Scala analysis: xen12-chalmers-tritriadic-mt-15-21-23
Tritriadic M->T scale built from 15:21:23
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 161/150 122.517825 2: 23/21 157.493440 3: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 4: 10/7 617.487807 Euler's tritone 5: 23/15 740.005633 6: 49/25 1165.024385 BP eighth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 1: 161/150 122.5178 2: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 3: 147/115 425.0188 4: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 5: 161/150 122.5178 6: 147/115 425.0188 7: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 50/49 34.976 cents Erlich's decatonic comma, tritonic diesis 1: 2 161/150 122.518 cents 1: 2 147/115 425.019 cents 2: 3 23/21 157.493 cents 2: 3 30/23 459.994 cents 2: 1 343/250 547.537 cents 3: 1 1150/1029 192.469 cents 3: 1 1500/1127 494.970 cents 3: 5 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 5 10/7 617.488 cents Euler's tritone 4: 1 1127/750 705.030 cents 4: 1 1029/575 1007.531 cents 5: 1 500/343 652.463 cents 5: 3 23/15 740.006 cents 5: 3 42/23 1042.507 cents 6: 2 230/147 774.981 cents 6: 2 300/161 1077.482 cents 6: 3 49/25 1165.024 cents BP eighth 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 : 122.5 157.5 582.5 617.5 740.0 1165.0 1200.0 122.5 : 35.0 460.0 495.0 617.5 1042.5 1077.5 1200.0 157.5 : 425.0 460.0 582.5 1007.5 1042.5 1165.0 1200.0 582.5 : 35.0 157.5 582.5 617.5 740.0 775.0 1200.0 617.5 : 122.5 547.5 582.5 705.0 740.0 1165.0 1200.0 740.0 : 425.0 460.0 582.5 617.5 1042.5 1077.5 1200.0 1165.0: 35.0 157.5 192.5 617.5 652.5 775.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 34.9756 .. 425.0188 cents 7203/5750, 390.0431 cents 50/49, 34.9756 cents 2: 157.4934 .. 547.5366 cents 7203/5750, 390.0431 cents 2645/3087,-267.5253 cents 3: 192.4691 .. 582.5122 cents 7203/5750, 390.0431 cents 287500/352947,-355.0675 cents 4: 617.4878 .. 1007.5309 cents 7203/5750, 390.0431 cents 50/49, 34.9756 cents 5: 652.4634 .. 1042.5066 cents 7203/5750, 390.0431 cents 287500/352947,-355.0675 cents 6: 774.9812 .. 1165.0244 cents 7203/5750, 390.0431 cents 2645/3087,-267.5253 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 50/49, 34.9756 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 147/115, 425.0188 cents Average / Smallest step : 4.901374 Largest / Average step : 2.479276 Largest / Smallest step : 12.151859 Median interval of one step : 161/150, 122.5178 cents, amount: 2 Most common interval of one step : 50/49, 34.9756 cents, amount: 3 Least squares average step : 169.60834 cents, oct.: 1187.25835 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABCBACB Step pattern size order : MSLSMLS Scale is a Constant Structure, by a margin of 34.97561 cents Scale diversity : 1.180038 Lumma stability : 0.087439 Lumma impropriety factor : 0.650072 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 : 50/49, 34.9756 cents Most common intervals : 7/5, 582.5122 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 157.493 617.488 cents Most common triad is 0.0 582.512 617.488 cents, amount: 3 Number of recognisable fifths : 1, average 705.0300 cents Scale contains a complete diamond : 5 7 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 23 Odd number limit : 1127 (O: 1127 U: 1127) Highest odd numerator or denominator: 161 Scale harmonicity : 0.010329 Average absolute harmonicity : 0.171240 Specific harmonicity : 0.050632 Fundamental : 