Scala analysis: xen15-chalmers-triadic-reversed-diamond-35-27
Triadic reversed diamond for M=35/27, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 36/35 48.770381 septimal diesis, 1/4-tone 2: 35/27 449.274618 septimal semi-diminished fourth, 9/4-tone 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 54/35 750.725382 septimal semi-augmented fifth 6: 35/18 1151.229619 septimal semi-diminished octave 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 36/35 48.7704 septimal diesis, 1/4-tone 1: 36/35 48.7704 septimal diesis, 1/4-tone 2: 1225/972 400.5042 3: 36/35 48.7704 septimal diesis, 1/4-tone 4: 9/8 203.9100 major whole tone 5: 36/35 48.7704 septimal diesis, 1/4-tone 6: 1225/972 400.5042 7: 36/35 48.7704 septimal diesis, 1/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 9/8 203.910 cents major whole tone 1: 2 1225/972 400.504 cents 2: 1 1296/1225 97.541 cents two (septimal diesis, 1/4-tone) 2: 2 81/70 252.680 cents Al-Hwarizmi's lute middle finger 2: 4 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 3: 1 1458/1225 301.451 cents 3: 4 4/3 498.045 cents perfect fourth 3: 2 35/24 653.185 cents septimal semi-diminished fifth 4: 2 48/35 546.815 cents septimal semi-augmented fourth 4: 4 3/2 701.955 cents perfect fifth 4: 1 1225/729 898.549 cents two (septimal semi-diminished fourth, 9/4-tone) 5: 4 54/35 750.725 cents septimal semi-augmented fifth 5: 2 140/81 947.320 cents 5: 1 1225/648 1102.459 cents 6: 2 1944/1225 799.496 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 4 35/18 1151.230 cents septimal semi-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 : 48.8 449.3 498.0 702.0 750.7 1151.2 1200.0 48.8 : 400.5 449.3 653.2 702.0 1102.5 1151.2 1200.0 449.3 : 48.8 252.7 301.5 702.0 750.7 799.5 1200.0 498.0 : 203.9 252.7 653.2 702.0 750.7 1151.2 1200.0 702.0 : 48.8 449.3 498.0 546.8 947.3 996.1 1200.0 750.7 : 400.5 449.3 498.0 898.5 947.3 1151.2 1200.0 1151.2: 48.8 97.5 498.0 546.8 750.7 799.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 400.5042 cents 42875/34992, 351.7339 cents 36/35, 48.7704 cents 2: 97.5408 .. 449.2746 cents 42875/34992, 351.7339 cents 1259712/1500625,-302.9635 cents 3: 301.4508 .. 653.1846 cents 42875/34992, 351.7339 cents 39366/42875,-147.8239 cents 4: 546.8154 .. 898.5492 cents 42875/34992, 351.7339 cents 1152/1225,-106.3692 cents 5: 750.7254 .. 1102.4592 cents 42875/34992, 351.7339 cents 39366/42875,-147.8239 cents 6: 799.4958 .. 1151.2296 cents 42875/34992, 351.7339 cents 1259712/1500625,-302.9635 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 1225/972, 400.5042 cents Average / Smallest step : 3.515014 Largest / Average step : 2.336275 Largest / Smallest step : 8.212038 Median interval of one step : 36/35, 48.7704 cents, amount: 4 Most common interval of one step : 36/35, 48.7704 cents, amount: 4 Least squares average step : 173.64485 cents, oct.: 1215.51396 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 48.77038 cents Scale diversity : 1.443042 Lumma stability : 0.081284 Lumma impropriety factor : 0.674864 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 : 36/35, 48.7704 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 : 9 27 35 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 : 7 Odd number limit : 1225 (O: 1225 U: 1225) Highest odd numerator or denominator: 35 Scale harmonicity : 0.019094 Average absolute harmonicity : 0.235932 Specific harmonicity : 0.102928 Fundamental : 1/1890, -10.8842 octaves, 0.1384 Hz. Guide tone : 3780, 11.8842 octaves, 988944.637 Hz. Exponens Consonantiae : 7.144200E+06, 22.76834 octaves Euler's gradus suavitatis : 36 Sum of Mann's harmonic distance : 145.0, average 20.71429 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 7.13051, average 1.01864 Sum of Tenney's harmonic distance : 14.30997, average 2.04428 Vogel's harmonic complexity : 22.57143 Wille's k value : 1837 Wilson's harmonic complexity : 42 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 93.13415, average 3.32622 Lattice compactness (without 2's) : 77.56742, average 2.77027 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.57143 8 1 3: -3 .. 