Scala analysis: xen15-chalmers-triadic-reversed-diamond-22-17
Triadic reversed diamond for M=22/17, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 34/33 51.682466 2: 22/17 446.362533 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 17/11 753.637467 6: 33/17 1148.317534 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 34/33 51.6825 1: 34/33 51.6825 2: 363/289 394.6801 3: 34/33 51.6825 4: 9/8 203.9100 major whole tone 5: 34/33 51.6825 6: 363/289 394.6801 7: 34/33 51.6825
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 34/33 51.682 cents 1: 1 9/8 203.910 cents major whole tone 1: 2 363/289 394.680 cents 2: 1 1156/1089 103.365 cents 2: 2 51/44 255.592 cents 2: 4 22/17 446.363 cents 3: 1 289/242 307.275 cents 3: 4 4/3 498.045 cents perfect fourth 3: 2 99/68 650.273 cents 4: 2 136/99 549.727 cents 4: 4 3/2 701.955 cents perfect fifth 4: 1 484/289 892.725 cents 5: 4 17/11 753.637 cents 5: 2 88/51 944.408 cents 5: 1 1089/578 1096.635 cents 6: 2 578/363 805.320 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 4 33/17 1148.318 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 : 51.7 446.4 498.0 702.0 753.6 1148.3 1200.0 51.7 : 394.7 446.4 650.3 702.0 1096.6 1148.3 1200.0 446.4 : 51.7 255.6 307.3 702.0 753.6 805.3 1200.0 498.0 : 203.9 255.6 650.3 702.0 753.6 1148.3 1200.0 702.0 : 51.7 446.4 498.0 549.7 944.4 996.1 1200.0 753.6 : 394.7 446.4 498.0 892.7 944.4 1148.3 1200.0 1148.3: 51.7 103.4 498.0 549.7 753.6 805.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 51.6825 .. 394.6801 cents 11979/9826, 342.9976 cents 34/33, 51.6825 cents 2: 103.3649 .. 446.3625 cents 11979/9826, 342.9976 cents 334084/395307,-291.3151 cents 3: 307.2749 .. 650.2725 cents 11979/9826, 342.9976 cents 4913/5324,-139.0876 cents 4: 549.7275 .. 892.7251 cents 11979/9826, 342.9976 cents 9248/9801,-100.5451 cents 5: 753.6375 .. 1096.6351 cents 11979/9826, 342.9976 cents 4913/5324,-139.0876 cents 6: 805.3199 .. 1148.3175 cents 11979/9826, 342.9976 cents 334084/395307,-291.3151 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 34/33, 51.6825 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 363/289, 394.6801 cents Average / Smallest step : 3.316958 Largest / Average step : 2.302300 Largest / Smallest step : 7.636634 Median interval of one step : 34/33, 51.6825 cents, amount: 4 Most common interval of one step : 34/33, 51.6825 cents, amount: 4 Least squares average step : 173.60325 cents, oct.: 1215.22275 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1277-tone equal temperament with octave 2/1 degrees: 55 475 530 747 802 1222 1277 Least number of segments generator : 639 of 600.470 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 802 of 753.641 cents and inv. generated superset size: 57 = 50 more = 814.286% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABACABA Step pattern size order : SLSMSLS Scale is a Constant Structure, by a margin of 51.68247 cents Scale diversity : 1.466424 