Scala analysis: xen15-chalmers-triadic-reversed-diamond-23-19
Triadic reversed 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: 76/69 167.283668 2: 23/19 330.761331 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 38/23 869.238669 6: 69/38 1032.716332 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 76/69 167.2837 1: 76/69 167.2837 2: 1587/1444 163.4777 3: 76/69 167.2837 4: 9/8 203.9100 major whole tone 5: 76/69 167.2837 6: 1587/1444 163.4777 7: 76/69 167.2837
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 1587/1444 163.478 cents 1: 4 76/69 167.284 cents 1: 1 9/8 203.910 cents major whole tone 2: 4 23/19 330.761 cents 2: 1 5776/4761 334.567 cents 2: 2 57/46 371.194 cents 3: 4 4/3 498.045 cents perfect fourth 3: 2 207/152 534.671 cents 3: 1 722/529 538.477 cents 4: 1 529/361 661.523 cents 4: 2 304/207 665.329 cents 4: 4 3/2 701.955 cents perfect fifth 5: 2 92/57 828.806 cents 5: 1 4761/2888 865.433 cents 5: 4 38/23 869.239 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 4 69/38 1032.716 cents 6: 2 2888/1587 1036.522 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 : 167.3 330.8 498.0 702.0 869.2 1032.7 1200.0 167.3 : 163.5 330.8 534.7 702.0 865.4 1032.7 1200.0 330.8 : 167.3 371.2 538.5 702.0 869.2 1036.5 1200.0 498.0 : 203.9 371.2 534.7 702.0 869.2 1032.7 1200.0 702.0 : 167.3 330.8 498.0 665.3 828.8 996.1 1200.0 869.2 : 163.5 330.8 498.0 661.5 828.8 1032.7 1200.0 1032.7: 167.3 334.6 498.0 665.3 869.2 1036.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 163.4777 .. 203.9100 cents 1083/1058, 40.4323 cents 1587/1444, 163.4777 cents 2: 330.7613 .. 371.1937 cents 1083/1058, 40.4323 cents 184/171, 126.8513 cents 3: 498.0450 .. 538.4773 cents 1083/1058, 40.4323 cents 184/171, 126.8513 cents 4: 661.5227 .. 701.9550 cents 1083/1058, 40.4323 cents 279841/260642, 123.0453 cents 5: 828.8063 .. 869.2387 cents 1083/1058, 40.4323 cents 184/171, 126.8513 cents 6: 996.0900 .. 1036.5223 cents 1083/1058, 40.4323 cents 184/171, 126.8513 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 1587/1444, 163.4777 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.048636 Largest / Average step : 1.189475 Largest / Smallest step : 1.247326 Median interval of one step : 76/69, 167.2837 cents, amount: 4 Most common interval of one step : 76/69, 167.2837 cents, amount: 4 Least squares average step : 171.95180 cents, oct.: 1203.66263 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABACABA Step pattern size order : MSMLMSM Scale is a Constant Structure, by a margin of 123.04532 cents Scale diversity : 1.193783 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.797838 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 : 109744/109503, 3.8060 cents Number of recognisable fifths : 4, average 701.9550 cents Scale is Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Scale is a complete diamond : 19 23 69 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 : 4761 (O: 4761 U: 4761) Highest odd numerator or denominator: 69 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 : 39749430 Sum of van Prooijen's expressibility: 7.35540, average 1.05077 Sum of Tenney's harmonic distance : 14.87865, average 2.12552 Vogel's harmonic complexity : 46.57143 Wille's k value : 2380 Wilson's harmonic complexity : 90 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 64.97815, average 2.32065 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 32| Scale is weakly epimorphic with val: <7 10 27 33| Scale is weakly epimorphic with val: <7 10 28 33| Scale is weakly epimorphic with val: <7 10 28 34| Scale is weakly epimorphic with val: <7 10 29 34| Scale is weakly epimorphic with val: <7 10 29 35| Scale is weakly epimorphic with val: <7 10 30 35| Scale is JI-epimorphic with val: <7 11 27 29| Scale is weakly epimorphic with val: <7 11 27 35| Scale is weakly epimorphic with val: <7 11 28 29| Scale is JI-epimorphic with val: <7 11 28 30| Scale is weakly epimorphic with val: <7 11 29 30| Scale is JI-epimorphic with val: <7 11 29 31| Scale is weakly epimorphic with val: <7 11 30 31| Scale is JI-epimorphic with val: <7 11 30 32| = patent Scale is weakly epimorphic with val: <7 11 31 32| Scale is JI-epimorphic with val: <7 11 31 33| Scale is weakly epimorphic with val: <7 11 32 33| Scale is JI-epimorphic with val: <7 11 32 34| Scale is weakly epimorphic with val: <7 11 33 34| Scale is JI-epimorphic with val: <7 11 33 35| Scale is weakly epimorphic with val: <7 12 27 30| Scale is weakly epimorphic with val: <7 12 27 33| Scale is weakly epimorphic with val: <7 12 28 31| Scale is weakly epimorphic with val: <7 12 28 34| Scale is weakly epimorphic with val: <7 12 29 32| Scale is weakly epimorphic with val: <7 12 29 35| Scale is weakly epimorphic with val: <7 12 30 33| Scale is weakly epimorphic with val: <7 12 31 34| Scale is weakly epimorphic with val: <7 12 32 35|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 11.0486 c. M:-16.2407 c. Lebeng 22: 3 3 3 4 3 3 3 SP M ME I SD: 4.6719 c. M:-7.1359 c. Minor quasi-equal Heptatonic, Miller's Porcupine-7 29: 4 4 4 5 4 4 4 SP M ME I SD: 1.2450 c. M: 1.7664 c. Miller's Porcupine-7 65: 9 9 9 11 9 9 9 SP M DE I SD: 1.0476 c. M:-1.5464 c. 94: 13 13 13 16 13 13 13 SP M DE I SD: 0.9441 c. M: 1.3262 c. 159: 22 22 22 27 22 22 22 SP M DE I SD: 0.9686 c. M:-1.3141 c. 171: 24 23 24 29 24 23 24 SP T3 I SD: 0.7949 c. M: 1.1374 c. 200: 28 27 28 34 28 27 28 SP T3 I SD: 0.5593 c. M:-0.7613 c. 207: 29 28 29 35 29 28 29 SP T3 I SD: 0.5490 c. M: 0.8323 c. 229: 32 31 32 39 32 31 32 SP T3 I SD: 0.4178 c. M: 0.6303 c. 236: 33 32 33 40 33 32 33 SP T3 I SD: 0.3358 c. M:-0.5129 c. 265: 37 36 37 45 37 36 37 SP T3 I SD: 0.1791 c. M:-0.2635 c. 294: 41 40 41 50 41 40 41 SP T3 I SD: 0.0980 c. M:-0.1491 c. 330: 46 45 46 56 46 45 46 SP T3 I SD: 0.1078 c. M:-0.1478 c. 595: 83 81 83 101 83 81 83 SP T3 I SD: 0.0823 c. M:-0.1113 c. 624: 87 85 87 106 87 85 87 SP T3 I SD: 0.0218 c. M:-0.0319 c. 1277: 178 174 178 217 178 174 178 SP T3 I SD: 0.0117 c. M: 0.0166 c. 1901: 265 259 265 323 265 259 265 SP T3 I SD: 0.0081 c. M:-0.0119 c. 2195: 306 299 306 373 306 299 306 SP T3 I SD: 0.0063 c. M:-0.0096 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: 5.0400 cents 4 x 5 x 6 x 7:8 S SD: 21.1661 cents 5 x 6:7 x 8:9:10 S SD: 20.6669 cents 6 x 7:8:9:10:11:12 S SD: 11.2888 cents 7:8 x 9:11:12:13:14 SD: 23.6491 cents 8:9:10:11:12:13:15:16 SD: 15.1023 cents 9:10:11:12:14:15:16:18 S SD: 11.1024 cents 10:11:12:13:15:17:18:20 SD: 9.9224 cents 12:13:15:16:18:20:22:24 SD: 9.4934 cents 14:15:17:19:21:23:25:28 SD: 9.2454 cents 16:18:19:21:24:26:29:32 SD: 9.0626 cents 17:19:21:23:26:28:31:34 SD: 8.7134 cents 18:20:22:24:27:30:33:36 S SD: 4.5433 cents 20:22:24:27:30:33:36:40 S SD: 4.3569 cents 28:31:34:37:42:46:51:56 SD: 3.1110 cents 38:42:46:51:57:63:69:76 SD: 2.0228 cents 48:53:58:64:72:79:87:96 SD: 1.2954 cents 66:73:80:88:99:109:120:132 SD: 1.1355 cents 80:88:97:107:120:132:145:160 SD: 1.0821 cents 90:99:109:120:135:149:163:180 SD: 0.8849 cents 108:119:131:144:162:178:196:216 SD: 0.7982 cents 118:130:143:157:177:195:214:236 SD: 0.6695 cents 120:132:145:160:180:198:218:240 SD: 0.6538 cents 138:152:167:184:207:228:251:276 SD: 0.4225 cents 186:205:225:248:279:307:338:372 SD: 0.3899 cents 218:240:264:291:327:360:396:436 SD: 0.3582 cents 228:251:276:304:342:377:414:456 SD: 0.2375 cents 276:304:334:368:414:456:501:552 SD: 0.1102 cents 570:628:690:760:855:942:1035:1140 SD: 0.0969 cents