Scala analysis: xen15-chalmers-triadic-reversed-diamond-33-28
Triadic reversed diamond for M=33/28, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 112/99 213.597962 2: 33/28 284.447037 undecimal minor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 56/33 915.552963 6: 99/56 986.402038 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 112/99 213.5980 1: 112/99 213.5980 2: 3267/3136 70.8491 3: 112/99 213.5980 4: 9/8 203.9100 major whole tone 5: 112/99 213.5980 6: 3267/3136 70.8491 7: 112/99 213.5980
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 3267/3136 70.849 cents 1: 1 9/8 203.910 cents major whole tone 1: 4 112/99 213.598 cents 2: 4 33/28 284.447 cents undecimal minor third 2: 2 14/11 417.508 cents undecimal diminished fourth or major third 2: 1 12544/9801 427.196 cents 3: 2 297/224 488.357 cents 3: 4 4/3 498.045 cents perfect fourth 3: 1 1568/1089 631.106 cents 4: 1 1089/784 568.894 cents two (undecimal minor third) 4: 4 3/2 701.955 cents perfect fifth 4: 2 448/297 711.643 cents 5: 1 9801/6272 772.804 cents 5: 2 11/7 782.492 cents undecimal augmented fifth 5: 4 56/33 915.553 cents 6: 4 99/56 986.402 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 6272/3267 1129.151 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 : 213.6 284.4 498.0 702.0 915.6 986.4 1200.0 213.6 : 70.8 284.4 488.4 702.0 772.8 986.4 1200.0 284.4 : 213.6 417.5 631.1 702.0 915.6 1129.2 1200.0 498.0 : 203.9 417.5 488.4 702.0 915.6 986.4 1200.0 702.0 : 213.6 284.4 498.0 711.6 782.5 996.1 1200.0 915.6 : 70.8 284.4 498.0 568.9 782.5 986.4 1200.0 986.4 : 213.6 427.2 498.0 711.6 915.6 1129.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.8491 .. 213.5980 cents 351232/323433, 142.7489 cents 3267/3136, 70.8491 cents 2: 284.4470 .. 427.1959 cents 351232/323433, 142.7489 cents 3267/3136, 70.8491 cents 3: 488.3570 .. 631.1059 cents 351232/323433, 142.7489 cents 2910897/2809856, 61.1611 cents 4: 568.8941 .. 711.6430 cents 351232/323433, 142.7489 cents 1185921/1229312,-62.2119 cents 5: 772.8041 .. 915.5530 cents 351232/323433, 142.7489 cents 2910897/2809856, 61.1611 cents 6: 986.4020 .. 1129.1509 cents 351232/323433, 142.7489 cents 3267/3136, 70.8491 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 3267/3136, 70.8491 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 112/99, 213.5980 cents Average / Smallest step : 2.419630 Largest / Average step : 1.245988 Largest / Smallest step : 3.014831 Median interval of one step : 112/99, 213.5980 cents, amount: 4 Most common interval of one step : 112/99, 213.5980 cents, amount: 4 Least squares average step : 171.29017 cents, oct.: 1199.03120 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2354-tone equal temperament with octave 2/1 degrees: 419 558 977 1377 1796 1935 2354 Least number of segments generator : 1179 of 601.020 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 2075 of 1057.774 cents and inv. generated superset size: 143 = 136 more = 2042.857% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABACABA Step pattern size order : LSLMLSL Scale is a Constant Structure, by a margin of 61.16111 cents Scale diversity : 1.308545 Lumma stability : 0.338099 Lumma impropriety factor : 0.051843 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 : 896/891, 9.6880 cents Number of recognisable fifths : 6, average 705.1843 cents Scale is Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords Best major thirds form a closed circle Scale is a complete diamond : 7 33 99 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 : 9801 (O: 9801 U: 9801) Highest odd numerator or denominator: 99 Scale harmonicity : 0.013405 Average absolute harmonicity : 0.228588 Specific harmonicity : 0.072352 Fundamental : 1/5544, -12.4367 octaves, 0.0472 Hz. Guide tone : 11088, 13.4367 octaves, 2900904.268 Hz. Exponens Consonantiae : 6.147187E+07, 25.87342 octaves Euler's gradus suavitatis : 48 Sum of Mann's harmonic distance : 265.5, average 37.92857 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 7.98254, average 1.14036 Sum of Tenney's harmonic distance : 16.17941, average 2.31134 Vogel's harmonic complexity : 27.57143 Wille's k value : 4900 Wilson's harmonic complexity : 48 Rectangular lattice diameter : 8 Triangular lattice diameter : 6 Lattice compactness : 103.40447, average 3.69302 Lattice compactness (without 2's) : 59.16021, average 2.11286 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 4 0.57143 16 1 3: -2 .. 