Scala analysis: xen15-chalmers-triadic-reversed-diamond-30-23
Triadic reversed diamond for M=30/23, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 46/45 38.050632 23rd-partial chroma 2: 30/23 459.994367 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 23/15 740.005633 6: 45/23 1161.949368 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 46/45 38.0506 23rd-partial chroma 1: 46/45 38.0506 23rd-partial chroma 2: 675/529 421.9437 3: 46/45 38.0506 23rd-partial chroma 4: 9/8 203.9100 major whole tone 5: 46/45 38.0506 23rd-partial chroma 6: 675/529 421.9437 7: 46/45 38.0506 23rd-partial chroma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 46/45 38.051 cents 23rd-partial chroma 1: 1 9/8 203.910 cents major whole tone 1: 2 675/529 421.944 cents 2: 1 2116/2025 76.101 cents two (23rd-partial chroma) 2: 2 23/20 241.961 cents 2: 4 30/23 459.994 cents 3: 1 529/450 280.011 cents 3: 4 4/3 498.045 cents perfect fourth 3: 2 135/92 663.904 cents 4: 2 184/135 536.096 cents 4: 4 3/2 701.955 cents perfect fifth 4: 1 900/529 919.989 cents 5: 4 23/15 740.006 cents 5: 2 40/23 958.039 cents 5: 1 2025/1058 1123.899 cents 6: 2 1058/675 778.056 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 4 45/23 1161.949 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 : 38.1 460.0 498.0 702.0 740.0 1161.9 1200.0 38.1 : 421.9 460.0 663.9 702.0 1123.9 1161.9 1200.0 460.0 : 38.1 242.0 280.0 702.0 740.0 778.1 1200.0 498.0 : 203.9 242.0 663.9 702.0 740.0 1161.9 1200.0 702.0 : 38.1 460.0 498.0 536.1 958.0 996.1 1200.0 740.0 : 421.9 460.0 498.0 920.0 958.0 1161.9 1200.0 1161.9: 38.1 76.1 498.0 536.1 740.0 778.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.0506 .. 421.9437 cents 30375/24334, 383.8931 cents 46/45, 38.0506 cents 2: 76.1013 .. 459.9944 cents 30375/24334, 383.8931 cents 1119364/1366875,-345.8425 cents 3: 280.0113 .. 663.9044 cents 30375/24334, 383.8931 cents 12167/13500,-179.9831 cents 4: 536.0956 .. 919.9887 cents 30375/24334, 383.8931 cents 16928/18225,-127.8087 cents 5: 740.0056 .. 1123.8987 cents 30375/24334, 383.8931 cents 12167/13500,-179.9831 cents 6: 778.0563 .. 1161.9494 cents 30375/24334, 383.8931 cents 1119364/1366875,-345.8425 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 46/45, 38.0506 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 675/529, 421.9437 cents Average / Smallest step : 4.505275 Largest / Average step : 2.461338 Largest / Smallest step : 11.089007 Median interval of one step : 46/45, 38.0506 cents, amount: 4 Most common interval of one step : 46/45, 38.0506 cents, amount: 4 Least squares average step : 173.79799 cents, oct.: 1216.58594 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 38.05063 cents Scale diversity : 1.323742 Lumma stability : 0.063418 Lumma impropriety factor : 0.746329 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 : 46/45, 38.0506 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 : 15 23 45 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 : 23 Odd number