Scala analysis: xen18-secor-13-limit-2-just
13-limit just scale, enharmonic alteration
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: 7/4 968.825906 harmonic seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole 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: 14/13 128.2982 2/3-tone 7: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 14/13 128.298 cents 2/3-tone 1: 2 13/12 138.573 cents tridecimal 2/3-tone 1: 1 9/8 203.910 cents major whole tone 1: 2 8/7 231.174 cents septimal whole tone 2: 2 7/6 266.871 cents septimal minor third 2: 1 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 2: 2 16/13 359.472 cents tridecimal neutral third 2: 1 26/21 369.747 cents 2: 1 9/7 435.084 cents septimal major third, BP third 3: 1 21/16 470.781 cents narrow fourth 3: 4 4/3 498.045 cents perfect 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: 4 3/2 701.955 cents perfect fifth 4: 1 32/21 729.219 cents wide fifth 5: 1 14/9 764.916 cents septimal minor sixth 5: 1 21/13 830.253 cents 5: 2 13/8 840.528 cents tridecimal neutral sixth 5: 1 64/39 857.517 cents 39th subharmonic 5: 2 12/7 933.129 cents septimal major sixth 6: 2 7/4 968.826 cents harmonic seventh 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 24/13 1061.427 cents tridecimal neutral seventh 6: 2 13/7 1071.702 cents 16/3-tone 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 : 138.6 266.9 498.0 702.0 840.5 968.8 1200.0 138.6 : 128.3 359.5 563.4 702.0 830.3 1061.4 1200.0 266.9 : 231.2 435.1 573.7 702.0 933.1 1071.7 1200.0 498.0 : 203.9 342.5 470.8 702.0 840.5 968.8 1200.0 702.0 : 138.6 266.9 498.0 636.6 764.9 996.1 1200.0 840.5 : 128.3 359.5 498.0 626.3 857.5 1061.4 1200.0 968.8 : 231.2 369.7 498.0 729.2 933.1 1071.7 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: 470.7809 .. 573.6568 cents 52/49, 102.8758 cents 49/48, 35.6968 cents 4: 626.3432 .. 729.2191 cents 52/49, 102.8758 cents 1568/1521, 52.6865 cents 5: 764.9159 .. 933.1291 cents 54/49, 168.2132 cents 49/48, 35.6968 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 : 13/12, 138.5727 cents, amount: 2 Least squares average step : 167.07045 cents, oct.: 1169.49316 cents Scale is strictly proper Step pattern alph. order: ABCDABC Step pattern size order : BADCBAD Scale is a Constant Structure, by a margin of 35.69681 cents Scale diversity : 1.472506 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.376725 Rothenberg efficiency : 0.421769 redundancy: 0.578231 Efficiency x scale size : 2.952381 Number of different interval sizes : 26 = 4.33333 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 169/168, 10.2744 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Number of recognisable fifths : 4, average 701.9550 cents Scale is Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords Scale contains a complete diamond : 1 3 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 42.8571% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 Scale is differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 5 and 6 combined Limited inverse transpositions with margin 168.2132 cents: 6 -- Rational properties -- Prime limit : 13 Odd number limit : 39 (O: 39 U: 39) Highest odd numerator or denominator: 13 Scale harmonicity : 0.023379 Average absolute