Scala analysis: xen10-chalmers-tritriadic-17-21-25
Tritriadic scale built from 17:21:25
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 625/578 135.344036 2: 21/17 365.825498 submajor third 3: 34/25 532.327982 4: 25/17 667.672018 5: 42/25 898.153480 quasi-equal major sixth 6: 525/289 1033.497516 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 578/525 166.5025 1: 625/578 135.3440 2: 714/625 230.4815 3: 578/525 166.5025 4: 625/578 135.3440 5: 714/625 230.4815 6: 625/578 135.3440 7: 578/525 166.5025
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 625/578 135.344 cents 1: 2 578/525 166.502 cents 1: 2 714/625 230.481 cents 2: 3 25/21 301.847 cents BP second, quasi-equal minor third 2: 3 21/17 365.825 cents submajor third 2: 1 19652/15625 396.984 cents 3: 1 15625/12138 437.191 cents 3: 1 13125/9826 501.170 cents 3: 5 34/25 532.328 cents 4: 5 25/17 667.672 cents 4: 1 19652/13125 698.830 cents 4: 1 24276/15625 762.809 cents 5: 1 15625/9826 803.016 cents 5: 3 34/21 834.175 cents supraminor sixth 5: 3 42/25 898.153 cents quasi-equal major sixth 6: 2 625/357 969.519 cents 6: 2 525/289 1033.498 cents 6: 3 1156/625 1064.656 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 : 135.3 365.8 532.3 667.7 898.2 1033.5 1200.0 135.3 : 230.5 397.0 532.3 762.8 898.2 1064.7 1200.0 365.8 : 166.5 301.8 532.3 667.7 834.2 969.5 1200.0 532.3 : 135.3 365.8 501.2 667.7 803.0 1033.5 1200.0 667.7 : 230.5 365.8 532.3 667.7 898.2 1064.7 1200.0 898.2 : 135.3 301.8 437.2 667.7 834.2 969.5 1200.0 1033.5: 166.5 301.8 532.3 698.8 834.2 1064.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 135.3440 .. 230.4815 cents 412692/390625, 95.1374 cents 625/578, 135.3440 cents 2: 301.8465 .. 396.9839 cents 412692/390625, 95.1374 cents 15625/14994, 71.3651 cents 3: 437.1906 .. 532.3280 cents 412692/390625, 95.1374 cents 244140625/238535976, 40.2066 cents 4: 667.6720 .. 762.8094 cents 412692/390625, 95.1374 cents 625/578, 135.3440 cents 5: 803.0161 .. 898.1535 cents 412692/390625, 95.1374 cents 244140625/238535976, 40.2066 cents 6: 969.5185 .. 1064.6560 cents 412692/390625, 95.1374 cents 15625/14994, 71.3651 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 625/578, 135.3440 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 714/625, 230.4815 cents Average / Smallest step : 1.266613 Largest / Average step : 1.344475 Largest / Smallest step : 1.702930 Median interval of one step : 578/525, 166.5025 cents, amount: 2 Most common interval of one step : 625/578, 135.3440 cents, amount: 3 Least squares average step : 173.04585 cents, oct.: 1211.32098 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1463-tone equal temperament with octave 2/1 degrees: 165 446 649 814 1095 1260 1463 Least number of segments generator : 732 of 600.410 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 872 of 715.243 cents and inv. generated superset size: 47 = 40 more = 671.429% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCABAC Step pattern size order : SLMSLSM Scale is a Constant Structure, by a margin of 40.20661 cents Scale diversity : 1.377106 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.524313 Rothenberg efficiency : 0.544218 redundancy: 0.455782 Efficiency x scale size : 3.809524 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 : 334084/328125, 