Scala analysis: xen15-chalmers-triadic-reversed-diamond-21-17
Triadic reversed diamond for M=21/17, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 68/63 132.219501 supraminor second 2: 21/17 365.825498 submajor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 34/21 834.174502 supraminor sixth 6: 63/34 1067.780499 submajor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 68/63 132.2195 supraminor second 1: 68/63 132.2195 supraminor second 2: 1323/1156 233.6060 3: 68/63 132.2195 supraminor second 4: 9/8 203.9100 major whole tone 5: 68/63 132.2195 supraminor second 6: 1323/1156 233.6060 7: 68/63 132.2195 supraminor second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 68/63 132.220 cents supraminor second 1: 1 9/8 203.910 cents major whole tone 1: 2 1323/1156 233.606 cents 2: 1 4624/3969 264.439 cents two (supraminor second) 2: 2 17/14 336.130 cents supraminor third 2: 4 21/17 365.825 cents submajor third 3: 1 578/441 468.349 cents 3: 4 4/3 498.045 cents perfect fourth 3: 2 189/136 569.735 cents 4: 2 272/189 630.265 cents 4: 4 3/2 701.955 cents perfect fifth 4: 1 441/289 731.651 cents two (submajor third) 5: 4 34/21 834.175 cents supraminor sixth 5: 2 28/17 863.870 cents submajor sixth 5: 1 3969/2312 935.561 cents 6: 2 2312/1323 966.394 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 4 63/34 1067.780 cents submajor 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 : 132.2 365.8 498.0 702.0 834.2 1067.8 1200.0 132.2 : 233.6 365.8 569.7 702.0 935.6 1067.8 1200.0 365.8 : 132.2 336.1 468.3 702.0 834.2 966.4 1200.0 498.0 : 203.9 336.1 569.7 702.0 834.2 1067.8 1200.0 702.0 : 132.2 365.8 498.0 630.3 863.9 996.1 1200.0 834.2 : 233.6 365.8 498.0 731.7 863.9 1067.8 1200.0 1067.8: 132.2 264.4 498.0 630.3 834.2 966.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 132.2195 .. 233.6060 cents 83349/78608, 101.3865 cents 68/63, 132.2195 cents 2: 264.4390 .. 365.8255 cents 83349/78608, 101.3865 cents 5345344/5250987, 30.8330 cents 3: 468.3490 .. 569.7355 cents 83349/78608, 101.3865 cents 9826/9261, 102.5235 cents 4: 630.2645 .. 731.6510 cents 83349/78608, 101.3865 cents 36992/35721, 60.5290 cents 5: 834.1745 .. 935.5610 cents 83349/78608, 101.3865 cents 9826/9261, 102.5235 cents 6: 966.3940 .. 1067.7805 cents 83349/78608, 101.3865 cents 5345344/5250987, 30.8330 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 68/63, 132.2195 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 1323/1156, 233.6060 cents Average / Smallest step : 1.296545 Largest / Average step : 1.362702 Largest / Smallest step : 1.766804 Median interval of one step : 68/63, 132.2195 cents, amount: 4 Most common interval of one step : 68/63, 132.2195 cents, amount: 4 Least squares average step : 172.45272 cents, oct.: 1207.16905 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 30.83301 cents Scale diversity : 1.382750 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.493068 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 : 294/289, 29.6960 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 : 17 21 63 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 : 3969 (O: 3969 U: 3969) Highest odd numerator or denominator: 63 Scale harmonicity : 0.010585 Average absolute harmonicity : 0.225038 Specific harmonicity : 0.056787 Fundamental : 1/2142, -11.0647 octaves, 0.1221 Hz. Guide tone : 4284, 12.0647 octaves, 1120803.922 Hz. Exponens Consonantiae : 9.176328E+06, 23.12949 octaves Euler's gradus suavitatis : 56 Sum of Mann's harmonic distance : 168.0, average 24.00000 Mersenne's string divisions : 557710230 Sum of van Prooijen's expressibility: 7.19736, average 1.02819 Sum of Tenney's harmonic distance : 14.52740, average 2.07534 Vogel's harmonic complexity : 31.57143 Wille's k value : 1984 Wilson's harmonic complexity : 60 Rectangular lattice diameter : 8 Triangular lattice diameter : 6 Lattice compactness : 74.52700, average 2.66168 Lattice compactness (without 2's) : 59.16021, average 2.11286 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.57143 8 1 3: -2 .. 