Scala analysis: xen15-chalmers-triadic-diamond-23-19
Triadic diamond for M=23/19, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 23/19 330.761331 2: 57/46 371.193670 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 92/57 828.806330 6: 38/23 869.238669 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 23/19 330.7613 1: 23/19 330.7613 2: 1083/1058 40.4323 3: 184/171 126.8513 4: 9/8 203.9100 major whole tone 5: 184/171 126.8513 6: 1083/1058 40.4323 7: 23/19 330.7613
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 1083/1058 40.432 cents 1: 2 184/171 126.851 cents 1: 1 9/8 203.910 cents major whole tone 1: 2 23/19 330.761 cents 2: 2 76/69 167.284 cents 2: 2 23/19 330.761 cents 2: 2 57/46 371.194 cents 2: 1 529/361 661.523 cents 3: 2 57/46 371.194 cents 3: 1 4232/3249 457.613 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: 1 3249/2116 742.387 cents 4: 2 92/57 828.806 cents 5: 1 722/529 538.477 cents 5: 2 92/57 828.806 cents 5: 2 38/23 869.239 cents 5: 2 69/38 1032.716 cents 6: 2 38/23 869.239 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 171/92 1073.149 cents 6: 2 2116/1083 1159.568 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 : 330.8 371.2 498.0 702.0 828.8 869.2 1200.0 330.8 : 40.4 167.3 371.2 498.0 538.5 869.2 1200.0 371.2 : 126.9 330.8 457.6 498.0 828.8 1159.6 1200.0 498.0 : 203.9 330.8 371.2 702.0 1032.7 1073.1 1200.0 702.0 : 126.9 167.3 498.0 828.8 869.2 996.1 1200.0 828.8 : 40.4 371.2 702.0 742.4 869.2 1073.1 1200.0 869.2 : 330.8 661.5 702.0 828.8 1032.7 1159.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 40.4323 .. 330.7613 cents 24334/20577, 290.3290 cents 1083/1058, 40.4323 cents 2: 167.2837 .. 661.5227 cents 36501/27436, 494.2390 cents 1444/1587,-163.4777 cents 3: 371.1937 .. 701.9550 cents 23/19, 330.7613 cents 20577/24334,-290.3290 cents 4: 498.0450 .. 828.8063 cents 23/19, 330.7613 cents 8/9,-203.9100 cents 5: 538.4773 .. 1032.7163 cents 36501/27436, 494.2390 cents 20577/24334,-290.3290 cents 6: 869.2387 .. 1159.5677 cents 24334/20577, 290.3290 cents 1444/1587,-163.4777 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 1083/1058, 40.4323 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 23/19, 330.7613 cents Average / Smallest step : 4.239888 Largest / Average step : 1.929441 Largest / Smallest step : 8.180613 Median interval of one step : 184/171, 126.8513 cents, amount: 2 Least squares average step : 165.24691 cents, oct.: 1156.72837 cents Scale is not proper Step pattern alph. order: ABCDCBA Step pattern size order : DABCBAD Scale is not a Constant Structure Scale diversity : 1.390452 Lumma stability : 0.067387 Lumma impropriety factor : 0.653807 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 : 621/608, 36.6263 cents Number of recognisable fifths : 4, average 701.9550 cents Scale is a complete diamond : 19 23 57 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 : 3249 (O: 3249 U: 3249) Highest odd numerator or denominator: 57 Scale harmonicity : 0.006222 Average absolute harmonicity : 0.219711 Specific harmonicity : 0.033115 Fundamental : 1/2622, -11.3565 octaves, 0.0998 Hz. Guide tone : 5244, 12.3565 octaves, 1371964.464 Hz. Exponens Consonantiae : 1.374977E+07, 23.71290 octaves Euler's gradus suavitatis : 88 Sum of Mann's harmonic distance : 185.0, average 26.42857 Mersenne's string divisions : 196595070 Sum of van Prooijen's expressibility: 7.18945, average 1.02706 Sum of Tenney's harmonic distance : 14.87865, average 2.12552 Vogel's harmonic complexity : 46.57143 Wille's k value : 1966 Wilson's harmonic complexity : 90 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 65.73531, average 2.34769 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 19: -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 27 29| Scale is weakly epimorphic with val: <7 10 27 35| Scale is weakly epimorphic with val: <7 10 28 29| Scale is weakly epimorphic with val: <7 10 28 30| Scale is weakly epimorphic with val: <7 10 29 30| Scale is weakly epimorphic with val: <7 10 29 31| Scale is weakly epimorphic with val: <7 10 30 31| Scale is weakly epimorphic with val: <7 10 30 32| Scale is weakly epimorphic with val: <7 10 31 32| Scale is weakly epimorphic with val: <7 10 31 33| Scale is