Scala analysis: xen15-gilson-archytas-chromatic
Archytas' Chromatic
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 28/27 62.960904 Archytas' 1/3-tone 2: 9/8 203.910002 major whole tone 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 14/9 764.915905 septimal minor sixth 6: 27/16 905.865003 Pythagorean major sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 32/27 294.1350 Pythagorean minor third 1: 28/27 62.9609 Archytas' 1/3-tone 2: 243/224 140.9491 Archytas' 2/3-tone 3: 32/27 294.1350 Pythagorean minor third 4: 9/8 203.9100 major whole tone 5: 28/27 62.9609 Archytas' 1/3-tone 6: 243/224 140.9491 Archytas' 2/3-tone 7: 32/27 294.1350 Pythagorean minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 2 243/224 140.949 cents Archytas' 2/3-tone 1: 1 9/8 203.910 cents major whole tone 1: 2 32/27 294.135 cents Pythagorean minor third 2: 2 9/8 203.910 cents major whole tone 2: 1 7/6 266.871 cents septimal minor third 2: 1 896/729 357.096 cents 2: 2 9/7 435.084 cents septimal major third, BP third 2: 1 4/3 498.045 cents perfect fourth 3: 1 81/64 407.820 cents Pythagorean major third 3: 4 4/3 498.045 cents perfect fourth 3: 1 112/81 561.006 cents 3: 1 81/56 638.994 cents 4: 1 112/81 561.006 cents 4: 1 81/56 638.994 cents 4: 4 3/2 701.955 cents perfect fifth 4: 1 128/81 792.180 cents Pythagorean minor sixth 5: 1 3/2 701.955 cents perfect fifth 5: 2 14/9 764.916 cents septimal minor sixth 5: 1 729/448 842.904 cents 5: 1 12/7 933.129 cents septimal major sixth 5: 2 16/9 996.090 cents Pythagorean minor seventh 6: 2 27/16 905.865 cents Pythagorean major sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 448/243 1059.051 cents 6: 2 27/14 1137.039 cents septimal 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 : 63.0 203.9 498.0 702.0 764.9 905.9 1200.0 63.0 : 140.9 435.1 639.0 702.0 842.9 1137.0 1200.0 203.9 : 294.1 498.0 561.0 702.0 996.1 1059.1 1200.0 498.0 : 203.9 266.9 407.8 702.0 764.9 905.9 1200.0 702.0 : 63.0 203.9 498.0 561.0 702.0 996.1 1200.0 764.9 : 140.9 435.1 498.0 639.0 933.1 1137.0 1200.0 905.9 : 294.1 357.1 498.0 792.2 996.1 1059.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 294.1350 cents 8/7, 231.1741 cents 28/27, 62.9609 cents 2: 203.9100 .. 498.0450 cents 32/27, 294.1350 cents 243/256,-90.2250 cents 3: 407.8200 .. 638.9941 cents 8/7, 231.1741 cents 243/256,-90.2250 cents 4: 561.0059 .. 792.1800 cents 8/7, 231.1741 cents 6272/6561,-77.9882 cents 5: 701.9550 .. 996.0900 cents 32/27, 294.1350 cents 243/256,-90.2250 cents 6: 905.8650 .. 1137.0391 cents 8/7, 231.1741 cents 243/256,-90.2250 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 28/27, 62.9609 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 32/27, 294.1350 cents Average / Smallest step : 2.722778 Largest / Average step : 1.715787 Largest / Smallest step : 4.671709 Median interval of one step : 243/224, 140.9491 cents, amount: 2 Least squares average step : 160.23218 cents, oct.: 1121.62527 cents Scale is not proper Step pattern alph. order: ABCDABC Step pattern size order : ABDCABD Scale is not a Constant Structure Scale diversity : 1.525876 Lumma stability : 0.104935 Lumma impropriety factor : 0.365740 Rothenberg efficiency : 0.540136 redundancy: 0.459864 Efficiency x scale size : 3.780952 Number of different interval sizes : 20 = 3.33333 / 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 : 64/63, 27.2641 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 5, 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 n-1 differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 7 Odd number limit : 729 (O: 729 U: 729) Highest odd numerator or denominator: 27 Scale harmonicity : 0.030973 Average