Scala analysis: xen15-chalmers-triadic-reversed-diamond-39-34
Triadic reversed diamond for M=39/34, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 39/34 237.527253 2: 136/117 260.517746 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 117/68 939.482254 6: 68/39 962.472747 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 39/34 237.5273 1: 39/34 237.5273 2: 4624/4563 22.9905 3: 39/34 237.5273 4: 9/8 203.9100 major whole tone 5: 39/34 237.5273 6: 4624/4563 22.9905 7: 39/34 237.5273
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 4624/4563 22.990 cents 1: 1 9/8 203.910 cents major whole tone 1: 4 39/34 237.527 cents 2: 4 136/117 260.518 cents 2: 2 351/272 441.437 cents 2: 1 1521/1156 475.055 cents 3: 2 17/13 464.428 cents 3: 4 4/3 498.045 cents perfect fourth 3: 1 13689/9248 678.965 cents 4: 1 18496/13689 521.035 cents 4: 4 3/2 701.955 cents perfect fifth 4: 2 26/17 735.572 cents 5: 1 2312/1521 724.945 cents 5: 2 544/351 758.563 cents 5: 4 117/68 939.482 cents 6: 4 68/39 962.473 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 4563/2312 1177.010 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 : 237.5 260.5 498.0 702.0 939.5 962.5 1200.0 237.5 : 23.0 260.5 464.4 702.0 724.9 962.5 1200.0 260.5 : 237.5 441.4 679.0 702.0 939.5 1177.0 1200.0 498.0 : 203.9 441.4 464.4 702.0 939.5 962.5 1200.0 702.0 : 237.5 260.5 498.0 735.6 758.6 996.1 1200.0 939.5 : 23.0 260.5 498.0 521.0 758.6 962.5 1200.0 962.5 : 237.5 475.1 498.0 735.6 939.5 1177.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 22.9905 .. 237.5273 cents 177957/157216, 214.5368 cents 4624/4563, 22.9905 cents 2: 260.5177 .. 475.0545 cents 177957/157216, 214.5368 cents 4624/4563, 22.9905 cents 3: 464.4277 .. 678.9645 cents 177957/157216, 214.5368 cents 19652/19773,-10.6268 cents 4: 521.0355 .. 735.5723 cents 177957/157216, 214.5368 cents 171051008/187388721,-157.9290 cents 5: 724.9455 .. 939.4823 cents 177957/157216, 214.5368 cents 19652/19773,-10.6268 cents 6: 962.4727 .. 1177.0095 cents 177957/157216, 214.5368 cents 4624/4563, 22.9905 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 4624/4563, 22.9905 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 39/34, 237.5273 cents Average / Smallest step : 7.456498 Largest / Average step : 1.385576 Largest / Smallest step : 10.331542 Median interval of one step : 39/34, 237.5273 cents, amount: 4 Most common interval of one step : 39/34, 237.5273 cents, amount: 4 Least squares average step : 170.94832 cents, oct.: 1196.63827 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 10.62676 cents Scale diversity : 1.117587 Lumma stability : 0.076635 Lumma impropriety factor : 0.149319 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 : 19773/19652, 10.6268 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 : 17 39 117 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 : 17 Odd number limit : 13689 (O: 13689 U: 13689) Highest odd numerator or denominator: 117 Scale harmonicity : 0.008319 Average absolute harmonicity : 0.222247 Specific harmonicity : 0.044697 Fundamental : 1/7956, -12.9578 octaves, 0.0329 Hz. Guide tone : 15912, 13.9578 octaves, 4162985.995 