Scala analysis: xen15-chalmers-triadic-diamond-23-20
Triadic diamond for M=23/20, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 23/20 241.960633 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: 40/23 958.039367 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 23/20 241.9606 1: 23/20 241.9606 2: 600/529 218.0337 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: 600/529 218.0337 7: 23/20 241.9606
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 46/45 38.051 cents 23rd-partial chroma 1: 1 9/8 203.910 cents major whole tone 1: 2 600/529 218.034 cents 1: 2 23/20 241.961 cents 2: 2 23/20 241.961 cents 2: 2 80/69 256.084 cents 2: 2 30/23 459.994 cents 2: 1 529/400 483.921 cents 3: 1 529/450 280.011 cents 3: 2 30/23 459.994 cents 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 23/15 740.006 cents 4: 1 900/529 919.989 cents 5: 1 800/529 716.079 cents 5: 2 23/15 740.006 cents 5: 2 69/40 943.916 cents 5: 2 40/23 958.039 cents 6: 2 40/23 958.039 cents 6: 2 529/300 981.966 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 45/23 1161.949 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 : 242.0 460.0 498.0 702.0 740.0 958.0 1200.0 242.0 : 218.0 256.1 460.0 498.0 716.1 958.0 1200.0 460.0 : 38.1 242.0 280.0 498.0 740.0 982.0 1200.0 498.0 : 203.9 242.0 460.0 702.0 943.9 1161.9 1200.0 702.0 : 38.1 256.1 498.0 740.0 958.0 996.1 1200.0 740.0 : 218.0 460.0 702.0 920.0 958.0 1161.9 1200.0 958.0 : 242.0 483.9 702.0 740.0 943.9 982.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.0506 .. 241.9606 cents 9/8, 203.9100 cents 46/45, 38.0506 cents 2: 241.9606 .. 483.9213 cents 23/20, 241.9606 cents 1/1, 0.0000 cents 3: 280.0113 .. 701.9550 cents 675/529, 421.9437 cents 8/9,-203.9100 cents 4: 498.0450 .. 919.9887 cents 675/529, 421.9437 cents 8/9,-203.9100 cents 5: 716.0787 .. 958.0394 cents 23/20, 241.9606 cents 8/9,-203.9100 cents 6: 958.0394 .. 1161.9494 cents 9/8, 203.9100 cents 1/1, 0.0000 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 : 23/20, 241.9606 cents Average / Smallest step : 4.505275 Largest / Average step : 1.411437 Largest / Smallest step : 6.358912 Median interval of one step : 600/529, 218.0337 cents, amount: 2 Least squares average step : 166.51549 cents, oct.: 1165.60844 cents Scale is not proper Step pattern alph. order: ABCDCBA Step pattern size order : DCABACD Scale is not a Constant Structure Scale diversity : 1.101291 Lumma stability : 0.063418 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 : 1600/1587, 14.1237 cents Number of recognisable fifths : 5, average 704.7797 cents Number of appreciable fifths : 4, average 701.9550 cents Scale is a complete diamond : 5 15 23 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 : 529 (O: 529 U: 529) Highest odd numerator or denominator: 23 Scale harmonicity : 0.009319 Average absolute harmonicity : 0.223566 Specific harmonicity : 0.049934 Fundamental : 1/1380, -10.4305 octaves, 0.1896 Hz. Guide tone : 2760, 11.4305 octaves, 722086.560 Hz. Exponens Consonantiae : 3.808800E+06, 21.86091 octaves Euler's gradus suavitatis : 62 Sum of Mann's harmonic distance : 106.0, average 15.14286 Mersenne's string divisions : 27279630 Sum of van Prooijen's expressibility: 6.40115, average 0.91445 Sum of Tenney's harmonic distance : 13.16158, average 1.88023 Vogel's harmonic complexity : 33.57143 Wille's k value : 793 Wilson's harmonic complexity : 62 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 76.11826, average 2.71851 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 10 1 3: -1 .. 