1/1050, -10.0362 octaves, 0.2492 Hz. Guide tone : 11270, 13.4602 octaves, 2948520.121 Hz. Exponens Consonantiae : 1.183350E+07, 23.49637 octaves Euler's gradus suavitatis : 57 Sum of Mann's harmonic distance : 249.5, average 35.64286 Mersenne's string divisions : 490612452 Sum of van Prooijen's expressibility: 8.31067, average 1.18724 Sum of Tenney's harmonic distance : 16.38302, average 2.34043 Vogel's harmonic complexity : 28.14286 Wille's k value : 563 Wilson's harmonic complexity : 62 Rectangular lattice diameter : 8 Triangular lattice diameter : 4 Lattice compactness : 65.73335, average 2.34762 Lattice compactness (without 2's) : 60.28697, average 2.15311 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 1 0.14286 3 1 3: -1 .. 0 -0.42857 3 5: -2 .. 1 -0.71429 7 7: -1 .. 2 0.28571 6 3 23: 0 .. 1 0.42857 3 3 Average exponent except 2's :-3 / 7 =-0.42857 Average absolute exponent except 2's: 19 / 7 = 2.71429 Scale is JI-epimorphic with val: <7 10 15 18 30| Scale is weakly epimorphic with val: <7 10 15 19 34| Scale is weakly epimorphic with val: <7 10 15 20 31| Scale is weakly epimorphic with val: <7 10 15 21 35| Scale is weakly epimorphic with val: <7 10 16 18 34| Scale is JI-epimorphic with val: <7 10 16 19 31| Scale is weakly epimorphic with val: <7 10 16 20 35| Scale is weakly epimorphic with val: <7 10 16 21 32| Scale is weakly epimorphic with val: <7 10 16 22 29| Scale is weakly epimorphic with val: <7 10 17 18 31| Scale is weakly epimorphic with val: <7 10 17 19 35| Scale is JI-epimorphic with val: <7 10 17 20 32| Scale is weakly epimorphic with val: <7 10 17 21 29| Scale is weakly epimorphic with val: <7 10 17 22 33| Scale is weakly epimorphic with val: <7 10 18 19 32| Scale is weakly epimorphic with val: <7 10 18 20 29| Scale is JI-epimorphic with val: <7 10 18 21 33| Scale is weakly epimorphic with val: <7 10 18 22 30| Scale is JI-epimorphic with val: <7 11 15 18 31| Scale is weakly epimorphic with val: <7 11 15 19 35| Scale is weakly epimorphic with val: <7 11 15 20 32| Scale is weakly epimorphic with val: <7 11 15 21 29| Scale is weakly epimorphic with val: <7 11 16 18 35| Scale is JI-epimorphic with val: <7 11 16 19 32| Scale is weakly epimorphic with val: <7 11 16 20 29| Scale is weakly epimorphic with val: <7 11 16 21 33| Scale is weakly epimorphic with val: <7 11 16 22 30| Scale is weakly epimorphic with val: <7 11 17 18 32| Scale is weakly epimorphic with val: <7 11 17 19 29| Scale is JI-epimorphic with val: <7 11 17 20 33| Scale is weakly epimorphic with val: <7 11 17 21 30| Scale is weakly epimorphic with val: <7 11 17 22 34| Scale is weakly epimorphic with val: <7 11 18 19 33| Scale is weakly epimorphic with val: <7 11 18 20 30| Scale is JI-epimorphic with val: <7 11 18 21 34| Scale is weakly epimorphic with val: <7 11 18 22 31| Scale is JI-epimorphic with val: <7 12 15 18 32| Scale is weakly epimorphic with val: <7 12 15 19 29| Scale is weakly epimorphic with val: <7 12 15 20 33| Scale is weakly epimorphic with val: <7 12 15 21 30| Scale is weakly epimorphic with val: <7 12 16 18 29| Scale is JI-epimorphic with val: <7 12 16 19 33| Scale is weakly epimorphic with val: <7 12 16 20 30| Scale is weakly epimorphic with val: <7 12 16 21 34| Scale is weakly epimorphic with val: <7 12 16 22 31| Scale is weakly epimorphic with val: <7 12 17 18 33| Scale is weakly epimorphic with val: <7 12 17 19 30| Scale is JI-epimorphic with val: <7 12 17 20 34| Scale is weakly epimorphic with val: <7 12 17 21 31| Scale is weakly epimorphic with val: <7 12 17 22 35| Scale is weakly epimorphic with val: <7 12 18 19 34| Scale is weakly epimorphic with val: <7 12 18 20 31| Scale is JI-epimorphic with val: <7 12 18 21 35| Scale is weakly epimorphic with val: <7 12 18 22 32|
