Scala analysis: xen09-chalmers-tritriadic-1-5-13
Tritriadic scale built from 1:5:13
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 65/64 26.841376 13th-partial chroma 2: 16/13 359.472338 tridecimal neutral third 3: 5/4 386.313714 major third 4: 169/128 481.055324 5: 20/13 745.786052 tridecimal semi-augmented fifth 6: 13/8 840.527662 tridecimal neutral sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/13 359.4723 tridecimal neutral third 1: 65/64 26.8414 13th-partial chroma 2: 1024/845 332.6310 3: 65/64 26.8414 13th-partial chroma 4: 169/160 94.7416 5: 2560/2197 264.7307 6: 169/160 94.7416 7: 16/13 359.4723 tridecimal neutral third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 65/64 26.841 cents 13th-partial chroma 1: 2 169/160 94.742 cents 1: 1 2560/2197 264.731 cents 1: 1 1024/845 332.631 cents 1: 1 16/13 359.472 cents tridecimal neutral third 2: 1 2197/2048 121.583 cents 2: 4 16/13 359.472 cents tridecimal neutral third 2: 1 5/4 386.314 cents major third 2: 1 13/10 454.214 cents tridecimal semi-diminished fourth 3: 2 5/4 386.314 cents major third 3: 2 13/10 454.214 cents tridecimal semi-diminished fourth 3: 1 169/128 481.055 cents 3: 2 256/169 718.945 cents two (tridecimal neutral third) 4: 2 169/128 481.055 cents 4: 1 256/169 718.945 cents two (tridecimal neutral third) 4: 2 20/13 745.786 cents tridecimal semi-augmented fifth 4: 2 8/5 813.686 cents minor sixth 5: 1 20/13 745.786 cents tridecimal semi-augmented fifth 5: 1 8/5 813.686 cents minor sixth 5: 4 13/8 840.528 cents tridecimal neutral sixth 5: 1 4096/2197 1078.417 cents 6: 1 13/8 840.528 cents tridecimal neutral sixth 6: 1 845/512 867.369 cents 6: 1 2197/1280 935.269 cents 6: 2 320/169 1105.258 cents 6: 2 128/65 1173.159 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 : 26.8 359.5 386.3 481.1 745.8 840.5 1200.0 26.8 : 332.6 359.5 454.2 718.9 813.7 1173.2 1200.0 359.5 : 26.8 121.6 386.3 481.1 840.5 867.4 1200.0 386.3 : 94.7 359.5 454.2 813.7 840.5 1173.2 1200.0 481.1 : 264.7 359.5 718.9 745.8 1078.4 1105.3 1200.0 745.8 : 94.7 454.2 481.1 813.7 840.5 935.3 1200.0 840.5 : 359.5 386.3 718.9 745.8 840.5 1105.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 26.8414 .. 359.4723 cents 1024/845, 332.6310 cents 65/64, 26.8414 cents 2: 121.5830 .. 454.2139 cents 1024/845, 332.6310 cents 28561/32768,-237.8894 cents 3: 386.3137 .. 718.9447 cents 1024/845, 332.6310 cents 25/26,-67.9002 cents 4: 481.0553 .. 813.6863 cents 1024/845, 332.6310 cents 28561/32768,-237.8894 cents 5: 745.7861 .. 1078.4170 cents 1024/845, 332.6310 cents 25/26,-67.9002 cents 6: 840.5277 .. 1173.1586 cents 1024/845, 332.6310 cents 28561/32768,-237.8894 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 65/64, 26.8414 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 16/13, 359.4723 cents Average / Smallest step : 6.386728 Largest / Average step : 2.096922 Largest / Smallest step : 13.392471 Median interval of one step : 169/160, 94.7416 cents, amount: 2 Least squares average step : 150.00746 cents, oct.: 1050.05224 cents Scale is not proper Scale is a mode of a 2280-tone equal temperament with octave 2/1 degrees: 51 683 734 914 1417 1597 2280 Least number of segments generator : 1141 of 600.526 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1631 of 858.421 cents and inv. generated superset size: 74 = 67 more = 1057.143% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABACDCE Step pattern size order : ADABCBE Scale is not a Constant Structure Scale diversity : 1.226295 Lumma stability : 0.044736 Lumma impropriety factor : 0.707890 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 : 5 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 65/64, 26.8414 cents Most common intervals : 16/13, 359.4723 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 386.314 840.528 cents Most common triad is 0.0 359.472 840.528 cents, amount: 3 Number of recognisable fifths : 3, average 718.9447 cents Number of appreciable fifths : 0 Scale contains a complete diamond : 1 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 : 0.011924 Average absolute harmonicity : 0.182599 Specific harmonicity : 0.065290 Fundamental : 1/1664, -10.7004 octaves, 