absolute harmonicity : 0.257116 Specific harmonicity : 0.168971 Fundamental : 1/432, -8.7549 octaves, 0.6056 Hz. Guide tone : 756, 9.5622 octaves, 197788.927 Hz. Exponens Consonantiae : 3.265920E+05, 18.31713 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 76.5, average 10.92857 Mersenne's string divisions : 19419015 Sum of van Prooijen's expressibility: 5.72546, average 0.81792 Sum of Tenney's harmonic distance : 11.63007, average 1.66144 Vogel's harmonic complexity : 14.71429 Wille's k value : 364 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 7 Triangular lattice diameter : 6 Lattice compactness : 105.65091, average 3.77325 Lattice compactness (without 2's) : 70.13626, average 2.50487 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -0.28571 14 1 3: -3 .. 3 0.00000 12 4 7: 0 .. 1 0.28571 2 2 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 14 / 7 = 2.00000 Scale is weakly epimorphic with val: <7 10 21| Scale is weakly epimorphic with val: <7 11 21| Scale is weakly epimorphic with val: <7 12 21|
FIT/MODE
7: 0 1 2 1 0 1 2 N T3 SD: 45.0292 c. M: 79.2016 c. 12: 1 1 3 2 1 1 3 N SD: 19.4940 c. M:-37.0391 c. Chromatic Dorian, Mela Kanakangi, Raga Kanakambari 14: 1 1 4 2 1 2 3 N SD: 22.3962 c. M:-36.9921 c. 16: 1 2 4 2 1 2 4 N T3 SD: 18.1256 c. M:-26.9550 c. 17: 1 2 4 3 1 2 4 N SD: 7.7740 c. M:-11.7821 c. 36: 2 4 9 6 2 4 9 N SD: 3.2542 c. M: 5.8650 c. Ratio 1:2 Chromatic Dorian 41: 2 5 10 7 2 5 10 N SD: 2.3487 c. M: 4.4243 c. 58: 3 7 14 10 3 7 14 N SD: 2.2234 c. M:-4.4798 c. Archchro 77: 4 9 19 13 4 9 19 N SD: 1.1011 c. M: 1.9689 c. 94: 5 11 23 16 5 11 23 N SD: 0.5716 c. M:-1.0415 c. 135: 7 16 33 23 7 16 33 N SD: 0.5126 c. M:-0.8017 c. 171: 9 20 42 29 9 20 42 N SD: 0.3030 c. M: 0.6018 c. 265: 14 31 65 45 14 31 65 N SD: 0.2373 c. M:-0.4353 c. 306: 16 36 75 52 16 36 75 N SD: 0.1141 c. M: 0.2158 c. 400: 21 47 98 68 21 47 98 N SD: 0.0746 c. M:-0.1350 c. 571: 30 67 140 97 30 67 140 N SD: 0.0574 c. M:-0.0864 c. 706: 37 83 173 120 37 83 173 N SD: 0.0517 c. M:-0.0840 c. 877: 46 103 215 149 46 103 215 N SD: 0.0287 c. M: 0.0497 c. 1277: 67 150 313 217 67 150 313 N SD: 0.0040 c. M:-0.0081 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: 7.1688 cents 4 x x 5:6 x 7:8 S SD: 32.0624 cents 5 x 6:7 x 8 x 10 S SD: 37.0786 cents 6 x 7:8:9 x 10:12 S SD: 13.3065 cents 7 x 8:9 x 11:12:14 SD: 15.1785 cents 8 x 9:11:12 x 14:16 SD: 16.4949 cents 9 x 10:12 x 14:15:18 S SD: 6.0829 cents 10 x 11:13:15:16:17:20 SD: 12.8848 cents 11 x 12:15 x 17:19:22 SD: 15.6274 cents 12 x 14:16:18:19:20:24 S SD: 12.2083 cents 13:14:15:17 x 20:22:26 SD: 14.6349 cents 14:15:16:19:21:22:24:28 SD: 10.9960 cents 15:16:17:20 x 23:25:30 SD: 10.0344 cents 16:17:18:21:24:25:27:32 SD: 7.2370 cents 17:18:19:23 x 26:29:34 SD: 9.5395 cents 18:19:20:24:27:28:30:36 S SD: 6.1677 cents 22:23:25:29:33:34:37:44 SD: 4.6322 cents 24:25:27:32:36:37:41:48 SD: 3.9170 cents 30:31:34:40:45:47:51:60 SD: 3.2472 cents 32:33:36:43:48:50:54:64 SD: 2.6141 cents 48:50:54:64:72:75:81:96 SD: 1.5580 cents 54:56:61:72:81:84:91:108 SD: 1.0709 cents 102:106:115:136:153:159:172:204 SD: 0.9278 cents 106:110:119:141:159:165:179:212 SD: 0.8341 cents 112:116:126:149:168:174:189:224 SD: 0.7104 cents 128:133:144:171:192:199:216:256 SD: 0.6963 cents 135:140:152:180:203:210:228:270 SD: 0.6744 cents 138:143:155:184:207:215:233:276 SD: 0.6005 cents 144:149:162:192:216:224:243:288 SD: 0.5527 cents 160:166:180:213:240:249:270:320 SD: 0.4171 cents 192:199:216:256:288:299:324:384 SD: 0.3085 cents 240:249:270:320:360:373:405:480 SD: 0.2470 cents 272:282:306:363:408:423:459:544 SD: 0.2451 cents 378:392:425:504:567:588:638:756 SD: 0.1533 cents 432:448:486:576:648:672:729:864 SD: 0.0000 cents