Hz. Exponens Consonantiae : 1.265959E+08, 26.91566 octaves Euler's gradus suavitatis : 70 Sum of Mann's harmonic distance : 316.5, average 45.21429 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 8.27274, average 1.18182 Sum of Tenney's harmonic distance : 16.80690, average 2.40099 Vogel's harmonic complexity : 38.57143 Wille's k value : 6844 Wilson's harmonic complexity : 72 Rectangular lattice diameter : 8 Triangular lattice diameter : 6 Lattice compactness : 86.13497, average 3.07625 Lattice compactness (without 2's) : 59.16021, average 2.11286 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 3 0.57143 12 1 3: -2 .. 2 0.00000 8 2 13: -1 .. 1 0.00000 4 17: -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 24 28| Scale is weakly epimorphic with val: <7 10 24 29| Scale is weakly epimorphic with val: <7 10 25 29| Scale is weakly epimorphic with val: <7 10 25 30| Scale is weakly epimorphic with val: <7 10 26 30| Scale is weakly epimorphic with val: <7 10 26 31| Scale is weakly epimorphic with val: <7 10 27 31| Scale is weakly epimorphic with val: <7 10 27 32| Scale is weakly epimorphic with val: <7 10 28 32| Scale is weakly epimorphic with val: <7 11 24 26| Scale is JI-epimorphic with val: <7 11 24 27| Scale is weakly epimorphic with val: <7 11 25 27| Scale is JI-epimorphic with val: <7 11 25 28| Scale is weakly epimorphic with val: <7 11 26 28| Scale is JI-epimorphic with val: <7 11 26 29| = patent Scale is weakly epimorphic with val: <7 11 27 29| Scale is JI-epimorphic with val: <7 11 27 30| Scale is weakly epimorphic with val: <7 11 28 30| Scale is JI-epimorphic with val: <7 11 28 31| Scale is weakly epimorphic with val: <7 11 29 31| Scale is JI-epimorphic with val: <7 11 29 32| Scale is weakly epimorphic with val: <7 12 24 26| Scale is weakly epimorphic with val: <7 12 24 30| Scale is weakly epimorphic with val: <7 12 25 27| Scale is weakly epimorphic with val: <7 12 25 31| Scale is weakly epimorphic with val: <7 12 26 28| Scale is weakly epimorphic with val: <7 12 26 32| Scale is weakly epimorphic with val: <7 12 27 29| Scale is weakly epimorphic with val: <7 12 28 30| Scale is weakly epimorphic with val: <7 12 29 31|
FIT/MODE
7: 1 0 2 1 1 0 2 N T3 SD: 66.2329 c. M: 105.3299 c. 8: 2 0 1 2 1 0 2 N I SD: 47.1169 c. M:-62.4727 c. 9: 2 0 2 1 2 0 2 N T3 I SD: 24.6819 c. M:-35.2883 c. 10: 2 0 2 2 2 0 2 N M DE I SD: 14.6650 c. M: 20.5177 c. 14: 3 0 3 2 3 0 3 N T3 I SD: 13.7313 c. M:-19.6156 c. 19: 4 0 4 3 4 0 4 N T3 I SD: 9.8913 c. M:-15.1043 c. 24: 5 0 5 4 5 0 5 N T3 I SD: 8.7833 c. M:-12.4727 c. 29: 6 0 6 5 6 0 6 N T3 I SD: 8.7444 c. M: 12.2419 c. 31: 6 1 6 5 6 1 6 N T3 I SD: 6.8412 c. M: 10.4500 c. 36: 7 1 7 6 7 1 7 N T3 I SD: 4.1134 c. M: 6.1489 c. 41: 8 1 8 7 8 1 8 N T3 I SD: 2.3938 c. M:-3.3809 c. 46: 9 1 9 8 9 1 9 N T3 I SD: 1.9554 c. M:-2.7446 c. 60: 12 1 12 10 12 1 12 N T3 I SD: 1.7075 c. M:-2.4727 c. 96: 19 2 19 16 19 2 19 N T3 I SD: 1.4882 c. M: 1.9823 c. 101: 20 2 20 17 20 2 20 N T3 I SD: 0.6958 c. M:-0.9649 c. 106: 21 2 21 18 21 2 21 N T3 I SD: 0.1393 c. M:-0.2086 c. 359: 71 7 71 61 71 7 71 N T3 I SD: 0.1542 c. M: 0.2065 c. 465: 92 9 92 79 92 9 92 N T3 I SD: 0.0899 