Scala analysis: xen09-chalmers-tritriadic-26-35-48
Tritriadic scale built from 26:35:48
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 13/12 138.572661 tridecimal 2/3-tone 2: 210/169 376.039298 3: 35/26 514.611959 4: 35/24 653.184619 septimal semi-diminished fifth 5: 288/169 922.854678 6: 24/13 1061.427339 tridecimal neutral seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 13/12 138.5727 tridecimal 2/3-tone 1: 13/12 138.5727 tridecimal 2/3-tone 2: 2520/2197 237.4666 3: 13/12 138.5727 tridecimal 2/3-tone 4: 13/12 138.5727 tridecimal 2/3-tone 5: 6912/5915 269.6701 6: 13/12 138.5727 tridecimal 2/3-tone 7: 13/12 138.5727 tridecimal 2/3-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 13/12 138.573 cents tridecimal 2/3-tone 1: 1 2520/2197 237.467 cents 1: 1 6912/5915 269.670 cents 2: 3 169/144 277.145 cents two (tridecimal 2/3-tone) 2: 2 210/169 376.039 cents 2: 2 576/455 408.243 cents 3: 1 2197/1728 415.718 cents 3: 3 35/26 514.612 cents 3: 3 48/35 546.815 cents septimal semi-augmented fourth 4: 3 35/24 653.185 cents septimal semi-diminished fifth 4: 3 52/35 685.388 cents 4: 1 3456/2197 784.282 cents 5: 2 455/288 791.757 cents 5: 2 169/105 823.961 cents 5: 3 288/169 922.855 cents 6: 1 5915/3456 930.330 cents 6: 1 2197/1260 962.533 cents 6: 5 24/13 1061.427 cents tridecimal neutral seventh 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 : 138.6 376.0 514.6 653.2 922.9 1061.4 1200.0 138.6 : 237.5 376.0 514.6 784.3 922.9 1061.4 1200.0 376.0 : 138.6 277.1 546.8 685.4 824.0 962.5 1200.0 514.6 : 138.6 408.2 546.8 685.4 824.0 1061.4 1200.0 653.2 : 269.7 408.2 546.8 685.4 922.9 1061.4 1200.0 922.9 : 138.6 277.1 415.7 653.2 791.8 930.3 1200.0 1061.4: 138.6 277.1 514.6 653.2 791.8 1061.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 138.5727 .. 269.6701 cents 82944/76895, 131.0974 cents 13/12, 138.5727 cents 2: 277.1453 .. 408.2427 cents 82944/76895, 131.0974 cents 999635/995328, 7.4753 cents 3: 415.7180 .. 546.8154 cents 82944/76895, 131.0974 cents 999635/995328, 7.4753 cents 4: 653.1846 .. 784.2820 cents 82944/76895, 131.0974 cents 1225/1152, 106.3692 cents 5: 791.7573 .. 922.8547 cents 82944/76895, 131.0974 cents 999635/995328, 7.4753 cents 6: 930.3299 .. 1061.4273 cents 82944/76895, 131.0974 cents 999635/995328, 7.4753 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 13/12, 138.5727 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 6912/5915, 269.6701 cents Average / Smallest step : 1.237102 Largest / Average step : 1.573075 Largest / Smallest step : 1.946055 Median interval of one step : 13/12, 138.5727 cents, amount: 5 Most common interval of one step : 13/12, 138.5727 cents, amount: 5 Least squares average step : 174.50045 cents, oct.: 1221.50315 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 2087-tone equal temperament with octave 2/1 degrees: 241 654 895 1136 1605 1846 2087 Least number of segments generator : 1044 of 600.287 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1945 of 1118.352 cents and inv. generated superset size: 48 = 41 more = 685.714% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAACAA Step pattern size order : SMSSLSS Scale is a Constant Structure, by a margin of 7.47526 cents Scale diversity : 1.299553 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.344513 