Lumma stability : 0.086137 Lumma impropriety factor : 0.655450 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 : 34/33, 51.6825 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 : 11 17 33 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 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 : 1089 (O: 1089 U: 1089) Highest odd numerator or denominator: 33 Scale harmonicity : 0.009530 Average absolute harmonicity : 0.223837 Specific harmonicity : 0.051069 Fundamental : 1/1122, -10.1319 octaves, 0.2332 Hz. Guide tone : 2244, 11.1319 octaves, 587087.769 Hz. Exponens Consonantiae : 2.517768E+06, 21.26371 octaves Euler's gradus suavitatis : 60 Sum of Mann's harmonic distance : 99.5, average 14.21429 Mersenne's string divisions : 1829100 Sum of van Prooijen's expressibility: 6.45217, average 0.92174 Sum of Tenney's harmonic distance : 12.80203, average 1.82886 Vogel's harmonic complexity : 32.57143 Wille's k value : 841 Wilson's harmonic complexity : 62 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 60.17688, average 2.14917 Lattice compactness (without 2's) : 47.53320, average 1.69761 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.57143 6 1 3: -1 .. 1 0.00000 4 2 11: -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: 12 / 7 = 1.71429 Scale is weakly epimorphic with val: <7 10 22 30| Scale is weakly epimorphic with val: <7 10 22 31| Scale is weakly epimorphic with val: <7 10 23 31| Scale is weakly epimorphic with val: <7 10 23 32| Scale is weakly epimorphic with val: <7 10 24 26| Scale is weakly epimorphic with val: <7 10 24 32| Scale is weakly epimorphic with val: <7 10 25 26| Scale is weakly epimorphic with val: <7 10 25 27| Scale is weakly epimorphic with val: <7 10 26 27| Scale is weakly epimorphic with val: <7 10 26 28| Scale is JI-epimorphic with val: <7 11 22 27| Scale is weakly epimorphic with val: <7 11 22 28| Scale is JI-epimorphic with val: <7 11 23 28| Scale is weakly epimorphic with val: <7 11 23 29| Scale is JI-epimorphic with val: <7 11 24 29| = patent Scale is weakly epimorphic with val: <7 11 24 30| Scale is JI-epimorphic with val: <7 11 25 30| Scale is weakly epimorphic with val: <7 11 25 31| Scale is JI-epimorphic with val: <7 11 26 31| Scale is weakly epimorphic with val: <7 11 26 32| Scale is weakly epimorphic with val: <7 12 22 26| Scale is weakly epimorphic with val: <7 12 22 30| Scale is weakly epimorphic with val: <7 12 23 27| Scale is weakly epimorphic with val: <7 12 23 31| Scale is weakly epimorphic with val: <7 12 24 28| Scale is weakly epimorphic with val: <7 12 24 32| Scale is weakly epimorphic with val: <7 12 25 26| Scale is weakly epimorphic with val: <7 12 25 29| Scale is weakly epimorphic with val: <7 12 26 27| Scale is weakly epimorphic with val: <7 12 26 30|
FIT/MODE
