Scala analysis: xen11-chalmers-tetrachordal-08-15
Transposition and Inversion by A/B, 8 tones, an Octony
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: 175/144 337.543332 4: 5/4 386.313714 major third 5: 35/27 449.274618 septimal semi-diminished fourth, 9/4-tone 6: 4/3 498.044999 perfect fourth 7: 35/18 1151.229619 septimal semi-diminished octave 8: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 36/35 48.7704 septimal diesis, 1/4-tone 1: 28/27 62.9609 Archytas' 1/3-tone 2: 36/35 48.7704 septimal diesis, 1/4-tone 3: 875/768 225.8120 4: 36/35 48.7704 septimal diesis, 1/4-tone 5: 28/27 62.9609 Archytas' 1/3-tone 6: 36/35 48.7704 septimal diesis, 1/4-tone 7: 35/24 653.1846 septimal semi-diminished fifth 8: 36/35 48.7704 septimal diesis, 1/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 36/35 48.770 cents septimal diesis, 1/4-tone 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 1 875/768 225.812 cents 1: 1 35/24 653.185 cents septimal semi-diminished fifth 2: 4 16/15 111.731 cents minor diatonic semitone 2: 2 75/64 274.582 cents classic augmented second 2: 2 3/2 701.955 cents perfect fifth 3: 2 192/175 160.502 cents septimal 4/5-tone 3: 1 135/112 323.353 cents septimal wide minor third 3: 2 175/144 337.543 cents 3: 1 54/35 750.725 cents septimal semi-augmented fifth 3: 2 14/9 764.916 cents septimal minor sixth 4: 4 5/4 386.314 cents major third 4: 4 8/5 813.686 cents minor sixth 5: 2 9/7 435.084 cents septimal major third, BP third 5: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 5: 2 288/175 862.457 cents 5: 1 224/135 876.647 cents narrow septimal major sixth 5: 2 175/96 1039.498 cents 6: 2 4/3 498.045 cents perfect fourth 6: 2 128/75 925.418 cents diminished seventh 6: 4 15/8 1088.269 cents classic major seventh 7: 1 48/35 546.815 cents septimal semi-augmented fourth 7: 1 1536/875 974.188 cents 7: 2 27/14 1137.039 cents septimal major seventh 7: 4 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: 3.71429 = 26/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 63.0 111.7 337.5 386.3 449.3 498.0 1151.2 1200.0 63.0 : 48.8 274.6 323.4 386.3 435.1 1088.3 1137.0 1200.0 111.7 : 225.8 274.6 337.5 386.3 1039.5 1088.3 1151.2 1200.0 337.5 : 48.8 111.7 160.5 813.7 862.5 925.4 974.2 1200.0 386.3 : 63.0 111.7 764.9 813.7 876.6 925.4 1151.2 1200.0 449.3 : 48.8 702.0 750.7 813.7 862.5 1088.3 1137.0 1200.0 498.0 : 653.2 702.0 764.9 813.7 1039.5 1088.3 1151.2 1200.0 1151.2: 48.8 111.7 160.5 386.3 435.1 498.0 546.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 653.1846 cents 1225/864, 604.4142 cents 36/35, 48.7704 cents 2: 111.7313 .. 701.9550 cents 45/32, 590.2237 cents 128/175,-541.4533 cents 3: 160.5017 .. 764.9159 cents 1225/864, 604.4142 cents 128/175,-541.4533 cents 4: 386.3137 .. 813.6863 cents 32/25, 427.3726 cents 45/56,-378.6022 cents 5: 435.0841 .. 1039.4983 cents 1225/864, 604.4142 cents 45/56,-378.6022 cents 6: 498.0450 .. 1088.2687 cents 45/32, 590.2237 cents 128/175,-541.4533 cents 7: 546.8154 .. 