Scala analysis: xen12-chalmers-tritriadic-dm-25-19-17
Tritriadic D->M scale built from 25:19:17
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: 578/475 339.770375 3: 34/25 532.327982 4: 38/25 724.885588 5: 722/425 917.443195 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: 9826/9025 147.2128 3: 19/17 192.5576 quasi-meantone 4: 19/17 192.5576 quasi-meantone 5: 19/17 192.5576 quasi-meantone 6: 7225/6859 89.9992 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 : 192.6 339.8 532.3 724.9 917.4 1007.4 1200.0 192.6 : 147.2 339.8 532.3 724.9 814.9 1007.4 1200.0 339.8 : 192.6 385.1 577.7 667.7 860.2 1052.8 1200.0 532.3 : 192.6 385.1 475.1 667.7 860.2 1007.4 1200.0 724.9 : 192.6 282.6 475.1 667.7 814.9 1007.4 1200.0 917.4 : 90.0 282.6 475.1 622.3 814.9 1007.4 1200.0 1007.4: 192.6 385.1 532.3 724.9 917.4 1110.0 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 : 174.28925 cents, oct.: 1220.02475 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1720-tone equal temperament with octave 2/1 degrees: 276 487 763 1039 1315 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: ABAAACA Step pattern size order : LMLLLSL 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 : 0.156101 Specific harmonicity : 0.026662 Fundamental : 1/8075, -12.9792 octaves, 0.0324 Hz. Guide tone : 208658, 17.6708 octaves, 54590267.205 Hz. Exponens Consonantiae : 1.684913E+09, 30.65003 octaves Euler's gradus suavitatis : 112 Sum of Mann's harmonic distance : 1207.0, average 172.42857 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.65847, average 1.52264 Sum of Tenney's harmonic distance : 22.45316, average 3.20759 Vogel's harmonic complexity : 51.42857 Wille's k value : 4512 Wilson's harmonic complexity : 118 Rectangular lattice diameter : 8 Triangular lattice diameter : 4 Lattice compactness : 70.02947, average 2.50105 Lattice compactness (without 2's) : 66.76217, average 2.38436 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 1 0.85714 6 1 5: -2 .. 0 -1.14286 8 17: -1 .. 2 0.28571 6 1 19: -1 .. 2 0.28571 6 5 Average exponent except 2's :-4 / 7 =-0.57143 Average absolute exponent except 2's: 20 / 7 = 2.85714 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: 30.2335 c. M: 60.3003 c. Lebeng 11: 2 1 2 2 1 1 2 P D3 S SD: 27.1052 c. M: 44.7159 c. 12: 2 1 2 2 2 1 2 P M ME I SD: 22.8696 c. M: 39.7704 c. G.Phrygian, M.Dorian, M.Hypomixolydian, Kafi That, Mela Kharaharapriya, Raga Bageshri, Bhimpalasi, Huseni, Kanara, Kapi, Nayaki Kanada, Ritigaula, Sriraga, Mischung 5, Gregorian nr.8, Eskimo Heptatonic, Yu: China, Hyojo, Oshikicho, Banshikicho: Japan, Nam: Vietnam 13: 2 2 2 2 2 1 2 SP M ME S SD: 15.4603 c. M:-29.4604 c. Karakalian 18: 3 2 3 3 3 1 3 P T3 SD: 