Scala analysis: xen10-chalmers-tritriadic-17-25-19
Tritriadic scale built from 17:25:19
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 19/17 192.557607 quasi-meantone 2: 361/289 385.115213 two (quasi-meantone) 3: 25/19 475.114412 4: 25/17 667.672018 5: 475/289 860.229625 6: 34/19 1007.442393 quasi-mean seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 19/17 192.5576 quasi-meantone 1: 19/17 192.5576 quasi-meantone 2: 19/17 192.5576 quasi-meantone 3: 7225/6859 89.9992 4: 19/17 192.5576 quasi-meantone 5: 19/17 192.5576 quasi-meantone 6: 9826/9025 147.2128 7: 19/17 192.5576 quasi-meantone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 7225/6859 89.999 cents 1: 1 9826/9025 147.213 cents 1: 5 19/17 192.558 cents quasi-meantone 2: 2 425/361 282.557 cents 2: 2 578/475 339.770 cents 2: 3 361/289 385.115 cents two (quasi-meantone) 3: 3 25/19 475.114 cents 3: 3 34/25 532.328 cents 3: 1 6859/4913 577.673 cents 4: 1 9826/6859 622.327 cents 4: 3 25/17 667.672 cents 4: 3 38/25 724.886 cents 5: 3 578/361 814.885 cents 5: 2 475/289 860.230 cents 5: 2 722/425 917.443 cents 6: 5 34/19 1007.442 cents quasi-mean seventh 6: 1 9025/4913 1052.787 cents 6: 1 13718/7225 1110.001 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 : 192.6 385.1 475.1 667.7 860.2 1007.4 1200.0 192.6 : 192.6 282.6 475.1 667.7 814.9 1007.4 1200.0 385.1 : 90.0 282.6 475.1 622.3 814.9 1007.4 1200.0 475.1 : 192.6 385.1 532.3 724.9 917.4 1110.0 1200.0 667.7 : 192.6 339.8 532.3 724.9 917.4 1007.4 1200.0 860.2 : 147.2 339.8 532.3 724.9 814.9 1007.4 1200.0 1007.4: 192.6 385.1 577.7 667.7 860.2 1052.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 89.9992 .. 192.5576 cents 130321/122825, 102.5584 cents 7225/6859, 89.9992 cents 2: 282.5568 .. 385.1152 cents 130321/122825, 102.5584 cents 7225/6859, 89.9992 cents 3: 475.1144 .. 577.6728 cents 130321/122825, 102.5584 cents 7225/6859, 89.9992 cents 4: 622.3272 .. 724.8856 cents 130321/122825, 102.5584 cents 48275138/47045881, 44.6544 cents 5: 814.8848 .. 917.4432 cents 130321/122825, 102.5584 cents 7225/6859, 89.9992 cents 6: 1007.4424 .. 1110.0008 cents 130321/122825, 102.5584 cents 7225/6859, 89.9992 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 7225/6859, 89.9992 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 19/17, 192.5576 cents Average / Smallest step : 1.904779 Largest / Average step : 1.123253 Largest / Smallest step : 2.139548 Median interval of one step : 19/17, 192.5576 cents, amount: 5 Most common interval of one step : 19/17, 192.5576 cents, amount: 5 Least squares average step : 170.03301 cents, oct.: 1190.23109 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1720-tone equal temperament with octave 2/1 degrees: 276 552 681 957 1233 1444 1720 Least number of segments generator : 861 of 600.698 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1403 of 978.837 cents and inv. generated superset size: 98 = 91 more = 1400.