weakly epimorphic with val: <7 10 32 33| Scale is weakly epimorphic with val: <7 10 32 34| Scale is weakly epimorphic with val: <7 10 33 34| Scale is weakly epimorphic with val: <7 10 33 35| Scale is weakly epimorphic with val: <7 11 27 32| Scale is weakly epimorphic with val: <7 11 27 33| Scale is weakly epimorphic with val: <7 11 28 33| Scale is weakly epimorphic with val: <7 11 28 34| Scale is weakly epimorphic with val: <7 11 29 34| Scale is weakly epimorphic with val: <7 11 29 35| Scale is weakly epimorphic with val: <7 11 30 35| Scale is weakly epimorphic with val: <7 12 27 31| Scale is weakly epimorphic with val: <7 12 27 35| Scale is weakly epimorphic with val: <7 12 28 29| Scale is weakly epimorphic with val: <7 12 28 32| Scale is weakly epimorphic with val: <7 12 29 30| Scale is weakly epimorphic with val: <7 12 29 33| Scale is weakly epimorphic with val: <7 12 30 31| Scale is weakly epimorphic with val: <7 12 30 34| Scale is weakly epimorphic with val: <7 12 31 32| Scale is weakly epimorphic with val: <7 12 31 35| Scale is weakly epimorphic with val: <7 12 32 33| Scale is weakly epimorphic with val: <7 12 33 34|
FIT/MODE
7: 2 0 1 1 1 0 2 N T3 I SD: 18.6166 c. M:-28.3365 c. 17: 5 0 2 3 2 0 5 N I SD: 15.4968 c. M:-22.1798 c. 19: 5 1 2 3 2 1 5 N I SD: 9.8035 c. M: 14.9719 c. 22: 6 1 2 4 2 1 6 N I SD: 7.0907 c. M:-10.6245 c. 26: 7 1 3 4 3 1 7 N I SD: 6.6756 c. M:-9.6473 c. 29: 8 1 3 5 3 1 8 N I SD: 1.0410 c. M: 1.4933 c. 94: 26 3 10 16 10 3 26 N I SD: 0.8146 c. M:-1.1536 c. 123: 34 4 13 21 13 4 34 N I SD: 0.6193 c. M:-0.9460 c. 152: 42 5 16 26 16 5 42 N I SD: 0.5723 c. M: 0.8176 c. 178: 49 6 19 30 19 6 49 N I SD: 0.5443 c. M:-0.8314 c. 181: 50 6 19 31 19 6 50 N I SD: 0.5834 c. M: 0.8074 c. 200: 55 7 21 34 21 7 55 N I SD: 0.5933 c. M:-0.8063 c. 207: 57 7 22 35 22 7 57 N I SD: 0.3357 c. M: 0.5057 c. 236: 65 8 25 40 25 8 65 N I SD: 0.1939 c. M:-0.2601 c. 265: 73 9 28 45 28 9 73 N I SD: 0.1298 c. M:-0.1953 c. 359: 99 12 38 61 38 12 99 N I SD: 0.1213 c. M:-0.1630 c. 388: 107 13 41 66 41 13 107 N I SD: 0.1105 c. M:-0.1665 c. 595: 164 20 63 101 63 20 164 N I SD: 0.0785 c. M:-0.1063 c. 624: 172 21 66 106 66 21 172 N I SD: 0.0276 c. M:-0.0398 c. 653: 180 22 69 111 69 22 180 N I SD: 0.0235 c. M:-0.0358 c. 1277: 352 43 135 217 135 43 352 N I SD: 0.0097 c. M:-0.0139 c. 2195: 605 74 232 373 232 74 605 N I SD: 0.0092 c. M:-0.0136 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: 5.0400 cents 4 x 5 x 6 x 7:8 S SD: 25.1821 cents 5:6 x 7 x 8 x 10 S SD: 21.7829 cents 6:7 x 8:9 x 10:12 S SD: 13.1310 cents 7:8 x 9 x 11:12:14 SD: 28.3610 cents 8 x 10:11:12:13 x 16 SD: 11.3208 cents 9:11 x 12:14 x 15:18 SD: 13.3713 cents 10:12 x 13:15:16:17:20 SD: 11.5699 cents 11:13:14:15:17 x 18:22 SD: 15.2146 cents 12 x 15:16:18:19:20:24 S SD: 6.5885 cents 13 x 16:17:20:21 x 26 SD: 11.2974 cents 14:17 x 19:21 x 23:28 SD: 6.5226 cents 16:19:20:21:24:26 x 32 SD: 7.8436 cents 17 x 21:23:26:27:28:34 SD: 8.5061 cents 18:22 x 24:27:29:30:36 SD: 3.7844 cents 19:23:24:25:29:31 x 38 SD: 8.9569 cents 20:24:25:27:30:32:33:40 SD: 4.8520 cents 22 x 27:29:33 x 36:44 SD: 6.1504 cents 24:29:30:32:36:39:40:48 SD: 3.5123 cents 27:33 x 36:41:44:45:54 SD: 5.8549 cents 28:34:35:37:42:45:46:56 SD: 3.6401 cents 31 x 38:41:47:50:51:62 SD: 5.1244 cents 32:39:40:43:48:52:53:64 SD: 3.7880 cents 33:40:41:44:50:53:55:66 SD: 3.5891 cents 34:41:42:45:51:55:56:68 SD: 2.3910 cents 38:46:47:51:57:61:63:76 SD: 2.3209 cents 42:51:52:56:63:68:69:84 SD: 1.7819 cents 54:65:67:72:81:87:89:108 SD: 1.6194 cents 62:75:77:83:93:100:102:124 SD: 1.5717 cents 66:80:82:88:99:107:109:132 SD: 1.3232 cents 72:87:89:96:108:116:119:144 SD: 0.8800 cents 96:116:119:128:144:155:159:192 SD: 0.7666 cents 104:126:129:139:156:168:172:208 SD: 0.7505 cents 114:138:141:152:171:184:188:228 SD: 0.6465 cents 138:167:171:184:207:223:228:276 SD: 0.3022 cents 204:247:253:272:306:329:337:408 SD: 0.2968 cents 210:254:260:280:315:339:347:420 SD: 0.2952 cents 276:334:342:368:414:445:456:552 SD: 0.2744 cents 314:380:389:419:471:507:519:628 SD: 0.2571 cents 318:385:394:424:477:513:525:636 SD: 0.2279 cents 342:414:424:456:513:552:565:684 SD: 0.1283 cents 414:501:513:552:621:668:684:828 SD: 0.1102 cents 552:668:684:736:828:891:912:1104 SD: 0.0793 cents