Scala analysis: xen15-chalmers-triadic-reversed-diamond-23-20
Triadic reversed 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: 80/69 256.084366 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 69/40 943.915634 6: 40/23 958.039367 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 23/20 241.9606 1: 23/20 241.9606 2: 1600/1587 14.1237 3: 23/20 241.9606 4: 9/8 203.9100 major whole tone 5: 23/20 241.9606 6: 1600/1587 14.1237 7: 23/20 241.9606
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 1600/1587 14.124 cents 1: 1 9/8 203.910 cents major whole tone 1: 4 23/20 241.961 cents 2: 4 80/69 256.084 cents 2: 2 207/160 445.871 cents 2: 1 529/400 483.921 cents 3: 2 30/23 459.994 cents 3: 4 4/3 498.045 cents perfect fourth 3: 1 4761/3200 687.831 cents 4: 1 6400/4761 512.169 cents 4: 4 3/2 701.955 cents perfect fifth 4: 2 23/15 740.006 cents 5: 1 800/529 716.079 cents 5: 2 320/207 754.129 cents 5: 4 69/40 943.916 cents 6: 4 40/23 958.039 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 1587/800 1185.876 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 : 242.0 256.1 498.0 702.0 943.9 958.0 1200.0 242.0 : 14.1 256.1 460.0 702.0 716.1 958.0 1200.0 256.1 : 242.0 445.9 687.8 702.0 943.9 1185.9 1200.0 498.0 : 203.9 445.9 460.0 702.0 943.9 958.0 1200.0 702.0 : 242.0 256.1 498.0 740.0 754.1 996.1 1200.0 943.9 : 14.1 256.1 498.0 512.2 754.1 958.0 1200.0 958.0 : 242.0 483.9 498.0 740.0 943.9 1185.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 14.1237 .. 241.9606 cents 36501/32000, 227.8369 cents 1600/1587, 14.1237 cents 2: 256.0844 .. 483.9213 cents 36501/32000, 227.8369 cents 1600/1587, 14.1237 cents 3: 459.9944 .. 687.8313 cents 36501/32000, 227.8369 cents 12000/12167,-23.9269 cents 4: 512.1687 .. 740.0056 cents 36501/32000, 227.8369 cents 20480000/22667121,-175.6625 cents 5: 716.0787 .. 943.9156 cents 36501/32000, 227.8369 cents 12000/12167,-23.9269 cents 6: 958.0394 .. 1185.8763 cents 36501/32000, 227.8369 cents 1600/1587, 14.1237 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 1600/1587, 14.1237 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 23/20, 241.9606 cents Average / Smallest step : 12.137625 Largest / Average step : 1.411437 Largest / Smallest step : 17.131494 Median interval of one step : 23/20, 241.9606 cents, amount: 4 Most common interval of one step : 23/20, 241.9606 cents, amount: 4 Least squares average step : 170.88499 cents, oct.: 1196.19494 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABACABA Step pattern size order : LSLMLSL Scale is a Constant Structure, by a margin of 14.12373 cents Scale diversity : 1.065865 Lumma stability : 0.047079 Lumma impropriety factor : 0.186264 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 : 1600/1587, 14.1237 cents Number of recognisable fifths : 6, average 701.9550 cents Number of appreciable 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 : 5 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 : 0.009149 Average absolute harmonicity : 0.223262 Specific harmonicity : 0.048792 Fundamental : 1/2760, -11.4305 octaves, 0.0948 Hz. Guide tone : 5520, 12.4305 octaves, 1444173.120 Hz. Exponens Consonantiae : 1.523520E+07, 23.86091 octaves Euler's gradus suavitatis : 64 Sum of Mann's harmonic distance : 189.5, average 27.07143 Mersenne's string divisions : 219984345 Sum of van Prooijen's expressibility: 7.35540, average 1.05077 Sum