Scala analysis: xen12-chalmers-tritriadic-dm-13-17-19
Tritriadic D->M scale built from 13:17:19
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: 289/247 271.870141 3: 17/13 464.427748 4: 19/13 656.985354 5: 361/221 849.542961 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: 4913/4693 79.3125 3: 19/17 192.5576 quasi-meantone 4: 19/17 192.5576 quasi-meantone 5: 19/17 192.5576 quasi-meantone 6: 7514/6859 157.8994 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 : 192.6 271.9 464.4 657.0 849.5 1007.4 1200.0 192.6 : 79.3 271.9 464.4 657.0 814.9 1007.4 1200.0 271.9 : 192.6 385.1 577.7 735.6 928.1 1120.7 1200.0 464.4 : 192.6 385.1 543.0 735.6 928.1 1007.4 1200.0 657.0 : 192.6 350.5 543.0 735.6 814.9 1007.4 1200.0 849.5 : 157.9 350.5 543.0 622.3 814.9 1007.4 1200.0 1007.4: 192.6 385.1 464.4 657.0 849.5 1042.1 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 : 167.49923 cents, oct.: 1172.49459 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABAAACA Step pattern size order : LSLLLML 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 : 0.154956 Specific harmonicity : 0.025097 Fundamental : 1/4199, -12.0358 octaves, 0.0623 Hz. Guide tone : 208658, 17.6708 octaves, 54590267.205 Hz. Exponens Consonantiae : 8.761549E+08, 29.70661 octaves Euler's gradus suavitatis : 116 Sum of Mann's harmonic distance : 636.0, average 90.85714 Mersenne's string divisions : 496003680 Sum of van Prooijen's expressibility: 10.08511, average 1.44073 Sum of Tenney's harmonic distance : 20.11305, average 2.87329 Vogel's harmonic complexity : 52.14286 Wille's k value : 3429 Wilson's harmonic complexity : 121 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 59.92009, average 2.14000 Lattice compactness (without 2's) : 56.12138, average 2.00433 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 1 0.28571 2 1 13: -1 .. 0 -0.57143 4 17: -1 .. 2 0.28571 6 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: 36.4514 c. M:-70.9870 c. Lebeng 8: 1 1 1 1 2 1 1 P M ME S SD: 38.5727 c. M: 56.9854 c. 11: 2 0 2 2 2 1 2 N T3 SD: 28.0985 c. M: 53.6883 c. 12: 2 1 2 2 2 1 2 P M ME I SD: 30.6212 c. M:-50.4570 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 1 2 2 2 2 2 SP M ME S SD: 9.4854 c. M: 18.7737 c. Tamashian 18: 3 1 3 3 3 2 3 P T3 SD: 8.6999 c. M:-17.1237 c. 25: 4 2 4 4 4 3 4 SP T3 SD: 11.5742 c. M:-16.1299 c. 30: 5 2 5 4 5 4 5 SP SD: 10.6834 c. M: 16.9854 c. 31: 5 2 5 5 5 4 5 SP T3 SD: 1.0846 c. M:-2.0699 c. 75: 12 5 12 12 12 10 12 SP T3 SD: 0.7721 c. M: 1.5430 c. 106: 17 7 17 17 17 14 17 SP T3 SD: 0.2700 c. M: 0.4864 c. 137: 22 9 22 22 22 18 22 SP T3 SD: 0.1705 c. M: 0.3373 c. 243: 39 16 39 39 39 32 39 SP T3 SD: 0.1646 c. M: 0.2652 c. 349: 56 23 56 56 56 46 56 SP T3 SD: 0.1877 c. M: 0.2593 c. 380: 61 25 61 61 61 50 61 SP T3 SD: 0.1550 c. M: 0.2912 c. 592: 95 39 95 95 95 78 95 SP T3 SD: 0.1768 c. M: 0.2485 c. 623: 100 41 100 100 100 82 100 SP T3 SD: 0.1572 c. M: 0.2811 c. 654: 105 43 105 105 105 86 105 SP T3 SD: 0.1566 c. M: 0.3105 c. 829: 133 55 133 133 133 109 133 SP T3 SD: 0.1630 c. M:-0.2650 c. 860: 138 57 138 138 138 113 138 SP T3 SD: 0.1691 c. M:-0.2245 c. 866: 139 57 139 139 139 114 139 SP T3 SD: 0.1588 c. M: 0.2766 c. 873: 