Scala analysis: xen15-chalmers-triadic-reversed-diamond-23-18
Triadic reversed 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: 24/23 73.680654 vicesimotertial minor semitone 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: 23/12 1126.319346 vicesimotertial major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 24/23 73.6807 vicesimotertial minor semitone 1: 24/23 73.6807 vicesimotertial minor semitone 2: 529/432 350.6837 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: 529/432 350.6837 7: 24/23 73.6807 vicesimotertial minor semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 24/23 73.681 cents vicesimotertial minor semitone 1: 1 9/8 203.910 cents major whole tone 1: 2 529/432 350.684 cents 2: 1 576/529 147.361 cents two (vicesimotertial minor semitone) 2: 2 27/23 277.591 cents vicesimotertial minor third 2: 4 23/18 424.364 cents vicesimotertial major third 3: 1 648/529 351.271 cents 3: 4 4/3 498.045 cents perfect fourth 3: 2 23/16 628.274 cents 23rd harmonic 4: 2 32/23 571.726 cents 23rd subharmonic 4: 4 3/2 701.955 cents perfect fifth 4: 1 529/324 848.729 cents two (vicesimotertial major third) 5: 4 36/23 775.636 cents 5: 2 46/27 922.409 cents 5: 1 529/288 1052.639 cents 6: 2 864/529 849.316 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 4 23/12 1126.319 cents vicesimotertial major 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 : 73.7 424.4 498.0 702.0 775.6 1126.3 1200.0 73.7 : 350.7 424.4 628.3 702.0 1052.6 1126.3 1200.0 424.4 : 73.7 277.6 351.3 702.0 775.6 849.3 1200.0 498.0 : 203.9 277.6 628.3 702.0 775.6 1126.3 1200.0 702.0 : 73.7 424.4 498.0 571.7 922.4 996.1 1200.0 775.6 : 350.7 424.4 498.0 848.7 922.4 1126.3 1200.0 1126.3: 73.7 147.4 498.0 571.7 775.6 849.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 73.6807 .. 350.6837 cents 12167/10368, 277.0030 cents 24/23, 73.6807 cents 2: 147.3613 .. 424.3643 cents 12167/10368, 277.0030 cents 248832/279841,-203.3224 cents 3: 351.2713 .. 628.2743 cents 12167/10368, 277.0030 cents 11664/12167,-73.0930 cents 4: 571.7257 .. 848.7287 cents 12167/10368, 277.0030 cents 512/529,-56.5487 cents 5: 775.6357 .. 1052.6387 cents 12167/10368, 277.0030 cents 11664/12167,-73.0930 cents 6: 849.3163 .. 1126.3193 cents 12167/10368, 277.0030 cents 248832/279841,-203.3224 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 : 529/432, 350.6837 cents Average / Smallest step : 2.326643 Largest / Average step : 2.045655 Largest / Smallest step : 4.759508 Median interval of one step : 24/23, 73.6807 cents, amount: 4 Most common interval of one step : 24/23, 73.6807 cents, amount: 4 Least squares average step : 173.28899 cents, oct.: 1213.02293 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2101-tone equal temperament with octave 2/1 degrees: 129 743 872 1229 1358 1972 2101 Least number of segments generator : 1051 of 600.286 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1099 of 627.701 cents and inv. generated superset