limit : 2025 (O: 2025 U: 2025) Highest odd numerator or denominator: 45 Scale harmonicity : 0.009038 Average absolute harmonicity : 0.223222 Specific harmonicity : 0.048816 Fundamental : 1/2070, -11.0154 octaves, 0.1264 Hz. Guide tone : 4140, 12.0154 octaves, 1083129.840 Hz. Exponens Consonantiae : 8.569800E+06, 23.03083 octaves Euler's gradus suavitatis : 64 Sum of Mann's harmonic distance : 132.5, average 18.92857 Mersenne's string divisions : 93469740 Sum of van Prooijen's expressibility: 6.98412, average 0.99773 Sum of Tenney's harmonic distance : 13.86594, average 1.98085 Vogel's harmonic complexity : 35.57143 Wille's k value : 1552 Wilson's harmonic complexity : 68 Rectangular lattice diameter : 8 Triangular lattice diameter : 6 Lattice compactness : 71.17734, average 2.54205 Lattice compactness (without 2's) : 59.16021, average 2.11286 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.57143 6 1 3: -2 .. 2 0.00000 8 2 5: -1 .. 1 0.00000 4 23: -1 .. 1 0.00000 4 4 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 16 / 7 = 2.28571 Scale is weakly epimorphic with val: <7 10 15 33| Scale is weakly epimorphic with val: <7 10 15 34| Scale is weakly epimorphic with val: <7 10 16 34| Scale is weakly epimorphic with val: <7 10 16 35| Scale is weakly epimorphic with val: <7 10 17 29| Scale is weakly epimorphic with val: <7 10 17 35| Scale is weakly epimorphic with val: <7 10 18 29| Scale is weakly epimorphic with val: <7 10 18 30| Scale is JI-epimorphic with val: <7 11 15 31| Scale is weakly epimorphic with val: <7 11 15 32| Scale is JI-epimorphic with val: <7 11 16 32| = patent Scale is weakly epimorphic with val: <7 11 16 33| Scale is JI-epimorphic with val: <7 11 17 33| Scale is weakly epimorphic with val: <7 11 17 34| Scale is JI-epimorphic with val: <7 11 18 34| Scale is weakly epimorphic with val: <7 11 18 35| Scale is weakly epimorphic with val: <7 12 15 31| Scale is weakly epimorphic with val: <7 12 15 35| Scale is weakly epimorphic with val: <7 12 16 29| Scale is weakly epimorphic with val: <7 12 16 32| Scale is weakly epimorphic with val: <7 12 17 30| Scale is weakly epimorphic with val: <7 12 17 33| Scale is weakly epimorphic with val: <7 12 18 31| Scale is weakly epimorphic with val: <7 12 18 34|
FIT/MODE
7: 0 3 0 1 0 3 0 N T3 I SD: 36.4855 c. M: 54.2913 c. 8: 0 3 0 2 0 3 0 N T3 I SD: 33.1923 c. M:-48.0450 c. 10: 0 4 0 2 0 4 0 N T3 I SD: 24.9210 c. M:-38.0506 c. 17: 0 6 1 3 0 6 1 N SD: 26.8101 c. M: 38.0506 c. 18: 0 7 0 3 1 6 1 N SD: 25.5947 c. M: 38.0506 c. 19: 1 6 1 3 1 6 1 N T3 I SD: 16.9242 c. M:-25.1073 c. 21: 1 7 1 3 1 7 1 N T3 I SD: 13.4844 c. M:-19.0922 c. 24: 1 8 1 4 1 8 1 N T3 I SD: 8.3921 c. M:-11.9494 c. 26: 1 9 1 4 1 9 1 N T3 I SD: 6.7848 c. M:-9.6473 c. 29: 1 10 1 5 1 10 1 N T3 I SD: 3.2320 c. M: 4.8220 c. 34: 1 12 1 6 1 12 1 N T3 I SD: 2.6400 c. M:-3.9274 c. 60: 2 21 2 10 2 21 2 N T3 I SD: 1.4757 c. M:-1.9550 c. 65: 2 23 2 11 2 23 2 N T3 I SD: 1.0460 c. M: 1.5441 c. 94: 3 33 3 16 3 33 3 N T3 I SD: 0.2763 