classic chromatic semitone, minor chroma 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: 48/25 1129.327573 classic diminished octave 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 25/24 70.6724 classic chromatic semitone, minor chroma 1: 25/24 70.6724 classic chromatic semitone, minor chroma 2: 768/625 356.7001 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: 768/625 356.7001 7: 25/24 70.6724 classic chromatic semitone, minor chroma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 1 9/8 203.910 cents major whole tone 1: 2 768/625 356.700 cents 2: 1 625/576 141.345 cents two (classic chromatic semitone, minor chroma) 2: 2 75/64 274.582 cents classic augmented second 2: 4 32/25 427.373 cents classic diminished fourth 3: 1 625/512 345.255 cents classic neutral third 3: 4 4/3 498.045 cents perfect fourth 3: 2 36/25 631.283 cents classic diminished fifth 4: 2 25/18 568.717 cents classic augmented fourth 4: 4 3/2 701.955 cents perfect fifth 4: 1 1024/625 854.745 cents two (classic diminished fourth) 5: 4 25/16 772.627 cents classic augmented fifth 5: 2 128/75 925.418 cents diminished seventh 5: 1 1152/625 1058.655 cents 6: 2 625/384 843.300 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 4 48/25 1129.328 cents classic diminished octave Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 70.7 427.4 498.0 702.0 772.6 1129.3 1200.0 70.7 : 356.7 427.4 631.3 702.0 1058.7 1129.3 1200.0 427.4 : 70.7 274.6 345.3 702.0 772.6 843.3 1200.0 498.0 : 203.9 274.6 631.3 702.0 772.6 1129.3 1200.0 702.0 : 70.7 427.4 498.0 568.7 925.4 996.1 1200.0 772.6 : 356.7 427.4 498.0 854.7 925.4 1129.3 1200.0 1129.3: 70.7 141.3 498.0 568.7 772.6 843.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 356.7001 cents 18432/15625, 286.0277 cents 25/24, 70.6724 cents 2: 141.3449 .. 427.3726 cents 18432/15625, 286.0277 cents 390625/442368,-215.3553 cents 3: 345.2549 .. 631.2826 cents 18432/15625, 286.0277 cents 15625/16384,-82.1177 cents 4: 568.7174 .. 854.7451 cents 18432/15625, 286.0277 cents 625/648,-62.5651 cents 5: 772.6274 .. 1058.6551 cents 18432/15625, 286.0277 cents 15625/16384,-82.1177 cents 6: 843.2999 .. 1129.3276 cents 18432/15625, 286.0277 cents 390625/442368,-215.3553 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 : 768/625, 356.7001 cents Average / Smallest step : 2.425678 Largest / Average step : 2.080751 Largest / Smallest step : 5.047232 Median interval of one step : 25/24, 70.6724 cents, amount: 4 Most common interval of one step : 25/24, 70.6724 cents, amount: 4 Least squares average step : 173.33197 cents, oct.: 1213.32376 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABACABA Step pattern size order : SLSMSLS Scale is a Constant Structure, by a margin of 11.44529 cents Scale diversity : 1.473110 Lumma stability : 0.117787 Lumma impropriety factor : 0.528850 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 : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 393216/390625, 11.4453 cents Number of recognisable fifths : 4, average 701.9550 cents Scale is Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords Scale is a complete diamond : 1 3 25 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 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 : 625 (O: 625 U: 625) Highest odd numerator or denominator: 25 Scale harmonicity : 0.025042 Average absolute harmonicity : 0.244034 Specific harmonicity : 0.133555 Fundamental : 1/1200, -10.2288 octaves, 0.2180 Hz. Guide tone : 2400, 11.2288 octaves, 627901.357 Hz. Exponens Consonantiae : 2.880000E+06, 21.45764 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 