Scala analysis: xen10-chalmers-tritriadic-17-13-19
Tritriadic scale built from 17:13:19
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: 26/19 543.014646 4: 26/17 735.572252 5: 494/289 928.129859 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: 7514/6859 157.8994 4: 19/17 192.5576 quasi-meantone 5: 19/17 192.5576 quasi-meantone 6: 4913/4693 79.3125 7: 19/17 192.5576 quasi-meantone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 4913/4693 79.313 cents 1: 1 7514/6859 157.899 cents 1: 5 19/17 192.558 cents quasi-meantone 2: 2 289/247 271.870 cents 2: 2 442/361 350.457 cents 2: 3 361/289 385.115 cents two (quasi-meantone) 3: 3 17/13 464.428 cents 3: 3 26/19 543.015 cents 3: 1 6859/4913 577.673 cents 4: 1 9826/6859 622.327 cents 4: 3 19/13 656.985 cents 4: 3 26/17 735.572 cents 5: 3 578/361 814.885 cents 5: 2 361/221 849.543 cents 5: 2 494/289 928.130 cents 6: 5 34/19 1007.442 cents quasi-mean seventh 6: 1 6859/3757 1042.101 cents 6: 1 9386/4913 1120.687 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 : 192.6 385.1 543.0 735.6 928.1 1007.4 1200.0 192.6 : 192.6 350.5 543.0 735.6 814.9 1007.4 1200.0 385.1 : 157.9 350.5 543.0 622.3 814.9 1007.4 1200.0 543.0 : 192.6 385.1 464.4 657.0 849.5 1042.1 1200.0 735.6 : 192.6 271.9 464.4 657.0 849.5 1007.4 1200.0 928.1 : 79.3 271.9 464.4 657.0 814.9 1007.4 1200.0 1007.4: 192.6 385.1 577.7 735.6 928.1 1120.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 79.3125 .. 192.5576 cents 89167/83521, 113.2451 cents 4913/4693, 79.3125 cents 2: 271.8701 .. 385.1152 cents 89167/83521, 113.2451 cents 4913/4693, 79.3125 cents 3: 464.4277 .. 577.6728 cents 89167/83521, 113.2451 cents 4913/4693, 79.3125 cents 4: 622.3272 .. 735.5723 cents 89167/83521, 113.2451 cents 48275138/47045881, 44.6544 cents 5: 814.8848 .. 928.1299 cents 89167/83521, 113.2451 cents 4913/4693, 79.3125 cents 6: 1007.4424 .. 1120.6875 cents 89167/83521, 113.2451 cents 4913/4693, 79.3125 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 4913/4693, 79.3125 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 19/17, 192.5576 cents Average / Smallest step : 2.161431 Largest / Average step : 1.123253 Largest / Smallest step : 2.427833 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 : 175.85303 cents, oct.: 1230.97123 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: AABAACA Step pattern size order : LLMLLSL Scale is a Constant Structure, by a margin of 44.65436 cents Scale diversity : 1.460288 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.433775 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 : 130321/127738, 34.6582 cents Most common intervals : 19/17, 192.5576 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 543.015 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 : 6859 (O: 6859 U: 6859) Highest odd numerator or denominator: 361 Scale harmonicity : 0.004633 Average absolute harmonicity : 0.154776 Specific harmonicity : 0.024990 Fundamental : 1/5491, -12.4229 octaves, 0.0476 Hz. Guide tone : 159562, 17.2838 octaves, 41745498.451 Hz. Exponens Consonantiae : 8.761549E+08, 29.70661 octaves Euler's gradus suavitatis : 116 Sum of Mann's harmonic distance : 806.5, average 115.21429 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.08511, average 1.44073 Sum of Tenney's harmonic distance : 21.13264, average 3.01895 Vogel's harmonic complexity : 52.57143 Wille's k value : 3429 Wilson's harmonic complexity : 121 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 60.90469, average 2.17517 Lattice compactness (without 2's) : 56.50032, average 2.01787 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 1 0.71429 5 1 13: 0 .. 1 0.42857 3 17: -2 .. 1 -0.71429 7 1 19: -1 .. 