c. M: 0.4199 c. 159: 5 56 5 27 5 56 5 N T3 I SD: 0.2675 c. M: 0.3830 c. 253: 8 89 8 43 8 89 8 N T3 I SD: 0.0734 c. M:-0.1060 c. 347: 11 122 11 59 11 122 11 N T3 I SD: 0.0437 c. M: 0.0623 c. 600: 19 211 19 102 19 211 19 N T3 I SD: 0.0363 c. M:-0.0506 c. 947: 30 333 30 161 30 333 30 N T3 I SD: 0.0345 c. M: 0.0513 c. 1260: 40 443 40 214 40 443 40 N T3 I SD: 0.0360 c. M:-0.0502 c. 1294: 41 455 41 220 41 455 41 N T3 I SD: 0.0356 c. M: 0.0543 c. 1513: 48 532 48 257 48 532 48 N T3 I SD: 0.0251 c. M:-0.0383 c. 1607: 51 565 51 273 51 565 51 N T3 I SD: 0.0226 c. M:-0.0328 c. 1766: 56 621 56 300 56 621 56 N T3 I SD: 0.0220 c. M:-0.0297 c. 1860: 59 654 59 316 59 654 59 N T3 I SD: 0.0132 c. M:-0.0195 c. 2113: 67 743 67 359 67 743 67 N T3 I SD: 0.0112 c. M: 0.0151 c. 2207: 70 776 70 375 70 776 70 N T3 I SD: 0.0067 c. M:-0.0101 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: 48.1177 cents 4 x 5 x 6 x x 8 S SD: 24.5602 cents 5 x x 7 x 8 x 10 SD: 37.3624 cents 6 x x 8:9 x x 12 S SD: 0.0000 cents 7:8:9 x x 11 x 14 SD: 49.8261 cents 8:9:10:11:12 x x 16 S SD: 37.8292 cents 9:10 x 12 x 14 x 18 SD: 36.6217 cents 10:11:13 x 15 x x 20 SD: 31.7713 cents 11:12:14:15 x 17 x 22 SD: 25.4403 cents 12:13 x 16:18 x 23:24 SD: 21.3300 cents 13:14:17 x x 20:25:26 SD: 19.0669 cents 14:15:18:19:21 x 27:28 SD: 15.6389 cents 15:16 x 20 x 23:29:30 SD: 15.3034 cents 16:17:21 x 24:25:31:32 SD: 12.8483 cents 17:18:22:23 x 26:33:34 SD: 11.4739 cents 18:19:23:24:27:28:35:36 SD: 10.1930 cents 19:20:25 x x 29:37:38 SD: 10.8317 cents 20:21:26:27:30:31:39:40 SD: 7.8690 cents 21:22:27:28 x 32:41:42 SD: 8.4252 cents 22:23:29 x 33:34:43:44 SD: 7.5206 cents 23:24:30:31 x 35:45:46 SD: 7.0563 cents 24:25:31:32:36:37:47:48 SD: 5.4227 cents 25:26 x 33 x 38:49:50 SD: 7.5679 cents 26:27:34:35:39:40:51:52 SD: 4.7202 cents 27:28:35:36 x 41:53:54 SD: 5.4015 cents 28:29 x 37:42:43:55:56 SD: 4.7453 cents 29:30:38:39 x 44:57:58 SD: 5.5443 cents 30:31:39:40:45:46:59:60 SD: 3.0768 cents 36:37:47:48:54:55:70:72 SD: 2.2361 cents 42:43:55:56:63:64:82:84 SD: 1.9380 cents 52:53:68:69:78:80:102:104 SD: 1.8521 cents 60:61:78:80:90:92:117:120 SD: 1.7834 cents 72:74:94:96:108:110:141:144 SD: 1.6455 cents 78:80:102:104:117:120:153:156 SD: 1.4717 cents 82:84:107:109:123:126:160:164 SD: 1.2570 cents 84:86:110:112:126:129:164:168 SD: 1.2363 cents 86:88:112:115:129:132:168:172 SD: 0.9669 cents 88:90:115:117:132:135:172:176 SD: 0.8980 cents 90:92:117:120:135:138:176:180 SD: 0.8348 cents 92:94:120:123:138:141:180:184 SD: 0.6912 cents 96:98:125:128:144:147:188:192 SD: 0.6806 cents 132:135:172:176:198:202:258:264 SD: 0.6158 cents 138:141:180:184:207:212:270:276 SD: 0.4815 cents 174:178:227:232:261:267:340:348 SD: 0.4133 cents 180:184:235:240:270:276:352:360 SD: 0.2595 cents 270:276:352:360:405:414:528:540 SD: 0.1728 cents 276:282:360:368:414:423:540:552 SD: 0.1653 cents 414:423:540:552:621:635:810:828 SD: 0.1405 cents 450:460:587:600:675:690:880:900 SD: 0.1235 cents 546:558:712:728:819:837:1068:1092 SD: 0.1195 cents