Scala analysis: xen15-chalmers-triadic-diamond-22-17
Triadic 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: 51/44 255.592468 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: 88/51 944.407532 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 51/44 255.5925 1: 51/44 255.5925 2: 968/867 190.7701 3: 34/33 51.6825 4: 9/8 203.9100 major whole tone 5: 34/33 51.6825 6: 968/867 190.7701 7: 51/44 255.5925
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 34/33 51.682 cents 1: 2 968/867 190.770 cents 1: 1 9/8 203.910 cents major whole tone 1: 2 51/44 255.592 cents 2: 2 176/153 242.453 cents 2: 2 51/44 255.592 cents 2: 2 22/17 446.363 cents 2: 1 2601/1936 511.185 cents 3: 1 289/242 307.275 cents 3: 2 22/17 446.363 cents 3: 2 4/3 498.045 cents perfect fourth 3: 2 3/2 701.955 cents perfect fifth 4: 2 4/3 498.045 cents perfect fourth 4: 2 3/2 701.955 cents perfect fifth 4: 2 17/11 753.637 cents 4: 1 484/289 892.725 cents 5: 1 3872/2601 688.815 cents 5: 2 17/11 753.637 cents 5: 2 88/51 944.408 cents 5: 2 153/88 957.547 cents 6: 2 88/51 944.408 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 867/484 1009.230 cents 6: 2 33/17 1148.318 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 255.6 446.4 498.0 702.0 753.6 944.4 1200.0 255.6 : 190.8 242.5 446.4 498.0 688.8 944.4 1200.0 446.4 : 51.7 255.6 307.3 498.0 753.6 1009.2 1200.0 498.0 : 203.9 255.6 446.4 702.0 957.5 1148.3 1200.0 702.0 : 51.7 242.5 498.0 753.6 944.4 996.1 1200.0 753.6 : 190.8 446.4 702.0 892.7 944.4 1148.3 1200.0 944.4 : 255.6 511.2 702.0 753.6 957.5 1009.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 51.6825 .. 255.5925 cents 9/8, 203.9100 cents 34/33, 51.6825 cents 2: 242.4525 .. 511.1849 cents 397953/340736, 268.7324 cents 7744/7803,-13.1399 cents 3: 307.2749 .. 701.9550 cents 363/289, 394.6801 cents 8/9,-203.9100 cents 4: 498.0450 .. 892.7251 cents 363/289, 394.6801 cents 8/9,-203.9100 cents 5: 688.8151 .. 957.5475 cents 397953/340736, 268.7324 cents 8/9,-203.9100 cents 6: 944.4075 .. 1148.3175 cents 9/8, 203.9100 cents 7744/7803,-13.1399 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 : 51/44, 255.5925 cents Average / Smallest step : 3.316958 Largest / Average step : 1.490956 Largest / Smallest step : 4.945439 Median interval of one step : 968/867, 190.7701 cents, amount: 2 Least squares average step : 166.32075 cents, oct.: 1164.24525 cents Scale is not proper Step pattern alph. order: ABCDCBA Step pattern size order : DBACABD Scale is not a Constant Structure Scale diversity : 1.239954 Lumma stability : 0.086137 Lumma impropriety factor : 0.509775 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 : 4 Highest interval variety : 4 Mean interval variety : 4.00000 = 4 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 7803/7744, 13.1399 cents Number of recognisable fifths : 5, average 699.3270 cents Number of appreciable fifths : 4, average 701.9550 cents Scale is a complete diamond : 11 17 51 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 : 2601 (O: 2601 U: 2601) Highest odd numerator or denominator: 51 Scale harmonicity : 0.009352 Average absolute harmonicity : 0.223630 Specific harmonicity : 0.050110 Fundamental : 1/2244, -11.1319 octaves, 0.1166 Hz. Guide tone : 4488, 12.1319 octaves, 1174175.537 Hz. Exponens Consonantiae : 1.007107E+07, 23.26371 octaves Euler's gradus suavitatis : 62 Sum of Mann's harmonic distance : 158.0, average 22.57143 Mersenne's string divisions : 14419860 Sum of van Prooijen's expressibility: 6.83028, average 0.97575 Sum of Tenney's harmonic distance : 14.00615, average 2.00088 Vogel's harmonic complexity : 33.57143 Wille's k value : 1300 Wilson's harmonic complexity : 62 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 74.59496, average 2.66411 Lattice compactness (without 2's) : 47.53320, average 1.69761 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 3 0.57143 10 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 27| Scale is weakly epimorphic with val: <7 10 22 28| Scale is weakly epimorphic with val: <7 10 23 28| Scale is weakly epimorphic with val: <7 10 23 29| Scale is