2 0.00000 8 2 7: -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 18 29| Scale is weakly epimorphic with val: <7 10 18 30| Scale is weakly epimorphic with val: <7 10 19 30| Scale is weakly epimorphic with val: <7 10 19 31| Scale is weakly epimorphic with val: <7 10 20 31| Scale is weakly epimorphic with val: <7 10 20 32| Scale is weakly epimorphic with val: <7 10 21 26| Scale is weakly epimorphic with val: <7 10 21 32| Scale is weakly epimorphic with val: <7 10 22 26| Scale is weakly epimorphic with val: <7 10 22 27| Scale is JI-epimorphic with val: <7 11 18 27| Scale is weakly epimorphic with val: <7 11 18 28| Scale is JI-epimorphic with val: <7 11 19 28| Scale is weakly epimorphic with val: <7 11 19 29| Scale is JI-epimorphic with val: <7 11 20 29| = patent Scale is weakly epimorphic with val: <7 11 20 30| Scale is JI-epimorphic with val: <7 11 21 30| Scale is weakly epimorphic with val: <7 11 21 31| Scale is JI-epimorphic with val: <7 11 22 31| Scale is weakly epimorphic with val: <7 11 22 32| Scale is weakly epimorphic with val: <7 12 18 27| Scale is weakly epimorphic with val: <7 12 18 31| Scale is weakly epimorphic with val: <7 12 19 28| Scale is weakly epimorphic with val: <7 12 19 32| Scale is weakly epimorphic with val: <7 12 20 26| Scale is weakly epimorphic with val: <7 12 20 29| Scale is weakly epimorphic with val: <7 12 21 27| Scale is weakly epimorphic with val: <7 12 21 30| Scale is weakly epimorphic with val: <7 12 22 28| Scale is weakly epimorphic with val: <7 12 22 31|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 25.7940 c. M: 39.2091 c. Lebeng 9: 1 2 1 1 1 2 1 P M ME I SD: 26.2646 c. M:-35.2883 c. 10: 1 2 1 2 1 2 1 P M ME I SD: 12.0579 c. M:-18.0450 c. 17: 2 3 2 3 2 3 2 SP M ME I SD: 8.6463 c. M: 12.8843 c. Neutral Dorian, Maqamic-7 19: 2 4 2 3 2 4 2 P T3 I SD: 8.6046 c. M: 13.1219 c. 26: 3 5 3 4 3 5 3 SP T3 I SD: 6.4060 c. M:-9.6473 c. 29: 3 6 3 5 3 6 3 P T3 I SD: 5.6302 c. M:-8.0816 c. 36: 4 7 4 6 4 7 4 SP T3 I SD: 1.2840 c. M: 1.9550 c. Savas Soft Chromatic 2nd Byzantine mode 82: 9 16 9 14 9 16 9 SP T3 I SD: 0.3770 c. M:-0.5122 c. 118: 13 23 13 20 13 23 13 SP T3 I SD: 0.2030 c. M: 0.2762 c. 200: 22 39 22 34 22 39 22 SP T3 I SD: 0.1518 c. M:-0.2195 c. 318: 35 62 35 54 35 62 35 SP T3 I SD: 0.1419 c. M:-0.2122 c. 518: 57 101 57 88 57 101 57 SP T3 I SD: 0.1411 c. M: 0.1977 c. 571: 63 111 63 97 63 111 63 SP T3 I SD: 0.1265 c. M:-0.1798 c. 653: 72 127 72 111 72 127 72 SP T3 I SD: 0.0870 c. M: 0.1287 c. 735: 81 143 81 125 81 143 81 SP T3 I SD: 0.0763 c. M: 0.1112 c. 771: 85 150 85 131 85 150 85 SP T3 I SD: 0.0544 c. M: 0.0762 c. 853: 94 166 94 145 94 166 94 SP T3 I SD: 0.0384 c. M: 0.0576 c. 971: 107 189 107 165 107 189 107 SP T3 I SD: 0.0123 c. M: 0.0171 c. 2060: 227 401 227 350 227 401 227 SP T3 I SD: 0.0101 c. M:-0.0135 c. 2142: 236 417 236 364 236 417 236 SP T3 I SD: 0.0047 c. M:-0.0066 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: 16.7281 cents 4 x 5 x 6 x 7:8 S SD: 25.2633 cents 5 x 6:7 x 8:9:10 S SD: 22.4423 cents 6 x 7:8:9:10:11:12 S SD: 18.7451 cents 7:8 x 9 x 11:13:14 SD: 25.6457 cents 8:9:10:11:12:13:15:16 SD: 13.4448 cents 10:11:12:13:15:16:19:20 SD: 12.6325 cents 12:13:15:16:18:19:22:24 SD: 6.8371 cents 18:19:22:24:27:29:33:36 SD: 6.7643 cents 21:23:26:28:32:34:39:42 SD: 5.3697 cents 22:24:27:29:33:36:41:44 SD: 5.1436 cents 24:26:30:32:36:39:44:48 SD: 4.1397 cents 26:28:32:35:39:42:48:52 SD: 2.8065 cents 34:37:42:45:51:55:63:68 SD: 2.7340 cents 39:42:48:52:59:63:72:78 SD: 2.5895 cents 42:45:52:56:63:68:78:84 SD: 1.9898 cents 48:52:59:64:72:78:89:96 SD: 1.7851 cents 60:65:74:80:90:97:111:120 SD: 1.1247 cents 76:82:94:101:114:123:141:152 SD: 0.9350 cents 90:97:111:120:135:146:167:180 SD: 0.8020 cents 102:110:126:136:153:165:189:204 SD: 0.3027 cents 252:272:311:336:378:408:467:504 SD: 0.2358 cents 276:298:341:368:414:447:511:552 SD: 0.2324 cents 352:380:435:469:528:570:652:704 SD: 0.2287 cents 354:382:437:472:531:573:656:708 SD: 0.1892 cents 378:408:467:504:567:612:700:756 SD: 0.1487 cents 468:505:578:624:702:758:867:936 SD: 0.1366 cents 480:518:593:640:720:777:889:960 SD: 0.1336 cents 552:596:682:736:828:894:1023:1104 SD: 0.1270 cents 570:615:704:760:855:923:1056:1140 SD: 0.1185 cents