1 0.00000 4 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: 12 / 7 = 1.71429 Scale is weakly epimorphic with val: <7 10 15 30| Scale is weakly epimorphic with val: <7 10 15 31| Scale is weakly epimorphic with val: <7 10 16 31| Scale is weakly epimorphic with val: <7 10 16 32| Scale is weakly epimorphic with val: <7 10 17 32| Scale is weakly epimorphic with val: <7 10 17 33| Scale is weakly epimorphic with val: <7 10 18 33| Scale is weakly epimorphic with val: <7 10 18 34| Scale is weakly epimorphic with val: <7 11 15 34| Scale is weakly epimorphic with val: <7 11 15 35| Scale is weakly epimorphic with val: <7 11 16 29| Scale is weakly epimorphic with val: <7 11 16 35| Scale is weakly epimorphic with val: <7 11 17 29| Scale is weakly epimorphic with val: <7 11 17 30| Scale is weakly epimorphic with val: <7 11 18 30| Scale is weakly epimorphic with val: <7 11 18 31| Scale is weakly epimorphic with val: <7 12 15 30| Scale is weakly epimorphic with val: <7 12 15 33| Scale is weakly epimorphic with val: <7 12 16 31| Scale is weakly epimorphic with val: <7 12 16 34| Scale is weakly epimorphic with val: <7 12 17 32| Scale is weakly epimorphic with val: <7 12 17 35| Scale is weakly epimorphic with val: <7 12 18 29| Scale is weakly epimorphic with val: <7 12 18 33|
FIT/MODE
7: 1 2 0 1 0 2 1 N T3 I SD: 48.3620 c. M:-70.5321 c. 8: 2 1 0 2 0 1 2 N I SD: 40.6264 c. M:-58.0394 c. 9: 2 1 1 1 1 1 2 N D3 I SD: 39.4787 c. M: 59.9944 c. 10: 2 2 0 2 0 2 2 N D3 I SD: 14.4389 c. M: 20.0056 c. 19: 4 3 1 3 1 3 4 N G I SD: 11.7837 c. M: 17.8891 c. 21: 4 4 1 3 1 4 4 N G I SD: 11.3536 c. M:-16.2407 c. 24: 5 4 1 4 1 4 5 N G I SD: 6.9352 c. M: 9.9944 c. 29: 6 5 1 5 1 5 6 N G I SD: 4.3215 c. M:-6.3152 c. 34: 7 6 1 6 1 6 7 N G I SD: 3.4964 c. M:-5.0982 c. 55: 11 10 2 9 2 10 11 N I SD: 2.4708 c. M:-3.7732 c. 60: 12 11 2 10 2 11 12 N I SD: 1.4800 c. M:-1.9606 c. 65: 13 12 2 11 2 12 13 N I SD: 1.3524 c. M:-1.9606 c. 89: 18 16 3 15 3 16 18 N I SD: 1.0267 c. M: 1.5674 c. 94: 19 17 3 16 3 17 19 N I SD: 0.3990 c. M:-0.5926 c. 159: 32 29 5 27 5 29 32 N I SD: 0.3184 c. M:-0.4512 c. 248: 50 45 8 42 8 45 50 N I SD: 0.2496 c. M:-0.3421 c. 253: 51 46 8 43 8 46 51 N I SD: 0.0577 c. M: 0.0847 c. 600: 121 109 19 102 19 109 121 N I SD: 0.0321 c. M:-0.0450 c. 853: 172 155 27 145 27 155 172 N I SD: 0.0260 c. M: 0.0380 c. 1354: 273 246 43 230 43 246 273 N I SD: 0.0233 c. M:-0.0348 c. 1607: 324 292 51 273 51 292 324 N I SD: 0.0176 c. M:-0.0259 c. 1860: 375 338 59 316 59 338 375 N I SD: 0.0173 c. M:-0.0251 c. 1954: 394 355 62 332 62 355 394 N I SD: 0.0100 c. M: 0.0148 c. 2207: 445 401 70 375 70 401 445 N I SD: 0.0044 c. M:-0.0067 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: 24.5602 cents 4 x 5 x 6 x 7:8 S SD: 18.6165 cents 5:6 x 7 x 8:9:10 S SD: 29.3526 cents 6:7 x 8:9 x 10:12 S SD: 15.5555 cents 7:8:9 x x 11:12:14 SD: 11.2472 cents 8:9:10:11:12 x 14:16 S SD: 16.5253 cents 9:10 x 12 x 14:16:18 S SD: 14.9872 cents 10:12:13 x 15 x 17:20 SD: 16.7504 cents 11:13:14:15 x 17:19:22 SD: 12.7773 cents 12:14 x 16:18 x 21:24 S SD: 5.4291 cents 13:15:17 x x 20:23:26 SD: 6.2258 cents 14:16:18:19:21 x 24:28 SD: 7.9867 cents 15:17 x 20 x 23:26:30 SD: 5.1853 cents 16:18:21 x 24:25:28:32 SD: 8.7317 cents 17:20:22:23 x 26:30:34 SD: 9.1821 cents 18:21:23:24:27:28:31:36 SD: 7.5547 cents 19:22:25 x x 29:33:38 SD: 4.1817 cents 21:24:27:28 x 32:37:42 SD: 6.1476 cents 22:25:29 x 33:34:38:44 SD: 5.4929 cents 23:26:30:31 x 35:40:46 SD: 6.2483 cents 24:28:31:32:36:37:42:48 SD: 4.7617 cents 25:29 x 33 x 38:43:50 SD: 6.7014 cents 26:30:34:35:39:40:45:52 SD: 2.9643 cents 27:31:35:36 x 41:47:54 SD: 3.3656 cents 28:32 x 37:42:43:49:56 SD: 3.6553 cents 29:33:38:39 x 44:50:58 SD: 5.7150 cents 30:35:39:40:45:46:52:60 SD: 3.7453 cents 32:37:42:43:48:49:56:64 SD: 3.2192 cents 34:39:44:45:51:52:59:68 SD: 2.8678 cents 39:45:51:52:59:60:68:78 SD: 2.5684 cents 42:48:55:56:63:64:73:84 SD: 2.3937 cents 46:53:60:61:69:71:80:92 SD: 2.1667 cents 52:60:68:69:78:80:90:104 SD: 2.1462 cents 54:62:70:72:81:83:94:108 SD: 1.7066 cents 60:69:78:80:90:92:104:120 SD: 1.1678 cents 66:76:86:88:99:101:115:132 SD: 0.7918 cents 108:124:141:144:162:166:188:216 SD: 0.7872 cents 114:131:149:152:171:175:198:228 SD: 0.6909 cents 126:145:164:168:189:193:219:252 SD: 0.6253 cents 154:177:201:205:231:236:268:308 SD: 0.5020 cents 174:200:227:232:261:267:303:348 SD: 0.3925 cents 180:207:235:240:270:276:313:360 SD: 0.2315 cents 246:283:321:328:369:377:428:492 SD: 0.2123 cents 306:352:399:408:459:469:532:612 SD: 0.1707 cents 414:476:540:552:621:635:720:828 SD: 0.0936 cents 480:552:626:640:720:736:835:960 SD: 0.0730 cents