Scala analysis: xen12-chalmers-tritriadic-mt-23-21-13
Tritriadic M->T scale built from 23:21:13
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 546/529 54.759875 2: 23/21 157.493440 3: 26/23 212.253315 4: 26/21 369.746754 5: 882/529 885.013120 6: 42/23 1042.506560 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 23/21 157.4934 1: 546/529 54.7599 2: 12167/11466 102.7336 3: 546/529 54.7599 4: 23/21 157.4934 5: 9261/6877 515.2664 6: 23/21 157.4934 7: 23/21 157.4934
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 546/529 54.760 cents 1: 1 12167/11466 102.734 cents 1: 3 23/21 157.493 cents 1: 1 9261/6877 515.266 cents 2: 2 23/21 157.493 cents 2: 2 26/23 212.253 cents 2: 1 529/441 314.987 cents 2: 2 441/299 672.760 cents 3: 1 26/23 212.253 cents 3: 2 529/441 314.987 cents 3: 1 26/21 369.747 cents 3: 1 18522/12167 727.520 cents 3: 2 21/13 830.253 cents 4: 2 26/21 369.747 cents 4: 1 12167/9261 472.480 cents 4: 1 21/13 830.253 cents 4: 2 882/529 885.013 cents 4: 1 23/13 987.747 cents 5: 2 598/441 527.240 cents 5: 1 882/529 885.013 cents 5: 2 23/13 987.747 cents 5: 2 42/23 1042.507 cents 6: 1 13754/9261 684.734 cents 6: 3 42/23 1042.507 cents 6: 1 22932/12167 1097.266 cents 6: 2 529/273 1145.240 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 : 54.8 157.5 212.3 369.7 885.0 1042.5 1200.0 54.8 : 102.7 157.5 315.0 830.3 987.7 1145.2 1200.0 157.5 : 54.8 212.3 727.5 885.0 1042.5 1097.3 1200.0 212.3 : 157.5 672.8 830.3 987.7 1042.5 1145.2 1200.0 369.7 : 515.3 672.8 830.3 885.0 987.7 1042.5 1200.0 885.0 : 157.5 315.0 369.7 472.5 527.2 684.7 1200.0 1042.5: 157.5 212.3 315.0 369.7 527.2 1042.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 54.7599 .. 515.2664 cents 441/338, 460.5065 cents 546/529, 54.7599 cents 2: 157.4934 .. 672.7598 cents 9261/6877, 515.2664 cents 158171/194481,-357.7729 cents 3: 212.2533 .. 830.2532 cents 483/338, 617.9999 cents 338/441,-460.5065 cents 4: 369.7468 .. 987.7467 cents 483/338, 617.9999 cents 338/441,-460.5065 cents 5: 527.2402 .. 1042.5066 cents 9261/6877, 515.2664 cents 338/441,-460.5065 cents 6: 684.7336 .. 1145.2401 cents 441/338, 460.5065 cents 158171/194481,-357.7729 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 546/529, 54.7599 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9261/6877, 515.2664 cents Average / Smallest step : 3.130551 Largest / Average step : 3.005720 Largest / Smallest step : 9.409561 Median interval of one step : 23/21, 157.4934 cents, amount: 3 Most common interval of one step : 23/21, 157.4934 cents, amount: 3 Least squares average step : 154.03999 cents, oct.: 1078.27993 cents Scale is not proper Step pattern alph. order: ABACDCC Step pattern size order : ABACDCC Scale is not a Constant Structure Scale diversity : 1.392022 Lumma stability : 0.091266 Lumma impropriety factor : 0.737511 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 : 4112446/4084101, 11.9738 cents Most common intervals : 23/21, 157.4934 cents & inv., amount: 5 Most common triad is 0.0 157.493 1042.507 cents, amount: 3 Number of recognisable fifths : 0 Scale contains a complete diamond : 21 23 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 23 Odd number limit : 12167 (O: 12167 U: 12167) Highest odd numerator or denominator: 529 Scale harmonicity : 0.005311 Average absolute harmonicity : 0.156622 Specific harmonicity : 0.028347 Fundamental : 1/11109, -13.4394 octaves, 0.0236 Hz. Guide tone : 263718, 18.0086 octaves, 68995370.830 Hz. Exponens Consonantiae : 2.929643E+09, 31.44808 octaves Euler's gradus suavitatis : 104 Sum of Mann's harmonic distance : 1347.0, average 192.42857 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.85431, average 1.55062 Sum of Tenney's harmonic distance : 22.61342, average 3.23049 Vogel's harmonic complexity : 48.85714 Wille's k value : 6083 Wilson's harmonic complexity : 112 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 70.36163, average 2.51292 Lattice compactness (without 2's) : 67.06225, average 2.39508 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 1 0.85714 6 1 3: -1 .. 