Scala analysis: xen09-chalmers-tritriadic-7-10-13
Tritriadic scale built from 7:10:13
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 14/13 128.298245 2/3-tone 2: 65/49 489.189563 3: 10/7 617.487807 Euler's tritone 4: 20/13 745.786052 tridecimal semi-augmented fifth 5: 169/98 943.403511 6: 13/7 1071.701755 16/3-tone 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 14/13 128.2982 2/3-tone 1: 14/13 128.2982 2/3-tone 2: 845/686 360.8913 3: 14/13 128.2982 2/3-tone 4: 14/13 128.2982 2/3-tone 5: 2197/1960 197.6175 6: 14/13 128.2982 2/3-tone 7: 14/13 128.2982 2/3-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 14/13 128.298 cents 2/3-tone 1: 1 2197/1960 197.617 cents 1: 1 845/686 360.891 cents 2: 3 196/169 256.596 cents two (2/3-tone) 2: 2 169/140 325.916 cents 2: 2 65/49 489.190 cents 3: 1 2744/2197 384.895 cents 3: 3 13/10 454.214 cents tridecimal semi-diminished fourth 3: 3 10/7 617.488 cents Euler's tritone 4: 3 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 3 20/13 745.786 cents tridecimal semi-augmented fifth 4: 1 2197/1372 815.105 cents 5: 2 98/65 710.810 cents 5: 2 280/169 874.084 cents 5: 3 169/98 943.404 cents 6: 1 1372/845 839.109 cents 6: 1 3920/2197 1002.383 cents 6: 5 13/7 1071.702 cents 16/3-tone 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 : 128.3 489.2 617.5 745.8 943.4 1071.7 1200.0 128.3 : 360.9 489.2 617.5 815.1 943.4 1071.7 1200.0 489.2 : 128.3 256.6 454.2 582.5 710.8 839.1 1200.0 617.5 : 128.3 325.9 454.2 582.5 710.8 1071.7 1200.0 745.8 : 197.6 325.9 454.2 582.5 943.4 1071.7 1200.0 943.4 : 128.3 256.6 384.9 745.8 874.1 1002.4 1200.0 1071.7: 128.3 256.6 617.5 745.8 874.1 1071.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 128.2982 .. 360.8913 cents 10985/9604, 232.5931 cents 14/13, 128.2982 cents 2: 256.5965 .. 489.1896 cents 10985/9604, 232.5931 cents 134456/142805,-104.2948 cents 3: 384.8947 .. 617.4878 cents 10985/9604, 232.5931 cents 134456/142805,-104.2948 cents 4: 582.5122 .. 815.1053 cents 10985/9604, 232.5931 cents 49/50,-34.9756 cents 5: 710.8104 .. 943.4035 cents 10985/9604, 232.5931 cents 134456/142805,-104.2948 cents 6: 839.1087 .. 1071.7018 cents 10985/9604, 232.5931 cents 134456/142805,-104.2948 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 14/13, 128.2982 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 845/686, 360.8913 cents Average / Smallest step : 1.336172 Largest / Average step : 2.105199 Largest / Smallest step : 2.812909 Median interval of one step : 14/13, 128.2982 cents, amount: 5 Most common interval of one step : 14/13, 128.2982 cents, amount: 5 Least squares average step : 182.06795 cents, oct.: 1274.47565 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABAACAA Step pattern size order : SLSSMSS Scale is a Constant Structure, by a margin of 24.00342 cents Scale diversity : 1.405795 Lumma stability : 0.213830 Lumma impropriety factor : 0.376796 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 : 1882384/1856465, 24.0034 cents Most common intervals : 14/13, 128.2982 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 617.488 1071.702 cents Number of recognisable fifths : 2, average 710.8104 cents Scale contains a complete diamond : 7 13 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 13 Odd number limit : 2197 (O: 2197 U: 2197) Highest odd numerator or denominator: 169 Scale harmonicity : 0.009370 Average absolute harmonicity : 0.169362 Specific harmonicity : 0.051644 Fundamental : 1/1274, -10.3151 octaves, 0.2054 Hz. Guide tone : 23660, 14.5302 octaves, 6190060.875 Hz. Exponens Consonantiae : 3.014284E+07, 24.84531 octaves Euler's gradus suavitatis : 62 Sum of Mann's harmonic distance : 240.5, average 34.35714 Mersenne's string divisions : 170757180 Sum of van Prooijen's expressibility: 8.22773, average 1.17539 Sum of Tenney's harmonic distance : 16.50244, average 2.35749 Vogel's harmonic complexity : 29.42857 Wille's k value : 1098 Wilson's harmonic complexity : 65 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 66.58357, average 2.37798 Lattice compactness (without 2's) : 56.50032, average 2.01787 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.57143 6 1 5: 0 .. 