1151.2296 cents 1225/864, 604.4142 cents 128/175,-541.4533 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 35/24, 653.1846 cents Average / Smallest step : 3.075637 Largest / Average step : 4.354564 Largest / Smallest step : 13.393059 Median interval of one step : 55.86564 cents, amount: 0 Most common interval of one step : 36/35, 48.7704 cents, amount: 4 Least squares average step : 126.16450 cents, oct.: 1009.31603 cents Scale is not proper Step pattern alph. order: ABCBABDB Step pattern size order : BACABADA Scale is a Constant Structure, by a margin of 48.77038 cents Scale diversity : 1.498282 Lumma stability : 0.081284 Lumma impropriety factor : 0.813781 Rothenberg efficiency : 0.421429 redundancy: 0.578571 Efficiency x scale size : 3.371429 Number of different interval sizes : 26 = 3.71429 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 3.71429 = 26/7 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 245/243, 14.1905 cents Number of recognisable fifths : 2, average 701.9550 cents Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 12.5000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 6-7 -- Rational properties -- Prime limit : 7 Odd number limit : 875 (O: 875 U: 875) Highest odd numerator or denominator: 175 Scale harmonicity : 0.021985 Average absolute harmonicity : 0.196744 Specific harmonicity : 0.119684 Fundamental : 1/2160, -11.0768 octaves, 0.1211 Hz. Guide tone : 2800, 11.4512 octaves, 732551.583 Hz. Exponens Consonantiae : 6.048000E+06, 22.52803 octaves Euler's gradus suavitatis : 33 Sum of Mann's harmonic distance : 269.5, average 33.68750 Mersenne's string divisions : 330193710 Sum of van Prooijen's expressibility: 9.11472, average 1.13934 Sum of Tenney's harmonic distance : 18.11615, average 2.26452 Vogel's harmonic complexity : 19.75000 Wille's k value : 1312 Wilson's harmonic complexity : 31 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 134.02573, average 3.72294 Lattice compactness (without 2's) : 74.64715, average 2.07353 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 4 0.25000 16 1 3: -3 .. 0 -1.50000 12 1 5: -1 .. 2 0.50000 6 2 7: 0 .. 1 0.50000 4 4 Average exponent except 2's :-4 / 8 =-0.50000 Average absolute exponent except 2's: 22 / 8 = 2.75000 Scale is weakly epimorphic with val: <8 13 17 21| Scale is weakly epimorphic with val: <8 13 18 20| Scale is weakly epimorphic with val: <8 13 20 20| Scale is weakly epimorphic with val: <8 13 20 24| Scale is weakly epimorphic with val: <8 14 20 21| Scale is weakly epimorphic with val: <8 14 20 23|
FIT/MODE
8: 0 0 2 0 1 0 4 1 N SD: 68.7966 c. M: 111.7313 c. 10: 1 0 2 0 1 0 6 0 N SD: 31.9507 c. M:-57.0391 c. 13: 0 1 2 1 1 0 7 1 N G SD: 38.2208 c. M: 62.9609 c. 14: 1 0 3 1 0 1 7 1 N SD: 25.1639 c. M:-42.2577 c. 15: 1 0 3 1 0 1 8 1 N SD: 26.2707 c. M: 49.2746 c. 17: 1 0 4 0 1 1 9 1 N SD: 23.0651 c. M: 41.1430 c. 18: 1 1 3 1 1 0 10 1 N SD: 16.9292 c. M: 31.3783 c. 19: 1 1 3 1 1 1 10 1 N D3 SD: 11.4605 c. M: 21.7539 c. 21: 1 1 4 1 1 1 11 1 N D3 SD: 9.0256 c. M:-16.2407 c. 22: 1 1 4 1 1 1 12 1 N D3 SD: 7.5370 c. M: 12.9110 c. 32: 2 1 6 1 2 1 18 1 N SD: 8.0022 c. M:-12.0391 c. 40: 2 2 7 2 2 2 21 2 N D3 SD: 7.2213 c. M:-11.9550 c. 43: 2 2 8 2 2 2 23 2 N D3 SD: 4.3725 c. M: 7.1470 c. 53: 3 2 10 2 3 2 29 2 N SD: 2.6910 c. M:-4.9636 c. 72: 4 3 13 3 4 3 39 3 N SD: 2.9698 c. M:-4.9354 c. 74: 4 3 14 3 4 3 40 3 N SD: 2.9284 c. M:-4.7794 c. 75: 4 3 