Scala analysis: xen15-chalmers-triadic-reversed-diamond-57-46
Triadic reversed diamond for M=57/46, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 184/171 126.851329 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: 171/92 1073.148671 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 184/171 126.8513 1: 184/171 126.8513 2: 9747/8464 244.3423 3: 184/171 126.8513 4: 9/8 203.9100 major whole tone 5: 184/171 126.8513 6: 9747/8464 244.3423 7: 184/171 126.8513
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 184/171 126.851 cents 1: 1 9/8 203.910 cents major whole tone 1: 2 9747/8464 244.342 cents 2: 1 33856/29241 253.703 cents 2: 2 23/19 330.761 cents 2: 4 57/46 371.194 cents 3: 1 4232/3249 457.613 cents 3: 4 4/3 498.045 cents perfect fourth 3: 2 513/368 575.104 cents 4: 2 736/513 624.896 cents 4: 4 3/2 701.955 cents perfect fifth 4: 1 3249/2116 742.387 cents 5: 4 92/57 828.806 cents 5: 2 38/23 869.239 cents 5: 1 29241/16928 946.297 cents 6: 2 16928/9747 955.658 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 4 171/92 1073.149 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 : 126.9 371.2 498.0 702.0 828.8 1073.1 1200.0 126.9 : 244.3 371.2 575.1 702.0 946.3 1073.1 1200.0 371.2 : 126.9 330.8 457.6 702.0 828.8 955.7 1200.0 498.0 : 203.9 330.8 575.1 702.0 828.8 1073.1 1200.0 702.0 : 126.9 371.2 498.0 624.9 869.2 996.1 1200.0 828.8 : 244.3 371.2 498.0 742.4 869.2 1073.1 1200.0 1073.1: 126.9 253.7 498.0 624.9 828.8 955.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 126.8513 .. 244.3423 cents 1666737/1557376, 117.4910 cents 184/171, 126.8513 cents 2: 253.7027 .. 371.1937 cents 1666737/1557376, 117.4910 cents 286557184/285012027, 9.3603 cents 3: 457.6127 .. 575.1037 cents 1666737/1557376, 117.4910 cents 194672/185193, 86.4190 cents 4: 624.8963 .. 742.3873 cents 1666737/1557376, 117.4910 cents 270848/263169, 49.7927 cents 5: 828.8063 .. 946.2973 cents 1666737/1557376, 117.4910 cents 194672/185193, 86.4190 cents 6: 955.6577 .. 1073.1487 cents 1666737/1557376, 117.4910 cents 286557184/285012027, 9.3603 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 184/171, 126.8513 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9747/8464, 244.3423 cents Average / Smallest step : 1.351413 Largest / Average step : 1.425330 Largest / Smallest step : 1.926210 Median interval of one step : 184/171, 126.8513 cents, amount: 4 Most common interval of one step : 184/171, 126.8513 cents, amount: 4 Least squares average step : 172.52941 cents, oct.: 1207.70587 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABACABA Step pattern size order : SLSMSLS Scale is a Constant Structure, by a margin of 9.36032 cents Scale diversity : 1.395907 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.412545 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 : 286557184/285012027, 9.3603 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 minor thirds form a closed circle Scale is a complete diamond : 23 57 171 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 : 29241 (O: 29241 U: 29241) Highest odd numerator or denominator: 171 Scale harmonicity : 0.005951 Average absolute harmonicity : 0.219386 Specific harmonicity : 0.031905 Fundamental : 1/15732, -13.9414 octaves, 0.0166 Hz. Guide tone : 31464, 14.9414 octaves, 8231786.787 Hz. Exponens Consonantiae : 4.949916E+08, 28.88283 octaves Euler's gradus suavitatis : 94 Sum of Mann's harmonic distance : 442.5, average 63.21429 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 8.93198, average 1.27600 Sum of Tenney's harmonic distance : 17.99126, average 2.57018 Vogel's harmonic complexity : 50.57143 Wille's k value : 14620 Wilson's harmonic complexity : 96 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 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: 16 / 7 = 2.28571 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 10 28 33| Scale is weakly epimorphic with val: <7 10 29 33| Scale is weakly