1 0.42857 3 7: -2 .. 1 -0.71429 7 1 13: -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 15 18 26| Scale is JI-epimorphic with val: <7 15 19 25| Scale is weakly epimorphic with val: <7 15 20 24| Scale is weakly epimorphic with val: <7 16 18 28| Scale is weakly epimorphic with val: <7 16 19 27| Scale is JI-epimorphic with val: <7 16 20 26| = patent Scale is weakly epimorphic with val: <7 16 21 25| Scale is weakly epimorphic with val: <7 16 22 24| Scale is weakly epimorphic with val: <7 17 19 29| Scale is weakly epimorphic with val: <7 17 20 28| Scale is JI-epimorphic with val: <7 17 21 27| Scale is weakly epimorphic with val: <7 17 22 26| Scale is weakly epimorphic with val: <7 18 19 24| Scale is weakly epimorphic with val: <7 18 21 29| Scale is JI-epimorphic with val: <7 18 22 28|
FIT/MODE
7: 0 2 1 1 1 1 1 N T3 SD: 93.6819 c. M: 146.3324 c. 8: 1 2 1 1 1 1 1 P M ME S SD: 25.8711 c. M: 43.4035 c. 10: 1 3 1 1 2 1 1 N T3 SD: 14.4833 c. M: 25.7861 c. 18: 2 5 2 2 3 2 2 N T3 SD: 12.6507 c. M: 22.5229 c. 19: 2 6 2 2 3 2 2 N T3 SD: 9.4651 c. M:-16.0736 c. 27: 3 8 3 3 4 3 3 N T3 SD: 6.2113 c. M: 10.0702 c. 29: 3 9 3 3 5 3 3 N T3 SD: 4.9168 c. M:-8.3206 c. 37: 4 11 4 4 6 4 4 N T3 SD: 1.7421 c. M: 2.8630 c. 66: 7 20 7 7 11 7 7 N T3 SD: 1.1867 c. M:-2.0510 c. 103: 11 31 11 11 17 11 11 N T3 SD: 0.1530 c. M:-0.2858 c. 243: 26 73 26 26 40 26 26 N T3 SD: 0.1689 c. M: 0.3007 c. 346: 37 104 37 37 57 37 37 N T3 SD: 0.0999 c. M: 0.1722 c. 449: 48 135 48 48 74 48 48 N T3 SD: 0.0771 c. M: 0.1290 c. 552: 59 166 59 59 91 59 59 N T3 SD: 0.0748 c. M: 0.1339 c. 954: 102 287 102 102 157 102 102 N T3 SD: 0.0801 c. M:-0.1259 c. 991: 106 298 106 106 163 106 106 N T3 SD: 0.0763 c. M:-0.1272 c. 1001: 107 301 107 107 165 107 107 N T3 SD: 0.0745 c. M: 0.1317 c. 1057: 113 318 113 113 174 113 113 N T3 SD: 0.0724 c. M:-0.1198 c. 1094: 117 329 117 117 180 117 117 N T3 SD: 0.0577 c. M:-0.1006 c. 1160: 124 349 124 124 191 124 124 N T3 SD: 0.0687 c. M:-0.1208 c. 1197: 128 360 128 128 197 128 128 N T3 SD: 0.0439 c. M:-0.0786 c. 1300: 139 391 139 139 214 139 139 N T3 SD: 0.0347 c. M:-0.0601 c. 1403: 150 422 150 150 231 150 150 N T3 SD: 0.0302 c. M:-0.0478 c. 1506: 161 453 161 161 248 161 161 N T3 SD: 0.0301 c. M:-0.0535 c. 1543: 165 464 165 165 254 165 165 N T3 SD: 0.0258 c. M: 0.0464 c. 1646: 176 495 176 176 271 176 176 N T3 SD: 0.0150 c. M: 0.0256 c. 1749: 187 526 187 187 288 187 187 N T3 SD: 0.0065 c. M:-0.0115 c. 1852: 198 557 198 198 305 198 198 N T3 SD: 0.0066 c. M:-0.0113 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: 21.9155 cents 3 x 4 x x 5 x 6 S SD: 19.9017 cents 4 x 5 x 6:7 x 8 S SD: 28.6693 cents 5 x x 7:8 x 9:10 SD: 23.4002 cents 6:7:8 x 9:10:11:12 S SD: 26.4508 cents 7:8:9:10:11:12:13:14 H SD: 17.4752 cents 8:9:11 x 12:14:15:16 SD: 18.5734 cents 9:10:12:13:14:16:17:18 S SD: 12.2680 cents 11:12:15:16:17:19:20:22 SD: 10.2718 cents 12:13:16:17:18:21:22:24 SD: 8.4035 cents 13:14:17:19:20:22:24:26 SD: 8.2591 cents 14:15:19:20:22:24:26:28 SD: 7.9429 cents 15:16:20:21:23:26:28:30 SD: 6.0041 cents 21:23:28:30:32:36:39:42 SD: 5.1722 cents 22:24:29:31:34:38:41:44 SD: 5.1299 cents 24:26:32:34:37:41:45:48 SD: 4.3959 cents 26:28:34:37:40:45:48:52 SD: 4.0477 cents 28:30:37:40:43:48:52:56 SD: 2.2042 cents 37:40:49:53:57:64:69:74 SD: 1.8031 cents 52:56:69:74:80:90:97:104 SD: 1.7091 cents 54:58:72:77:83:93:100:108 SD: 1.7018 cents 61:66:81:87:94:105:113:122 SD: 1.5247 cents 65:70:86:93:100:112:121:130 SD: 0.9712 cents 91:98:121:130:140:157:169:182 SD: 0.5954 cents 117:126:155:167:180:202:217:234 SD: 0.5824 cents 119:128:158:170:183:205:221:238 SD: 0.4646 cents 156:168:207:223:240:269:290:312 SD: 0.3004 cents 236:254:313:337:363:407:438:472 SD: 0.2543 cents 273:294:362:390:420:471:507:546 SD: 0.1490 cents 364:392:483:520:560:628:676:728 SD: 0.1342 cents 392:422:520:560:603:676:728:784 SD: 0.0955 cents