of Tenney's harmonic distance : 14.96776, average 2.13825 Vogel's harmonic complexity : 34.57143 Wille's k value : 2380 Wilson's harmonic complexity : 62 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 97.63630, average 3.48701 Lattice compactness (without 2's) : 47.53320, average 1.69761 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 4 0.57143 16 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 34| Scale is weakly epimorphic with val: <7 10 15 35| Scale is weakly epimorphic with val: <7 10 16 29| Scale is weakly epimorphic with val: <7 10 16 35| Scale is weakly epimorphic with val: <7 10 17 29| Scale is weakly epimorphic with val: <7 10 17 30| Scale is weakly epimorphic with val: <7 10 18 30| Scale is weakly epimorphic with val: <7 10 18 31| Scale is JI-epimorphic with val: <7 11 15 30| Scale is weakly epimorphic with val: <7 11 15 31| Scale is JI-epimorphic with val: <7 11 16 31| Scale is weakly epimorphic with val: <7 11 16 32| = patent Scale is JI-epimorphic with val: <7 11 17 32| Scale is weakly epimorphic with val: <7 11 17 33| Scale is JI-epimorphic with val: <7 11 18 33| Scale is weakly epimorphic with val: <7 11 18 34| Scale is weakly epimorphic with val: <7 12 15 32| Scale is weakly epimorphic with val: <7 12 15 35| Scale is weakly epimorphic with val: <7 12 16 29| Scale is weakly epimorphic with val: <7 12 16 33| Scale is weakly epimorphic with val: <7 12 17 30| Scale is weakly epimorphic with val: <7 12 17 34| Scale is weakly epimorphic with val: <7 12 18 31| Scale is weakly epimorphic with val: <7 12 18 35|
FIT/MODE
7: 1 0 2 1 1 0 2 N T3 SD: 65.8771 c. M: 100.8965 c. 8: 1 0 2 1 2 0 2 N T3 SD: 73.3981 c. M: 106.0844 c. 9: 2 0 2 1 2 0 2 N T3 I SD: 23.7104 c. M:-35.2883 c. 10: 2 0 2 2 2 0 2 N M DE I SD: 12.9634 c. M:-18.0450 c. 14: 3 0 3 2 3 0 3 N T3 I SD: 11.8970 c. M:-16.2407 c. 19: 4 0 4 3 4 0 4 N T3 I SD: 7.1293 c. M:-10.6709 c. 24: 5 0 5 4 5 0 5 N T3 I SD: 5.4895 c. M:-8.0394 c. 29: 6 0 6 5 6 0 6 N T3 I SD: 5.4270 c. M: 7.8085 c. 46: 9 1 9 8 9 1 9 N T3 I SD: 4.7853 c. M:-7.1780 c. 51: 10 1 10 9 10 1 10 N T3 I SD: 4.3873 c. M:-6.6665 c. 55: 11 1 11 9 11 1 11 N T3 I SD: 3.8157 c. M: 5.7338 c. 60: 12 1 12 10 12 1 12 N T3 I SD: 2.5634 c. M: 3.9156 c. 65: 13 1 13 11 13 1 13 N T3 I SD: 1.6621 c. M:-2.3772 c. 70: 14 1 14 12 14 1 14 N T3 I SD: 1.2849 c. M:-1.9606 c. 84: 17 1 17 14 17 1 17 N T3 I SD: 1.2813 c. M: 1.9550 c. 89: 18 1 18 15 18 1 18 N T3 I SD: 0.5957 c. M:-0.8314 c. 94: 19 1 19 16 19 1 19 N T3 I SD: 0.5255 c. M: 0.7652 c. 159: 32 2 32 27 32 2 32 N T3 I SD: 0.3696 c. M: 0.5194 c. 164: 33 2 33 28 33 2 33 N T3 I SD: 0.3710 c. M:-0.4972 c. 248: 50 3 50 42 50 3 50 N T3 I SD: 0.2686 c. M: 0.3672 c. 253: 51 3 51 43 51 3 51 N T3 I SD: 0.0422 c. M:-0.0634 c. 853: 172 10 172 145 172 10 172 N T3 I SD: 0.0326 c. M: 0.0469 c. 1106: 223 13 223 188 223 13 223 N T3 I SD: 0.0235 c. M: 0.0341 c. 1359: 274 16 274 231 274 16 274 N T3 I SD: 0.0209 c. M:-0.0318 c. 1448: 292 17 292 246 292 17 292 N T3 I SD: 0.0193 c. M:-0.0283 c. 1701: 343 20 343 289 343 20 343 N T3 I SD: 0.0112 c. M:-0.0150 c. 1954: 394 23 394 332 394 23 394 N T3 I SD: 0.0067 c. M:-0.0103 c. 2207: 445 26 445 375 445 26 445 N T3 I SD: 0.0066 c. M: 0.0099 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: 19.8523 cents 4 x x 5:6 x 7:8 S SD: 28.0627 cents 5 x 6:7:8 x 9:10 S SD: 32.6880 cents 6 x 7:8:9:10 x 12 S SD: 12.1052 cents 7:8 x 9:11:12 