Scala analysis: xen15-chalmers-triadic-reversed-diamond-17-14
Triadic reversed diamond for M=17/14, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 56/51 161.915496 2: 17/14 336.129503 supraminor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 28/17 863.870497 submajor sixth 6: 51/28 1038.084504 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 56/51 161.9155 1: 56/51 161.9155 2: 867/784 174.2140 3: 56/51 161.9155 4: 9/8 203.9100 major whole tone 5: 56/51 161.9155 6: 867/784 174.2140 7: 56/51 161.9155
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 56/51 161.915 cents 1: 2 867/784 174.214 cents 1: 1 9/8 203.910 cents major whole tone 2: 1 3136/2601 323.831 cents 2: 4 17/14 336.130 cents supraminor third 2: 2 21/17 365.825 cents submajor third 3: 4 4/3 498.045 cents perfect fourth 3: 1 392/289 527.741 cents 3: 2 153/112 540.040 cents 4: 2 224/153 659.960 cents 4: 1 289/196 672.259 cents two (supraminor third) 4: 4 3/2 701.955 cents perfect fifth 5: 2 34/21 834.175 cents supraminor sixth 5: 4 28/17 863.870 cents submajor sixth 5: 1 2601/1568 876.169 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 1568/867 1025.786 cents 6: 4 51/28 1038.085 cents 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 : 161.9 336.1 498.0 702.0 863.9 1038.1 1200.0 161.9 : 174.2 336.1 540.0 702.0 876.2 1038.1 1200.0 336.1 : 161.9 365.8 527.7 702.0 863.9 1025.8 1200.0 498.0 : 203.9 365.8 540.0 702.0 863.9 1038.1 1200.0 702.0 : 161.9 336.1 498.0 660.0 834.2 996.1 1200.0 863.9 : 174.2 336.1 498.0 672.3 834.2 1038.1 1200.0 1038.1: 161.9 323.8 498.0 660.0 863.9 1025.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 161.9155 .. 203.9100 cents 459/448, 41.9945 cents 56/51, 161.9155 cents 2: 323.8310 .. 365.8255 cents 459/448, 41.9945 cents 25088/23409, 119.9210 cents 3: 498.0450 .. 540.0395 cents 459/448, 41.9945 cents 68/63, 132.2195 cents 4: 659.9605 .. 701.9550 cents 459/448, 41.9945 cents 25088/23409, 119.9210 cents 5: 834.1745 .. 876.1690 cents 459/448, 41.9945 cents 68/63, 132.2195 cents 6: 996.0900 .. 1038.0845 cents 459/448, 41.9945 cents 25088/23409, 119.9210 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 56/51, 161.9155 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.058753 Largest / Average step : 1.189475 Largest / Smallest step : 1.259361 Median interval of one step : 56/51, 161.9155 cents, amount: 4 Most common interval of one step : 56/51, 161.9155 cents, amount: 4 Least squares average step : 172.02849 cents, oct.: 1204.19945 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABACABA Step pattern size order : SMSLSMS Scale is a Constant Structure, by a margin of 119.92099 cents Scale diversity : 1.209883 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.790027 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 : 44217/43904, 12.2985 cents Number of recognisable fifths : 4, average 701.9550 cents Scale is Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Scale is a complete diamond : 7 17 51 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 : 17 Odd number limit : 2601 (O: 2601 U: 2601) Highest odd numerator or denominator: 51 Scale harmonicity : 0.010972 Average absolute harmonicity : 0.225520 Specific harmonicity : 0.058518 Fundamental : 1/1428, -10.4798 octaves, 0.1832 Hz. Guide tone : 2856, 11.4798 octaves, 747202.614 Hz. Exponens Consonantiae : 4.078368E+06, 21.95956 octaves Euler's gradus suavitatis : 54 Sum of Mann's harmonic distance : 138.5, average 19.78571 Mersenne's string divisions : 82543545 Sum of van Prooijen's expressibility: 6.83028, average 0.97575 Sum of Tenney's harmonic distance : 13.82303, average 1.97472 Vogel's harmonic complexity : 29.57143 Wille's k value : 1300 Wilson's harmonic complexity : 54 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 78.76043, average 2.81287 Lattice compactness (without 2's) : 47.53320, average 1.69761 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 3 0.57143 12 1 3: -1 .. 1 0.00000 4 2 7: -1 .. 1 0.00000 4 17: -1 .. 