Scala analysis: xen15-chalmers-triadic-diamond-15-13
Triadic diamond for M=15/13, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 15/13 247.741053 tridecimal 5/4-tone 2: 13/10 454.213948 tridecimal semi-diminished fourth 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 20/13 745.786052 tridecimal semi-augmented fifth 6: 26/15 952.258947 tridecimal semi-augmented sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 15/13 247.7411 tridecimal 5/4-tone 1: 15/13 247.7411 tridecimal 5/4-tone 2: 169/150 206.4729 3: 40/39 43.8311 tridecimal minor diesis 4: 9/8 203.9100 major whole tone 5: 40/39 43.8311 tridecimal minor diesis 6: 169/150 206.4729 7: 15/13 247.7411 tridecimal 5/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 40/39 43.831 cents tridecimal minor diesis 1: 1 9/8 203.910 cents major whole tone 1: 2 169/150 206.473 cents 1: 2 15/13 247.741 cents tridecimal 5/4-tone 2: 2 15/13 247.741 cents tridecimal 5/4-tone 2: 2 52/45 250.304 cents 2: 2 13/10 454.214 cents tridecimal semi-diminished fourth 2: 1 225/169 495.482 cents two (tridecimal 5/4-tone) 3: 1 200/169 291.572 cents 3: 2 13/10 454.214 cents tridecimal semi-diminished fourth 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 20/13 745.786 cents tridecimal semi-augmented fifth 4: 1 169/100 908.428 cents two (tridecimal semi-diminished fourth) 5: 1 338/225 704.518 cents 5: 2 20/13 745.786 cents tridecimal semi-augmented fifth 5: 2 45/26 949.696 cents 5: 2 26/15 952.259 cents tridecimal semi-augmented sixth 6: 2 26/15 952.259 cents tridecimal semi-augmented sixth 6: 2 300/169 993.527 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 39/20 1156.169 cents 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 : 247.7 454.2 498.0 702.0 745.8 952.3 1200.0 247.7 : 206.5 250.3 454.2 498.0 704.5 952.3 1200.0 454.2 : 43.8 247.7 291.6 498.0 745.8 993.5 1200.0 498.0 : 203.9 247.7 454.2 702.0 949.7 1156.2 1200.0 702.0 : 43.8 250.3 498.0 745.8 952.3 996.1 1200.0 745.8 : 206.5 454.2 702.0 908.4 952.3 1156.2 1200.0 952.3 : 247.7 495.5 702.0 745.8 949.7 993.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.8311 .. 247.7411 cents 9/8, 203.9100 cents 40/39, 43.8311 cents 2: 247.7411 .. 495.4821 cents 15/13, 247.7411 cents 1/1, 0.0000 cents 3: 291.5721 .. 701.9550 cents 507/400, 410.3829 cents 8/9,-203.9100 cents 4: 498.0450 .. 908.4279 cents 507/400, 410.3829 cents 8/9,-203.9100 cents 5: 704.5179 .. 952.2589 cents 15/13, 247.7411 cents 8/9,-203.9100 cents 6: 952.2589 .. 