Scala analysis: xen11-chalmers-tetrachordal-06-03
Transposition by 4/3, Mixolydian Mode
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: 16/15 111.731285 minor diatonic semitone 3: 4/3 498.044999 perfect fourth 4: 112/81 561.005903 5: 64/45 609.776284 2nd tritone 6: 16/9 996.089998 Pythagorean minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 1: 28/27 62.9609 Archytas' 1/3-tone 2: 36/35 48.7704 septimal diesis, 1/4-tone 3: 5/4 386.3137 major third 4: 28/27 62.9609 Archytas' 1/3-tone 5: 36/35 48.7704 septimal diesis, 1/4-tone 6: 5/4 386.3137 major third 7: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 36/35 48.770 cents septimal diesis, 1/4-tone 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 1 9/8 203.910 cents major whole tone 1: 2 5/4 386.314 cents major third 2: 2 16/15 111.731 cents minor diatonic semitone 2: 1 7/6 266.871 cents septimal minor third 2: 2 9/7 435.084 cents septimal major third, BP third 2: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 2: 1 45/32 590.224 cents diatonic tritone 3: 1 6/5 315.641 cents minor third 3: 4 4/3 498.045 cents perfect fourth 3: 1 81/56 638.994 cents 3: 1 35/24 653.185 cents septimal semi-diminished fifth 4: 1 48/35 546.815 cents septimal semi-augmented fourth 4: 1 112/81 561.006 cents 4: 4 3/2 701.955 cents perfect fifth 4: 1 5/3 884.359 cents major sixth, BP sixth 5: 1 64/45 609.776 cents 2nd tritone 5: 1 54/35 750.725 cents septimal semi-augmented fifth 5: 2 14/9 764.916 cents septimal minor sixth 5: 1 12/7 933.129 cents septimal major sixth 5: 2 15/8 1088.269 cents classic major seventh 6: 2 8/5 813.686 cents minor sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 27/14 1137.039 cents septimal major seventh 6: 2 35/18 1151.230 cents septimal semi-diminished octave 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 : 63.0 111.7 498.0 561.0 609.8 996.1 1200.0 63.0 : 48.8 435.1 498.0 546.8 933.1 1137.0 1200.0 111.7 : 386.3 449.3 498.0 884.4 1088.3 1151.2 1200.0 498.0 : 63.0 111.7 498.0 702.0 764.9 813.7 1200.0 561.0 : 48.8 435.1 639.0 702.0 750.7 1137.0 1200.0 609.8 : 386.3 590.2 653.2 702.0 1088.3 1151.2 1200.0 996.1 : 203.9 266.9 315.6 702.0 764.9 813.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 386.3137 cents 175/144, 337.5433 cents 36/35, 48.7704 cents 2: 111.7313 .. 590.2237 cents 675/512, 478.4924 cents 64/75,-274.5824 cents 3: 315.6413 .. 653.1846 cents 175/144, 337.5433 cents 64/75,-274.5824 cents 4: 546.8154 .. 884.3587 cents 175/144, 337.5433 cents 1152/1225,-106.3692 cents 5: 609.7763 .. 1088.2687 cents 675/512, 478.4924 cents 64/75,-274.5824 cents 6: 813.6863 .. 