2 0.28571 6 7: -1 .. 2 0.28571 6 13: 0 .. 1 0.42857 3 1 23: -2 .. 1 -0.71429 7 5 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 22 / 7 = 3.14286 Scale is weakly epimorphic with val: <7 10 18 24 34| Scale is weakly epimorphic with val: <7 10 18 25 29| Scale is weakly epimorphic with val: <7 10 18 26 31| Scale is weakly epimorphic with val: <7 10 18 27 33| Scale is weakly epimorphic with val: <7 10 18 29 30| Scale is weakly epimorphic with val: <7 10 19 24 33| Scale is weakly epimorphic with val: <7 10 19 25 35| Scale is weakly epimorphic with val: <7 10 19 26 30| Scale is weakly epimorphic with val: <7 10 19 27 32| Scale is weakly epimorphic with val: <7 10 19 28 34| Scale is weakly epimorphic with val: <7 10 20 24 32| Scale is weakly epimorphic with val: <7 10 20 25 34| Scale is weakly epimorphic with val: <7 10 20 26 29| Scale is weakly epimorphic with val: <7 10 20 27 31| Scale is weakly epimorphic with val: <7 10 20 28 33| Scale is weakly epimorphic with val: <7 10 20 29 35| Scale is weakly epimorphic with val: <7 10 21 25 33| Scale is weakly epimorphic with val: <7 10 21 26 35| Scale is weakly epimorphic with val: <7 10 21 27 30| Scale is weakly epimorphic with val: <7 10 21 28 32| Scale is weakly epimorphic with val: <7 10 21 29 34| Scale is weakly epimorphic with val: <7 10 22 24 30| Scale is weakly epimorphic with val: <7 10 22 26 34| Scale is weakly epimorphic with val: <7 10 22 27 29| Scale is weakly epimorphic with val: <7 10 22 28 31| Scale is weakly epimorphic with val: <7 10 22 29 33| Scale is weakly epimorphic with val: <7 11 18 24 33| Scale is weakly epimorphic with val: <7 11 18 25 35| Scale is weakly epimorphic with val: <7 11 18 26 30| Scale is weakly epimorphic with val: <7 11 18 27 32| Scale is weakly epimorphic with val: <7 11 18 28 34| Scale is weakly epimorphic with val: <7 11 19 24 32| Scale is weakly epimorphic with val: <7 11 19 25 34| Scale is weakly epimorphic with val: <7 11 19 26 29| Scale is weakly epimorphic with val: <7 11 19 27 31| Scale is weakly epimorphic with val: <7 11 19 28 33| Scale is weakly epimorphic with val: <7 11 19 29 35| Scale is weakly epimorphic with val: <7 11 20 25 33| Scale is weakly epimorphic with val: <7 11 20 26 35| Scale is weakly epimorphic with val: <7 11 20 27 30| Scale is weakly epimorphic with val: <7 11 20 28 32| Scale is weakly epimorphic with val: <7 11 20 29 34| Scale is weakly epimorphic with val: <7 11 21 24 30| Scale is weakly epimorphic with val: <7 11 21 26 34| Scale is weakly epimorphic with val: <7 11 21 27 29| Scale is weakly epimorphic with val: <7 11 21 28 31| Scale is weakly epimorphic with val: <7 11 21 29 33| Scale is weakly epimorphic with val: <7 11 22 24 29| Scale is weakly epimorphic with val: <7 11 22 25 31| Scale is weakly epimorphic with val: <7 11 22 27 35| Scale is weakly epimorphic with val: <7 11 22 28 30| Scale is weakly epimorphic with val: <7 11 22 29 32| Scale is weakly epimorphic with val: <7 12 18 24 32| Scale is weakly epimorphic with val: <7 12 18 25 34| Scale is weakly epimorphic with val: <7 12 18 26 29| Scale is weakly epimorphic with val: <7 12 18 27 31| Scale is weakly epimorphic with val: <7 12 18 28 33| Scale is weakly epimorphic with val: <7 12 18 29 35| Scale is weakly epimorphic with val: <7 12 19 25 33| Scale is weakly epimorphic