1 0.00000 4 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 18 30| Scale is weakly epimorphic with val: <7 10 18 31| Scale is weakly epimorphic with val: <7 10 19 31| Scale is weakly epimorphic with val: <7 10 19 32| Scale is weakly epimorphic with val: <7 10 20 26| Scale is weakly epimorphic with val: <7 10 20 32| Scale is weakly epimorphic with val: <7 10 21 26| Scale is weakly epimorphic with val: <7 10 21 27| Scale is weakly epimorphic with val: <7 10 22 27| Scale is weakly epimorphic with val: <7 10 22 28| Scale is weakly epimorphic with val: <7 11 18 26| Scale is JI-epimorphic with val: <7 11 18 27| Scale is weakly epimorphic with val: <7 11 19 27| Scale is JI-epimorphic with val: <7 11 19 28| Scale is weakly epimorphic with val: <7 11 20 28| Scale is JI-epimorphic with val: <7 11 20 29| = patent Scale is weakly epimorphic with val: <7 11 21 29| Scale is JI-epimorphic with val: <7 11 21 30| Scale is weakly epimorphic with val: <7 11 22 30| Scale is JI-epimorphic with val: <7 11 22 31| Scale is weakly epimorphic with val: <7 12 18 28| Scale is weakly epimorphic with val: <7 12 18 31| Scale is weakly epimorphic with val: <7 12 19 29| Scale is weakly epimorphic with val: <7 12 19 32| Scale is weakly epimorphic with val: <7 12 20 26| Scale is weakly epimorphic with val: <7 12 20 30| Scale is weakly epimorphic with val: <7 12 21 27| Scale is weakly epimorphic with val: <7 12 21 31| Scale is weakly epimorphic with val: <7 12 22 28| Scale is weakly epimorphic with val: <7 12 22 32|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 10.6840 c. M:-16.2407 c. Lebeng 22: 3 3 3 4 3 3 3 SP M ME I SD: 6.1488 c. M:-8.8568 c. Minor quasi-equal Heptatonic, Miller's Porcupine-7 29: 4 4 4 5 4 4 4 SP M ME I SD: 3.4294 c. M:-5.0950 c. Miller's Porcupine-7 36: 5 5 5 6 5 5 5 SP M ME I SD: 3.1266 c. M: 4.7512 c. Equal Diatonic Dorian 53: 7 8 7 9 7 8 7 SP T3 I SD: 2.6152 c. M:-3.4931 c. 60: 8 9 8 10 8 9 8 SP T3 I SD: 2.5339 c. M:-3.8705 c. 75: 10 11 10 13 10 11 10 SP T3 I SD: 1.4993 c. M:-2.0450 c. 82: 11 12 11 14 11 12 11 SP T3 I SD: 0.6154 c. M: 0.9399 c. 118: 16 17 16 20 16 17 16 SP T3 I SD: 0.5317 c. M: 0.7964 c. 171: 23 25 23 29 23 25 23 SP T3 I SD: 0.4811 c. M:-0.7126 c. 193: 26 28 26 33 26 28 26 SP T3 I SD: 0.4186 c. M:-0.6357 c. 200: 27 29 27 34 27 29 27 SP T3 I SD: 0.0861 c. M:-0.1295 c. 482: 65 70 65 82 65 70 65 SP T3 I SD: 0.0816 c. M:-0.1197 c. 489: 66 71 66 83 66 71 66 SP T3 I SD: 0.0753 c. M:-0.1145 c. 682: 92 99 92 116 92 99 92 SP T3 I SD: 0.0645 c. M:-0.0978 c. 689: 93 100 93 117 93 100 93 SP T3 I SD: 0.0483 c. M:-0.0682 c. 771: 104 112 104 131 104 112 104 SP T3 I SD: 0.0402 c. M:-0.0573 c. 971: 131 141 131 165 131 141 131 SP T3 I SD: 0.0149 c. M: 0.0205 c. 1171: 158 170 158 199 158 170 158 SP T3 I SD: 0.0062 c. M: 0.0091 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: 6.8294 cents 4 x 5 x 6 x 7:8 S SD: 21.3822 cents 5 x 6:7 x 8:9:10 S SD: 20.4868 cents 6 x 7:8:9:10:11:12 S SD: 12.1835 cents 7:8 x 9:11:12:13:14 SD: 24.2521 cents 8:9:10:11:12:13:15:16 SD: 14.4161 cents 9:10:11:12:14:15:16:18 S SD: 11.6884 cents 10:11:12:13:15:16:18:20 SD: 10.3891 cents 12:13:15:16:18:20:22:24 SD: 8.5837 cents 17:19:21:23:26:28:31:34 SD: 8.5639 cents 18:20:22:24:27:30:33:36 S SD: 4.7250 cents 22:24:27:29:33:36:40:44 SD: 4.5054 cents 28:31:34:37:42:46:51:56 SD: 3.0804 cents 32:35:39:43:48:53:58:64 SD: 2.9726 cents 40:44:49:53:60:66:73:80 SD: 2.7837 cents 42:46:51:56:63:69:77:84 SD: 1.8423 cents 51:56:62:68:77:84:93:102 SD: 1.6609 cents 60:66:73:80:90:99:109:120 SD: 1.0214 cents 84:92:102:112:126:138:153:168 SD: 0.8934 cents 90:99:109:120:135:148:164:180 SD: 0.8831 cents 102:112:124:136:153:168:186:204 SD: 0.4032 cents 192:211:233:256:288:316:350:384 SD: 0.3748 cents 224:246:272:299:336:369:408:448 SD: 0.2815 cents 252:277:306:336:378:415:459:504 SD: 0.2651 cents 318:349:386:424:477:524:579:636 SD: 0.2115 cents 336:369:408:448:504:553:612:672 SD: 0.1883 cents 396:435:481:528:594:652:721:792 SD: 0.1817 cents 420:461:510:560:630:692:765:840 SD: 0.1266 cents 510:560:619:680:765:840:929:1020 SD: 0.1157 cents 570:626:692:760:855:939:1038:1140 SD: 0.0976 cents