x 14 SD: 20.6717 cents 8:9 x 11:12 x 14:16 SD: 13.2698 cents 9:10 x 12:14 x 16:18 S SD: 18.9303 cents 10 x 12:13:15:17 x 20 SD: 15.6294 cents 11 x 13:15:17:19 x 22 SD: 14.5427 cents 12 x 14:16:18 x 21:24 S SD: 3.0509 cents 13:15 x 17:20:22:23:26 SD: 11.8609 cents 14:16 x 19:21:24 x 28 SD: 6.8458 cents 15:17 x 20:23 x 26:30 SD: 9.2088 cents 16:18:19:21:24 x 28:32 SD: 10.5723 cents 17 x 20:23:26:29:30:34 SD: 9.7449 cents 18 x 21:24:27:31 x 36 SD: 2.2283 cents 19 x 22:25:29 x 33:38 SD: 7.5968 cents 20:23 x 27:30 x 35:40 SD: 4.8119 cents 21:24 x 28:32:36:37:42 SD: 6.4190 cents 22:25:26:29:33:38 x 44 SD: 7.3038 cents 23:26:27:31:35 x 40:46 SD: 8.0206 cents 24 x 28:32:36:41:42:48 SD: 3.7831 cents 25 x 29:33:38:43 x 50 SD: 5.8466 cents 26:30 x 35:39:45 x 52 SD: 3.6948 cents 27:31 x 36:41 x 47:54 SD: 4.2969 cents 28:32 x 37:42:48:49:56 SD: 4.0488 cents 29:33:34:39:44:50 x 58 SD: 6.0528 cents 30 x 35:40:45 x 52:60 SD: 2.4476 cents 31 x 36:41:47:53:54:62 SD: 4.6949 cents 32 x 37:43:48:55:56:64 SD: 3.1615 cents 33:38 x 44:50:57 x 66 SD: 3.5391 cents 34:39 x 45:51 x 59:68 SD: 2.8108 cents 37 x 43:49:56:64 x 74 SD: 4.0892 cents 38 x 44:51:57 x 66:76 SD: 2.3602 cents 39:45 x 52:59:67:68:78 SD: 2.9835 cents 40:46 x 53:60:69:70:80 SD: 2.5504 cents 41:47:48:55:62:71 x 82 SD: 4.2991 cents 42:48:49:56:63:72:73:84 SD: 2.6730 cents 44 x 51:59:66:76:77:88 SD: 2.4608 cents 45 x 52:60:68 x 78:90 SD: 3.0336 cents 46:53 x 61:69:79:80:92 SD: 2.0968 cents 47:54 x 63:71:81:82:94 SD: 2.7366 cents 48:55:56:64:72:83 x 96 SD: 2.1939 cents 49:56:57:65:74 x 85:98 SD: 3.2700 cents 50 x 58:67:75:86:87:100 SD: 1.6775 cents 51 x 59:68:77:88:89:102 SD: 2.2188 cents 52:60 x 69:78:90 x 104 SD: 2.3361 cents 53:61 x 71:80:91:92:106 SD: 2.6975 cents 54:62:63:72:81:93:94:108 SD: 1.6567 cents 56:64:65:75:84 x 97:112 SD: 2.5173 cents 57 x 66:76:86:98:99:114 SD: 2.0080 cents 58 x 67:77:87:100:101:116 SD: 1.6837 cents 59:68 x 79:89:102:103:118 SD: 2.4798 cents 60:69:70:80:90 x 104:120 SD: 2.0396 cents 62:71:72:83:93:107:108:124 SD: 1.5521 cents 64 x 74:85:96:110:111:128 SD: 1.9028 cents 65:75 x 87:98:112:113:130 SD: 2.1093 cents 66:76:77:88:99:114:115:132 SD: 1.6750 cents 68:78:79:91:102:117:118:136 SD: 1.4744 cents 70 x 81:93:105:121:122:140 SD: 1.4578 cents 71 x 82:95:107:122:123:142 SD: 2.5729 cents 72:83 x 96:108:124:125:144 SD: 0.9758 cents 77 x 89:103:116:133:134:154 SD: 1.8445 cents 78:90 x 104:117:135:136:156 SD: 1.5499 cents 80:92:93:107:120:138:139:160 SD: 1.0391 cents 84 x 97:112:126:145:146:168 SD: 1.1910 cents 87:100:101:116:131:150:151:174 SD: 1.1292 cents 88:101:102:117:132:152:153:176 SD: 0.9221 cents 90 x 104:120:135:155:157:180 SD: 1.3854 cents 92:106:107:123:138:159:160:184 SD: 1.2175 cents 94:108:109:125:141:162:163:188 SD: 1.0319 cents 97:112 x 129:146:167:169:194 SD: 1.8625 cents 98:113:114:131:147:169:170:196 SD: 1.3799 cents 99:114:115:132:149:171:172:198 SD: 1.0884 cents 100:115:116:133:150:173:174:200 SD: 0.9624 cents 106:122:123:141:159:183:184:212 SD: 0.8265 cents 108:124:125:144:162:186:188:216 SD: 0.7449 cents 114:131:132:152:171:197:198:228 SD: 0.6642 cents 120:138:139:160:180:207:209:240 SD: 0.4286 cents 200:230:232:267:300:345:348:400 SD: 0.3550 cents 226:260:262:301:339:390:393:452 SD: 0.3075 cents 288:331:334:384:432:497:501:576 SD: 0.2013 cents 306:352:355:408:459:528:532:612 SD: 0.1984 cents 414:476:480:552:621:714:720:828 SD: 0.0735 cents