3 0.00000 12 2 5: -1 .. 1 0.00000 4 7: -1 .. 1 0.00000 4 4 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 20 / 7 = 2.85714 Scale is weakly epimorphic with val: <7 10 15 20| Scale is weakly epimorphic with val: <7 10 15 21| Scale is weakly epimorphic with val: <7 10 16 19| Scale is weakly epimorphic with val: <7 10 16 20| Scale is weakly epimorphic with val: <7 10 17 18| Scale is weakly epimorphic with val: <7 10 17 19| Scale is weakly epimorphic with val: <7 10 18 18| Scale is weakly epimorphic with val: <7 11 15 19| Scale is JI-epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 11 16 18| Scale is JI-epimorphic with val: <7 11 16 19| Scale is JI-epimorphic with val: <7 11 17 18| Scale is weakly epimorphic with val: <7 12 15 20| Scale is weakly epimorphic with val: <7 12 16 19| Scale is weakly epimorphic with val: <7 12 17 18| Scale is weakly epimorphic with val: <7 12 17 22| Scale is weakly epimorphic with val: <7 12 18 21|
FIT/MODE
7: 0 3 0 1 0 3 0 N T3 I SD: 44.3001 c. M: 65.0111 c. 8: 0 3 0 2 0 3 0 N T3 I SD: 36.5959 c. M:-48.7704 c. 10: 0 4 0 2 0 4 0 N T3 I SD: 32.2854 c. M:-48.7704 c. 12: 0 4 1 2 0 4 1 N SD: 37.8186 c. M: 51.2296 c. 14: 1 4 1 2 1 4 1 N T3 I SD: 24.2442 c. M:-36.9439 c. 16: 1 5 1 2 1 5 1 N T3 I SD: 20.1075 c. M:-26.9550 c. 17: 1 5 1 3 1 5 1 N T3 I SD: 18.1601 c. M: 25.7452 c. 19: 1 6 1 3 1 6 1 N T3 I SD: 9.4189 c. M:-14.3875 c. 22: 1 7 1 4 1 7 1 N T3 I SD: 8.4679 c. M: 12.9110 c. 24: 1 8 1 4 1 8 1 N T3 I SD: 1.2940 c. M: 1.9550 c. 99: 4 33 4 17 4 33 4 N T3 I SD: 0.7293 c. M:-1.0753 c. 123: 5 41 5 21 5 41 5 N T3 I SD: 0.3698 c. M: 0.4941 c. 147: 6 49 6 25 6 49 6 N T3 I SD: 0.1987 c. M: 0.2950 c. 318: 13 106 13 54 13 106 13 N T3 I SD: 0.1957 c. M:-0.2862 c. 465: 19 155 19 79 19 155 19 N T3 I SD: 0.1910 c. M:-0.2619 c. 470: 19 157 19 80 19 157 19 N T3 I SD: 0.1731 c. M:-0.2597 c. 494: 20 165 20 84 20 165 20 N T3 I SD: 0.1241 c. M:-0.1874 c. 518: 21 173 21 88 21 173 21 N T3 I SD: 0.1025 c. M: 0.1462 c. 641: 26 214 26 109 26 214 26 N T3 I SD: 0.0659 c. M:-0.0964 c. 665: 27 222 27 113 27 222 27 N T3 I SD: 0.0368 c. M: 0.0487 c. 812: 33 271 33 138 33 271 33 N T3 I SD: 0.0110 c. M:-0.0154 c. 2289: 93 764 93 389 93 764 93 N T3 I SD: 0.0104 c. M:-0.0155 c. 2313: 94 772 94 393 94 772 94 N T3 I SD: 0.0083 c. M: 0.0120 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: 44.5444 cents 4 x 5 x 6 x x 8 S SD: 20.9870 cents 5 x x 7 x 8 x 10 SD: 35.1169 cents 6 x x 8:9 x x 12 S SD: 0.0000 cents 7:8:9 x x 11 x 14 SD: 46.4231 cents 8:9:10:11:12 x x 16 S SD: 35.1399 cents 9:10 x 12 x 14 x 18 SD: 33.5962 cents 10:11:13 x 15 x 19:20 SD: 24.6066 cents 11:12:14:15 x 17:21:22 SD: 19.6619 cents 12:13 x 16:18:19:23:24 SD: 17.2361 cents 13:14:17 x x 20:25:26 SD: 16.6669 cents 14:15:18:19:21:22:27:28 SD: 12.2436 cents 15:16:19:20 x 23:29:30 SD: 12.6709 cents 16:17:21 x 24:25:31:32 SD: 10.7204 cents 17:18:22:23 x 26:33:34 SD: 9.7237 cents 18:19:23:24:27:28:35:36 SD: 7.6022 cents 19:20 x 25 x 29:37:38 SD: 9.9664 cents 20:21:26:27:30:31:39:40 SD: 6.1437 cents 21:22:27:28 x 32:41:42 SD: 6.9177 cents 22:23 x 29:33:34:43:44 SD: 5.9509 cents 23:24:30:31 x 35:45:46 SD: 7.0118 cents 24:25:31:32:36:37:47:48 SD: 3.7024 cents 30:31:39:40:45:46:58:60 SD: 2.4813 cents 40:41:52:53:60:62:78:80 SD: 2.3335 cents 48:49:62:64:72:74:93:96 SD: 2.2562 cents 54:56:70:72:81:83:105:108 SD: 2.2323 cents 57:59:74:76:86:88:111:114 SD: 2.1957 cents 60:62:78:80:90:93:117:120 SD: 1.8989 cents 64:66:83:85:96:99:124:128 SD: 1.5999 cents 66:68:86:88:99:102:128:132 SD: 1.5498 cents 68:70:88:91:102:105:132:136 SD: 1.1187 cents 72:74:93:96:108:111:140:144 SD: 0.9251 cents 102:105:132:136:153:157:198:204 SD: 0.8535 cents 105:108:136:140:158:162:204:210 SD: 0.8343 cents 108:111:140:144:162:167:210:216 SD: 0.5828 cents 138:142:179:184:207:213:268:276 SD: 0.3714 cents 210:216:272:280:315:324:408:420 SD: 0.2856 cents 216:222:280:288:324:333:420:432 SD: 0.2700 cents 276:284:358:368:414:426:537:552 SD: 0.2588 cents 324:333:420:432:486:500:630:648 SD: 0.1991 cents 348:358:451:464:522:537:677:696 SD: 0.1472 cents 486:500:630:648:729:750:945:972 SD: 0.0800 cents