Scala analysis: xen18-secor-13-limit-1-just
13-limit just scale
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: 7/6 266.870906 septimal minor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 13/8 840.527662 tridecimal neutral sixth 6: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-tone 1: 13/12 138.5727 tridecimal 2/3-tone 2: 14/13 128.2982 2/3-tone 3: 8/7 231.1741 septimal whole tone 4: 9/8 203.9100 major whole tone 5: 13/12 138.5727 tridecimal 2/3-tone 6: 44/39 208.8353 7: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 14/13 128.298 cents 2/3-tone 1: 2 13/12 138.573 cents tridecimal 2/3-tone 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 9/8 203.910 cents major whole tone 1: 1 44/39 208.835 cents 1: 1 8/7 231.174 cents septimal whole tone 2: 1 7/6 266.871 cents septimal minor third 2: 1 13/11 289.210 cents tridecimal minor third 2: 1 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 2: 1 11/9 347.408 cents undecimal neutral third 2: 2 16/13 359.472 cents tridecimal neutral third 2: 1 9/7 435.084 cents septimal major third, BP third 3: 1 14/11 417.508 cents undecimal diminished fourth or major third 3: 3 4/3 498.045 cents perfect fourth 3: 1 11/8 551.318 cents undecimal semi-augmented fourth 3: 1 18/13 563.382 cents tridecimal augmented fourth 3: 1 39/28 573.657 cents 4: 1 56/39 626.343 cents 4: 1 13/9 636.618 cents tridecimal diminished fifth 4: 1 16/11 648.682 cents undecimal semi-diminished fifth 4: 3 3/2 701.955 cents perfect fifth 4: 1 11/7 782.492 cents undecimal augmented fifth 5: 1 14/9 764.916 cents septimal minor sixth 5: 2 13/8 840.528 cents tridecimal neutral sixth 5: 1 18/11 852.592 cents undecimal neutral sixth 5: 1 64/39 857.517 cents 39th subharmonic 5: 1 22/13 910.790 cents tridecimal major sixth 5: 1 12/7 933.129 cents septimal major sixth 6: 1 7/4 968.826 cents harmonic seventh 6: 1 39/22 991.165 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 2 24/13 1061.427 cents tridecimal neutral seventh 6: 1 13/7 1071.702 cents 16/3-tone Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.66667 = 17/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 138.6 266.9 498.0 702.0 840.5 1049.4 1200.0 138.6 : 128.3 359.5 563.4 702.0 910.8 1061.4 1200.0 266.9 : 231.2 435.1 573.7 782.5 933.1 1071.7 1200.0 498.0 : 203.9 342.5 551.3 702.0 840.5 968.8 1200.0 702.0 : 138.6 347.4 498.0 636.6 764.9 996.1 1200.0 840.5 : 208.8 359.5 498.0 626.3 857.5 1061.4 1200.0 1049.4: 150.6 289.2 417.5 648.7 852.6 991.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 128.2982 .. 231.1741 cents 52/49, 102.8758 cents 14/13, 128.2982 cents 2: 266.8709 .. 435.0841 cents 54/49, 168.2132 cents 49/48, 35.6968 cents 3: 417.5080 .. 573.6568 cents 429/392, 156.1488 cents 98/99,-17.5761 cents 4: 626.3432 .. 782.4920 cents 429/392, 156.1488 cents 1568/1521, 52.6865 cents 5: 764.9159 .. 933.1291 cents 54/49, 168.2132 cents 98/99,-17.5761 cents 6: 968.8259 .. 