31.1584 cents Most common intervals : 34/25, 532.3280 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 365.825 667.672 cents Most common triad is 0.0 532.328 667.672 cents, amount: 3 Number of recognisable fifths : 1, average 698.8305 cents Best fifths form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 17 25 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 17 Odd number limit : 15625 (O: 15625 U: 15625) Highest odd numerator or denominator: 625 Scale harmonicity : 0.006959 Average absolute harmonicity : 0.161402 Specific harmonicity : 0.037523 Fundamental : 1/14450, -13.8188 octaves, 0.0181 Hz. Guide tone : 446250, 18.7675 octaves, 116750408.516 Hz. Exponens Consonantiae : 6.448313E+09, 32.58627 octaves Euler's gradus suavitatis : 83 Sum of Mann's harmonic distance : 1113.0, average 159.00000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 11.03208, average 1.57601 Sum of Tenney's harmonic distance : 22.17156, average 3.16737 Vogel's harmonic complexity : 40.28571 Wille's k value : 7812 Wilson's harmonic complexity : 91 Rectangular lattice diameter : 11 Triangular lattice diameter : 6 Lattice compactness : 91.35314, average 3.26261 Lattice compactness (without 2's) : 86.85691, average 3.10203 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 1 0.28571 4 1 3: 0 .. 1 0.42857 3 5: -2 .. 4 0.57143 12 7: 0 .. 1 0.42857 3 1 17: -2 .. 1 -0.71429 7 5 Average exponent except 2's : 5 / 7 = 0.71429 Average absolute exponent except 2's: 25 / 7 = 3.57143 Scale is JI-epimorphic with val: <7 10 15 18 26| Scale is weakly epimorphic with val: <7 10 15 19 28| Scale is weakly epimorphic with val: <7 10 15 21 32| Scale is weakly epimorphic with val: <7 10 15 22 27| Scale is weakly epimorphic with val: <7 10 16 18 31| Scale is weakly epimorphic with val: <7 10 16 19 26| Scale is JI-epimorphic with val: <7 10 16 20 28| Scale is weakly epimorphic with val: <7 10 16 21 30| Scale is weakly epimorphic with val: <7 10 17 18 29| Scale is weakly epimorphic with val: <7 10 17 19 31| Scale is weakly epimorphic with val: <7 10 17 20 26| Scale is weakly epimorphic with val: <7 10 17 21 28| Scale is JI-epimorphic with val: <7 10 17 22 30| Scale is weakly epimorphic with val: <7 10 18 18 27| Scale is weakly epimorphic with val: <7 10 18 20 31| Scale is weakly epimorphic with val: <7 10 18 21 26| Scale is weakly epimorphic with val: <7 10 18 22 28| Scale is weakly epimorphic with val: <7 11 15 18 28| Scale is weakly epimorphic with val: <7 11 15 20 32| Scale is weakly epimorphic with val: <7 11 15 21 27| Scale is weakly epimorphic with val: <7 11 15 22 29| Scale is weakly epimorphic with val: <7 11 16 18 26| Scale is JI-epimorphic with val: <7 11 16 19 28| Scale is weakly epimorphic with val: <7 11 16 20 30| Scale is weakly epimorphic with val: <7 11 16 22 27| Scale is weakly epimorphic with val: <7 11 17 18 31| Scale is weakly epimorphic with val: <7 11 17 19 26| Scale is weakly epimorphic with val: <7 11 17 20 28| Scale is JI-epimorphic with val: <7 11 17 21 30| Scale is weakly epimorphic with val: <7 11 17 22 32| Scale is weakly epimorphic with val: <7 11 18 19 31| Scale is weakly epimorphic with val: <7 11 18 20 26| Scale is weakly epimorphic with val: <7 11 18 21 28| Scale is weakly epimorphic with val: <7 11 18 22 30| Scale is weakly