2 0.00000 8 2 7: -1 .. 1 0.00000 4 11: -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 19 22| Scale is weakly epimorphic with val: <7 10 20 22| Scale is weakly epimorphic with val: <7 10 20 23| Scale is weakly epimorphic with val: <7 10 21 23| Scale is weakly epimorphic with val: <7 10 21 24| Scale is weakly epimorphic with val: <7 10 22 24| Scale is weakly epimorphic with val: <7 10 22 25| Scale is weakly epimorphic with val: <7 11 18 22| Scale is JI-epimorphic with val: <7 11 18 23| Scale is weakly epimorphic with val: <7 11 19 23| Scale is JI-epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 11 20 24| = patent Scale is JI-epimorphic with val: <7 11 20 25| Scale is weakly epimorphic with val: <7 11 21 25| Scale is JI-epimorphic with val: <7 11 21 26| Scale is weakly epimorphic with val: <7 11 22 26| Scale is weakly epimorphic with val: <7 12 18 23| Scale is weakly epimorphic with val: <7 12 18 26| Scale is weakly epimorphic with val: <7 12 19 24| Scale is weakly epimorphic with val: <7 12 20 25| Scale is weakly epimorphic with val: <7 12 21 22| Scale is weakly epimorphic with val: <7 12 21 26| Scale is weakly epimorphic with val: <7 12 22 23|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 39.4743 c. M: 58.4101 c. Lebeng 9: 2 0 2 1 2 0 2 N T3 I SD: 35.3662 c. M: 53.0687 c. 10: 2 0 2 2 2 0 2 N M DE I SD: 29.2684 c. M: 44.4470 c. 12: 2 1 2 2 2 1 2 P M ME I SD: 11.0921 c. M: 15.5530 c. G.Phrygian, M.Dorian, M.Hypomixolydian, Kafi That, Mela Kharaharapriya, Raga Bageshri, Bhimpalasi, Huseni, Kanara, Kapi, Nayaki Kanada, Ritigaula, Sriraga, Mischung 5, Gregorian nr.8, Eskimo Heptatonic, Yu: China, Hyojo, Oshikicho, Banshikicho: Japan, Nam: Vietnam 17: 3 1 3 3 3 1 3 N M DE I SD: 2.5729 c. M:-3.9274 c. Supra-7 67: 12 4 12 11 12 4 12 N T3 I SD: 2.2767 c. M:-3.4475 c. 72: 13 4 13 12 13 4 13 N T3 I SD: 2.0339 c. M:-3.0687 c. 84: 15 5 15 14 15 5 15 N T3 I SD: 1.2985 c. M: 1.9550 c. 101: 18 6 18 17 18 6 18 N T3 I SD: 0.6530 c. M:-0.9649 c. 118: 21 7 21 20 21 7 21 N T3 I SD: 0.2127 c. M: 0.2987 c. 135: 24 8 24 23 24 8 24 N T3 I SD: 0.2010 c. M:-0.2672 c. 253: 45 15 45 43 45 15 45 N T3 I SD: 0.1132 c. M: 0.1592 c. 612: 109 36 109 104 109 36 109 N T3 I SD: 0.0987 c. M:-0.1333 c. 730: 130 43 130 124 130 43 130 N T3 I SD: 0.0666 c. M:-0.1007 c. 848: 151 50 151 144 151 50 151 N T3 I SD: 0.0571 c. M:-0.0813 c. 865: 154 51 154 147 154 51 154 N T3 I SD: 0.0375 c. M:-0.0540 c. 983: 175 58 175 167 175 58 175 N T3 I SD: 0.0225 c. M:-0.0338 c. 1118: 199 66 199 190 199 66 199 N T3 I SD: 0.0089 c. M:-0.0128 c. 2354: 419 139 419 400 419 139 419 N T3 I SD: 0.0035 c. M: 0.0050 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: 10.3981 cents 4 x 5 x 6 x 7:8 S SD: 25.8430 cents 5 x 6:7 x 8:9:10 S SD: 27.8982 cents 6 x 7:8:9:10:11:12 S SD: 12.0716 cents 7:8 x 9:11:12 x 14 SD: 21.0410 cents 8:9 x 11:12 x 14:16 SD: 11.3856 cents 10:11:12:13:15:17:18:20 SD: 11.2832 cents 11:12:13:15:17:19 x 22 SD: 15.9081 cents 12 x 14:16:18:20:21:24 S SD: 6.6477 cents 13:15 x 17:20:22:23:26 SD: 10.8545 cents 14:16:17:19:21:24:25:28 SD: 9.6157 cents 15:17:18:20:23:25:27:30 SD: 9.4509 cents 16:18:19:21:24:27:28:32 SD: 5.3656 cents 19 x 22:25:29:32:34:38 SD: 9.1054 cents 20:23:24:27:30:34:35:40 SD: 7.2260 cents 21:24:25:28:32:36:37:42 SD: 5.8867 cents 22:25:26:29:33:37:39:44 SD: 3.8793 cents 30:34:35:40:45:51:53:60 SD: 2.5926 cents 39:44:46:52:59:66:69:78 SD: 2.3302 cents 44:50:52:59:66:75:78:88 SD: 2.3058 cents 46:52:54:61:69:78:81:92 SD: 1.9517 cents 52:59:61:69:78:88:92:104 SD: 1.9431 cents 56:63:66:75:84:95:99:112 SD: 1.7707 cents 60:68:71:80:90:102:106:120 SD: 1.1881 cents 78:88:92:104:117:132:138:156 SD: 0.9998 cents 90:102:106:120:135:153:159:180 SD: 0.6670 cents 129:146:152:172:194:219:228:258 SD: 0.6597 cents 138:156:163:184:207:234:244:276 SD: 0.6078 cents 146:165:172:195:219:248:258:292 SD: 0.5699 cents 152:172:179:203:228:258:269:304 SD: 0.5291 cents 162:183:191:216:243:275:286:324 SD: 0.5159 cents 168:190:198:224:252:285:297:336 SD: 0.1115 cents 426:482:502:568:639:723:753:852 SD: 0.0664 cents 594:672:700:792:891:1008:1050:1188 SD: 0.0357 cents