2 0.28571 6 5 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 24 26 29| Scale is JI-epimorphic with val: <7 24 27 28| Scale is weakly epimorphic with val: <7 24 29 33| Scale is weakly epimorphic with val: <7 24 30 32| Scale is weakly epimorphic with val: <7 25 26 31| Scale is weakly epimorphic with val: <7 25 27 30| Scale is JI-epimorphic with val: <7 25 28 29| Scale is weakly epimorphic with val: <7 25 31 33| Scale is weakly epimorphic with val: <7 26 27 32| Scale is weakly epimorphic with val: <7 26 28 31| Scale is JI-epimorphic with val: <7 26 29 30| = patent Scale is weakly epimorphic with val: <7 27 28 33| Scale is weakly epimorphic with val: <7 27 29 32| Scale is JI-epimorphic with val: <7 27 30 31| Scale is weakly epimorphic with val: <7 28 30 33| Scale is JI-epimorphic with val: <7 28 31 32| Scale is JI-epimorphic with val: <7 29 32 33|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 39.6934 c. M: 70.9870 c. Lebeng 8: 1 2 1 1 1 1 1 P M ME S SD: 41.5402 c. M:-64.8848 c. 11: 2 2 1 2 2 0 2 N T3 SD: 32.9839 c. M:-53.6883 c. 12: 2 2 1 2 2 1 2 P M ME S SD: 24.6091 c. M: 43.0146 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 2 2 2 1 2 SP M ME S SD: 8.6987 c. M: 15.8844 c. Karakalian 18: 3 3 2 3 3 1 3 P T3 SD: 8.0901 c. M:-14.8848 c. 31: 5 5 4 5 5 2 5 SP T3 SD: 1.0608 c. M:-1.9816 c. 75: 12 12 10 12 12 5 12 SP T3 SD: 0.6586 c. M: 1.1152 c. 106: 17 17 14 17 17 7 17 SP T3 SD: 0.2130 c. M:-0.3816 c. 137: 22 22 18 22 22 9 22 SP T3 SD: 0.1989 c. M:-0.3373 c. 243: 39 39 32 39 39 16 39 SP T3 SD: 0.1553 c. M:-0.2652 c. 349: 56 56 46 56 56 23 56 SP T3 SD: 0.1602 c. M:-0.2518 c. 592: 95 95 78 95 95 39 95 SP T3 SD: 0.1565 c. M:-0.2485 c. 829: 133 133 109 133 133 55 133 SP T3 SD: 0.1546 c. M: 0.2650 c. 860: 138 138 113 138 138 57 138 SP T3 SD: 0.1463 c. M: 0.2239 c. 904: 145 145 119 145 145 60 145 SP T3 SD: 0.1423 c. M: 0.2538 c. 935: 150 150 123 150 150 62 150 SP T3 SD: 0.1216 c. M: 0.2154 c. 966: 155 155 127 155 155 64 155 SP T3 SD: 0.1110 c. M: 0.1795 c. 997: 160 160 131 160 160 66 160 SP T3 SD: 0.1108 c. M: 0.1862 c. 1041: 167 167 137 167 167 69 167 SP T3 SD: 0.0983 c. M: 0.1760 c. 1072: 172 172 141 172 172 71 172 SP T3 SD: 0.0843 c. M: 0.1448 c. 1103: 177 177 145 177 177 73 177 SP T3 SD: 0.0813 c. M: 0.1316 c. 1178: 189 189 155 189 189 78 189 SP T3 SD: 0.0651 c. M: 0.1163 c. 1209: 194 194 159 194 194 80 194 SP T3 SD: 0.0579 c. M: 0.0902 c. 1284: 206 206 169 206 206 85 206 SP T3 SD: 0.0529 c. M: 0.0925 c. 1315: 211 211 173 211 211 87 211 SP T3 SD: 0.0401 c. M: 0.0690 c. 1421: 228 228 187 228 228 94 228 SP T3 SD: 0.0288 c. M: 0.0510 c. 1452: 233 233 191 233 233 96 233 SP T3 SD: 0.0234 c. M: 0.0394 c. 1558: 250 250 205 250 250 103 250 SP T3 SD: 0.0096 c. M: 0.0169 c. 1695: 272 272 223 272 272 112 272 SP T3 SD: 0.0096 c. M:-0.0175 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: 16.8086 cents 3 x x 4 x 5 x 6 S SD: 20.9183 cents 4 x 5 x 6 x 7:8 S SD: 12.8033 cents 5 x 6:7:8 x 9:10 S SD: 22.4424 cents 6:7 x 8:9:10:11:12 S SD: 18.5203 cents 7:8:9:10:11:12:13:14 H SD: 18.0080 cents 8:9:10:11:12 x 14:16 S SD: 8.8516 cents 12:13:15:16:18 x 21:24 SD: 14.4908 cents 13:15:16:18:20:22:23:26 SD: 10.0107 cents 15:17:19:21:23:26:27:30 SD: 8.3659 cents 16:18:20:22:24:27:29:32 SD: 6.8736 cents 17:19:21:23:26:29:30:34 SD: 5.2577 cents 24:27:30:33:37:41:43:48 SD: 2.8418 cents 32:36:40:44:49:55:57:64 SD: 2.7009 cents 41:46:51:56:63:70:73:82 SD: 2.2744 cents 44:49:55:60:67:75:79:88 SD: 1.9768 cents 49:55:61:67:75:84:88:98 SD: 1.7906 cents 51:57:64:70:78:87:91:102 SD: 1.6168 cents 60:67:75:82:92:103:107:120 SD: 1.5553 cents 68:76:85:93:104:116:122:136 SD: 0.8432 cents 76:85:95:104:116:130:136:152 SD: 0.5823 cents 128:143:160:175:196:219:229:256 SD: 0.4838 cents 144:161:180:197:220:246:258:288 SD: 0.4742 cents 185:207:231:253:283:316:331:370 SD: 0.3851 cents 196:219:245:268:300:335:351:392 SD: 0.3795 cents 204:228:255:279:312:349:365:408 SD: 0.3060 cents 261:292:326:357:399:446:467:522 SD: 0.3050 cents 272:304:340:372:416:465:487:544 SD: 0.2603 cents 342:382:427:468:523:585:612:684 SD: 0.2593 cents 366:409:457:501:560:626:655:732 SD: 0.2259 cents 374:418:467:512:572:639:669:748 SD: 0.2037 cents 410:458:512:561:627:701:734:820 SD: 0.1925 cents 434:485:542:594:664:742:777:868 SD: 0.1727 cents 450:503:562:616:688:769:805:900 SD: 0.1684 cents 461:515:576:631:705:788:825:922 SD: 0.1461 cents 502:561:627:687:768:858:898:1004 SD: 0.1252 cents 570:637:712:780:872:974:1020:1140 SD: 0.1086 cents 578:646:722:791:884:988:1034:1156 SD: 0.0773 cents