Scala analysis: xen15-chalmers-triadic-reversed-diamond-27-22
Triadic reversed diamond for M=27/22, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 88/81 143.497939 2nd undecimal neutral second 2: 27/22 354.547060 neutral third, Zalzal wosta of al-Farabi 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 44/27 845.452940 neutral sixth 6: 81/44 1056.502061 2nd undecimal neutral seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 88/81 143.4979 2nd undecimal neutral second 1: 88/81 143.4979 2nd undecimal neutral second 2: 2187/1936 211.0491 3: 88/81 143.4979 2nd undecimal neutral second 4: 9/8 203.9100 major whole tone 5: 88/81 143.4979 2nd undecimal neutral second 6: 2187/1936 211.0491 7: 88/81 143.4979 2nd undecimal neutral second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 88/81 143.498 cents 2nd undecimal neutral second 1: 1 9/8 203.910 cents major whole tone 1: 2 2187/1936 211.049 cents 2: 1 7744/6561 286.996 cents two (2nd undecimal neutral second) 2: 2 11/9 347.408 cents undecimal neutral third 2: 4 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 3: 1 968/729 490.906 cents 3: 4 4/3 498.045 cents perfect fourth 3: 2 243/176 558.457 cents 4: 2 352/243 641.543 cents 4: 4 3/2 701.955 cents perfect fifth 4: 1 729/484 709.094 cents two (neutral third, Zalzal wosta of al-Farabi) 5: 4 44/27 845.453 cents neutral sixth 5: 2 18/11 852.592 cents undecimal neutral sixth 5: 1 6561/3872 913.004 cents 6: 2 3872/2187 988.951 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 4 81/44 1056.502 cents 2nd undecimal neutral seventh 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 : 143.5 354.5 498.0 702.0 845.5 1056.5 1200.0 143.5 : 211.0 354.5 558.5 702.0 913.0 1056.5 1200.0 354.5 : 143.5 347.4 490.9 702.0 845.5 989.0 1200.0 498.0 : 203.9 347.4 558.5 702.0 845.5 1056.5 1200.0 702.0 : 143.5 354.5 498.0 641.5 852.6 996.1 1200.0 845.5 : 211.0 354.5 498.0 709.1 852.6 1056.5 1200.0 1056.5: 143.5 287.0 498.0 641.5 845.5 989.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 143.4979 .. 211.0491 cents 177147/170368, 67.5512 cents 88/81, 143.4979 cents 2: 286.9959 .. 354.5471 cents 177147/170368, 67.5512 cents 14992384/14348907, 75.9468 cents 3: 490.9059 .. 558.4571 cents 177147/170368, 67.5512 cents 21296/19683, 136.3588 cents 4: 641.5429 .. 709.0941 cents 177147/170368, 67.5512 cents 61952/59049, 83.0859 cents 5: 845.4529 .. 913.0041 cents 177147/170368, 67.5512 cents 21296/19683, 136.3588 cents 6: 988.9509 .. 1056.5021 cents 177147/170368, 67.5512 cents 14992384/14348907, 75.9468 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 88/81, 143.4979 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 2187/1936, 211.0491 cents Average / Smallest step : 1.194641 Largest / Average step : 1.231120 Largest / Smallest step : 1.470747 Median interval of one step : 88/81, 143.4979 cents, amount: 4 Most common interval of one step : 88/81, 143.4979 cents, amount: 4 Least squares average step : 172.29160 cents, oct.: 1206.04121 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 75.94676 cents Scale diversity : 1.281232 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.662244 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 : 243/242, 7.1391 cents Number of recognisable fifths : 5, average 703.3828 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 : 11 27 81 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 : 11 Odd number limit : 6561 (O: 6561 U: 6561) Highest odd numerator or denominator: 81 Scale harmonicity : 0.015950 Average absolute harmonicity : 0.231871 Specific harmonicity : 0.086288 Fundamental : 1/3564, -11.7993 octaves, 0.0734 Hz. Guide tone : 7128, 12.7993 octaves, 