Scala analysis: xen15-chalmers-triadic-diamond-23-18
Triadic diamond for M=23/18, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 27/23 277.590655 vicesimotertial minor third 2: 23/18 424.364346 vicesimotertial major third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 36/23 775.635654 6: 46/27 922.409345 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 27/23 277.5907 vicesimotertial minor third 1: 27/23 277.5907 vicesimotertial minor third 2: 529/486 146.7737 3: 24/23 73.6807 vicesimotertial minor semitone 4: 9/8 203.9100 major whole tone 5: 24/23 73.6807 vicesimotertial minor semitone 6: 529/486 146.7737 7: 27/23 277.5907 vicesimotertial minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 24/23 73.681 cents vicesimotertial minor semitone 1: 2 529/486 146.774 cents 1: 1 9/8 203.910 cents major whole tone 1: 2 27/23 277.591 cents vicesimotertial minor third 2: 2 92/81 220.454 cents 2: 2 27/23 277.591 cents vicesimotertial minor third 2: 2 23/18 424.364 cents vicesimotertial major third 2: 1 729/529 555.181 cents two (vicesimotertial minor third) 3: 1 648/529 351.271 cents 3: 2 23/18 424.364 cents vicesimotertial major third 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 36/23 775.636 cents 4: 1 529/324 848.729 cents two (vicesimotertial major third) 5: 1 1058/729 644.819 cents 5: 2 36/23 775.636 cents 5: 2 46/27 922.409 cents 5: 2 81/46 979.546 cents 6: 2 46/27 922.409 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 972/529 1053.226 cents 6: 2 23/12 1126.319 cents vicesimotertial major seventh 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 : 277.6 424.4 498.0 702.0 775.6 922.4 1200.0 277.6 : 146.8 220.5 424.4 498.0 644.8 922.4 1200.0 424.4 : 73.7 277.6 351.3 498.0 775.6 1053.2 1200.0 498.0 : 203.9 277.6 424.4 702.0 979.5 1126.3 1200.0 702.0 : 73.7 220.5 498.0 775.6 922.4 996.1 1200.0 775.6 : 146.8 424.4 702.0 848.7 922.4 1126.3 1200.0 922.4 : 277.6 555.2 702.0 775.6 979.5 1053.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 73.6807 .. 277.5907 cents 9/8, 203.9100 cents 24/23, 73.6807 cents 2: 220.4543 .. 555.1813 cents 59049/48668, 334.7270 cents 2116/2187,-57.1363 cents 3: 351.2713 .. 701.9550 cents 529/432, 350.6837 cents 8/9,-203.9100 cents 4: 498.0450 .. 848.7287 cents 529/432, 350.6837 cents 8/9,-203.9100 cents 5: 644.8187 .. 979.5457 cents 59049/48668, 334.7270 cents 8/9,-203.9100 cents 6: 922.4093 .. 1126.3193 cents 9/8, 203.9100 cents 2116/2187,-57.1363 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 24/23, 73.6807 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 27/23, 277.5907 cents Average / Smallest step : 2.326643 Largest / Average step : 1.619279 Largest / Smallest step : 3.767484 Median interval of one step : 529/486, 146.7737 cents, amount: 2 Least squares average step : 166.00649 cents, oct.: 1162.04543 cents Scale is not proper Step pattern alph. order: ABCDCBA Step pattern size order : DBACABD Scale is not a Constant Structure Scale diversity : 1.471960 Lumma stability : 0.122801 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 : 736/729, 16.5443 cents Number of recognisable fifths : 4, average 701.9550 cents Scale is a complete diamond : 9 23 27 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 : 729 (O: 729 U: 729) Highest odd numerator or denominator: 27 Scale harmonicity : 0.009692 Average absolute harmonicity : 0.223920 Specific harmonicity : 0.051972 Fundamental : 1/1242, -10.2784 octaves, 0.2106 Hz. Guide tone : 2484, 11.2784 octaves, 649877.904 Hz. Exponens Consonantiae : 3.085128E+06, 21.55690 octaves Euler's gradus suavitatis : 60 Sum of Mann's harmonic distance : 119.0, average 17.00000 Mersenne's string divisions : 185416350 Sum of van Prooijen's expressibility: 6.54043, average 0.93435 Sum of Tenney's harmonic distance : 13.58061, average 1.94009 Vogel's harmonic complexity : 33.57143 Wille's k value : 931 Wilson's harmonic complexity : 64 Rectangular lattice diameter : 8 Triangular lattice diameter : 6 Lattice compactness : 89.99971, average 3.21428 Lattice compactness (without 2's) : 73.03173, average 2.60828 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.57143 8 1 3: -3 .. 3 0.00000 12 2 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 29| Scale is weakly epimorphic with val: <7 10 35| Scale is weakly epimorphic with val: <7 11 34| Scale is weakly epimorphic with val: <7 11 35| Scale is weakly epimorphic with val: <7 12 32| Scale is weakly epimorphic with val: <7 12 35|
