Scala analysis: xen12-chalmers-tritriadic-mt-25-23-7
Tritriadic M->T scale built from 25:23:7
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 644/625 51.845398 2: 25/23 144.353080 3: 28/25 196.198479 middle second 4: 28/23 340.551559 5: 1058/625 911.293839 6: 46/25 1055.646920 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 25/23 144.3531 1: 644/625 51.8454 2: 15625/14812 92.5077 3: 644/625 51.8454 4: 25/23 144.3531 5: 12167/8750 570.7423 6: 25/23 144.3531 7: 25/23 144.3531
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 644/625 51.845 cents 1: 1 15625/14812 92.508 cents 1: 3 25/23 144.353 cents 1: 1 12167/8750 570.742 cents 2: 2 25/23 144.353 cents 2: 2 28/25 196.198 cents middle second 2: 1 625/529 288.706 cents 2: 2 529/350 715.095 cents 3: 1 28/25 196.198 cents middle second 3: 2 625/529 288.706 cents 3: 1 28/23 340.552 cents 3: 1 24334/15625 766.941 cents 3: 2 23/14 859.448 cents 4: 2 28/23 340.552 cents 4: 1 15625/12167 433.059 cents 4: 1 23/14 859.448 cents 4: 2 1058/625 911.294 cents 4: 1 25/14 1003.802 cents middle minor seventh 5: 2 700/529 484.905 cents 5: 1 1058/625 911.294 cents 5: 2 25/14 1003.802 cents middle minor seventh 5: 2 46/25 1055.647 cents 6: 1 17500/12167 629.258 cents 6: 3 46/25 1055.647 cents 6: 1 29624/15625 1107.492 cents 6: 2 625/322 1148.155 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 51.8 144.4 196.2 340.6 911.3 1055.6 1200.0 51.8 : 92.5 144.4 288.7 859.4 1003.8 1148.2 1200.0 144.4 : 51.8 196.2 766.9 911.3 1055.6 1107.5 1200.0 196.2 : 144.4 715.1 859.4 1003.8 1055.6 1148.2 1200.0 340.6 : 570.7 715.1 859.4 911.3 1003.8 1055.6 1200.0 911.3 : 144.4 288.7 340.6 433.1 484.9 629.3 1200.0 1055.6: 144.4 196.2 288.7 340.6 484.9 1055.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 51.8454 .. 570.7423 cents 529/392, 518.8969 cents 644/625, 51.8454 cents 2: 144.3531 .. 715.0954 cents 12167/8750, 570.7423 cents 218750/279841,-426.3892 cents 3: 196.1985 .. 859.4484 cents 575/392, 663.2500 cents 392/529,-518.8969 cents 4: 340.5516 .. 1003.8015 cents 575/392, 663.2500 cents 392/529,-518.8969 cents 5: 484.9046 .. 1055.6469 cents 12167/8750, 570.7423 cents 392/529,-518.8969 cents 6: 629.2577 .. 1148.1546 cents 529/392, 518.8969 cents 218750/279841,-426.3892 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 644/625, 51.8454 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 12167/8750, 570.7423 cents Average / Smallest step : 3.306534 Largest / Average step : 3.329330 Largest / Smallest step : 11.008543 Median interval of one step : 25/23, 144.3531 cents, amount: 3 Most common interval of one step : 25/23, 144.3531 cents, amount: 3 Least squares average step : 154.15503 cents, oct.: 1079.08520 cents Scale is not proper Step pattern alph. order: ABACDCC Step pattern size order : ABACDCC Scale is not a Constant Structure Scale diversity : 1.469063 Lumma stability : 0.086409 Lumma impropriety factor : 0.759412 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 : 4 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 9765625/9538928, 40.6623 cents Most common intervals : 25/23, 144.3531 cents & inv., amount: 5 Most common triad is 0.0 144.353 1055.647 cents, amount: 3 Number of recognisable fifths : 2, average 715.0954 cents Number of appreciable fifths : 0 Scale contains a complete diamond : 23 25 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 23 Odd number limit : 15625 (O: 15625 U: 15625) Highest odd numerator or denominator: 625 Scale harmonicity : 0.005651 Average absolute harmonicity : 0.159414 Specific harmonicity : 0.031064 Fundamental : 1/14375, -13.8113 octaves, 0.0182 Hz. Guide tone : 370300, 18.4983 octaves, 96879946.831 Hz. Exponens Consonantiae : 5.323063E+09, 32.30961 octaves Euler's gradus suavitatis : 99 Sum of Mann's harmonic distance : 1589.0, average 227.00000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 11.14731, average 1.59247 Sum of Tenney's harmonic distance : 23.20051, average 3.31436 Vogel's harmonic complexity : 46.71429 Wille's k value : 7812 Wilson's harmonic complexity : 106 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 92.48434, average 3.30301 Lattice compactness (without 2's) : 85.08042, average 3.03859 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 1.28571 9 1 5: -4 .. 