14 3 4 3 41 3 N SD: 1.3824 c. M: 2.3137 c. 96: 5 4 18 4 5 4 52 4 N SD: 1.0045 c. M:-1.9550 c. 149: 8 6 28 6 8 6 81 6 N SD: 1.0382 c. M:-1.7321 c. 152: 8 6 29 6 8 6 83 6 N SD: 1.0275 c. M:-1.9304 c. 171: 9 7 32 7 9 7 93 7 N SD: 0.3777 c. M: 0.7012 c. 270: 14 11 51 11 14 11 147 11 N SD: 0.4099 c. M: 0.7387 c. 323: 17 13 61 13 17 13 176 13 N SD: 0.3051 c. M:-0.5372 c. 419: 22 17 79 17 22 17 228 17 N SD: 0.2482 c. M:-0.4042 c. 441: 23 18 83 18 23 18 240 18 N SD: 0.2032 c. M: 0.3759 c. 494: 26 20 93 20 26 20 269 20 N SD: 0.1177 c. M:-0.1970 c. 665: 35 27 125 27 35 27 362 27 N SD: 0.1104 c. M:-0.1970 c. 935: 49 38 176 38 49 38 509 38 N SD: 0.0532 c. M: 0.0771 c. 1429: 75 58 269 58 75 58 778 58 N SD: 0.0424 c. M: 0.0744 c. 1525: 80 62 287 62 80 62 830 62 N SD: 0.0311 c. M:-0.0534 c. 2019: 106 82 380 82 106 82 1099 82 N SD: 0.0341 c. M:-0.0567 c. 2190: 115 89 412 89 115 89 1192 89 N SD: 0.0326 c. M:-0.0528 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x 4 S SD: 101.9550 cents 3 x x x x x 4 x 6 S SD: 0.0000 cents 4 x x x 5 x x x 8 SD: 0.0000 cents 5 x x 6 x x 7 x 10 SD: 29.0869 cents 6 x x 7 x x 8 x 12 S SD: 23.5575 cents 7 x x x x 9 x x 14 SD: 7.0953 cents 8 x 9 x 10 x 11 x 16 SD: 26.6164 cents 9 x 10:11 x x 12 x 18 S SD: 17.8394 cents 10 x 11:12 x 13 x 19:20 SD: 14.0635 cents 11 x 12:13:14 x 15:21:22 SD: 14.2845 cents 12 x 13 x 15 x 16:23:24 SD: 7.3239 cents 13 x 14:16 x 17 x 25:26 SD: 7.3510 cents 14 x 15:17 x 18:19:27:28 SD: 6.2431 cents 15 x 16:18:19 x 20:29:30 SD: 5.5376 cents 16 x 17:19:20:21 x 31:32 SD: 7.7266 cents 17 x 18 x 21:22:23:33:34 SD: 5.8660 cents 18 x 19:22 x 23:24:35:36 SD: 5.3915 cents 19 x 20:23:24 x 25:37:38 SD: 6.3092 cents 20:21 x 24:25:26:27:39:40 SD: 5.4465 cents 21:22 x x 26:27:28:41:42 SD: 4.8146 cents 22:23 x 27:28 x 29:43:44 SD: 7.3220 cents 23:24:25:28:29:30:31:45:46 SD: 5.5803 cents 24:25:26:29:30:31:32:47:48 SD: 4.0861 cents 27:28:29:33:34:35:36:53:54 SD: 3.2437 cents 33:34:35:40:41:43:44:64:66 SD: 2.6701 cents 47:49:50:57:59:61:63:91:94 SD: 2.2212 cents 48:50:51:58:60:62:64:93:96 SD: 2.0937 cents 51:53:54:62:64:66:68:99:102 SD: 1.9351 cents 56:58:60:68:70:73:75:109:112 SD: 1.8659 cents 57:59:61:69:71:74:76:111:114 SD: 1.4763 cents 60:62:64:73:75:78:80:117:120 SD: 1.1929 cents 75:78:80:91:94:97:100:146:150 SD: 1.0676 cents 88:91:94:107:110:114:117:171:176 SD: 0.9511 cents 105:109:112:128:131:136:140:204:210 SD: 0.8548 cents 107:111:114:130:134:139:143:208:214 SD: 0.8411 cents 108:112:115:131:135:140:144:210:216 SD: 0.5582 cents 135:140:144:164:169:175:180:263:270 SD: 0.5282 cents 168:174:179:204:210:218:224:327:336 SD: 0.5132 cents 192:199:205:233:240:249:256:373:384 SD: 0.4490 cents 195:202:208:237:244:253:260:379:390 SD: 0.3891 cents 213:221:227:259:266:276:284:414:426 SD: 0.3457 cents 240:249:256:292:300:311:320:467:480 SD: 0.3167 cents 273:283:291:332:341:354:364:531:546 SD: 0.2933 cents 297:308:317:361:371:385:396:578:594 SD: 0.2764 cents 344:357:367:418:430:446:459:669:688 SD: 0.2332 cents 348:361:371:423:435:451:464:677:696 SD: 0.1845 cents 408:423:435:496:510:529:544:793:816 SD: 0.1696 cents 432:448:461:525:540:560:576:840:864 SD: 0.0939 cents 540:560:576:656:675:700:720:1050:1080 SD: 0.0825 cents