with val: <7 12 19 26 35| Scale is weakly epimorphic with val: <7 12 19 27 30| Scale is weakly epimorphic with val: <7 12 19 28 32| Scale is weakly epimorphic with val: <7 12 19 29 34| Scale is weakly epimorphic with val: <7 12 20 24 30| Scale is weakly epimorphic with val: <7 12 20 26 34| Scale is weakly epimorphic with val: <7 12 20 27 29| Scale is weakly epimorphic with val: <7 12 20 28 31| Scale is weakly epimorphic with val: <7 12 20 29 33| Scale is weakly epimorphic with val: <7 12 21 24 29| Scale is weakly epimorphic with val: <7 12 21 25 31| Scale is weakly epimorphic with val: <7 12 21 27 35| Scale is weakly epimorphic with val: <7 12 21 28 30| Scale is weakly epimorphic with val: <7 12 21 29 32| Scale is weakly epimorphic with val: <7 12 22 24 35| Scale is weakly epimorphic with val: <7 12 22 25 30| Scale is weakly epimorphic with val: <7 12 22 26 32| Scale is weakly epimorphic with val: <7 12 22 28 29| Scale is weakly epimorphic with val: <7 12 22 29 31|
FIT/MODE
7: 0 1 0 1 3 1 1 N SD: 30.5976 c. M: 54.7599 c. 15: 1 1 1 2 6 2 2 N SD: 18.3611 c. M:-30.2532 c. 16: 1 1 1 2 7 2 2 N SD: 11.5675 c. M:-20.2401 c. 22: 1 2 1 3 9 3 3 N SD: 7.6282 c. M: 12.2858 c. 23: 1 2 1 3 10 3 3 N SD: 2.5502 c. M: 4.5294 c. 61: 3 5 3 8 26 8 8 N SD: 2.7132 c. M:-4.2565 c. 68: 3 6 3 9 29 9 9 N SD: 1.4575 c. M: 2.6602 c. 84: 4 7 4 11 36 11 11 N SD: 1.3823 c. M:-2.3830 c. 91: 4 8 4 12 39 12 12 N SD: 1.1511 c. M: 2.0126 c. 107: 5 9 5 14 46 14 14 N SD: 0.7508 c. M:-1.3149 c. 130: 6 11 6 17 56 17 17 N SD: 0.6108 c. M:-1.1407 c. 175: 8 15 8 23 75 23 23 N SD: 0.3148 c. M:-0.5390 c. 198: 9 17 9 26 85 26 26 N SD: 0.1234 c. M: 0.2144 c. 503: 23 43 23 66 216 66 66 N SD: 0.0627 c. M:-0.1109 c. 701: 32 60 32 92 301 92 92 N SD: 0.0107 c. M:-0.0190 c. 1600: 73 137 73 210 687 210 210 N SD: 0.0073 c. M: 0.0131 c. 2301: 105 197 105 302 988 302 302 N SD: 0.0038 c. M: 0.0066 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: 91.5291 cents 3 x x x 4:5 x 6 S SD: 42.7666 cents 4 x x x 5 x 7:8 SD: 25.1734 cents 5 x x x 6:8:9:10 S SD: 23.2318 cents 6 x x 7 x 10:11:12 SD: 13.7625 cents 7 x x 8:9:12:13:14 S SD: 17.6573 cents 8 x x 9:10:13:15:16 SD: 13.2924 cents 9 x 10 x 11:15:16:18 SD: 11.4446 cents 10 x 11 x 12:17:18:20 SD: 13.7626 cents 11 x 12 x 14:18:20:22 SD: 11.7229 cents 12 x 13:14:15:20:22:24 S SD: 10.0871 cents 13 x 14:15:16:22:24:26 SD: 9.4865 cents 14 x 15:16:17:23:26:28 SD: 11.1079 cents 15 x 16:17:19:25:27:30 SD: 10.9225 cents 16:17 x 18:20:27:29:32 SD: 9.8116 cents 17:18 x 19:21:28:31:34 SD: 8.8339 cents 18:19:20 x 22:30:33:36 SD: 8.6213 cents 19:20:21 x 24:32:35:38 SD: 9.3472 cents 20:21:22:23:25:33:37:40 SD: 7.7317 cents 21:22:23:24:26:35:38:42 SD: 5.0945 cents 22:23:24:25:27:37:40:44 SD: 4.8119 cents 24:25:26:27:30:40:44:48 S SD: 4.5237 cents 29:30:32:33:36:48:53:58 SD: 3.1824 cents 30:31:33:34:37:50:55:60 SD: 1.8738 cents 54:56:59:61:67:90:99:108 SD: 1.7344 cents 62:64:68:70:77:103:113:124 SD: 1.3508 cents 63:65:69:71:78:105:115:126 SD: 0.7732 cents 93:96:102:105:115:155:170:186 SD: 0.6184 cents 156:161:171:176:193:260:285:312 SD: 0.5802 cents 159:164:174:180:197:265:290:318 SD: 0.5710 cents 160:165:175:181:198:267:292:320 SD: 0.5218 cents 189:195:207:214:234:315:345:378 SD: 0.4337 cents 190:196:208:215:235:317:347:380 SD: 0.4298 cents 222:229:243:251:275:370:405:444 SD: 0.3553 cents 252:260:276:285:312:420:460:504 SD: 0.1976 cents 315:325:345:356:390:525:575:630 SD: 0.1728 cents 345:356:378:390:427:575:630:690 SD: 0.1672 cents 505:521:553:571:625:842:922:1010 SD: 0.1669 cents 529:546:579:598:655:882:966:1058 SD: 0.1637 cents 558:576:611:631:691:930:1019:1116 SD: 0.1514 cents 559:577:612:632:692:932:1021:1118 SD: 0.1209 cents