1071.7018 cents 52/49, 102.8758 cents 49/48, 35.6968 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 : 8/7, 231.1741 cents Average / Smallest step : 1.336172 Largest / Average step : 1.348516 Largest / Smallest step : 1.801849 Median interval of one step : 12/11, 150.6371 cents, amount: 1 Most common interval of one step : 13/12, 138.5727 cents, amount: 2 Least squares average step : 170.52204 cents, oct.: 1193.65427 cents Scale is not proper Step pattern alph. order: ABCDAEF Step pattern size order : BAFDBEC Scale is a Constant Structure, by a margin of 17.57613 cents Scale diversity : 1.525809 Lumma stability : 0.317231 Lumma impropriety factor : 0.029294 Rothenberg efficiency : 0.341497 redundancy: 0.658503 Efficiency x scale size : 2.390476 Number of different interval sizes : 34 = 5.66667 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 5.66667 = 17/3 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 352/351, 4.9253 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 3 Number of recognisable fifths : 3, average 701.9550 cents Scale contains a complete diamond : 1 3 Length of longest harmonic part : 3 at degree 6 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 42.8571% Scale is n-1 differentially coherent in interval class 1 Scale is differentially coherent in interval class 2 Scale is n-1 differentially coherent in interval class 3 Scale is n-1 differentially coherent in interval classes 4 and 5 combined -- Rational properties -- Prime limit : 13 Odd number limit : 39 (O: 39 U: 39) Highest odd numerator or denominator: 13 Scale harmonicity : 0.016406 Average absolute harmonicity : 0.240213 Specific harmonicity : 0.110449 Fundamental : 1/24, -4.5850 octaves, 10.9011 Hz. Guide tone : 12012, 13.5522 octaves, 3142646.290 Hz. Exponens Consonantiae : 2.882880E+05, 18.13715 octaves Euler's gradus suavitatis : 38 Sum of Mann's harmonic distance : 45.5, average 6.50000 Mersenne's string divisions : 116025 Sum of van Prooijen's expressibility: 5.06862, average 0.72409 Sum of Tenney's harmonic distance : 9.81131, average 1.40162 Vogel's harmonic complexity : 10.28571 Wille's k value : 19 Wilson's harmonic complexity : 37 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 69.91965, average 2.49713 Lattice compactness (without 2's) : 37.72865, average 1.34745 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.71429 11 1 3: -1 .. 1 -0.42857 5 2 7: 0 .. 1 0.14286 1 1 11: 0 .. 1 0.14286 1 1 13: 0 .. 1 0.28571 2 2 Average exponent except 2's : 1 / 7 = 0.14286 Average absolute exponent except 2's: 9 / 7 = 1.28571 Scale is weakly epimorphic with val: <7 10 18 23 26| Scale is weakly epimorphic with val: <7 10 19 23 29| Scale is weakly epimorphic with val: <7 11 19 23 27| Scale is JI-epimorphic with val: <7 11 20 24 26| = patent Scale is weakly epimorphic with val: <7 12 18 23 29| Scale is weakly epimorphic with val: <7 12 20 22 25| Scale