1864867.029 Hz. Exponens Consonantiae : 2.540419E+07, 24.59856 octaves Euler's gradus suavitatis : 42 Sum of Mann's harmonic distance : 214.5, average 30.64286 Mersenne's string divisions : 220481625 Sum of van Prooijen's expressibility: 7.63394, average 1.09056 Sum of Tenney's harmonic distance : 15.41187, average 2.20170 Vogel's harmonic complexity : 25.57143 Wille's k value : 3280 Wilson's harmonic complexity : 46 Rectangular lattice diameter : 10 Triangular lattice diameter : 8 Lattice compactness : 115.73610, average 4.13343 Lattice compactness (without 2's) : 95.51346, average 3.41120 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 3 0.57143 12 1 3: -4 .. 4 0.00000 16 2 11: -1 .. 1 0.00000 4 4 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 20 / 7 = 2.85714 Scale is weakly epimorphic with val: <7 10 24| Scale is weakly epimorphic with val: <7 10 25| Scale is JI-epimorphic with val: <7 11 24| = patent Scale is weakly epimorphic with val: <7 11 25| Scale is weakly epimorphic with val: <7 12 23| Scale is weakly epimorphic with val: <7 12 26|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 18.3656 c. M:-27.9306 c. Lebeng 10: 1 2 1 2 1 2 1 P M ME I SD: 16.1024 c. M:-23.4979 c. 17: 2 3 2 3 2 3 2 SP M ME I SD: 2.5852 c. M:-3.9274 c. Neutral Dorian, Maqamic-7 41: 5 7 5 7 5 7 5 SP M DE I SD: 2.3539 c. M:-3.3275 c. Maqamic-7 58: 7 10 7 10 7 10 7 SP M DE I SD: 1.8491 c. M: 2.8229 c. 75: 9 13 9 13 9 13 9 SP M DE I SD: 1.7665 c. M:-2.5471 c. 92: 11 16 11 16 11 16 11 SP M DE I SD: 1.8014 c. M: 2.3928 c. 101: 12 18 12 17 12 18 12 SP T3 I SD: 1.2365 c. M:-1.8886 c. 118: 14 21 14 20 14 21 14 SP T3 I SD: 0.9639 c. M:-1.3851 c. 125: 15 22 15 21 15 22 15 SP T3 I SD: 0.7583 c. M:-1.1550 c. 142: 17 25 17 24 17 25 17 SP T3 I SD: 0.3672 c. M:-0.5466 c. 159: 19 28 19 27 19 28 19 SP T3 I SD: 0.1120 c. M:-0.1699 c. 518: 62 91 62 88 62 91 62 SP T3 I SD: 0.0915 c. M:-0.1314 c. 677: 81 119 81 115 81 119 81 SP T3 I SD: 0.0503 c. M:-0.0767 c. 836: 100 147 100 142 100 147 100 SP T3 I SD: 0.0317 c. M:-0.0427 c. 853: 102 150 102 145 102 150 102 SP T3 I SD: 0.0272 c. M: 0.0380 c. 1012: 121 178 121 172 121 178 121 SP T3 I SD: 0.0155 c. M: 0.0213 c. 1689: 202 297 202 287 202 297 202 SP T3 I SD: 0.0139 c. M: 0.0189 c. 1848: 221 325 221 314 221 325 221 SP T3 I SD: 0.0060 c. M:-0.0086 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: 12.9686 cents 4 x 5 x 6 x 7:8 S SD: 23.3134 cents 5 x 6:7 x 8:9:10 S SD: 21.1387 cents 6 x 7:8:9:10:11:12 S SD: 16.0310 cents 7:8 x 9 x 11:13:14 SD: 25.1764 cents 8:9:10:11:12:13:15:16 SD: 13.1941 cents 10:11:12:13:15:16:18:20 SD: 11.4465 cents 12:13:15:16:18:20:22:24 SD: 7.2815 cents 14:15:17:19:21:23:26:28 SD: 6.8269 cents 18:20:22:24:27:29:33:36 SD: 6.4000 cents 21:23:26:28:32:34:39:42 SD: 5.5851 cents 22:24:27:29:33:36:41:44 SD: 4.3907 cents 24:26:29:32:36:39:44:48 SD: 4.1018 cents 26:28:32:35:39:42:48:52 SD: 4.0027 cents 30:33:37:40:45:49:55:60 SD: 3.5041 cents 32:35:39:43:48:52:59:64 SD: 3.1751 cents 36:39:44:48:54:59:66:72 SD: 2.1305 cents 44:48:54:59:66:72:81:88 SD: 2.0109 cents 48:52:59:64:72:78:88:96 SD: 1.4750 cents 70:76:86:93:105:114:129:140 SD: 0.9856 cents 84:91:103:112:126:137:155:168 SD: 0.9594 cents 92:100:113:123:138:150:169:184 SD: 0.8958 cents 102:111:125:136:153:166:188:204 SD: 0.7062 cents 114:124:140:152:171:186:210:228 SD: 0.4759 cents 162:176:199:216:243:264:298:324 SD: 0.2944 cents 246:267:302:328:369:401:453:492 SD: 0.2709 cents 264:287:324:352:396:430:486:528 SD: 0.2045 cents 300:326:368:400:450:489:552:600 SD: 0.1902 cents 348:378:427:464:522:567:641:696 SD: 0.1648 cents 440:478:540:587:660:717:810:880 SD: 0.1416 cents 510:554:626:680:765:831:939:1020 SD: 0.0690 cents