epimorphic with val: <7 10 29 34| Scale is weakly epimorphic with val: <7 10 30 34| Scale is weakly epimorphic with val: <7 10 30 35| Scale is weakly epimorphic with val: <7 10 31 35| Scale is JI-epimorphic with val: <7 11 27 29| Scale is weakly epimorphic with val: <7 11 27 30| Scale is JI-epimorphic with val: <7 11 28 30| Scale is weakly epimorphic with val: <7 11 28 31| Scale is JI-epimorphic with val: <7 11 29 31| Scale is weakly epimorphic with val: <7 11 29 32| Scale is JI-epimorphic with val: <7 11 30 32| = patent Scale is weakly epimorphic with val: <7 11 30 33| Scale is JI-epimorphic with val: <7 11 31 33| Scale is weakly epimorphic with val: <7 11 31 34| Scale is JI-epimorphic with val: <7 11 32 34| Scale is weakly epimorphic with val: <7 11 32 35| Scale is JI-epimorphic with val: <7 11 33 35| Scale is weakly epimorphic with val: <7 12 27 29| Scale is weakly epimorphic with val: <7 12 27 33| Scale is weakly epimorphic with val: <7 12 28 30| Scale is weakly epimorphic with val: <7 12 28 34| Scale is weakly epimorphic with val: <7 12 29 31| Scale is weakly epimorphic with val: <7 12 29 35| Scale is weakly epimorphic with val: <7 12 30 32| Scale is weakly epimorphic with val: <7 12 31 33| Scale is weakly epimorphic with val: <7 12 32 34| Scale is weakly epimorphic with val: <7 12 33 35|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 29.5386 c. M:-44.5772 c. Lebeng 9: 1 2 1 1 1 2 1 P M ME I SD: 24.5944 c. M:-35.2883 c. 10: 1 2 1 2 1 2 1 P M ME I SD: 11.9267 c. M:-18.0450 c. 19: 2 4 2 3 2 4 2 P T3 I SD: 5.6697 c. M:-7.7537 c. 29: 3 6 3 5 3 6 3 P T3 I SD: 1.7793 c. M:-2.7134 c. 65: 7 13 7 11 7 13 7 SP T3 I SD: 1.6637 c. M:-2.3794 c. 84: 9 17 9 14 9 17 9 SP T3 I SD: 1.3975 c. M: 1.9550 c. 94: 10 19 10 16 10 19 10 SP T3 I SD: 0.6856 c. M:-0.9809 c. 123: 13 25 13 21 13 25 13 SP T3 I SD: 0.3578 c. M:-0.4840 c. 236: 25 48 25 40 25 48 25 SP T3 I SD: 0.1994 c. M:-0.2673 c. 265: 28 54 28 45 28 54 28 SP T3 I SD: 0.0833 c. M:-0.1271 c. 388: 41 79 41 66 41 79 41 SP T3 I SD: 0.0701 c. M:-0.1069 c. 624: 66 127 66 106 66 127 66 SP T3 I SD: 0.0471 c. M:-0.0717 c. 653: 69 133 69 111 69 133 69 SP T3 I SD: 0.0348 c. M:-0.0519 c. 889: 94 181 94 151 94 181 94 SP T3 I SD: 0.0293 c. M:-0.0427 c. 1277: 135 260 135 217 135 260 135 SP T3 I SD: 0.0077 c. M:-0.0112 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: 18.5175 cents 4 x 5 x 6 x 7:8 S SD: 26.3532 cents 5 x 6:7 x 8:9:10 S SD: 23.2684 cents 6 x 7:8:9:10:11:12 S SD: 20.0936 cents 7:8 x 9 x 11:13:14 SD: 26.0725 cents 8:9:10:11:12:13:15:16 SD: 13.8289 cents 10:11:12:13:15:16:19:20 SD: 12.8883 cents 12:13:15:16:18:19:22:24 SD: 6.4479 cents 16:17:20:21:24:26:30:32 SD: 6.0901 cents 21:23:26:28:32:34:39:42 SD: 5.9166 cents 24:26:30:32:36:39:45:48 SD: 3.8651 cents 26:28:32:35:39:42:48:52 SD: 3.3607 cents 36:39:45:48:54:58:67:72 SD: 2.7881 cents 38:41:47:51:57:61:71:76 SD: 2.6023 cents 42:45:52:56:63:68:78:84 SD: 1.3393 cents 54:58:67:72:81:87:100:108 SD: 1.1566 cents 78:84:97:104:117:126:145:156 SD: 0.9360 cents 104:112:129:139:156:168:193:208 SD: 0.8078 cents 108:116:134:144:162:174:201:216 SD: 0.7801 cents 120:129:149:160:180:194:223:240 SD: 0.6898 cents 130:140:161:173:195:210:242:260 SD: 0.6876 cents 134:144:166:179:201:216:249:268 SD: 0.6536 cents 142:153:176:189:213:229:264:284 SD: 0.5920 cents 156:168:193:208:234:252:290:312 SD: 0.4886 cents 168:181:208:224:252:271:312:336 SD: 0.4510 cents 184:198:228:245:276:297:342:368 SD: 0.3369 cents 210:226:260:280:315:339:390:420 SD: 0.2973 cents 234:252:290:312:351:378:435:468 SD: 0.2970 cents 264:284:327:352:396:426:491:528 SD: 0.2018 cents 318:342:394:424:477:513:591:636 SD: 0.1835 cents 342:368:424:456:513:552:636:684 SD: 0.1794 cents 368:396:456:491:552:594:684:736 SD: 0.1692 cents 474:510:587:632:711:765:881:948 SD: 0.1486 cents 498:536:617:664:747:804:926:996 SD: 0.1391 cents 510:549:632:680:765:823:948:1020 SD: 0.1157 cents 552:594:684:736:828:891:1026:1104 SD: 0.0207 cents