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 : 999635/995328, 7.4753 cents Most common intervals : 13/12, 138.5727 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 514.612 1061.427 cents Number of recognisable fifths : 0 Best fifths form a closed circle Scale contains a complete diamond : 3 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 : 5915 (O: 5915 U: 5915) Highest odd numerator or denominator: 169 Scale harmonicity : 0.010086 Average absolute harmonicity : 0.168119 Specific harmonicity : 0.053141 Fundamental : 1/4056, -11.9858 octaves, 0.0645 Hz. Guide tone : 131040, 16.9996 octaves, 34283414.077 Hz. Exponens Consonantiae : 5.314982E+08, 28.98549 octaves Euler's gradus suavitatis : 61 Sum of Mann's harmonic distance : 510.5, average 72.92857 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.77180, average 1.39597 Sum of Tenney's harmonic distance : 20.10902, average 2.87272 Vogel's harmonic complexity : 29.28571 Wille's k value : 2957 Wilson's harmonic complexity : 60 Rectangular lattice diameter : 8 Triangular lattice diameter : 4 Lattice compactness : 110.39009, average 3.94250 Lattice compactness (without 2's) : 60.28697, average 2.15311 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -3 .. 5 0.57143 16 1 3: -1 .. 2 0.28571 6 5: 0 .. 1 0.42857 3 7: 0 .. 1 0.42857 3 1 13: -2 .. 1 -0.71429 7 5 Average exponent except 2's : 3 / 7 = 0.42857 Average absolute exponent except 2's: 19 / 7 = 2.71429 Scale is weakly epimorphic with val: <7 10 15 18 28| Scale is JI-epimorphic with val: <7 10 15 20 25| Scale is weakly epimorphic with val: <7 10 15 21 27| Scale is weakly epimorphic with val: <7 10 15 22 29| Scale is JI-epimorphic with val: <7 10 16 19 25| Scale is weakly epimorphic with val: <7 10 16 20 27| Scale is weakly epimorphic with val: <7 10 16 21 29| Scale is JI-epimorphic with val: <7 10 17 18 25| Scale is weakly epimorphic with val: <7 10 17 19 27| Scale is weakly epimorphic with val: <7 10 17 20 29| Scale is weakly epimorphic with val: <7 10 17 22 26| Scale is weakly epimorphic with val: <7 10 18 18 27| Scale is weakly epimorphic with val: <7 10 18 19 29| Scale is weakly epimorphic with val: <7 10 18 21 26| Scale is weakly epimorphic with val: <7 10 18 22 28| Scale is weakly epimorphic with val: <7 11 15 18 27| Scale is weakly epimorphic with val: <7 11 15 19 29| Scale is weakly epimorphic with val: <7 11 15 20 24| Scale is JI-epimorphic with val: <7 11 15 21 26| Scale is weakly epimorphic with val: <7 11 15 22 28| Scale is weakly epimorphic with val: <7 11 16 18 29| Scale is weakly epimorphic with val: <7 11 16 19 24| Scale is JI-epimorphic with val: <7 11 16 20 26| = patent Scale is weakly epimorphic with val: <7 11 16 21 28| Scale is weakly epimorphic with val: <7 11 17 18 24| Scale is JI-epimorphic with val: <7 11 17 19 26| Scale is weakly epimorphic with val: <7 11 17 20 28| Scale is JI-epimorphic with val: <7 11 18 18 26| Scale is weakly epimorphic with val: <7 11 18 19 28| Scale is weakly epimorphic with val: <7 11 18 22 27| Scale is weakly epimorphic with val: <7 12 15 19 28| Scale is weakly epimorphic with val: <7 12 15 21 25| Scale is JI-epimorphic with val: <7 12 15 22 27| Scale is weakly epimorphic with val: <7 12 16 18 28| Scale is weakly epimorphic