Scala analysis: xen11-chalmers-tetrachordal-06-11
Transposition by B/A
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 36/35 48.770381 septimal diesis, 1/4-tone 2: 28/27 62.960904 Archytas' 1/3-tone 3: 16/15 111.731285 minor diatonic semitone 4: 192/175 160.501667 septimal 4/5-tone 5: 4/3 498.044999 perfect fourth 6: 48/35 546.815381 septimal semi-augmented fourth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 35/24 653.1846 septimal semi-diminished fifth 1: 36/35 48.7704 septimal diesis, 1/4-tone 2: 245/243 14.1905 minor BP diesis, Sensamagic comma 3: 36/35 48.7704 septimal diesis, 1/4-tone 4: 36/35 48.7704 septimal diesis, 1/4-tone 5: 175/144 337.5433 6: 36/35 48.7704 septimal diesis, 1/4-tone 7: 35/24 653.1846 septimal semi-diminished fifth
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 245/243 14.191 cents minor BP diesis, Sensamagic comma 1: 4 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 175/144 337.543 cents 1: 1 35/24 653.185 cents septimal semi-diminished fifth 2: 2 28/27 62.961 cents Archytas' 1/3-tone 2: 1 1296/1225 97.541 cents two (septimal diesis, 1/4-tone) 2: 2 5/4 386.314 cents major third 2: 2 3/2 701.955 cents perfect fifth 3: 2 16/15 111.731 cents minor diatonic semitone 3: 2 9/7 435.084 cents septimal major third, BP third 3: 1 245/162 716.146 cents 3: 1 54/35 750.725 cents septimal semi-augmented fifth 3: 1 175/96 1039.498 cents 4: 1 192/175 160.502 cents septimal 4/5-tone 4: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 4: 1 324/245 483.854 cents 4: 2 14/9 764.916 cents septimal minor sixth 4: 2 15/8 1088.269 cents classic major seventh 5: 2 4/3 498.045 cents perfect fourth 5: 2 8/5 813.686 cents minor sixth 5: 1 1225/648 1102.459 cents 5: 2 27/14 1137.039 cents septimal major seventh 6: 1 48/35 546.815 cents septimal semi-augmented fourth 6: 1 288/175 862.457 cents 6: 4 35/18 1151.230 cents septimal semi-diminished octave 6: 1 486/245 1185.809 cents 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 : 48.8 63.0 111.7 160.5 498.0 546.8 1200.0 48.8 : 14.2 63.0 111.7 449.3 498.0 1151.2 1200.0 63.0 : 48.8 97.5 435.1 483.9 1137.0 1185.8 1200.0 111.7 : 48.8 386.3 435.1 1088.3 1137.0 1151.2 1200.0 160.5 : 337.5 386.3 1039.5 1088.3 1102.5 1151.2 1200.0 498.0 : 48.8 702.0 750.7 764.9 813.7 862.5 1200.0 546.8 : 653.2 702.0 716.1 764.9 813.7 1151.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 14.1905 .. 653.1846 cents 81/56, 638.9941 cents 245/243, 14.1905 cents 2: 62.9609 .. 701.9550 cents 81/56, 638.9941 cents 32/45,-590.2237 cents 3: 111.7313 .. 1039.4983 cents 875/512, 927.7670 cents 32/45,-590.2237 cents 4: 160.5017 .. 1088.2687 cents 875/512, 927.7670 cents 18432/30625,-878.9967 cents 5: 498.0450 .. 1137.0391 cents 81/56, 638.9941 cents 32/45,-590.2237 cents 6: 546.8154 .. 1185.8095 cents 81/56, 638.9941 cents 32/45,-590.2237 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 245/243, 14.1905 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 35/24, 653.1846 cents Average / Smallest step : 12.080498 Largest / Average step : 3.810244 Largest / Smallest step : 46.029638 Median interval of one step : 36/35, 48.7704 cents, amount: 4 Most common interval of one step : 36/35, 48.7704 cents, amount: 4 Least squares average step : 109.45007 cents, oct.: 766.15050 cents Scale is not proper Step pattern alph. order: ABAACAD Step pattern size order : BABBCBD Scale is a Constant Structure, by a margin of 14.19052 cents Scale diversity : 1.359407 Lumma stability : 0.023651 Lumma impropriety factor : 0.895065 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 : 36/35, 48.7704 cents & inv., amount: 4 Number of recognisable fifths : 3, average 706.6852 cents Number of appreciable 