117.5, average 16.78571 Mersenne's string divisions : 41797245 Sum of van Prooijen's expressibility: 6.54600, average 0.93514 Sum of Tenney's harmonic distance : 13.52084, average 1.93155 Vogel's harmonic complexity : 17.57143 Wille's k value : 937 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 125.24119, average 4.47290 Lattice compactness (without 2's) : 60.26375, average 2.15228 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 5 0.57143 20 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 15| Scale is weakly epimorphic with val: <7 10 18| Scale is weakly epimorphic with val: <7 11 17| Scale is weakly epimorphic with val: <7 12 16| Scale is weakly epimorphic with val: <7 12 18|
FIT/MODE
7: 0 2 1 1 0 2 1 N T3 SD: 65.8686 c. M: 100.7561 c. 8: 0 2 1 1 1 2 1 N D3 SD: 76.2762 c. M: 127.3726 c. 9: 1 2 1 1 1 2 1 P M ME I SD: 41.1302 c. M: 62.6609 c. 12: 1 3 1 2 1 3 1 N T3 I SD: 21.4688 c. M: 29.3276 c. Double Harmonic Major, Major Gipsy, Bhairav That, Mela Mayamalavagaula, Raga Paraj, Kalingada, Gaulipantu, Lalitapancamam, Gandhakriya, Kalingda, Manjiri, Chromatic 2nd Byzantine Liturgical, Hitzazkiar: Greece, Maqam Zengule, Hijaz Kar, Suzidil 14: 1 4 1 2 1 4 1 N T3 I SD: 11.8497 c. M:-16.2407 c. 17: 1 5 1 3 1 5 1 N T3 I SD: 2.9375 c. M:-3.9274 c. 48: 3 14 3 8 3 14 3 N T3 I SD: 2.8375 c. M:-4.3276 c. 53: 3 16 3 9 3 16 3 N T3 I SD: 2.1035 c. M: 2.8161 c. 70: 4 21 4 12 4 21 4 N T3 I SD: 1.3800 c. M: 2.1010 c. 84: 5 25 5 14 5 25 5 N T3 I SD: 1.2907 c. M: 1.9550 c. 87: 5 26 5 15 5 26 5 N T3 I SD: 1.2176 c. M: 1.7069 c. 101: 6 30 6 17 6 30 6 N T3 I SD: 0.6395 c. M:-0.9649 c. 118: 7 35 7 20 7 35 7 N T3 I SD: 0.3365 c. M:-0.5140 c. 188: 11 56 11 32 11 56 11 N T3 I SD: 0.3040 c. M: 0.4597 c. 289: 17 86 17 49 17 86 17 N T3 I SD: 0.2092 c. M: 0.3091 c. 306: 18 91 18 52 18 91 18 N T3 I SD: 0.0616 c. M: 0.0842 c. 424: 25 126 25 72 25 126 25 N T3 I SD: 0.0576 c. M: 0.0823 c. 730: 43 217 43 124 43 217 43 N T3 I SD: 0.0248 c. M:-0.0372 c. 1359: 80 404 80 231 80 404 80 N T3 I SD: 0.0242 c. M: 0.0323 c. 1477: 87 439 87 251 87 439 87 N T3 I SD: 0.0130 c. M: 0.0198 c. 1783: 105 530 105 303 105 530 105 N T3 I SD: 0.0053 c. M:-0.0080 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 5 x 6 S SD: 37.2438 cents 4 x 5 x 6 x x 8 S SD: 13.6863 cents 5 x 6:7 x 8 x 10 S SD: 36.4901 cents 6 x x 8:9 x x 12 S SD: 0.0000 cents 7:8:9 x x 11:13:14 SD: 34.1984 cents 8:9:10:11:12:13:15:16 SD: 24.1477 cents 9:10 x 12 x 14:17:18 SD: 23.1026 cents 10:11:13 x 15:16:19:20 SD: 17.9764 cents 11:12:14:15 x 17:21:22 SD: 15.3326 cents 12:13:15:16:18:19:23:24 SD: 11.8072 cents 13:14 x 17 x 20:25:26 SD: 14.3931 cents 14:15:18:19:21:22:27:28 SD: 8.4922 cents 15:16:19:20 x 23:29:30 SD: 9.4607 cents 16:17:20:21:24:25:31:32 SD: 8.8655 cents 18:19:23:24:27:28:35:36 SD: 4.6818 cents 22:23:28:29:33:34:42:44 SD: 4.4863 cents 24:25:31:32:36:38:46:48 SD: 3.9939 cents 26:27:33:35:39:41:50:52 SD: 3.9837 cents 28:29:36:37:42:44:54:56 SD: 3.3678 cents 39:41:50:52:59:61:75:78 SD: 3.1579 cents 42:44:54:56:63:66:81:84 SD: 2.5296 cents 46:48:59:61:69:72:88:92 SD: 1.8015 cents 50:52:64:67:75:78:96:100 SD: 1.3547 cents 72:75:92:96:108:113:138:144 SD: 1.2539 cents 75:78:96:100:113:117:144:150 SD: 1.2315 cents 78:81:100:104:117:122:150:156 SD: 0.9792 cents 96:100:123:128:144:150:184:192 SD: 0.4929 cents 174:181:223:232:261:272:334:348 SD: 0.4791 cents 186:194:238:248:279:291:357:372 SD: 0.4661 cents 190:198:243:253:285:297:365:380 SD: 0.4330 cents 192:200:246:256:288:300:369:384 SD: 0.3414 cents 240:250:307:320:360:375:461:480 SD: 0.1935 cents 336:350:430:448:504:525:645:672 SD: 0.0651 cents