harmonicity : 0.245303 Specific harmonicity : 0.126998 Fundamental : 1/24, -4.5850 octaves, 10.9011 Hz. Guide tone : 1092, 10.0928 octaves, 285695.117 Hz. Exponens Consonantiae : 2.620800E+04, 14.67772 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 42.5, average 6.07143 Mersenne's string divisions : 75075 Sum of van Prooijen's expressibility: 4.87233, average 0.69605 Sum of Tenney's harmonic distance : 9.43893, average 1.34842 Vogel's harmonic complexity : 10.00000 Wille's k value : 19 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 70.79910, average 2.52854 Lattice compactness (without 2's) : 36.07837, average 1.28851 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.85714 12 1 3: -1 .. 1 -0.28571 4 2 7: 0 .. 1 0.28571 2 2 13: 0 .. 1 0.28571 2 2 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 8 / 7 = 1.14286 Scale is weakly epimorphic with val: <7 11 19 27| Scale is JI-epimorphic with val: <7 11 20 26| = patent Scale is weakly epimorphic with val: <7 12 18 29| Scale is weakly epimorphic with val: <7 12 22 25|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 40.0474 c. M:-75.9862 c. Lebeng 9: 1 1 2 1 1 1 2 P M ME S SD: 27.8266 c. M: 40.5277 c. Pseudo Pelog, Pelogic-7, Antiionian 10: 1 1 2 2 1 1 2 P D3 S SD: 16.0197 c. M: 26.8709 c. 17: 2 2 3 3 2 2 3 SP D3 S SD: 9.9764 c. M:-19.4094 c. 24: 3 2 5 4 3 2 5 P SD: 11.1291 c. M: 18.8259 c. 26: 3 3 5 4 3 3 5 SP SD: 7.3930 c. M:-10.0522 c. 27: 3 3 5 5 3 3 5 SP D3 S SD: 6.4436 c. M: 9.1561 c. 36: 4 4 7 6 4 4 7 SP SD: 3.6166 c. M: 7.1943 c. 53: 6 6 10 9 6 6 10 SP SD: 2.9561 c. M:-4.8272 c. 63: 7 7 12 11 7 7 12 SP SD: 2.8269 c. M: 5.2393 c. 67: 8 7 13 11 8 7 13 SP SD: 2.7648 c. M:-4.7109 c. 77: 9 8 15 13 9 8 15 SP SD: 1.4754 c. M: 2.5921 c. 94: 11 10 18 16 11 10 18 SP SD: 1.2532 c. M:-2.0255 c. 104: 12 11 20 18 12 11 20 SP SD: 1.3473 c. M:-1.8912 c. 130: 15 14 25 22 15 14 25 SP SD: 0.4593 c. M:-0.8214 c. 207: 24 22 40 35 24 22 40 SP SD: 0.4426 c. M: 0.7100 c. 234: 27 25 45 40 27 25 45 SP SD: 0.4154 c. M:-0.6091 c. 270: 31 29 52 46 31 29 52 SP SD: 0.3962 c. M: 0.7949 c. 337: 39 36 65 57 39 36 65 SP SD: 0.3113 c. M:-0.4713 c. 347: 40 37 67 59 40 37 67 SP SD: 0.3215 c. M: 0.5885 c. 364: 42 39 70 62 42 39 70 SP SD: 0.2197 c. M:-0.4049 c. 441: 51 47 85 75 51 47 85 SP SD: 0.1669 c. M:-0.2887 c. 477: 55 51 92 81 55 51 92 SP SD: 0.1870 c. M: 0.2761 c. 571: 66 61 110 97 66 61 110 SP SD: 0.0658 c. M:-0.1314 c. 1048: 121 112 202 178 121 112 202 SP SD: 0.0665 c. M: 0.1236 c. 1178: 136 126 227 200 136 126 227 SP SD: 0.0713 c. M: 0.1202 c. 1272: 147 136 245 216 147 136 245 SP SD: 0.0718 c. M:-0.1102 c. 1282: 148 137 247 218 148 137 247 SP SD: 0.0587 c. M: 0.1002 c. 1412: 163 151 272 240 163 151 272 SP SD: 0.0250 c. M: 0.0457 c. 1983: 229 212 382 337 229 212 382 SP SD: 0.0099 c. M:-0.0170 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: 27.9328 cents 5 x 6:7 x 8:9:10 S SD: 22.4609 cents 6 x 7:8:9:10:11:12 S SD: 15.2820 cents 7 x 8:9 x 11:12:14 SD: 19.8804 cents 8 x 9:11:12:13:14:16 SD: 13.7458 cents 10:11:12:13:15:16:18:20 SD: 12.8550 cents 11:12:13:15:17:18:19:22 SD: 10.5821 cents 12:13:14:16:18:20:21:24 S SD: 6.2616 cents 22:24:26:29:33:36:39:44 SD: 5.8565 cents 23:25:27:31:35:37:40:46 SD: 5.6066 cents 24:26:28:32:36:39:42:48 S SD: 0.0000 cents