c. M: 0.1274 c. 571: 113 11 113 97 113 11 113 N T3 I SD: 0.0515 c. M: 0.0777 c. 677: 134 13 134 115 134 13 134 N T3 I SD: 0.0302 c. M: 0.0436 c. 783: 155 15 155 133 155 15 155 N T3 I SD: 0.0257 c. M:-0.0393 c. 1359: 269 26 269 231 269 26 269 N T3 I SD: 0.0241 c. M: 0.0321 c. 1824: 361 35 361 310 361 35 361 N T3 I SD: 0.0182 c. M:-0.0273 c. 1930: 382 37 382 328 382 37 382 N T3 I SD: 0.0107 c. M:-0.0143 c. 2036: 403 39 403 346 403 39 403 N T3 I SD: 0.0065 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: 18.3745 cents 4 x x 5:6 x 7:8 S SD: 27.9779 cents 5 x 6:7:8 x 9:10 S SD: 32.0598 cents 6 x 7:8:9:10 x 12 S SD: 11.0977 cents 7:8 x 9:11:12 x 14 SD: 20.5241 cents 8:9 x 11:12 x 14:16 SD: 12.6625 cents 9:10 x 12:14:15:16:18 S SD: 17.6158 cents 10:11:12:13:15:17 x 20 SD: 17.2028 cents 11 x 13:15:17:19 x 22 SD: 14.2169 cents 12 x 14:16:18 x 21:24 S SD: 1.7969 cents 13:15 x 17:20:22:23:26 SD: 11.3255 cents 14:16 x 19:21:24 x 28 SD: 6.3864 cents 15:17 x 20:23 x 26:30 SD: 8.9140 cents 16:18:19:21:24 x 28:32 SD: 9.5488 cents 17 x 20:23:26:29:30:34 SD: 8.9106 cents 18 x 21:24:27:31 x 36 SD: 1.3125 cents 19 x 22:25:29 x 33:38 SD: 7.8038 cents 20:23 x 27:30:34:35:40 SD: 5.1555 cents 21:24 x 28:32:36:37:42 SD: 5.6552 cents 22:25:26:29:33:38 x 44 SD: 6.5038 cents 23:26:27:31:35 x 40:46 SD: 7.3044 cents 24 x 28:32:36:41:42:48 SD: 2.5488 cents 25 x 29:33:38:43:44:50 SD: 5.5394 cents 26:30 x 35:39:45 x 52 SD: 4.3959 cents 27:31 x 36:41:46:47:54 SD: 4.5748 cents 28:32:33:37:42:48:49:56 SD: 4.3677 cents 30:34:35:40:45 x 52:60 SD: 4.0104 cents 31 x 36:41:47:53:54:62 SD: 4.3013 cents 32 x 37:43:48:55:56:64 SD: 2.9319 cents 33:38 x 44:50:57:58:66 SD: 4.0283 cents 34:39:40:45:51 x 59:68 SD: 4.3003 cents 35:40:41:47:53:60:61:70 SD: 3.7309 cents 36:41:42:48:54:62:63:72 SD: 2.1972 cents 38 x 44:51:57:65:66:76 SD: 2.9912 cents 39:45 x 52:59:67:68:78 SD: 3.0207 cents 40:46 x 53:60:69:70:80 SD: 2.3422 cents 41:47:48:55:62:71 x 82 SD: 4.0344 cents 42:48:49:56:63:72:73:84 SD: 1.7551 cents 45 x 52:60:68:77:78:90 SD: 3.5875 cents 46:53 x 61:69:79:80:92 SD: 2.2259 cents 48:55:56:64:72:83:84:96 SD: 1.7973 cents 51 x 59:68:77:88:89:102 SD: 2.4826 cents 52:60 x 69:78:89:91:104 SD: 2.8754 cents 54:62:63:72:81:93:94:108 SD: 1.0476 cents 58 x 67:77:87:100:101:116 SD: 2.2965 cents 60:69:70:80:90:103:105:120 SD: 1.5385 cents 62:71:72:83:93:107:108:124 SD: 1.3525 cents 68:78:79:91:102:117:119:136 SD: 1.2905 cents 74:85:86:99:111:127:129:148 SD: 1.1018 cents 90:103:105:120:135:155:157:180 SD: 1.1009 cents 94:108:109:125:141:162:164:188 SD: 1.0703 cents 104:119:121:139:156:179:181:208 SD: 0.9953 cents 110:126:128:147:165:189:192:220 SD: 0.8335 cents 122:140:142:163:183:210:213:244 SD: 0.7019 cents 129:148:150:172:194:222:225:258 SD: 0.6531 cents 136:156:158:181:204:234:237:272 SD: 0.4928 cents 190:218:221:253:285:327:331:380 SD: 0.4310 cents 198:227:230:264:297:341:345:396 SD: 0.3553 cents 204:234:237:272:306:351:356:408 SD: 0.2522 cents 246:282:286:328:369:423:429:492 SD: 0.2276 cents 258:296:300:344:387:444:450:516 SD: 0.1383 cents 456:523:530:608:684:785:795:912 SD: 0.1370 cents 468:537:544:624:702:805:816:936 SD: 0.1088 cents