8.2556 c. M:-15.8901 c. 25: 4 3 4 4 4 2 4 SP T3 SD: 3.5268 c. M: 5.4432 c. 43: 7 5 7 7 7 3 7 SP T3 SD: 2.8409 c. M: 4.8867 c. 56: 9 7 9 9 9 4 9 SP T3 SD: 2.6897 c. M:-3.9854 c. 63: 10 8 10 10 10 5 10 SP T3 SD: 2.0816 c. M: 3.1575 c. 81: 13 10 13 13 13 6 13 SP T3 SD: 0.7740 c. M:-1.0753 c. 106: 17 13 17 17 17 8 17 SP T3 SD: 0.2532 c. M: 0.4621 c. 187: 30 23 30 30 30 14 30 SP T3 SD: 0.2090 c. M:-0.3366 c. 293: 47 36 47 47 47 22 47 SP T3 SD: 0.0811 c. M:-0.1614 c. 399: 64 49 64 64 64 30 64 SP T3 SD: 0.0809 c. M: 0.1500 c. 692: 111 85 111 111 111 52 111 SP T3 SD: 0.0722 c. M:-0.1140 c. 922: 148 113 148 148 148 69 148 SP T3 SD: 0.0701 c. M:-0.1273 c. 1028: 165 126 165 165 165 77 165 SP T3 SD: 0.0497 c. M: 0.0817 c. 1134: 182 139 182 182 182 85 182 SP T3 SD: 0.0440 c. M: 0.0878 c. 1215: 195 149 195 195 195 91 195 SP T3 SD: 0.0440 c. M:-0.0877 c. 1240: 199 152 199 199 199 93 199 SP T3 SD: 0.0498 c. M: 0.0930 c. 1321: 212 162 212 212 212 99 212 SP T3 SD: 0.0245 c. M:-0.0436 c. 1427: 229 175 229 229 229 107 229 SP T3 SD: 0.0183 c. M: 0.0367 c. 1614: 259 198 259 259 259 121 259 SP T3 SD: 0.0153 c. M:-0.0289 c. 1720: 276 211 276 276 276 129 276 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: 11.4653 cents 3 x x 4 x 5 x 6 S SD: 15.8812 cents 4 x 5 x 6 x 7:8 S SD: 16.1697 cents 5 x 6:7:8 x 9:10 S SD: 21.0612 cents 6 x 7:8:9:10:11:12 S SD: 16.5558 cents 8:9:10:11:12 x 14:16 S SD: 11.3930 cents 9:10:11:12:14:15:16:18 S SD: 9.2169 cents 14:16:17:19:21:24:25:28 SD: 6.8554 cents 17:19:21:23:26:29:30:34 SD: 5.5475 cents 19:21:23:26:29:32:34:38 SD: 4.1470 cents 23:26:28:31:35:39:41:46 SD: 3.7512 cents 27:30:33:37:41:46:48:54 SD: 3.1648 cents 33:37:40:45:50:56:59:66 SD: 1.6513 cents 50:56:61:68:76:85:89:100 SD: 1.5602 cents 69:77:84:94:105:117:123:138 SD: 1.2368 cents 77:86:94:105:117:131:138:154 SD: 1.1757 cents 83:93:101:113:126:141:149:166 SD: 1.0864 cents 86:96:105:117:131:146:154:172 SD: 1.0600 cents 92:103:112:125:140:156:165:184 SD: 0.9208 cents 100:112:122:136:152:170:179:200 SD: 0.8462 cents 110:123:134:150:167:187:197:220 SD: 0.8249 cents 119:133:145:162:181:202:213:238 SD: 0.4903 cents 152:170:185:207:231:258:272:304 SD: 0.4370 cents 189:211:230:257:287:321:338:378 SD: 0.4040 cents 236:264:287:321:359:401:422:472 SD: 0.3821 cents 239:267:291:325:363:406:428:478 SD: 0.3235 cents 272:304:331:370:413:462:487:544 SD: 0.3035 cents 281:314:342:382:427:477:503:562 SD: 0.2505 cents 323:361:393:439:491:549:578:646 SD: 0.2045 cents 356:398:433:484:541:605:637:712 SD: 0.1896 cents 375:419:456:510:570:637:671:750 SD: 0.1872 cents 425:475:517:578:646:722:761:850 SD: 0.1715 cents 442:494:538:601:672:751:791:884 SD: 0.1134 cents 475:531:578:646:722:807:850:950 SD: 0.0577 cents