1151.2296 cents 175/144, 337.5433 cents 64/75,-274.5824 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 5/4, 386.3137 cents Average / Smallest step : 3.515014 Largest / Average step : 2.253497 Largest / Smallest step : 7.921072 Median interval of one step : 28/27, 62.9609 cents, amount: 2 Least squares average step : 153.21431 cents, oct.: 1072.50017 cents Scale is not proper Step pattern alph. order: ABCABCD Step pattern size order : BADBADC Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.578397 Lumma stability : 0.081284 Lumma impropriety factor : 0.813781 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 : 245/243, 14.1905 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Number of recognisable fifths : 4, average 701.9550 cents Scale is Mixolydian octave species of abstract tetrachord Scale contains two identical conjunct tetrachords All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 14.2857% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 7 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 81 Scale harmonicity : 0.029983 Average absolute harmonicity : 0.220531 Specific harmonicity : 0.163866 Fundamental : 1/405, -8.6618 octaves, 0.6460 Hz. Guide tone : 448, 8.8074 octaves, 117208.253 Hz. Exponens Consonantiae : 1.814400E+05, 17.46913 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 211.5, average 30.21429 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 7.60052, average 1.08579 Sum of Tenney's harmonic distance : 16.21440, average 2.31634 Vogel's harmonic complexity : 15.28571 Wille's k value : 202 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 91.57000, average 3.27036 Lattice compactness (without 2's) : 54.69604, average 1.95343 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 6 3.28571 23 1 3: -4 .. 0 -1.85714 13 2 5: -1 .. 0 -0.28571 2 2 7: 0 .. 1 0.28571 2 2 Average exponent except 2's :-13 / 7 =-1.85714 Average absolute exponent except 2's: 17 / 7 = 2.42857 Scale is JI-epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 11 16 21| Scale is weakly epimorphic with val: <7 12 17 18|
FIT/MODE
7: 0 1 2 0 1 2 1 N T3 SD: 48.9840 c. M:-75.9380 c. 8: 0 1 2 1 0 3 1 N SD: 41.8489 c. M: 62.9609 c. 9: 0 1 3 0 0 3 2 N SD: 48.1422 c. M: 76.4430 c. 10: 1 0 3 1 0 3 2 N SD: 30.6269 c. M:-57.0391 c. 12: 1 0 4 1 0 4 2 N SD: 21.1955 c. M:-38.9941 c. 13: 1 0 4 1 1 4 2 N SD: 24.8369 c. M: 36.5065 c. 14: 1 0 5 1 0 5 2 N SD: 24.2885 c. M:-38.9941 c. 16: 1 0 6 0 1 5 3 N SD: 24.0757 c. M: 36.7313 c. 17: 1 1 5 1 1 5 3 N SD: 15.4326 c. M:-29.4452 c. 19: 1 1 6 1 1 6 3 N SD: 11.9738 c. M:-21.8027 c. 22: 1 1 7 1 1 7 4 N SD: 9.7820 c. M: 15.5514 c. 24: 1 1 8 1 1 8 4 N SD: 8.7947 c. M: 12.9609 c. Enharmonic Mixolydian 34: 2 1 11 2 1 11 6 N SD: 6.3107 c. M: 9.7763 c. 41: 2 2 13 2 2 13 7 N SD: 3.7220 c. M:-5.3419 c. 53: 3 2 17 3 2 17 9 N SD: 2.7914 c. M:-5.0318 c. 75: 4 3 24 4 3 24 13 N SD: 1.9357 c. M: 4.0900 c. 77: 4 3 25 4 3 25 13 N SD: 1.3862 c. M: 2.6404 c. 118: 6 5 38 6 5 38 20 N SD: 1.0089 c. M: 1.9440 c. 152: 