Scala analysis: xen15-chalmers-triadic-reversed-diamond-16-13
Triadic reversed diamond for M=16/13, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 13/12 138.572661 tridecimal 2/3-tone 2: 16/13 359.472338 tridecimal neutral third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 13/8 840.527662 tridecimal neutral sixth 6: 24/13 1061.427339 tridecimal neutral seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 13/12 138.5727 tridecimal 2/3-tone 1: 13/12 138.5727 tridecimal 2/3-tone 2: 192/169 220.8997 3: 13/12 138.5727 tridecimal 2/3-tone 4: 9/8 203.9100 major whole tone 5: 13/12 138.5727 tridecimal 2/3-tone 6: 192/169 220.8997 7: 13/12 138.5727 tridecimal 2/3-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 13/12 138.573 cents tridecimal 2/3-tone 1: 1 9/8 203.910 cents major whole tone 1: 2 192/169 220.900 cents 2: 1 169/144 277.145 cents two (tridecimal 2/3-tone) 2: 2 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 2: 4 16/13 359.472 cents tridecimal neutral third 3: 1 169/128 481.055 cents 3: 4 4/3 498.045 cents perfect fourth 3: 2 18/13 563.382 cents tridecimal augmented fourth 4: 2 13/9 636.618 cents tridecimal diminished fifth 4: 4 3/2 701.955 cents perfect fifth 4: 1 256/169 718.945 cents two (tridecimal neutral third) 5: 4 13/8 840.528 cents tridecimal neutral sixth 5: 2 64/39 857.517 cents 39th subharmonic 5: 1 288/169 922.855 cents 6: 2 169/96 979.100 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 4 24/13 1061.427 cents tridecimal neutral seventh 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 : 138.6 359.5 498.0 702.0 840.5 1061.4 1200.0 138.6 : 220.9 359.5 563.4 702.0 922.9 1061.4 1200.0 359.5 : 138.6 342.5 481.1 702.0 840.5 979.1 1200.0 498.0 : 203.9 342.5 563.4 702.0 840.5 1061.4 1200.0 702.0 : 138.6 359.5 498.0 636.6 857.5 996.1 1200.0 840.5 : 220.9 359.5 498.0 718.9 857.5 1061.4 1200.0 1061.4: 138.6 277.1 498.0 636.6 840.5 979.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 138.5727 .. 220.8997 cents 2304/2197, 82.3270 cents 13/12, 138.5727 cents 2: 277.1453 .. 359.4723 cents 2304/2197, 82.3270 cents 28561/27648, 56.2456 cents 3: 481.0553 .. 563.3823 cents 2304/2197, 82.3270 cents 2197/2048, 121.5830 cents 4: 636.6177 .. 718.9447 cents 2304/2197, 82.3270 cents 169/162, 73.2353 cents 5: 840.5277 .. 922.8547 cents 2304/2197, 82.3270 cents 2197/2048, 121.5830 cents 6: 979.1003 .. 1061.4273 cents 2304/2197, 82.3270 cents 28561/27648, 56.2456 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 13/12, 138.5727 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 192/169, 220.8997 cents Average / Smallest step : 1.237102 Largest / Average step : 1.288581 Largest / Smallest step : 1.594107 Median interval of one step : 13/12, 138.5727 cents, amount: 4 Most common interval of one step : 13/12, 138.5727 cents, amount: 4 Least squares average step : 172.36196 cents, oct.: 1206.53373 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABACABA Step pattern size order : SLSMSLS Scale is a Constant Structure, by a margin of 56.24564 cents Scale diversity : 1.335886 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.588365 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 : 512/507, 16.9897 cents Number of recognisable fifths : 5, average 705.3529 cents Number of appreciable 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 : 1 3 13 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 1 and 2 combined 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 : 13 Odd number limit : 169 (O: 169 U: 169) Highest odd numerator or denominator: 13 Scale harmonicity : 0.017655 Average absolute harmonicity : 0.234033 Specific harmonicity : 0.094160 Fundamental : 1/312, -8.2854 octaves, 0.8385 Hz. Guide tone : 624, 9.2854 octaves, 163254.353 Hz. Exponens Consonantiae : 1.946880E+05, 17.57080 octaves Euler's gradus suavitatis : 36 Sum of Mann's harmonic distance : 63.5, average 9.07143 Mersenne's string divisions : 563325 Sum of van Prooijen's expressibility: 5.41002, average 0.77286 Sum of Tenney's harmonic distance : 11.18074, average 1.59725 Vogel's harmonic complexity : 19.57143 Wille's k value : 253 Wilson's harmonic complexity : 32 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 95.10493, average 3.39660 Lattice compactness (without 2's) : 39.08641, average 1.39594 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 4 0.57143 16 1 3: -1 .. 1 0.00000 4 2 13: -1 .. 1 0.00000 4 4 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 8 / 7 = 1.14286 Scale is weakly epimorphic with val: <7 10 29| Scale is JI-epimorphic with val: <7 11 26| = patent Scale is weakly epimorphic with val: <7 11 27| Scale is weakly epimorphic with val: <7 12 25| Scale is weakly epimorphic with val: <7 12 29|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 21.5097 c. M: 32.8559 c. Lebeng 10: 1 2 1 2 1 2 1 P M ME I SD: 13.8445 c. M:-18.5727 c. 17: 2 3 2 3 2 3 2 SP M ME I SD: 4.3048 c. M: 6.5312 c. Neutral Dorian, Maqamic-7 43: 5 8 5 7 5 8 5 SP T3 I SD: 2.9404 c. M:-4.2806 c. 53: 6 10 6 9 6 10 6 SP T3 I SD: 2.0851 c. M: 2.7918 c. 60: 7 11 7 10 7 11 7 SP T3 I SD: 1.3243 c. M:-1.9550 c. 70: 8 13 8 12 8 13 8 SP T3 I SD: 0.9467 c. M: 1.4298 c. 130: 15 24 15 22 15 24 15 SP T3 I SD: 0.3642 c. M:-0.5277 c. 147: 17 27 17 25 17 27 17 SP T3 I SD: 0.1941 c. M: 0.2887 c. 277: 32 51 32 47 32 51 32 SP T3 I SD: 0.0993 c. M:-0.1499 c. 424: 49 78 49 72 49 78 49 SP T3 I SD: 0.0707 c. M:-0.1066 c. 641: 74 118 74 109 74 118 74 SP T3 I SD: 0.0479 c. M:-0.0731 c. 771: 89 142 89 131 89 142 89 SP T3 I SD: 0.0428 c. M: 0.0607 c. 918: 106 169 106 156 106 169 106 SP T3 I SD: 0.0069 c. M:-0.0106 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: 14.6104 cents 4 x 5 x 6 x 7:8 S SD: 24.1033 cents 5 x 6:7 x 8:9:10 S SD: 21.6310 cents 6 x 7:8:9:10:11:12 S SD: 17.1931 cents 7:8 x 9 x 11:13:14 SD: 25.3083 cents 8:9:10:11:12:13:15:16 SD: 13.2078 cents 10:11:12:13:15:16:18:20 SD: 12.1071 cents 12:13:15:16:18:20:22:24 SD: 7.5420 cents 14:15:17:19:21:23:26:28 SD: 6.8710 cents 21:23:26:28:32:34:39:42 SD: 5.2544 cents 22:24:27:29:33:36:41:44 SD: 4.4563 cents 24:26:30:32:36:39:44:48 SD: 4.2040 cents 26:28:32:35:39:42:48:52 SD: 3.1480 cents 34:37:42:45:51:55:63:68 SD: 2.7356 cents 38:41:47:51:57:62:70:76 SD: 2.5322 cents 46:50:57:61:69:75:85:92 SD: 2.4565 cents 48:52:59:64:72:78:89:96 SD: 1.1185 cents 72:78:89:96:108:117:133:144 SD: 1.0806 cents 86:93:106:115:129:140:159:172 SD: 1.0793 cents 96:104:118:128:144:156:177:192 SD: 0.4557 cents 144:156:177:192:216:234:266:288 SD: 0.3526 cents 168:182:207:224:252:273:310:336 SD: 0.3019 cents 216:234:266:288:324:351:399:432 SD: 0.2024 cents 312:338:384:416:468:507:576:624 SD: 0.0000 cents