is weakly epimorphic with val: <7 12 22 23 27|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 33.9943 c. M:-75.9862 c. Lebeng 8: 1 1 1 2 1 1 1 P M ME I SD: 36.6102 c. M:-59.4723 c. 9: 1 1 2 1 1 2 1 P M ME S SD: 25.2415 c. M: 40.5277 c. 10: 1 1 2 2 1 2 1 N D3 SD: 19.4831 c. M:-30.6371 c. 14: 2 1 3 2 2 2 2 P T3 SD: 18.5550 c. M:-32.8559 c. 17: 2 2 3 3 2 3 2 P D3 SD: 7.6483 c. M:-15.4820 c. 26: 3 3 5 4 3 5 3 P SD: 8.7069 c. M:-12.1755 c. 27: 3 3 5 5 3 5 3 N D3 SD: 8.5350 c. M:-17.3037 c. 31: 4 3 6 5 4 5 4 P SD: 8.2426 c. M:-16.2660 c. 36: 4 4 7 6 4 6 5 P SD: 7.0086 c. M: 16.0296 c. 40: 5 4 8 6 5 7 5 P SD: 7.8094 c. M:-11.9550 c. 41: 5 4 8 7 5 7 5 N SD: 4.7709 c. M:-8.2528 c. 46: 5 5 9 8 5 8 6 N SD: 5.0896 c. M: 8.1379 c. 50: 6 5 10 8 6 9 6 N SD: 4.6744 c. M:-6.6371 c. 53: 6 6 10 9 6 9 7 P SD: 3.7834 c. M: 7.8535 c. 58: 7 6 11 10 7 10 7 N SD: 4.5001 c. M:-7.7482 c. 63: 7 7 12 11 7 11 8 N SD: 2.7310 c. M: 5.2393 c. 77: 9 8 15 13 9 13 10 N SD: 2.2562 c. M: 5.2071 c. 80: 9 9 15 14 9 14 10 N SD: 2.4432 c. M: 3.5727 c. 87: 10 9 17 15 10 15 11 N SD: 2.0646 c. M: 4.8019 c. 94: 11 10 18 16 11 16 12 N SD: 1.4926 c. M: 2.5544 c. 104: 12 11 20 18 12 18 13 N SD: 1.3601 c. M:-1.8912 c. 113: 13 12 22 19 13 20 14 N SD: 1.2457 c. M:-1.9645 c. 130: 15 14 25 22 15 23 16 N SD: 1.1943 c. M:-2.9448 c. 157: 18 17 30 27 18 27 20 N SD: 1.1620 c. M: 2.2292 c. 166: 19 18 32 28 19 29 21 N SD: 1.0853 c. M: 1.9734 c. 181: 21 19 35 31 21 31 23 N SD: 1.2012 c. M: 1.8491 c. 183: 21 20 35 31 21 32 23 N SD: 0.9496 c. M:-1.9816 c. 190: 22 20 37 32 22 33 24 N SD: 0.8880 c. M: 1.6077 c. 207: 24 22 40 35 24 36 26 N SD: 0.3535 c. M:-0.5578 c. 431: 50 46 83 73 50 75 54 N SD: 0.3735 c. M:-0.6385 c. 477: 55 51 92 81 55 83 60 N SD: 0.1943 c. M: 0.3063 c. 494: 57 53 95 84 57 86 62 N SD: 0.1400 c. M:-0.3356 c. 684: 79 73 132 116 79 119 86 N SD: 0.1739 c. M: 0.2401 c. 701: 81 75 135 119 81 122 88 N SD: 0.0918 c. M:-0.1762 c. 971: 112 104 187 165 112 169 122 N SD: 0.1022 c. M: 0.1587 c. 1012: 117 108 195 172 117 176 127 N SD: 0.0988 c. M:-0.1838 c. 1178: 136 126 227 200 136 205 148 N SD: 0.0823 c. M: 0.1269 c. 1282: 148 137 247 218 148 223 161 N SD: 0.0628 c. M: 0.1002 c. 1489: 172 159 287 253 172 259 187 N SD: 0.0550 c. M: 0.1147 c. 1506: 174 161 290 256 174 262 189 N SD: 0.0603 c. M:-0.1098 c. 1776: 205 190 342 302 205 309 223 N SD: 0.0478 c. M:-0.0720 c. 1983: 229 212 382 337 229 345 249 N SD: 0.0189 c. M: 0.0437 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: 0.0000 cents 3 x x 4 x 5 x 6 S SD: 14.6104 cents 4 x x 5:6 x 7:8 S SD: 34.4330 cents 5 x 6:7 x 8:9:10 S SD: 21.2064 cents 6 x 7:8:9:10:11:12 S SD: 7.3052 cents 7 x 8:9 x 11:13:14 SD: 19.0845 cents 8 x 9:11:12:13:15:16 SD: 15.1984 cents 10:11:12:13:15:16:18:20 SD: 11.7177 cents 11:12:13:15:17:18:20:22 SD: 10.2830 cents 12:13:14:16:18:20:22:24 S SD: 6.2616 cents 22:24:26:29:33:36:40:44 SD: 5.3223 cents 24:26:28:32:36:39:44:48 SD: 0.0000 cents