FIT/MODE
7: 2 0 1 1 1 0 2 N T3 I SD: 56.4849 c. M: 81.5072 c. 8: 2 1 0 2 0 1 2 N I SD: 31.4765 c. M:-48.0450 c. 9: 2 1 1 1 1 1 2 N D3 I SD: 23.6536 c. M:-35.2883 c. 12: 3 1 1 2 1 1 3 N I SD: 17.7251 c. M: 24.3643 c. Mela Yagapriya, Raga Kalahamsa 14: 3 2 1 2 1 2 3 N G I SD: 14.1378 c. M: 20.4478 c. 17: 4 2 1 3 1 2 4 N I SD: 3.3295 c. M: 4.7623 c. 48: 11 6 3 8 3 6 11 N I SD: 1.7678 c. M: 2.5907 c. 65: 15 8 4 11 4 8 15 N I SD: 0.4415 c. M: 0.6676 c. 82: 19 10 5 14 5 10 19 N I SD: 0.3565 c. M:-0.4840 c. 147: 34 18 9 25 9 18 34 N I SD: 0.0840 c. M:-0.1255 c. 964: 223 118 59 164 59 118 223 N I SD: 0.0895 c. M:-0.1197 c. 1007: 233 123 62 171 62 123 233 N I SD: 0.0877 c. M:-0.1340 c. 1072: 248 131 66 182 66 131 248 N I SD: 0.0768 c. M: 0.1106 c. 1137: 263 139 70 193 70 139 263 N I SD: 0.0758 c. M:-0.1080 c. 1154: 267 141 71 196 71 141 267 N I SD: 0.0661 c. M: 0.1009 c. 1219: 282 149 75 207 75 149 282 N I SD: 0.0576 c. M:-0.0821 c. 1301: 301 159 80 221 80 159 301 N I SD: 0.0494 c. M: 0.0753 c. 1366: 316 167 84 232 84 167 316 N I SD: 0.0425 c. M:-0.0598 c. 1448: 335 177 89 246 89 177 335 N I SD: 0.0363 c. M:-0.0550 c. 1513: 350 185 93 257 93 185 350 N I SD: 0.0304 c. M: 0.0418 c. 1595: 369 195 98 271 98 195 369 N I SD: 0.0258 c. M:-0.0383 c. 1660: 384 203 102 282 102 203 384 N I SD: 0.0205 c. M:-0.0273 c. 1742: 403 213 107 296 107 213 403 N I SD: 0.0174 c. M:-0.0245 c. 1807: 418 221 111 307 111 221 418 N I SD: 0.0126 c. M: 0.0181 c. 1889: 437 231 116 321 116 231 437 N I SD: 0.0114 c. M: 0.0165 c. 1954: 452 239 120 332 120 239 452 N I SD: 0.0068 c. M:-0.0103 c. 2101: 486 257 129 357 129 257 486 N I SD: 0.0056 c. M: 0.0086 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: 12.6835 cents 4 x 5 x 6 x 7:8 S SD: 15.0049 cents 5:6 x 7 x 8:9:10 S SD: 27.6340 cents 6:7 x 8:9 x 10:12 S SD: 7.9064 cents 7:8:9 x x 11:12:14 SD: 9.8617 cents 9:11 x 12 x 14:15:18 SD: 16.0465 cents 10:12:13 x 15:16:17:20 SD: 10.2752 cents 11:13:14:15 x 17:19:22 SD: 8.7327 cents 12:14:15:16:18:19:20:24 S SD: 8.3391 cents 13:15 x 17 x 20:22:26 SD: 11.0401 cents 14:16:18:19:21:22:24:28 SD: 8.2934 cents 15:18:19:20 x 23:26:30 SD: 10.3239 cents 16:19:20:21:24:25:27:32 SD: 7.6543 cents 18:21:23:24:27:28:31:36 SD: 3.4408 cents 28:33:36:37:42:44:48:56 SD: 3.3955 cents 30:35:38:40:45:47:51:60 SD: 2.7116 cents 36:42:46:48:54:56:61:72 SD: 2.5509 cents 40:47:51:53:60:63:68:80 SD: 2.3261 cents 46:54:59:61:69:72:78:92 SD: 2.0150 cents 51:60:65:68:77:80:87:102 SD: 1.9174 cents 57:67:73:76:86:89:97:114 SD: 1.7166 cents 58:68:74:77:87:91:99:116 SD: 1.3940 cents 64:75:82:85:96:100:109:128 SD: 1.3281 cents 80:94:102:107:120:125:136:160 SD: 1.1883 cents 87:102:111:116:131:136:148:174 SD: 1.1703 cents 90:106:115:120:135:141:153:180 SD: 1.0014 cents 98:115:125:131:147:153:167:196 SD: 1.0004 cents 104:122:133:139:156:163:177:208 SD: 0.7760 cents 108:127:138:144:162:169:184:216 SD: 0.4285 cents 202:237:258:269:303:316:344:404 SD: 0.3918 cents 212:249:271:283:318:332:361:424 SD: 0.3807 cents 230:270:294:307:345:360:392:460 SD: 0.2994 cents 270:317:345:360:405:423:460:540 SD: 0.2314 cents 288:338:368:384:432:451:491:576 SD: 0.2156 cents 368:432:470:491:552:576:627:736 SD: 0.2052 cents 396:465:506:528:594:620:675:792 SD: 0.1567 cents 414:486:529:552:621:648:705:828 SD: 0.1169 cents 432:507:552:576:648:676:736:864 SD: 0.0900 cents 540:634:690:720:810:845:920:1080 SD: 0.0721 cents