weakly epimorphic with val: <7 10 24 29| Scale is weakly epimorphic with val: <7 10 24 30| Scale is weakly epimorphic with val: <7 10 25 30| Scale is weakly epimorphic with val: <7 10 25 31| Scale is weakly epimorphic with val: <7 10 26 31| Scale is weakly epimorphic with val: <7 10 26 32| Scale is weakly epimorphic with val: <7 11 22 30| Scale is weakly epimorphic with val: <7 11 22 31| Scale is weakly epimorphic with val: <7 11 23 31| Scale is weakly epimorphic with val: <7 11 23 32| Scale is weakly epimorphic with val: <7 11 24 26| Scale is weakly epimorphic with val: <7 11 24 32| Scale is weakly epimorphic with val: <7 11 25 26| Scale is weakly epimorphic with val: <7 11 25 27| Scale is weakly epimorphic with val: <7 11 26 27| Scale is weakly epimorphic with val: <7 11 26 28| Scale is weakly epimorphic with val: <7 12 22 28| Scale is weakly epimorphic with val: <7 12 22 32| Scale is weakly epimorphic with val: <7 12 23 26| Scale is weakly epimorphic with val: <7 12 23 29| Scale is weakly epimorphic with val: <7 12 24 27| Scale is weakly epimorphic with val: <7 12 24 30| Scale is weakly epimorphic with val: <7 12 25 28| Scale is weakly epimorphic with val: <7 12 25 31| Scale is weakly epimorphic with val: <7 12 26 29| Scale is weakly epimorphic with val: <7 12 26 32|
FIT/MODE
7: 1 1 1 1 0 1 2 N T3 SD: 66.0661 c. M: 103.5054 c. 8: 2 1 0 2 0 1 2 N I SD: 35.0248 c. M:-48.0450 c. 9: 2 1 1 1 1 1 2 N D3 I SD: 31.7012 c. M: 46.3625 c. 10: 2 2 0 2 0 2 2 N D3 I SD: 22.0404 c. M:-33.6375 c. 14: 3 2 1 2 1 2 3 N G I SD: 12.9028 c. M: 17.7911 c. 19: 4 3 1 3 1 3 4 N G I SD: 4.7507 c. M:-7.2182 c. 24: 5 4 1 4 1 4 5 N G I SD: 3.7159 c. M: 5.5925 c. 43: 9 7 2 7 2 7 9 N G I SD: 3.2936 c. M: 4.4297 c. 51: 11 8 2 9 2 8 11 N I SD: 2.7438 c. M:-3.9274 c. 65: 14 10 3 11 3 10 14 N I SD: 2.3422 c. M: 3.2856 c. 70: 15 11 3 12 3 11 15 N I SD: 1.0195 c. M: 1.5504 c. 89: 19 14 4 15 4 14 19 N I SD: 0.9333 c. M: 1.4187 c. 94: 20 15 4 16 4 15 20 N I SD: 0.2944 c. M: 0.4460 c. 258: 55 41 11 44 11 41 55 N I SD: 0.2441 c. M:-0.3706 c. 277: 59 44 12 47 12 44 59 N I SD: 0.1146 c. M: 0.1531 c. 371: 79 59 16 63 16 59 79 N I SD: 0.0511 c. M:-0.0682 c. 812: 173 129 35 138 35 129 173 N I SD: 0.0500 c. M: 0.0726 c. 906: 193 144 39 154 39 144 193 N I SD: 0.0261 c. M: 0.0367 c. 1277: 272 203 55 217 55 203 272 N I SD: 0.0043 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 x 5:6 S SD: 20.0163 cents 4 x 5 x 6 x 7:8 S SD: 16.2059 cents 5:6 x 7 x 8:9:10 S SD: 28.0735 cents 6:7 x 8:9 x 10:12 S SD: 12.2198 cents 7:8:9 x x 11:12:14 SD: 8.2055 cents 8:9:10:11:12 x 14:16 S SD: 16.4242 cents 9:10 x 12 x 14:16:18 S SD: 18.0609 cents 10:12:13 x 15 x 17:20 SD: 13.1626 cents 11:13:14:15 x 17:19:22 SD: 9.8313 cents 12:14 x 16:18:19:21:24 SD: 8.3013 cents 13:15:17 x x 20:22:26 SD: 7.9492 cents 14:16:18:19:21:22:24:28 SD: 7.3153 cents 15:17:19:20 x 23:26:30 SD: 9.3376 cents 16:19:21 x 24:25:28:32 SD: 9.5894 cents 17:20:22:23 x 26:29:34 SD: 7.4916 cents 18:21:23:24:27:28:31:36 SD: 3.9100 cents 19:22 x 25 x 29:33:38 SD: 6.7031 cents 20:23:26:27:30:31:35:40 SD: 5.2140 cents 21:24:27:28 x 32:36:42 S SD: 6.3397 cents 24:28:31:32:36:37:41:48 SD: 3.0483 cents 30:35:39:40:45:46:52:60 SD: 2.9840 cents 38:44:49:51:57:59:66:76 SD: 2.7256 cents 44:51:57:59:66:68:76:88 SD: 1.4470 cents 62:72:80:83:93:96:107:124 SD: 1.3999 cents 68:79:88:91:102:105:117:136 SD: 1.2997 cents 81:94:105:108:122:125:140:162 SD: 1.2635 cents 84:97:109:112:126:130:145:168 SD: 1.1970 cents 88:102:114:117:132:136:152:176 SD: 0.7909 cents 102:118:132:136:153:158:176:204 SD: 0.7424 cents 108:125:140:144:162:167:186:216 SD: 0.7350 cents 126:146:163:168:189:195:217:252 SD: 0.5946 cents 132:153:171:176:198:204:228:264 SD: 0.3611 cents 150:174:194:200:225:232:259:300 SD: 0.3551 cents 156:181:202:208:234:241:269:312 SD: 0.3429 cents 252:292:326:336:378:389:435:504 SD: 0.3277 cents 258:299:334:344:387:399:445:516 SD: 0.2173 cents 378:438:489:504:567:584:652:756 SD: 0.1667 cents 466:540:603:621:699:720:804:932 SD: 0.1630 cents 504:584:652:672:756:779:870:1008 SD: 0.1575 cents 510:591:660:680:765:788:880:1020 SD: 0.0807 cents