0.1572 Hz. Guide tone : 13520, 13.7228 octaves, 3537177.643 Hz. Exponens Consonantiae : 2.249728E+07, 24.42325 octaves Euler's gradus suavitatis : 52 Sum of Mann's harmonic distance : 260.5, average 37.21429 Mersenne's string divisions : 2592513 Sum of van Prooijen's expressibility: 8.08160, average 1.15451 Sum of Tenney's harmonic distance : 16.30632, average 2.32947 Vogel's harmonic complexity : 24.28571 Wille's k value : 1098 Wilson's harmonic complexity : 44 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 139.04786, average 4.96600 Lattice compactness (without 2's) : 41.76998, average 1.49178 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -7 .. 4 -1.57143 25 1 5: 0 .. 1 0.42857 3 1 13: -1 .. 2 0.28571 6 5 Average exponent except 2's : 5 / 7 = 0.71429 Average absolute exponent except 2's: 9 / 7 = 1.28571 Scale is weakly epimorphic with val: <7 16 25| Scale is weakly epimorphic with val: <7 17 27| Scale is weakly epimorphic with val: <7 18 29|
FIT/MODE
7: 0 2 0 1 1 1 2 N T3 SD: 33.5388 c. M: 60.0718 c. 9: 0 3 0 1 2 0 3 N SD: 37.5403 c. M:-54.2139 c. 10: 0 3 0 1 2 1 3 N SD: 17.2356 c. M: 26.8414 c. 13: 0 4 0 1 3 1 4 N SD: 15.2938 c. M: 26.8414 c. 23: 0 7 0 2 5 2 7 N SD: 15.1148 c. M: 26.8414 c. 24: 1 6 1 2 5 2 7 N SD: 13.5211 c. M:-23.1586 c. 27: 1 7 1 2 6 2 8 N SD: 9.8899 c. M:-17.6031 c. 30: 1 8 1 2 7 2 9 N SD: 8.9775 c. M:-14.2139 c. 34: 1 9 1 3 7 3 10 N SD: 7.0945 c. M:-13.0623 c. 37: 1 10 1 3 8 3 11 N SD: 3.4600 c. M:-5.5911 c. 40: 1 11 1 3 9 3 12 N SD: 2.4783 c. M:-4.2139 c. 50: 1 14 1 4 11 4 15 N SD: 1.6163 c. M: 2.8414 c. 87: 2 24 2 7 19 7 26 N SD: 0.9131 c. M:-1.7033 c. 90: 2 25 2 7 20 7 27 N SD: 0.6096 c. M: 1.0553 c. 140: 3 39 3 11 31 11 42 N SD: 0.6872 c. M: 1.1271 c. 177: 4 49 4 14 39 14 53 N SD: 0.1809 c. M:-0.3006 c. 267: 6 74 6 21 59 21 80 N SD: 0.1571 c. M:-0.2814 c. 404: 9 112 9 32 89 32 121 N SD: 0.1348 c. M: 0.2415 c. 444: 10 123 10 35 98 35 133 N SD: 0.1139 c. M:-0.1857 c. 494: 11 137 11 39 109 39 148 N SD: 0.0683 c. M: 0.1207 c. 671: 15 186 15 53 148 53 201 N SD: 0.0187 c. M: 0.0334 c. 1609: 36 446 36 127 355 127 482 N SD: 0.0105 c. M:-0.0188 c. 2280: 51 632 51 180 503 180 683 N SD: 0.0020 c. M:-0.0034 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: 21.9155 cents 3 x x x 4 x 5:6 S SD: 15.6695 cents 4 x x 5 x 6:7:8 S SD: 33.8947 cents 5 x 6 x 7 x 8:10 S SD: 28.4332 cents 6 x 7 x 8:9:10:12 S SD: 22.5442 cents 7 x x x 9:11 x 14 SD: 19.6092 cents 8 x x 10:11:12:13:16 SD: 16.5626 cents 9:10:11 x 12:14:15:18 S SD: 27.3460 cents 10:11:12 x 13:15:16:20 SD: 26.0193 cents 11:12 x 14:15:17:18:22 SD: 23.3512 cents 12:13 x 15:16:18:20:24 SD: 21.4831 cents 13:14:16 x 17:20:21:26 SD: 17.2204 cents 14:15:17 x 18:22:23:28 SD: 18.9580 cents 15:16:18:19:20:23:24:30 SD: 14.7744 cents 16:17 x 20:21:25:26:32 SD: 13.8723 cents 17:18:21 x 22:26:28:34 SD: 14.0371 cents 18:19:22:23:24:28:29:36 SD: 11.8889 cents 19:20:23:24:25:29:31:38 SD: 10.3652 cents 20:21 x 25:26:31:33:40 SD: 11.6752 cents 21:22:26 x 28:32:34:42 SD: 9.9892 cents 22:23:27:28:29:34:36:44 SD: 8.7176 cents 24:25 x 30:32:37:39:48 SD: 7.8577 cents 25:26:31 x 33:38:41:50 SD: 8.4050 cents 26:27:32:33:34:40:42:52 SD: 7.2317 cents 27:28:33:34:36:42:44:54 SD: 6.8397 cents 28:29:34:35:37:43:46:56 SD: 6.4909 cents 29:30 x 36:38:45:47:58 SD: 6.6082 cents 30:31:37:38:40:46:49:60 SD: 6.1192 cents 31:32:38:39:41:48:50:62 SD: 5.0788 cents 32:33:39:40:42:49:52:64 SD: 4.8635 cents 33:34 x 41:44:51:54:66 SD: 5.8302 cents 34:35:42:43:45:52:55:68 SD: 4.9052 cents 35:36:43:44:46:54:57:70 SD: 3.7508 cents 37:38 x 46:49:57:60:74 SD: 3.7551 cents 40:41:49:50:53:62:65:80 SD: 3.2707 cents 43:44:53:54:57:66:70:86 SD: 2.5240 cents 47:48:58:59:62:72:76:94 SD: 2.4616 cents 48:49:59:60:63:74:78:96 SD: 2.0306 cents 56:57:69:70:74:86:91:112 SD: 0.7810 cents 125:127:154:156:165:192:203:250 SD: 0.6401 cents 181:184:223:226:239:278:294:362 SD: 0.6113 cents 184:187:226:230:243:283:299:368 SD: 0.5390 cents 187:190:230:234:247:288:304:374 SD: 0.4452 cents 200:203:246:250:264:308:325:400 SD: 0.3341 cents 256:260:315:320:338:394:416:512 SD: 0.1139 cents 312:317:384:390:412:480:507:624 SD: 0.1045 cents 568:577:699:710:750:874:923:1136 SD: 0.0770 cents