7: 0 3 0 1 0 3 0 N T3 I SD: 46.4401 c. M: 67.9232 c. 8: 0 3 0 2 0 3 0 N T3 I SD: 37.7686 c. M: 51.6825 c. 12: 0 4 1 2 0 4 1 N SD: 37.8715 c. M: 53.6375 c. 14: 1 4 1 2 1 4 1 N T3 I SD: 22.2868 c. M: 34.0318 c. 16: 1 5 1 2 1 5 1 N T3 I SD: 19.1499 c. M:-26.9550 c. 17: 1 5 1 3 1 5 1 N T3 I SD: 15.9840 c. M: 22.8331 c. 19: 1 6 1 3 1 6 1 N T3 I SD: 7.5953 c. M: 11.4754 c. 22: 1 7 1 4 1 7 1 N T3 I SD: 6.7421 c. M: 9.9989 c. 24: 1 8 1 4 1 8 1 N T3 I SD: 2.3835 c. M: 3.6375 c. 46: 2 15 2 8 2 15 2 N T3 I SD: 2.0203 c. M: 2.8843 c. 70: 3 23 3 12 3 23 3 N T3 I SD: 0.6091 c. M:-0.9021 c. 94: 4 31 4 16 4 31 4 N T3 I SD: 0.4180 c. M: 0.6186 c. 164: 7 54 7 28 7 54 7 N T3 I SD: 0.3582 c. M:-0.4840 c. 258: 11 85 11 44 11 85 11 N T3 I SD: 0.3504 c. M:-0.5197 c. 277: 12 91 12 47 12 91 12 N T3 I SD: 0.1984 c. M:-0.3031 c. 301: 13 99 13 51 13 99 13 N T3 I SD: 0.1924 c. M:-0.2939 c. 347: 15 114 15 59 15 114 15 N T3 I SD: 0.1726 c. M: 0.2530 c. 371: 16 122 16 63 16 122 16 N T3 I SD: 0.0521 c. M:-0.0696 c. 812: 35 267 35 138 35 267 35 N T3 I SD: 0.0387 c. M: 0.0571 c. 836: 36 275 36 142 36 275 36 N T3 I SD: 0.0344 c. M: 0.0490 c. 906: 39 298 39 154 39 298 39 N T3 I SD: 0.0224 c. M:-0.0318 c. 1277: 55 420 55 217 55 420 55 N T3 I SD: 0.0026 c. M: 0.0039 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: 43.5737 cents 4 x 5 x 6 x x 8 S SD: 20.0163 cents 5 x 6:7 x 8 x 10 S SD: 41.7048 cents 6 x x 8:9 x x 12 S SD: 0.0000 cents 7:8:9 x x 11 x 14 SD: 45.5364 cents 8:9:10:11:12 x x 16 S SD: 34.4192 cents 9:10 x 12 x 14:17:18 SD: 27.8926 cents 10:11:13 x 15 x 19:20 SD: 23.9008 cents 11:12:14:15 x 17:21:22 SD: 18.9816 cents 12:13 x 16:18:19:23:24 SD: 16.4917 cents 13:14:17 x x 20:25:26 SD: 16.1505 cents 14:15:18:19:21:22:27:28 SD: 11.6211 cents 15:16:19:20 x 23:29:30 SD: 12.0400 cents 16:17:21 x 24:25:31:32 SD: 10.2817 cents 17:18:22:23 x 26:33:34 SD: 9.4278 cents 18:19:23:24:27:28:35:36 SD: 6.9648 cents 19:20 x 25 x 29:37:38 SD: 9.7967 cents 20:21:26:27:30:31:39:40 SD: 5.8667 cents 21:22:27:28 x 32:41:42 SD: 6.7810 cents 22:23:28:29:33:34:43:44 SD: 6.3952 cents 24:25:31:32:36:37:47:48 SD: 3.5615 cents 30:31:39:40:45:46:58:60 SD: 2.5653 cents 38:39:49:51:57:59:74:76 SD: 2.5047 cents 48:49:62:64:72:74:93:96 SD: 2.4542 cents 54:56:70:72:81:83:105:108 SD: 2.1833 cents 57:59:74:76:86:88:111:114 SD: 2.1676 cents 58:60:75:77:87:90:113:116 SD: 1.9998 cents 60:62:78:80:90:93:116:120 SD: 1.8209 cents 62:64:80:83:93:96:120:124 SD: 1.5765 cents 64:66:83:85:96:99:124:128 SD: 1.2398 cents 66:68:85:88:99:102:128:132 SD: 1.2166 cents 68:70:88:91:102:105:132:136 SD: 0.9567 cents 96:99:124:128:144:148:186:192 SD: 0.9272 cents 99:102:128:132:149:153:192:198 SD: 0.8913 cents 102:105:132:136:153:158:198:204 SD: 0.6087 cents 132:136:171:176:198:204:256:264 SD: 0.3418 cents 198:204:256:264:297:306:384:396 SD: 0.3213 cents 204:210:264:272:306:315:396:408 SD: 0.3027 cents 258:266:334:344:387:399:501:516 SD: 0.2690 cents 306:315:396:408:459:473:594:612 SD: 0.2193 cents 330:340:427:440:495:510:641:660 SD: 0.1625 cents 456:470:590:608:684:705:885:912 SD: 0.1522 cents 462:476:598:616:693:714:897:924 SD: 0.0688 cents