1156.1689 cents 9/8, 203.9100 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 40/39, 43.8311 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 15/13, 247.7411 cents Average / Smallest step : 3.911122 Largest / Average step : 1.445156 Largest / Smallest step : 5.652181 Median interval of one step : 169/150, 206.4729 cents, amount: 2 Least squares average step : 166.43291 cents, oct.: 1165.03039 cents Scale is not proper Step pattern alph. order: ABCDCBA Step pattern size order : DCABACD Scale is not a Constant Structure Scale diversity : 1.129681 Lumma stability : 0.073052 Lumma impropriety factor : 0.509775 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 : 4 Highest interval variety : 4 Mean interval variety : 4.00000 = 4 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 676/675, 2.5629 cents Number of recognisable fifths : 5, average 702.4676 cents Scale is a complete diamond : 5 13 15 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 : 13 Odd number limit : 225 (O: 225 U: 225) Highest odd numerator or denominator: 15 Scale harmonicity : 0.015281 Average absolute harmonicity : 0.230949 Specific harmonicity : 0.081085 Fundamental : 1/390, -8.6073 octaves, 0.6708 Hz. Guide tone : 780, 9.6073 octaves, 204067.941 Hz. Exponens Consonantiae : 3.042000E+05, 18.21466 octaves Euler's gradus suavitatis : 40 Sum of Mann's harmonic distance : 70.0, average 10.00000 Mersenne's string divisions : 4356660 Sum of van Prooijen's expressibility: 5.53431, average 0.79062 Sum of Tenney's harmonic distance : 11.56838, average 1.65263 Vogel's harmonic complexity : 22.57143 Wille's k value : 292 Wilson's harmonic complexity : 42 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 66.43961, average 2.37284 Lattice compactness (without 2's) : 47.53320, average 1.69761 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.57143 8 1 3: -1 .. 1 0.00000 4 2 5: -1 .. 1 0.00000 4 13: -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 15 24| Scale is weakly epimorphic with val: <7 10 16 24| Scale is weakly epimorphic with val: <7 10 16 25| Scale is weakly epimorphic with val: <7 10 17 25| Scale is weakly epimorphic with val: <7 10 17 26| Scale is weakly epimorphic with val: <7 10 18 26| Scale is weakly epimorphic with val: <7 10 18 27| Scale is weakly epimorphic with val: <7 11 15 27| Scale is weakly epimorphic with val: <7 11 15 28| Scale is weakly epimorphic with val: <7 11 16 28| Scale is weakly epimorphic with val: <7 11 16 29| Scale is weakly epimorphic with val: <7 11 17 29| Scale is weakly epimorphic with val: <7 11 18 24| Scale is weakly epimorphic with val: <7 12 15 26| Scale is weakly epimorphic with val: <7 12 16 24| Scale is weakly epimorphic with val: <7 12 16 27| Scale is weakly epimorphic with val: <7 12 17 25| Scale is weakly epimorphic with val: <7 12 17 28| Scale is weakly epimorphic with val: <7 12 18 26| Scale is weakly epimorphic with val: <7 12 18 29|
FIT/MODE