epimorphic with val: <7 12 15 19 32| Scale is weakly epimorphic with val: <7 12 15 20 27| Scale is weakly epimorphic with val: <7 12 15 21 29| Scale is weakly epimorphic with val: <7 12 15 22 31| Scale is JI-epimorphic with val: <7 12 16 18 28| Scale is weakly epimorphic with val: <7 12 16 19 30| Scale is weakly epimorphic with val: <7 12 16 21 27| Scale is weakly epimorphic with val: <7 12 16 22 29| Scale is weakly epimorphic with val: <7 12 17 18 26| Scale is weakly epimorphic with val: <7 12 17 19 28| Scale is JI-epimorphic with val: <7 12 17 20 30| Scale is weakly epimorphic with val: <7 12 17 21 32| Scale is weakly epimorphic with val: <7 12 18 18 31| Scale is weakly epimorphic with val: <7 12 18 19 26| Scale is weakly epimorphic with val: <7 12 18 20 28| Scale is weakly epimorphic with val: <7 12 18 21 30| Scale is JI-epimorphic with val: <7 12 18 22 32|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 24.4564 c. M: 41.0106 c. Lebeng 9: 1 2 1 1 2 1 1 P M ME S SD: 22.3983 c. M:-35.1799 c. Pelog Saptanada: Sunda 15: 2 3 2 1 3 2 2 P D3 SD: 22.9257 c. M:-34.1745 c. 16: 2 3 2 2 3 2 2 SP M ME S SD: 9.8714 c. M:-16.5025 c. Mavila-7, Antiaeolian 20: 2 4 3 2 4 2 3 P T3 SD: 9.0450 c. M: 15.3440 c. 27: 3 5 4 3 5 3 4 SP T3 SD: 6.8086 c. M: 11.2753 c. 36: 4 7 5 4 7 4 5 SP T3 SD: 1.2076 c. M: 2.0107 c. 79: 9 15 11 9 15 9 11 SP T3 SD: 1.1054 c. M: 1.9509 c. 115: 13 22 16 13 22 13 16 SP T3 SD: 0.4308 c. M: 0.7622 c. 151: 17 29 21 17 29 17 21 SP T3 SD: 0.2160 c. M: 0.3849 c. 390: 44 75 54 44 75 44 54 SP T3 SD: 0.2160 c. M:-0.3486 c. 469: 53 90 65 53 90 53 65 SP T3 SD: 0.1462 c. M:-0.2636 c. 505: 57 97 70 57 97 57 70 SP T3 SD: 0.0929 c. M:-0.1659 c. 620: 70 119 86 70 119 70 86 SP T3 SD: 0.0758 c. M:-0.1398 c. 656: 74 126 91 74 126 74 91 SP T3 SD: 0.0218 c. M:-0.0391 c. 1463: 165 281 203 165 281 165 203 SP T3 SD: 0.0033 c. M: 0.0057 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: 17.1415 cents 3 x x 4 x 5 x 6 S SD: 12.3181 cents 4 x 5 x 6 x 7:8 S SD: 19.0025 cents 5 x 6:7 x 8:9:10 S SD: 22.2930 cents 6 x 7:8:9:10:11:12 S SD: 18.6969 cents 7:8:9 x 10:12:13:14 S SD: 23.0829 cents 8:9:10:11:12:13:15:16 SD: 16.2742 cents 9:10:11:12:13:15:16:18 SD: 11.3237 cents 11:12:14:15:16:18:20:22 S SD: 10.4638 cents 12:13:15:16:18:20:22:24 SD: 8.1100 cents 13:14:16:18:19:22:24:26 SD: 6.5595 cents 21:23:26:29:31:35:38:42 SD: 5.5068 cents 22:24:27:30:32:37:40:44 SD: 3.9092 cents 25:27:31:34:37:42:45:50 SD: 2.9367 cents 34:37:42:46:50:57:62:68 SD: 2.3023 cents 38:41:47:52:56:64:69:76 SD: 1.8403 cents 47:51:58:64:69:79:85:94 SD: 1.5239 cents 59:64:73:80:87:99:107:118 SD: 1.4258 cents 72:78:89:98:106:121:131:144 SD: 0.7150 cents 119:129:147:162:175:200:216:238 SD: 0.7043 cents 136:147:168:185:200:228:247:272 SD: 0.5354 cents 170:184:210:231:250:286:309:340 SD: 0.4918 cents 187:202:231:254:275:314:340:374 SD: 0.4713 cents 197:213:243:268:290:331:358:394 SD: 0.4544 cents 200:216:247:272:294:336:363:400 SD: 0.3897 cents 208:225:257:283:306:349:378:416 SD: 0.3721 cents 225:243:278:306:331:378:409:450 SD: 0.3554 cents 234:253:289:318:344:393:425:468 SD: 0.2312 cents 272:294:336:370:400:457:494:544 SD: 0.1288 cents 344:372:425:468:506:578:625:688 SD: 0.1196 cents 506:547:625:688:744:850:919:1012 SD: 0.1151 cents 578:625:714:786:850:971:1050:1156 SD: 0.0272 cents