Scala analysis: xen15-gilson-aristoxenus-diatonic-malakon
Aristoxenus' Diatonic Malakon
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 20/19 88.800698 small undevicesimal semitone 2: 8/7 231.174094 septimal whole tone 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 30/19 790.755699 smaller undevicesimal minor sixth 6: 12/7 933.129094 septimal major sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 7/6 266.8709 septimal minor third 1: 20/19 88.8007 small undevicesimal semitone 2: 38/35 142.3734 3: 7/6 266.8709 septimal minor third 4: 9/8 203.9100 major whole tone 5: 20/19 88.8007 small undevicesimal semitone 6: 38/35 142.3734 7: 7/6 266.8709 septimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 20/19 88.801 cents small undevicesimal semitone 1: 2 38/35 142.373 cents 1: 1 9/8 203.910 cents major whole tone 1: 2 7/6 266.871 cents septimal minor third 2: 2 8/7 231.174 cents septimal whole tone 2: 1 45/38 292.711 cents 2: 1 70/57 355.672 cents 2: 2 19/15 409.244 cents undevicesimal ditone 2: 1 21/16 470.781 cents narrow fourth 3: 1 9/7 435.084 cents septimal major third, BP third 3: 4 4/3 498.045 cents perfect fourth 3: 1 105/76 559.582 cents 3: 1 57/40 613.154 cents 4: 1 80/57 586.846 cents 4: 1 152/105 640.418 cents 4: 4 3/2 701.955 cents perfect fifth 4: 1 14/9 764.916 cents septimal minor sixth 5: 1 32/21 729.219 cents wide fifth 5: 2 30/19 790.756 cents smaller undevicesimal minor sixth 5: 1 57/35 844.328 cents 5: 1 76/45 907.289 cents 5: 2 7/4 968.826 cents harmonic seventh 6: 2 12/7 933.129 cents septimal major sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 35/19 1057.627 cents 6: 2 19/10 1111.199 cents undevicesimal major seventh 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 : 88.8 231.2 498.0 702.0 790.8 933.1 1200.0 88.8 : 142.4 409.2 613.2 702.0 844.3 1111.2 1200.0 231.2 : 266.9 470.8 559.6 702.0 968.8 1057.6 1200.0 498.0 : 203.9 292.7 435.1 702.0 790.8 933.1 1200.0 702.0 : 88.8 231.2 498.0 586.8 729.2 996.1 1200.0 790.8 : 142.4 409.2 498.0 640.4 907.3 1111.2 1200.0 933.1 : 266.9 355.7 498.0 764.9 968.8 1057.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 88.8007 .. 266.8709 cents 133/120, 178.0702 cents 20/19, 88.8007 cents 2: 231.1741 .. 470.7809 cents 147/128, 239.6068 cents 48/49,-35.6968 cents 3: 435.0841 .. 613.1543 cents 133/120, 178.0702 cents 48/49,-35.6968 cents 4: 586.8457 .. 764.9159 cents 133/120, 178.0702 cents 3200/3249,-26.3086 cents 5: 729.2191 .. 968.8259 cents 147/128, 239.6068 cents 48/49,-35.6968 cents 6: 933.1291 .. 1111.1993 cents 133/120, 178.0702 cents 48/49,-35.6968 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 20/19, 88.8007 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 1.930487 Largest / Average step : 1.556747 Largest / Smallest step : 3.005279 Median interval of one step : 38/35, 142.3734 cents, amount: 2 Least squares average step : 162.89755 cents, oct.: 1140.28285 cents Scale is not proper Step pattern alph. order: ABCDABC Step pattern size order : ABDCABD Scale is a Constant Structure, by a margin of 25.83979 cents Scale diversity : 1.606118 Lumma stability : 0.148001 Lumma impropriety factor : 0.140913 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 : 135/133, 25.8398 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 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% Scale is differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 19 Odd number limit : 105 (O: 105 U: 105) Highest odd numerator or denominator: 19 Scale harmonicity : 0.016632 Average absolute harmonicity : 0.239332 Specific harmonicity : 0.090120 Fundamental : 1/798, -9.6402 octaves, 0.3279 Hz. Guide tone : 120, 6.9069 octaves, 31395.068 Hz. Exponens Consonantiae : 9.576000E+04, 16.54714 octaves Euler's gradus suavitatis : 37 Sum of Mann's harmonic distance : 68.5, average 9.78571 Mersenne's string divisions : 181545 Sum of van Prooijen's expressibility: 5.20195, average 0.74314 Sum of Tenney's harmonic distance : 11.16649, average 1.59521 Vogel's harmonic complexity : 26.28571 Wille's k value : 598 Wilson's harmonic complexity : 37 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 62.72088, average 2.24003 Lattice compactness (without 2's) : 39.97736, average 1.42776 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 1.42857 12 1 3: -1 .. 