with val: <7 12 16 20 25| Scale is JI-epimorphic with val: <7 12 16 21 27| Scale is weakly epimorphic with val: <7 12 16 22 29| Scale is weakly epimorphic with val: <7 12 17 19 25| Scale is JI-epimorphic with val: <7 12 17 20 27| Scale is weakly epimorphic with val: <7 12 17 21 29| Scale is weakly epimorphic with val: <7 12 17 22 24| Scale is weakly epimorphic with val: <7 12 18 18 25| Scale is JI-epimorphic with val: <7 12 18 19 27| Scale is weakly epimorphic with val: <7 12 18 20 29| Scale is weakly epimorphic with val: <7 12 18 21 24|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 35.1251 c. M: 65.7118 c. Lebeng 9: 1 2 1 1 2 1 1 P M ME S SD: 13.4752 c. M:-23.9607 c. Pelog Saptanada: Sunda 16: 2 3 2 2 3 2 2 SP M ME S SD: 13.9817 c. M: 22.8547 c. Mavila-7, Antiaeolian 17: 2 3 2 2 4 2 2 P T3 SD: 13.7024 c. M: 23.0981 c. 25: 3 5 3 3 5 3 3 SP M DE S SD: 10.5110 c. M:-18.8154 c. Mavila-7, Antiaeolian 26: 3 5 3 3 6 3 3 P T3 SD: 4.5315 c. M: 7.0308 c. 35: 4 7 4 4 8 4 4 P T3 SD: 1.5434 c. M:-2.8596 c. 86: 10 17 10 10 19 10 10 SP T3 SD: 1.4998 c. M:-2.6293 c. 112: 13 22 13 13 25 13 13 SP T3 SD: 0.7916 c. M: 1.4261 c. 121: 14 24 14 14 27 14 14 SP T3 SD: 0.7702 c. M:-1.3608 c. 147: 17 29 17 17 33 17 17 SP T3 SD: 0.3044 c. M: 0.5291 c. 182: 21 36 21 21 41 21 21 SP T3 SD: 0.2444 c. M: 0.4374 c. 303: 35 60 35 35 68 35 35 SP T3 SD: 0.1629 c. M:-0.2807 c. 338: 39 67 39 39 76 39 39 SP T3 SD: 0.1678 c. M:-0.2921 c. 450: 52 89 52 52 101 52 52 SP T3 SD: 0.1067 c. M: 0.1880 c. 485: 56 96 56 56 109 56 56 SP T3 SD: 0.0247 c. M:-0.0432 c. 1117: 129 221 129 129 251 129 129 SP T3 SD: 0.0187 c. M: 0.0321 c. 1602: 185 317 185 185 360 185 185 SP T3 SD: 0.0056 c. M: 0.0093 c. 2087: 241 413 241 241 469 241 241 SP T3 SD: 0.0016 c. M:-0.0029 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: 24.3852 cents 3 x x 4 x 5 x 6 S SD: 13.9698 cents 4 x 5 x 6:7 x 8 S SD: 16.9512 cents 5 x 6:7 x x 9:10 SD: 25.2234 cents 6 x 7:8:9:10:11:12 S SD: 21.2121 cents 7:8:9 x 10:12:13:14 S SD: 19.3984 cents 8:9:10:11:12:14:15:16 S SD: 14.9381 cents 9:10:11:12:13:15:17:18 SD: 11.3761 cents 11:12:14:15:16:19:20:22 SD: 8.6046 cents 13:14:16:18:19:22:24:26 SD: 7.7177 cents 17:18:21:23:25:29:31:34 SD: 7.0254 cents 20:22:25:27:29:34:37:40 SD: 4.4211 cents 24:26:30:32:35:41:44:48 SD: 3.3309 cents 26:28:32:35:38:44:48:52 SD: 3.3198 cents 33:36:41:44:48:56:61:66 SD: 3.1894 cents 34:37:42:46:50:58:63:68 SD: 3.1771 cents 37:40:46:50:54:63:68:74 SD: 1.5863 cents 58:63:72:78:85:99:107:116 SD: 1.4887 cents 61:66:76:82:89:104:113:122 SD: 1.1770 cents 70:76:87:94:102:119:129:140 SD: 1.1241 cents 87:94:108:117:127:148:161:174 SD: 1.0717 cents 95:103:118:128:139:162:175:190 SD: 1.0432 cents 96:104:119:129:140:164:177:192 SD: 1.0152 cents 98:106:122:132:143:167:181:196 SD: 0.6417 cents 144:156:179:194:210:245:266:288 SD: 0.4764 cents 168:182:209:226:245:286:310:336 SD: 0.4374 cents 190:206:236:256:277:324:351:380 SD: 0.3976 cents 203:220:252:273:296:346:375:406 SD: 0.3922 cents 214:232:266:288:312:365:395:428 SD: 0.3062 cents 240:260:298:323:350:409:443:480 SD: 0.2003 cents 301:326:374:405:439:513:556:602 SD: 0.1949 cents 338:366:420:455:493:576:624:676 SD: 0.1201 cents 552:598:686:743:805:941:1019:1104 SD: 0.0932 cents 598:648:743:805:872:1019:1104:1196 SD: 0.0749 cents