size: 95 = 88 more = 1357.143% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABACABA Step pattern size order : SLSMSLS Scale is a Constant Structure, by a margin of 0.58762 cents Scale diversity : 1.452677 Lumma stability : 0.122801 Lumma impropriety factor : 0.507816 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 : 279936/279841, 0.5876 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 : 3 9 23 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 : 529 (O: 529 U: 529) Highest odd numerator or denominator: 23 Scale harmonicity : 0.010016 Average absolute harmonicity : 0.224318 Specific harmonicity : 0.053898 Fundamental : 1/828, -9.6935 octaves, 0.3160 Hz. Guide tone : 1656, 10.6935 octaves, 433251.936 Hz. Exponens Consonantiae : 1.371168E+06, 20.38697 octaves Euler's gradus suavitatis : 58 Sum of Mann's harmonic distance : 98.5, average 14.07143 Mersenne's string divisions : 11937765 Sum of van Prooijen's expressibility: 6.40115, average 0.91445 Sum of Tenney's harmonic distance : 12.87624, average 1.83946 Vogel's harmonic complexity : 31.57143 Wille's k value : 793 Wilson's harmonic complexity : 58 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 85.16880, average 3.04174 Lattice compactness (without 2's) : 52.73791, average 1.88350 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 3 0.57143 12 1 3: -2 .. 2 0.00000 8 2 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 32| Scale is weakly epimorphic with val: <7 10 33| Scale is weakly epimorphic with val: <7 11 30| Scale is JI-epimorphic with val: <7 11 31| Scale is weakly epimorphic with val: <7 12 30| Scale is weakly epimorphic with val: <7 12 34|
FIT/MODE
7: 0 2 1 1 0 2 1 N T3 SD: 65.7270 c. M: 97.7479 c. 8: 0 2 1 1 1 2 1 N D3 SD: 75.6687 c. M: 124.3643 c. 9: 1 2 1 1 1 2 1 P M ME I SD: 39.2695 c. M: 59.6527 c. 12: 1 3 1 2 1 3 1 N T3 I SD: 19.1993 c. M: 26.3193 c. Double Harmonic Major, Major Gipsy, Bhairav That, Mela Mayamalavagaula, Raga Paraj, Kalingada, Gaulipantu, Lalitapancamam, Gandhakriya, Kalingda, Manjiri, Chromatic 2nd Byzantine Liturgical, Hitzazkiar: Greece, Maqam Zengule, Hijaz Kar, Suzidil 14: 1 4 1 2 1 4 1 N T3 I SD: 11.0359 c. M:-16.2407 c. 17: 1 5 1 3 1 5 1 N T3 I SD: 2.7089 c. M:-3.9274 c. 48: 3 14 3 8 3 14 3 N T3 I SD: 1.3057 c. M: 1.9550 c. 65: 4 19 4 11 4 19 4 N T3 I SD: 0.2746 c. M:-0.4165 c. 147: 9 43 9 25 9 43 9 N T3 I SD: 0.1391 c. M: 0.2113 c. 212: 13 62 13 36 13 62 13 N T3 I SD: 0.1078 c. M:-0.1640 c. 359: 22 105 22 61 22 105 22 N T3 I SD: 0.1101 c. M:-0.1482 c. 571: 35 167 35 97 35 167 35 N T3 I SD: 0.1073 c. M:-0.1540 c. 783: 48 229 48 133 48 229 48 N T3 I SD: 0.1068 c. M:-0.1567 c. 995: 61 291 61 169 61 291 61 N T3 I SD: 0.1067 c. M:-0.1583 c. 1024: 63 299 63 174 63 299 63 N T3 I SD: 0.1108 c. M: 0.1475 c. 1041: 64 304 64 177 64 304 64 N T3 I SD: 0.1034 c. M: 0.1569 c. 1106: 68 323 68 188 68 323 68 N T3 I SD: 0.0904 c. M:-0.1329 c. 1171: 72 342 72 199 72 342 72 N T3 I SD: 0.0811 c. M:-0.1116 