1 0.28571 4 2 5: 0 .. 1 0.28571 2 7: -1 .. 0 -0.28571 2 2 19: -1 .. 0 -0.28571 2 2 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 10 / 7 = 1.42857 Scale is weakly epimorphic with val: <7 10 15 22 31| Scale is weakly epimorphic with val: <7 10 16 22 32| Scale is weakly epimorphic with val: <7 10 17 22 33| Scale is weakly epimorphic with val: <7 10 18 22 27| Scale is JI-epimorphic with val: <7 11 15 19 28| Scale is weakly epimorphic with val: <7 11 15 20 27| Scale is JI-epimorphic with val: <7 11 16 19 29| Scale is weakly epimorphic with val: <7 11 16 20 28| Scale is JI-epimorphic with val: <7 11 17 19 30| Scale is weakly epimorphic with val: <7 11 17 20 29| Scale is JI-epimorphic with val: <7 11 18 19 31| Scale is weakly epimorphic with val: <7 11 18 20 30| Scale is weakly epimorphic with val: <7 12 15 18 30| Scale is weakly epimorphic with val: <7 12 15 22 33| Scale is weakly epimorphic with val: <7 12 16 18 31| Scale is weakly epimorphic with val: <7 12 16 22 27| Scale is weakly epimorphic with val: <7 12 17 18 32| Scale is weakly epimorphic with val: <7 12 17 22 28| Scale is weakly epimorphic with val: <7 12 18 18 33| Scale is weakly epimorphic with val: <7 12 18 22 29|
FIT/MODE
7: 0 1 1 2 0 1 2 N T3 SD: 86.6930 c. M: 155.1879 c. 8: 0 1 2 1 1 1 2 N D3 SD: 65.3961 c. M: 101.9550 c. 9: 1 1 2 1 1 1 2 P M ME S SD: 28.8318 c. M:-44.5326 c. Pseudo Pelog, Pelogic-7, Antiionian 10: 1 1 2 2 1 1 2 P D3 S SD: 26.3211 c. M:-49.2443 c. 12: 1 1 3 2 1 1 3 N SD: 18.0787 c. M: 33.1291 c. Chromatic Dorian, Mela Kanakangi, Raga Kanakambari 14: 1 2 3 2 1 2 3 P T3 SD: 15.4901 c. M:-25.9688 c. Superpelog-Pelog 15: 1 2 3 3 1 2 3 N SD: 15.1850 c. M:-26.8709 c. 17: 1 2 4 3 1 2 4 N SD: 13.0001 c. M: 19.4094 c. 24: 2 3 5 4 2 3 5 P SD: 11.0684 c. M:-18.8259 c. Soft Diatonic Dorian 26: 2 3 6 4 2 3 6 N SD: 6.9421 c. M: 10.0522 c. 27: 2 3 6 5 2 3 6 N SD: 6.9004 c. M:-9.2443 c. 36: 3 4 8 6 3 4 8 N SD: 5.6471 c. M:-11.1993 c. 41: 3 5 9 7 3 5 9 N SD: 1.7929 c. M:-3.4563 c. 67: 5 8 15 11 5 8 15 N SD: 2.3162 c. M:-3.4475 c. 94: 7 11 21 16 7 11 21 N SD: 0.7847 c. M: 1.3869 c. 135: 10 16 30 23 10 16 30 N SD: 0.2147 c. M:-0.3554 c. 472: 35 56 105 80 35 56 105 N SD: 0.1748 c. M:-0.2601 c. 566: 42 67 126 96 42 67 126 N SD: 0.1739 c. M: 0.2669 c. 607: 45 72 135 103 45 72 135 N SD: 0.1093 c. M:-0.1614 c. 742: 55 88 165 126 55 88 165 N SD: 0.0818 c. M:-0.1481 c. 877: 65 104 195 149 65 104 195 N SD: 0.0777 c. M:-0.1389 c. 1407: 104 167 313 239 104 167 313 N SD: 0.0757 c. M: 0.1374 c. 1542: 114 183 343 262 114 183 343 N SD: 0.0553 c. M: 0.0942 c. 1677: 124 199 373 285 124 199 373 N SD: 0.0416 c. M: 0.0708 c. 1812: 134 215 403 308 134 215 403 N SD: 0.0355 c. M: 0.0590 c. 1947: 144 231 433 331 144 231 433 N SD: 0.0367 c. M: 0.0493 c. 2284: 169 271 508 388 169 271 508 N SD: 0.0239 c. M: 0.0377 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 x 5:6 S SD: 16.2568 cents 4 x x 5:6 x 7:8 S SD: 29.3238 cents 5 x 6:7 x 8:9:10 S SD: 29.6175 cents 6 x 7:8:9 x 10:12 S SD: 12.0877 cents 7 x 8:9 x 11:12:14 SD: 12.7002 cents 8 x 9:11:12:13:14:16 SD: 14.2720 cents 9 x 10:12 x 14:15:18 S SD: 14.7306 cents 10 x 11:13:15:16:17:20 SD: 13.9795 cents 11:12:13:15 x 17:19:22 SD: 16.8770 cents 12:13:14:16:18:19:21:24 SD: 10.1507 cents 14:15:16:19:21:22:24:28 SD: 6.3022 cents 20:21:23:27:30:32:34:40 SD: 5.2164 cents 21:22:24:28:32:33:36:42 S SD: 4.2376 cents 33:35:38:44:50:52:57:66 SD: 4.1086 cents 34:36:39:45:51:54:58:68 SD: 3.1370 cents 36:38:41:48:54:57:62:72 SD: 1.7281 cents 42:44:48:56:63:66:72:84 S SD: 1.6695 cents 56:59:64:75:84:88:96:112 SD: 1.6297 cents 72:76:82:96:108:114:123:144 SD: 1.5561 cents 76:80:87:101:114:120:130:152 SD: 1.0602 cents 78:82:89:104:117:123:134:156 SD: 0.7983 cents 112:118:128:149:168:177:192:224 SD: 0.6347 cents 154:162:176:205:231:243:264:308 SD: 0.4616 cents 168:177:192:224:252:265:288:336 SD: 0.3301 cents 210:221:240:280:315:332:360:420 SD: 0.3193 cents 252:265:288:336:378:398:432:504 SD: 0.2540 cents 266:280:304:355:399:420:456:532 SD: 0.2323 cents 342:360:391:456:513:540:586:684 SD: 0.1507 cents 378:398:432:504:567:597:648:756 SD: 0.0925 cents 420:442:480:560:630:663:720:840 SD: 0.0833 cents