7: 1 2 0 1 0 2 1 N T3 I SD: 52.6334 c. M: 76.3125 c. 8: 2 1 0 2 0 1 2 N I SD: 38.0116 c. M:-52.2589 c. 9: 2 1 1 1 1 1 2 N D3 I SD: 36.0262 c. M: 54.2139 c. 10: 2 2 0 2 0 2 2 N D3 I SD: 17.3244 c. M:-25.7861 c. 14: 3 2 1 2 1 2 3 N G I SD: 16.9848 c. M: 25.6425 c. 19: 4 3 1 3 1 3 4 N G I SD: 7.9757 c. M: 12.1087 c. 24: 5 4 1 4 1 4 5 N G I SD: 2.7611 c. M: 4.2139 c. 29: 6 5 1 5 1 5 6 N G I SD: 0.9906 c. M: 1.4933 c. 53: 11 9 2 9 2 9 11 N G I SD: 1.0212 c. M: 1.3838 c. 82: 17 14 3 14 3 14 17 N G I SD: 0.6810 c. M:-1.0394 c. 111: 23 19 4 19 4 19 23 N G I SD: 0.6343 c. M:-0.9076 c. 140: 29 24 5 24 5 24 29 N G I SD: 0.6565 c. M:-0.9021 c. 193: 40 33 7 33 7 33 40 N G I SD: 0.6415 c. M:-0.9636 c. 243: 50 42 9 41 9 42 50 N I SD: 0.5892 c. M:-0.8275 c. 267: 55 46 10 45 10 46 55 N I SD: 0.5537 c. M:-0.8314 c. 272: 56 47 10 46 10 47 56 N I SD: 0.4596 c. M: 0.6822 c. 296: 61 51 11 50 11 51 61 N I SD: 0.4095 c. M:-0.6036 c. 301: 62 52 11 51 11 52 62 N I SD: 0.3700 c. M:-0.5650 c. 325: 67 56 12 55 12 56 67 N I SD: 0.2948 c. M:-0.4165 c. 354: 73 61 13 60 13 61 73 N I SD: 0.2060 c. M: 0.2834 c. 383: 79 66 14 65 14 66 79 N I SD: 0.1455 c. M:-0.2215 c. 412: 85 71 15 70 15 71 85 N I SD: 0.1225 c. M:-0.1682 c. 436: 90 75 16 74 16 75 90 N I SD: 0.0810 c. M:-0.1201 c. 465: 96 80 17 79 17 80 96 N I SD: 0.0151 c. M: 0.0204 c. 1424: 294 245 52 242 52 245 294 N I SD: 0.0087 c. M:-0.0118 c. 1889: 390 325 69 321 69 325 390 N I SD: 0.0060 c. M:-0.0091 c. 2354: 486 405 86 400 86 405 486 N I SD: 0.0060 c. M: 0.0083 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: 22.6334 cents 4 x 5 x 6 x 7:8 S SD: 17.4730 cents 5:6 x 7 x 8:9:10 S SD: 28.7225 cents 6:7 x 8:9 x 10:12 S SD: 14.1087 cents 7:8:9 x x 11:12:14 SD: 9.7030 cents 8:9:10:11:12 x 14:16 S SD: 16.3674 cents 9:10 x 12 x 14:16:18 S SD: 16.1939 cents 10:12:13 x 15 x 17:20 SD: 15.1533 cents 11:13:14:15 x 17:19:22 SD: 11.4006 cents 12:14 x 16:18 x 21:24 S SD: 5.0613 cents 13:15:17 x x 20:23:26 SD: 7.3857 cents 15:17 x 20 x 23:26:30 SD: 6.3176 cents 16:18:21 x 24:25:28:32 SD: 9.4142 cents 17:20:22:23 x 26:29:34 SD: 8.6581 cents 18:21:23:24:27:28:31:36 SD: 5.9708 cents 19:22:25 x x 29:33:38 SD: 5.1929 cents 20:23:26:27:30:31:35:40 SD: 4.3746 cents 21:24:27:28 x 32:36:42 S SD: 5.9648 cents 22:25 x 29:33:34:38:44 SD: 5.7458 cents 23:27:30:31 x 35:40:46 SD: 6.8030 cents 24:28:31:32:36:37:42:48 SD: 3.9830 cents 25:29 x 33 x 38:43:50 SD: 6.3343 cents 26:30:34:35:39:40:45:52 SD: 2.8043 cents 44:51:57:59:66:68:76:88 SD: 2.4455 cents 46:53:60:61:69:71:80:92 SD: 1.9893 cents 52:60:68:69:78:80:90:104 SD: 1.9193 cents 54:62:70:72:81:83:94:108 SD: 1.7781 cents 60:69:78:80:90:92:104:120 SD: 1.1678 cents 78:90:101:104:117:120:135:156 SD: 1.0439 cents 84:97:109:112:126:129:146:168 SD: 0.9486 cents 90:104:117:120:135:138:156:180 SD: 0.9033 cents 104:120:135:139:156:160:180:208 SD: 0.7878 cents 117:135:152:156:176:180:203:234 SD: 0.7622 cents 124:143:161:165:186:191:215:248 SD: 0.6756 cents 130:150:169:173:195:200:225:260 SD: 0.6006 cents 150:173:195:200:225:231:260:300 SD: 0.2705 cents 240:277:312:320:360:369:416:480 SD: 0.1692 cents 390:450:507:520:585:600:676:780 SD: 0.0000 cents