c. 1188: 73 347 73 202 73 347 73 N T3 I SD: 0.0799 c. M: 0.1219 c. 1236: 76 361 76 210 76 361 76 N T3 I SD: 0.0754 c. M:-0.1058 c. 1253: 77 366 77 213 77 366 77 N T3 I SD: 0.0677 c. M:-0.1026 c. 1318: 81 385 81 224 81 385 81 N T3 I SD: 0.0588 c. M:-0.0851 c. 1383: 85 404 85 235 85 404 85 N T3 I SD: 0.0535 c. M: 0.0721 c. 1400: 86 409 86 238 86 409 86 N T3 I SD: 0.0517 c. M:-0.0786 c. 1448: 89 423 89 246 89 423 89 N T3 I SD: 0.0515 c. M: 0.0763 c. 1465: 90 428 90 249 90 428 90 N T3 I SD: 0.0423 c. M:-0.0640 c. 1530: 94 447 94 260 94 447 94 N T3 I SD: 0.0363 c. M: 0.0506 c. 1595: 98 466 98 271 98 466 98 N T3 I SD: 0.0341 c. M:-0.0498 c. 1612: 99 471 99 274 99 471 99 N T3 I SD: 0.0310 c. M:-0.0467 c. 1677: 103 490 103 285 103 490 103 N T3 I SD: 0.0233 c. M: 0.0352 c. 1742: 107 509 107 296 107 509 107 N T3 I SD: 0.0199 c. M:-0.0277 c. 1824: 112 533 112 310 112 533 112 N T3 I SD: 0.0156 c. M: 0.0222 c. 1889: 116 552 116 321 116 552 116 N T3 I SD: 0.0086 c. M:-0.0128 c. 2036: 125 595 125 346 125 595 125 N T3 I SD: 0.0065 c. M: 0.0096 c. 2101: 129 614 129 357 129 614 129 N T3 I SD: 0.0034 c. M:-0.0050 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: 36.2410 cents 4 x 5 x 6 x x 8 S SD: 12.6835 cents 5 x 6:7 x 8 x 10 S SD: 35.7100 cents 6 x x 8:9 x x 12 S SD: 0.0000 cents 7:8:9 x x 11:13:14 SD: 33.4360 cents 8:9:10:11:12:13:15:16 SD: 23.4322 cents 9:10 x 12 x 14:17:18 SD: 22.4271 cents 10:11:13 x 15:16:19:20 SD: 17.4065 cents 11:12:14:15 x 17:21:22 SD: 14.9201 cents 12:13:15:16:18:19:23:24 SD: 11.1169 cents 13:14 x 17 x 20:25:26 SD: 14.1952 cents 14:15:18:19:21:22:27:28 SD: 8.2189 cents 15:16:19:20 x 23:29:30 SD: 9.3847 cents 16:17:20:21:24:25:31:32 SD: 8.4860 cents 18:19:23:24:27:28:35:36 SD: 4.8072 cents 21:22:27:28:32:33:40:42 SD: 4.6699 cents 22:23:28:29:33:34:42:44 SD: 4.4725 cents 24:25:31:32:36:38:46:48 SD: 3.9286 cents 26:27:33:35:39:41:50:52 SD: 3.7222 cents 36:38:46:48:54:56:69:72 SD: 3.2319 cents 39:41:50:52:59:61:75:78 SD: 3.0366 cents 40:42:51:53:60:63:77:80 SD: 2.9316 cents 42:44:54:56:63:66:81:84 SD: 2.5708 cents 44:46:56:59:66:69:84:88 SD: 2.0785 cents 46:48:59:61:69:72:88:92 SD: 1.7049 cents 48:50:61:64:72:75:92:96 SD: 1.4785 cents 69:72:88:92:104:108:132:138 SD: 1.3633 cents 72:75:92:96:108:113:138:144 SD: 0.7935 cents 90:94:115:120:135:141:173:180 SD: 0.7856 cents 108:113:138:144:162:169:207:216 SD: 0.6700 cents 138:144:176:184:207:216:265:276 SD: 0.6612 cents 140:146:179:187:210:219:268:280 SD: 0.5968 cents 156:163:199:208:234:244:299:312 SD: 0.5580 cents 166:173:212:221:249:260:318:332 SD: 0.5444 cents 180:188:230:240:270:282:345:360 SD: 0.3237 cents 228:238:291:304:342:357:437:456 SD: 0.3106 cents 230:240:294:307:345:360:441:460 SD: 0.2994 cents 252:263:322:336:378:394:483:504 SD: 0.2758 cents 274:286:350:365:411:429:525:548 SD: 0.2731 cents 276:288:353:368:414:432:529:552 SD: 0.2337 cents 324:338:414:432:486:507:621:648 SD: 0.0900 cents 504:526:644:672:756:789:966:1008 SD: 0.0578 cents