8 6 49 8 6 49 26 N SD: 1.0385 c. M: 1.8815 c. 171: 9 7 55 9 7 55 29 N SD: 0.4247 c. M:-0.7500 c. 248: 13 10 80 13 10 80 42 N SD: 0.3533 c. M:-0.6842 c. 289: 15 12 93 15 12 93 49 N SD: 0.4512 c. M: 0.6772 c. 323: 17 13 104 17 13 104 55 N SD: 0.2876 c. M: 0.4884 c. 419: 22 17 135 22 17 135 71 N SD: 0.2874 c. M:-0.5687 c. 441: 23 18 142 23 18 142 75 N SD: 0.2626 c. M: 0.4617 c. 494: 26 20 159 26 20 159 84 N SD: 0.1087 c. M:-0.1970 c. 612: 32 25 197 32 25 197 104 N SD: 0.1182 c. M: 0.2216 c. 665: 35 27 214 35 27 214 113 N SD: 0.1319 c. M:-0.1971 c. 742: 39 30 239 39 30 239 126 N SD: 0.1155 c. M:-0.1801 c. 783: 41 32 252 41 32 252 133 N SD: 0.1113 c. M:-0.1854 c. 913: 48 37 294 48 37 294 155 N SD: 0.1282 c. M:-0.2208 c. 935: 49 38 301 49 38 301 159 N SD: 0.1107 c. M: 0.1542 c. 1106: 58 45 356 58 45 356 188 N SD: 0.0410 c. M: 0.0683 c. 1848: 97 75 595 97 75 595 314 N SD: 0.0272 c. M: 0.0430 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: 46.0894 cents 3 x x 4 x x 5:6 S SD: 37.2438 cents 4 x x 5 x 6:7:8 S SD: 36.8478 cents 5 x x x 7 x 9:10 SD: 10.1382 cents 6 x 7:8 x 9:11:12 SD: 37.6315 cents 7 x 8:9 x 10:12:14 S SD: 29.8357 cents 8 x 9 x 11 x 14:16 SD: 24.1533 cents 9 x 10:12 x 13:16:18 SD: 15.1196 cents 10 x 11:13:14 x 18:20 SD: 15.0787 cents 11 x 12 x 15:16:20:22 S SD: 14.3103 cents 12 x 13:16 x 17:21:24 SD: 7.7710 cents 13 x 14:17:18 x 23:26 SD: 7.6937 cents 14 x 15:19 x 20:25:28 SD: 6.6853 cents 15 x 16:20:21 x 27:30 SD: 6.0829 cents 16 x 17:21:22:23:28:32 SD: 7.3948 cents 17 x 18:23 x 24:30:34 SD: 6.7186 cents 18 x 19:24:25:26:32:36 SD: 5.5492 cents 19 x 20:25:26:27:34:38 SD: 6.4683 cents 20:21 x 27:28 x 36:40 SD: 8.6025 cents 21:22 x 28:29:30:37:42 SD: 4.1310 cents 22:23 x 29:30:31:39:44 SD: 6.3424 cents 23:24:25:31:32:33:41:46 SD: 6.2239 cents 24:25:26:32:33:34:43:48 SD: 4.7406 cents 26:27:28:35:36:37:46:52 SD: 3.5883 cents 28:29:30:37:39:40:50:56 SD: 3.4535 cents 31:32:33:41:43:44:55:62 SD: 2.5836 cents 45:47:48:60:62:64:80:90 SD: 1.9702 cents 57:59:61:76:79:81:101:114 SD: 1.3851 cents 76:79:81:101:105:108:135:152 SD: 1.0801 cents 78:81:83:104:108:111:139:156 SD: 0.9795 cents 102:106:109:136:141:145:181:204 SD: 0.8366 cents 104:108:111:139:144:148:185:208 SD: 0.8058 cents 107:111:114:143:148:152:190:214 SD: 0.7730 cents 133:138:142:177:184:189:236:266 SD: 0.7508 cents 135:140:144:180:187:192:240:270 SD: 0.4412 cents 211:219:225:281:292:300:375:422 SD: 0.4355 cents 222:230:237:296:307:316:395:444 SD: 0.4344 cents 225:233:240:300:311:320:400:450 SD: 0.3644 cents 240:249:256:320:332:341:427:480 SD: 0.3465 cents 243:252:259:324:336:346:432:486 SD: 0.3439 cents 267:277:285:356:369:380:475:534 SD: 0.3401 cents 270:280:288:360:373:384:480:540 SD: 0.2209 cents 374:388:399:499:517:532:665:748 SD: 0.2135 cents 405:420:432:540:560:576:720:810 S SD: 0.0000 cents