140 58 140 140 140 115 140 SP T3 SD: 0.1478 c. M:-0.2948 c. 904: 145 60 145 145 145 119 145 SP T3 SD: 0.1290 c. M:-0.2538 c. 935: 150 62 150 150 150 123 150 SP T3 SD: 0.1211 c. M:-0.2154 c. 966: 155 64 155 155 155 127 155 SP T3 SD: 0.1237 c. M:-0.1795 c. 1010: 162 67 162 162 162 133 162 SP T3 SD: 0.1047 c. M:-0.2091 c. 1041: 167 69 167 167 167 137 167 SP T3 SD: 0.0911 c. M:-0.1760 c. 1072: 172 71 172 172 172 141 172 SP T3 SD: 0.0888 c. M:-0.1448 c. 1103: 177 73 177 177 177 145 177 SP T3 SD: 0.0968 c. M:-0.1397 c. 1116: 179 74 179 179 179 147 179 SP T3 SD: 0.0914 c. M:-0.1729 c. 1147: 184 76 184 184 184 151 184 SP T3 SD: 0.0719 c. M:-0.1438 c. 1178: 189 78 189 189 189 155 189 SP T3 SD: 0.0628 c. M:-0.1163 c. 1209: 194 80 194 194 194 159 194 SP T3 SD: 0.0662 c. M:-0.0902 c. 1253: 201 83 201 201 201 165 201 SP T3 SD: 0.0632 c. M:-0.1171 c. 1284: 206 85 206 206 206 169 206 SP T3 SD: 0.0462 c. M:-0.0925 c. 1315: 211 87 211 211 211 173 211 SP T3 SD: 0.0420 c. M:-0.0690 c. 1390: 223 92 223 223 223 183 223 SP T3 SD: 0.0408 c. M:-0.0723 c. 1421: 228 94 228 228 228 187 228 SP T3 SD: 0.0257 c. M:-0.0510 c. 1452: 233 96 233 233 233 191 233 SP T3 SD: 0.0285 c. M:-0.0438 c. 1527: 245 101 245 245 245 201 245 SP T3 SD: 0.0232 c. M:-0.0356 c. 1558: 250 103 250 250 250 205 250 SP T3 SD: 0.0098 c. M:-0.0169 c. 1695: 272 112 272 272 272 223 272 SP T3 SD: 0.0088 c. M:-0.0146 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: 22.4848 cents 3 x x 4 x 5 x 6 S SD: 16.1323 cents 4 x x 5:6 x 7:8 S SD: 24.5144 cents 5 x 6 x 7:8:9:10 S SD: 18.8159 cents 6 x 7:8:9:10:11:12 S SD: 13.0670 cents 7:8 x 9:10:11:13:14 SD: 18.6618 cents 8:9 x 10:12:13:14:16 S SD: 16.5206 cents 9:10:11:12:13:15:16:18 SD: 13.3210 cents 10:11:12:13:15:16:18:20 SD: 11.2400 cents 11:12:13:14:16:18:20:22 S SD: 10.1989 cents 13 x 15:17:19:21:23:26 SD: 6.1061 cents 14:16 x 18:20:23:25:28 SD: 10.5721 cents 15:17:18:20:22:25:27:30 SD: 10.0816 cents 16:18:19:21:23:26:29:32 SD: 6.7345 cents 17:19:20:22:25:28:30:34 SD: 5.1865 cents 19:21:22:25:28:31:34:38 SD: 4.5670 cents 24:27:28:31:35:39:43:48 SD: 3.8060 cents 33:37:39:43:48:54:59:66 SD: 3.0302 cents 35:39:41:46:51:57:63:70 SD: 2.3242 cents 43:48:50:56:63:70:77:86 SD: 2.1445 cents 52:58:61:68:76:85:93:104 SD: 0.8432 cents 95:106:111:124:139:155:170:190 SD: 0.8102 cents 117:131:137:153:171:191:209:234 SD: 0.6684 cents 136:152:159:178:199:222:243:272 SD: 0.5796 cents 147:164:172:192:215:240:263:294 SD: 0.5782 cents 152:170:178:199:222:248:272:304 SD: 0.5197 cents 153:171:179:200:224:250:274:306 SD: 0.4818 cents 188:210:220:246:275:307:336:376 SD: 0.4351 cents 195:218:228:255:285:319:349:390 SD: 0.4104 cents 205:229:240:268:300:335:367:410 SD: 0.4056 cents 247:276:289:323:361:403:442:494 SD: 0.2934 cents 289:323:338:378:422:472:517:578 SD: 0.2672 cents 305:341:357:399:446:498:546:610 SD: 0.2492 cents 341:381:399:446:498:557:610:682 SD: 0.2271 cents 347:388:406:454:507:567:621:694 SD: 0.2019 cents 390:436:456:510:570:637:698:780 SD: 0.1889 cents 399:446:467:522:583:652:714:798 SD: 0.1794 cents 423:473:495:553:618:691:757:846 SD: 0.1738 cents 442:494:517:578:646:722:791:884 SD: 0.0773 cents 494:552:578:646:722:807:884:988 SD: 0.0557 cents