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: AABAACA Step pattern size order : LLSLLML Scale is a Constant Structure, by a margin of 44.65436 cents Scale diversity : 1.469105 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.487208 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 : 48275138/47045881, 44.6544 cents Most common intervals : 19/17, 192.5576 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 475.114 1007.442 cents Most common triad is 0.0 192.558 1007.442 cents, amount: 3 Number of recognisable fifths : 0 Best fifths form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 17 19 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 19 Odd number limit : 9025 (O: 9025 U: 9025) Highest odd numerator or denominator: 475 Scale harmonicity : 0.004843 Average absolute harmonicity : 0.156091 Specific harmonicity : 0.026471 Fundamental : 1/5491, -12.4229 octaves, 0.0476 Hz. Guide tone : 306850, 18.2272 octaves, 80279804.713 Hz. Exponens Consonantiae : 1.684913E+09, 30.65003 octaves Euler's gradus suavitatis : 112 Sum of Mann's harmonic distance : 796.0, average 113.71429 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.58759, average 1.51251 Sum of Tenney's harmonic distance : 21.08154, average 3.01165 Vogel's harmonic complexity : 50.85714 Wille's k value : 4512 Wilson's harmonic complexity : 118 Rectangular lattice diameter : 8 Triangular lattice diameter : 4 Lattice compactness : 69.77003, average 2.49179 Lattice compactness (without 2's) : 66.59060, average 2.37824 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 1 0.28571 2 1 5: 0 .. 2 0.85714 6 17: -2 .. 1 -0.71429 7 1 19: -1 .. 2 0.28571 6 5 Average exponent except 2's : 3 / 7 = 0.42857 Average absolute exponent except 2's: 19 / 7 = 2.71429 Scale is JI-epimorphic with val: <7 15 26 27| Scale is weakly epimorphic with val: <7 15 27 33| Scale is weakly epimorphic with val: <7 15 28 32| Scale is weakly epimorphic with val: <7 15 29 31| Scale is weakly epimorphic with val: <7 16 26 31| Scale is weakly epimorphic with val: <7 16 27 30| Scale is JI-epimorphic with val: <7 16 28 29| Scale is weakly epimorphic with val: <7 16 31 33| Scale is weakly epimorphic with val: <7 17 26 28| Scale is weakly epimorphic with val: <7 17 28 33| Scale is weakly epimorphic with val: <7 17 29 32| Scale is JI-epimorphic with val: <7 17 30 31| Scale is weakly epimorphic with val: <7 18 26 32| Scale is weakly epimorphic with val: <7 18 27 31| Scale is weakly epimorphic with val: <7 18 28 30| Scale is JI-epimorphic with val: <7 18 32 33|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 25.4897 c. M: 42.2581 c. Lebeng 12: 2 2 1 2 2 1 2 P M ME S SD: 22.6098 c. M:-39.7704 c. G.Hypophrygian, G.Ionian (Iastian), M.Mixolydian, G.M.Hypoionian, Hypermixolydian, Mischung 3, Khamaj That, Mela Harikambhoji, Raga Balahamsa, Bhim, Devamanohari, Harini, Janjhuti, Kaamaai, Khambhavati, Surati, Gregorian nr.7, Enharmonic Byzantine Liturgical, Rast descending: Greece, Ching, Shang: China 13: 2 2 1 2 2 2 2 SP M ME S SD: 16.4479 c. M: 29.4604 c. Oukranian 18: 3 3 1 3 3 2 3 P T3 SD: 7.9834 c. M:-14.8848 c. 25: 4 4 2 4 4 3 4 SP T3 SD: 2.8954 c. M:-4.8856 c. 56: 9 9 4 9 9 7 9 SP T3 SD: 2.2399 c. M: 3.6858 c. 81: 13 13 6 13 13 10 13 SP T3 SD: 0.6592 c. M: 1.0403 c. 106: 17 17 8 17 17 13 17 SP T3 SD: 0.1997 c. M:-0.3573 c. 187: 30 30 14 30 30 23 30 SP T3 SD: 0.1971 c. M: 0.3366 c. 293: 47 47 22 47 47 36 47 SP T3 SD: 0.0943 c. M: 0.1614 c. 399: 64 64 30 64 64 49 64 SP T3 SD: 0.0817 c. M: 0.1528 c. 692: 111 111 52 111 111 85 111 SP T3 SD: 0.0818 c. M: 0.1441 c. 922: 148 148 69 148 148 113 148 SP T3 SD: 0.0719 c. M:-0.1342 c. 1028: 165 165 77 165 165 126 165 SP T3 SD: 0.0569 c. M:-0.0988 c. 1109: 178 178 83 178 178 136 178 SP T3 SD: 0.0590 c. M:-0.0967 c. 1134: 182 182 85 182 182 139 182 SP T3 SD: 0.0510 c. M:-0.0878 c. 1215: 195 195 91 195 195 149 195 SP T3 SD: 0.0392 c. M:-0.0700 c. 1321: 212 212 99 212 212 162 212 SP T3 SD: 0.0255 c. M:-0.0475 c. 1427: 229 229 107 229 229 175 229 SP T3 SD: 0.0211 c. M:-0.0367 c. 1614: 259 259 121 259 259 198 259 SP T3 SD: 0.0122 c. M: 0.0215 c. 1720: 276 276 129 276 276 211 276 SP T3 SD: 0.0017 c. M:-0.0029 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: 11.0957 cents 4 x 5 x 6 x 7:8 S SD: 12.9132 cents 5 x 6 x 7:8:9:10 S SD: 23.9568 cents 6:7 x 8:9:10:11:12 S SD: 16.2986 cents 7:8 x 9:10:12:13:14 S SD: 20.4503 cents 8:9:10:11:12:13:14:16 S SD: 13.5466 cents 9:10:11:12:13:15:16:18 SD: 8.7204 cents 10:11 x 13:15:16:18:20 SD: 11.3538 cents 11:12:14 x 16:18:20:22 S SD: 10.5208 cents 13:15:16:17:19:21:23:26 SD: 10.3191 cents 15:17:19:20:22:25:27:30 SD: 6.9941 cents 16:18:20:21:24:26:29:32 SD: 6.7044 cents 17:19:21:22:25:28:30:34 SD: 6.0512 cents 19:21:24:25:28:31:34:38 SD: 4.3339 cents 25:28:31:33:37:41:45:50 SD: 3.0129 cents 28:31:35:37:41:46:50:56 SD: 2.8308 cents 41:46:51:54:60:67:73:82 SD: 2.6622 cents 44:49:55:58:65:72:79:88 SD: 2.0374 cents 51:57:64:67:75:84:91:102 SD: 1.4930 cents 60:67:75:79:88:99:107:120 SD: 1.4787 cents 76:85:95:100:112:125:136:152 SD: 0.5987 cents 161:180:201:212:237:265:288:322 SD: 0.5039 cents 168:188:210:221:247:276:301:336 SD: 0.4862 cents 177:198:221:233:260:291:317:354 SD: 0.4452 cents 196:219:245:258:288:322:351:392 SD: 0.3627 cents 213:238:266:280:313:350:381:426 SD: 0.3320 cents 238:266:297:313:350:391:426:476 SD: 0.3028 cents 253:283:316:333:372:416:453:506 SD: 0.2853 cents 272:304:340:358:400:447:487:544 SD: 0.2314 cents 289:323:361:380:425:475:517:578 SD: 0.1871 cents 357:399:446:470:525:587:639:714 SD: 0.1839 cents 393:439:491:517:578:646:703:786 SD: 0.1788 cents 418:467:522:550:615:687:748:836 SD: 0.1646 cents 466:521:582:613:685:766:834:932 SD: 0.1604 cents 485:542:606:638:713:797:868:970 SD: 0.1373 cents 510:570:637:671:750:838:913:1020 SD: 0.1252 cents 542:606:677:713:797:891:970:1084 SD: 0.1250 cents 561:627:701:738:825:922:1004:1122 SD: 0.1030 cents 570:637:712:750:838:937:1020:1140 SD: 0.0830 cents