2 -1.42857 14 7: 0 .. 1 0.42857 3 1 23: -1 .. 2 0.28571 6 5 Average exponent except 2's :-5 / 7 =-0.71429 Average absolute exponent except 2's: 23 / 7 = 3.28571 Scale is weakly epimorphic with val: <7 15 18 34| Scale is weakly epimorphic with val: <7 15 19 29| Scale is weakly epimorphic with val: <7 15 20 31| Scale is weakly epimorphic with val: <7 15 21 33| Scale is weakly epimorphic with val: <7 15 22 35| Scale is weakly epimorphic with val: <7 16 19 34| Scale is weakly epimorphic with val: <7 16 20 29| Scale is weakly epimorphic with val: <7 16 21 31| Scale is weakly epimorphic with val: <7 16 22 33| Scale is weakly epimorphic with val: <7 17 18 30| Scale is weakly epimorphic with val: <7 17 19 32| Scale is weakly epimorphic with val: <7 17 21 29| Scale is weakly epimorphic with val: <7 17 22 31| Scale is weakly epimorphic with val: <7 18 18 35| Scale is weakly epimorphic with val: <7 18 19 30| Scale is weakly epimorphic with val: <7 18 20 32| Scale is weakly epimorphic with val: <7 18 21 34|
FIT/MODE
7: 0 1 0 1 3 1 1 N SD: 33.1777 c. M: 54.1510 c. 8: 0 1 0 1 4 1 1 N SD: 30.8406 c. M: 51.8454 c. 15: 0 2 0 2 7 2 2 N SD: 29.0064 c. M: 51.8454 c. 16: 1 1 1 2 7 2 2 N SD: 19.7979 c. M:-34.4484 c. 17: 1 1 1 2 8 2 2 N SD: 10.7414 c. M:-18.7428 c. 24: 1 2 1 3 11 3 3 N SD: 6.5297 c. M: 11.2938 c. 25: 1 2 1 3 12 3 3 N SD: 2.7743 c. M: 4.5516 c. 42: 2 3 2 5 20 5 5 N SD: 2.9582 c. M:-5.2975 c. 49: 2 4 2 6 23 6 6 N SD: 2.7703 c. M: 5.1714 c. 66: 3 5 3 8 31 8 8 N SD: 2.7532 c. M:-4.9030 c. 67: 3 5 3 8 32 8 8 N SD: 1.2621 c. M:-2.1390 c. 92: 4 7 4 11 44 11 11 N SD: 1.0013 c. M:-1.7496 c. 116: 5 9 5 14 55 14 14 N SD: 0.5575 c. M: 0.9490 c. 141: 6 11 6 17 67 17 17 N SD: 0.4594 c. M: 0.7816 c. 183: 8 14 8 22 87 22 22 N SD: 0.3558 c. M:-0.6136 c. 208: 9 16 9 25 99 25 25 N SD: 0.1340 c. M:-0.2446 c. 324: 14 25 14 39 154 39 39 N SD: 0.1168 c. M:-0.1892 c. 532: 23 41 23 64 253 64 64 N SD: 0.0288 c. M:-0.0499 c. 1272: 55 98 55 153 605 153 153 N SD: 0.0233 c. M:-0.0414 c. 1413: 61 109 61 170 672 170 170 N SD: 0.0257 c. M: 0.0412 c. 1621: 70 125 70 195 771 195 195 N SD: 0.0154 c. M: 0.0255 c. 2153: 93 166 93 259 1024 259 259 N SD: 0.0061 c. M: 0.0107 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x 4 S SD: 104.6694 cents 3 x x x 4:5 x 6 S SD: 53.2600 cents 4 x x x 5:7 x 8 SD: 24.5042 cents 5 x x x 6:8:9:10 S SD: 26.9207 cents 6 x x 7 x 10:11:12 SD: 18.9730 cents 7 x x 8:9:12:13:14 S SD: 20.8751 cents 8 x x 9:10:14:15:16 SD: 16.1589 cents 9 x x 10:11:15:17:18 SD: 10.9979 cents 10 x 11 x 12:17:18:20 SD: 10.0972 cents 11 x 12 x 13:19:20:22 SD: 13.1454 cents 12 x 13 x 15:20:22:24 SD: 10.7565 cents 13 x 14:15:16:22:24:26 SD: 9.5831 cents 14 x 15:16:17:24:26:28 SD: 8.4949 cents 15 x 16:17:18:25:28:30 SD: 9.7901 cents 16 x 17:18:19:27:29:32 SD: 10.7665 cents 17 x 18:19:21:29:31:34 SD: 9.3289 cents 18:19 x 20:22:30:33:36 SD: 8.7337 cents 19:20 x 21:23:32:35:38 SD: 7.5807 cents 20:21:22 x 24:34:37:40 SD: 7.9113 cents 22:23:24:25:27:37:40:44 SD: 6.4680 cents 23:24:25:26:28:39:42:46 SD: 4.3229 cents 24:25:26:27:29:41:44:48 SD: 4.2954 cents 26:27:28:29:32:44:48:52 SD: 4.2440 cents 29:30 x 32:35:49:53:58 SD: 5.4864 cents 30:31:33:34:37:51:55:60 SD: 5.4796 cents 31:32:34:35:38:52:57:62 SD: 4.1375 cents 32:33:35:36:39:54:59:64 SD: 2.1356 cents 33:34:36:37:40:56:61:66 SD: 1.9220 cents 58:60:63:65:71:98:107:116 SD: 1.8731 cents 59:61:64:66:72:100:109:118 SD: 1.5811 cents 68:70:74:76:83:115:125:136 SD: 0.9720 cents 92:95:100:103:112:156:169:184 SD: 0.7941 cents 101:104:110:113:123:171:186:202 SD: 0.6251 cents 160:165:174:179:195:271:294:320 SD: 0.5844 cents 175:180:190:196:213:296:322:350 SD: 0.5619 cents 192:198:209:215:234:325:353:384 SD: 0.5370 cents 193:199:210:216:235:327:355:386 SD: 0.4284 cents 231:238:251:259:281:391:425:462 SD: 0.3422 cents 266:274:289:298:324:450:489:532 SD: 0.3384 cents 267:275:290:299:325:452:491:534 SD: 0.2600 cents 299:308:325:335:364:506:550:598 SD: 0.1529 cents 492:507:535:551:599:833:905:984 SD: 0.1372 cents 599:617:651:671:729:1014:1102:1198 SD: 0.1298 cents