FIT/MODE
7: 1 0 2 1 0 3 0 N SD: 47.9091 c. M:-68.2265 c. 8: 1 0 3 0 1 3 0 N T3 SD: 19.8071 c. M:-34.9756 c. 18: 2 0 7 0 2 6 1 N SD: 18.3660 c. M: 31.6911 c. 19: 2 0 7 1 2 6 1 N SD: 18.8901 c. M: 31.1777 c. 21: 2 1 7 1 2 7 1 N T3 SD: 11.9950 c. M: 22.1672 c. 23: 2 1 8 1 2 8 1 N T3 SD: 11.1250 c. M: 18.1700 c. 29: 3 1 10 1 3 10 1 N T3 SD: 4.6563 c. M:-8.0238 c. 31: 3 1 11 1 3 11 1 N T3 SD: 3.5702 c. M: 6.3888 c. 39: 4 1 14 1 4 14 1 N T3 SD: 2.4652 c. M:-4.2064 c. 68: 7 2 24 2 7 24 2 N T3 SD: 0.7852 c. M:-1.3301 c. 107: 11 3 38 3 11 38 3 N T3 SD: 0.7212 c. M:-1.3308 c. 138: 14 4 49 4 14 49 4 N T3 SD: 0.5822 c. M: 0.9717 c. 167: 17 5 59 5 17 59 5 N T3 SD: 0.5146 c. M: 0.9525 c. 175: 18 5 62 5 18 62 5 N T3 SD: 0.5227 c. M:-0.9107 c. 206: 21 6 73 6 21 73 6 N T3 SD: 0.1314 c. M: 0.2119 c. 274: 28 8 97 8 28 97 8 N T3 SD: 0.0975 c. M:-0.1708 c. 480: 49 14 170 14 49 170 14 N T3 SD: 0.0135 c. M: 0.0244 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: 19.0253 cents 3 x x 4 x 5 x 6 S SD: 55.7500 cents 4 x x x x 6 x 8 S SD: 19.0253 cents 5 x 6:7 x 8 x 10 S SD: 43.6174 cents 6 x 7:8 x 9 x 12 S SD: 35.8347 cents 7 x 8 x 10:11 x 14 SD: 21.2631 cents 8 x 9:11 x 12 x 16 SD: 16.9105 cents 9 x 10 x 13:14 x 18 SD: 10.0218 cents 10 x 11:14 x 15 x 20 SD: 9.6962 cents 11 x 12:15:16:17 x 22 SD: 11.4573 cents 12:13 x x 17:18 x 24 SD: 10.9416 cents 13:14 x 18:19:20:25:26 SD: 9.2449 cents 14:15 x x 20:21:27:28 SD: 9.4667 cents 15:16 x 21 x 23:29:30 SD: 5.2107 cents 17:18:19:24 x 26:33:34 SD: 7.9815 cents 18:19:20:25:26:28:35:36 S SD: 7.5911 cents 19:20:21 x 27:29:37:38 SD: 6.7854 cents 21 x 23:29:30:32:41:42 SD: 4.4853 cents 22 x 24:31 x 34:43:44 SD: 3.9073 cents 23 x 25:32:33:35:45:46 SD: 3.8281 cents 24:26 x x 34:37:47:48 SD: 4.7238 cents 25:27 x 35:36:38:49:50 SD: 3.8508 cents 26:28 x 36:37:40:51:52 SD: 3.6482 cents 28:30:31:39:40:43:55:56 SD: 3.0629 cents 29:31:32:41 x 44:57:58 SD: 4.8944 cents 30:32:33:42:43:46:59:60 SD: 2.2155 cents 35 x 38:49:50:54:69:70 SD: 3.5152 cents 36:39 x 50:51:55:71:72 SD: 4.7529 cents 37:40:41:52:53:57:73:74 SD: 4.1077 cents 38:41:42:53:54:58:74:76 SD: 3.6274 cents 39:42:43:55:56:60:76:78 SD: 3.3136 cents 40:43:44:56:57:61:78:80 SD: 2.2580 cents 42:45:46:59:60:64:82:84 SD: 2.0495 cents 52:56:57:73:74:80:102:104 SD: 1.6772 cents 53:57:58:74:76:81:104:106 SD: 1.5294 cents 70:75:77:98:100:107:137:140 SD: 1.4374 cents 73:78:80:102:104:112:143:146 SD: 1.4167 cents 82:88:90:115:117:126:161:164 SD: 1.0061 cents 95:102:104:133:136:146:186:190 SD: 0.8247 cents 105:113:115:147:150:161:206:210 SD: 0.7000 cents 135:145:148:189:193:207:265:270 SD: 0.5092 cents 177:190:194:248:253:271:347:354 SD: 0.4791 cents 178:191:195:249:254:273:349:356 SD: 0.3688 cents 231:248:253:323:330:354:453:462 SD: 0.3660 cents 270:290:296:378:386:414:529:540 SD: 0.3584 cents 272:292:298:381:389:417:533:544 SD: 0.3227 cents 273:293:299:382:390:419:535:546 SD: 0.2724 cents 285:306:312:399:407:437:559:570 SD: 0.2413 cents 315:338:345:441:450:483:617:630 SD: 0.1762 cents 420:451:460:588:600:644:823:840 SD: 0.1251 cents 450:483:493:630:643:690:882:900 SD: 0.0903 cents 600:644:657:840:857:920:1176:1200 SD: 0.0678 cents