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 = 14.2857% Scale is differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval class 2 -- Rational properties -- Prime limit : 7 Odd number limit : 1225 (O: 1225 U: 1225) Highest odd numerator or denominator: 175 Scale harmonicity : 0.018974 Average absolute harmonicity : 0.208008 Specific harmonicity : 0.111793 Fundamental : 1/4725, -12.2061 octaves, 0.0554 Hz. Guide tone : 4032, 11.9773 octaves, 1054874.279 Hz. Exponens Consonantiae : 1.905120E+07, 24.18338 octaves Euler's gradus suavitatis : 37 Sum of Mann's harmonic distance : 308.5, average 44.07143 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 8.41575, average 1.20225 Sum of Tenney's harmonic distance : 17.49096, average 2.49871 Vogel's harmonic complexity : 23.00000 Wille's k value : 2362 Wilson's harmonic complexity : 39 Rectangular lattice diameter : 9 Triangular lattice diameter : 5 Lattice compactness : 98.71724, average 3.52562 Lattice compactness (without 2's) : 65.08754, average 2.32456 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 6 3.00000 21 1 3: -3 .. 2 -0.14286 9 1 5: -2 .. 0 -0.71429 5 1 7: -1 .. 1 -0.28571 4 4 Average exponent except 2's :-8 / 7 =-1.14286 Average absolute exponent except 2's: 18 / 7 = 2.57143 Scale is weakly epimorphic with val: <7 10 17 19| Scale is weakly epimorphic with val: <7 12 18 19|
FIT/MODE
7: 0 0 1 0 2 0 4 N SD: 40.2629 c. M: 62.9609 c. 9: 0 0 1 0 3 0 5 N SD: 35.8059 c. M: 62.9609 c. 10: 0 0 1 0 3 0 6 N SD: 42.8307 c. M: 66.8154 c. 11: 0 1 0 0 4 0 6 N SD: 36.6569 c. M: 51.4108 c. 12: 0 0 1 0 4 0 7 N SD: 41.9799 c. M: 62.9609 c. 13: 1 0 0 1 3 1 7 N SD: 26.9858 c. M:-43.5373 c. 14: 1 0 0 1 4 0 8 N G SD: 23.9069 c. M:-36.9439 c. 15: 1 0 0 1 4 1 8 N SD: 19.9005 c. M: 31.7313 c. 17: 1 0 1 0 5 1 9 N SD: 17.3624 c. M:-29.4452 c. 19: 1 0 1 1 5 1 10 N SD: 15.9375 c. M:-28.9720 c. 20: 1 0 1 1 5 1 11 N SD: 11.6833 c. M:-19.4983 c. 21: 1 0 1 1 6 1 11 N SD: 12.5325 c. M:-24.6132 c. 22: 1 0 1 1 6 1 12 N SD: 4.9820 c. M: 8.4154 c. 46: 2 0 2 2 13 2 25 N SD: 5.4122 c. M: 10.7870 c. 50: 2 1 2 2 14 2 27 N SD: 6.2018 c. M:-9.0391 c. 51: 2 1 2 2 14 2 28 N SD: 4.7958 c. M:-7.6273 c. 53: 2 1 2 2 15 2 29 N SD: 2.7959 c. M:-4.9636 c. 73: 3 1 3 3 20 3 40 N SD: 3.3204 c. M: 4.8943 c. 74: 3 1 3 3 21 3 40 N SD: 2.7214 c. M:-4.6577 c. 75: 3 1 3 3 21 3 41 N SD: 1.4195 c. M: 2.8154 c. 96: 4 1 4 4 27 4 52 N SD: 1.7018 c. M:-3.1846 c. 97: 4 1 4 4 27 4 53 N SD: 1.6215 c. M: 3.1996 c. 99: 4 1 4 4 28 4 54 N SD: 1.8581 c. M: 2.9259 c. 118: 5 1 5 5 33 5 64 N SD: 1.6268 c. M:-2.3372 c. 149: 6 2 6 6 42 6 81 N SD: 0.9314 c. M:-1.4686 c. 171: 7 2 7 7 48 7 93 N SD: 0.4817 c. M:-0.9018 c. 246: 10 3 10 10 69 10 134 N SD: 0.3972 c. M: 0.4840 c. 345: 14 4 14 14 97 14 188 N SD: 0.4662 c. M: 0.7284 c. 366: 15 4 15 15 103 15 199 N SD: 0.4354 c. M:-0.7256 c. 397: 16 5 16 16 112 16 216 N SD: 0.3964 c. M:-0.6956 c. 417: 17 5 17 17 117 17 227 N SD: 0.3503 c. M:-0.6494 c. 419: 17 5 17 17 118 17 228 N SD: 0.1445 c. M:-0.2844 c. 494: 20 6 20 20 139 20 269 N SD: 0.1587 c. M: 0.2567 c. 590: 24 7 24 24 166 24 321 N SD: 0.1766 c. M:-0.3033 c. 665: 27 8 27 27 187 27 362 N SD: 0.1039 c. M:-0.1970 c. 860: 35 10 35 35 242 35 468 N SD: 0.1072 c. M: 0.1702 c. 913: 37 11 37 37 257 37 497 N SD: 0.0997 c. M: 0.1512 c. 935: 38 11 38 38 263 38 509 N SD: 0.0634 c. M: 0.0774 c. 1106: 45 13 45 45 311 45 602 N SD: 0.0413 c. M:-0.0770 c. 1525: 62 18 62 62 429 62 830 N SD: 0.0352 c. M:-0.0699 c. 1600: 65 19 65 65 450 65 871 N SD: 0.0350 c. M: 0.0654 c. 2019: 82 24 82 82 568 82 1099 N SD: 0.0243 c. M:-0.0406 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3:4 S SD: 77.5698 cents 3 x x x x 4 x 6 S SD: 0.0000 cents 4 x x x x 5:6:8 S SD: 63.7287 cents 5 x x x 6 x 7:10 SD: 53.0645 cents 6 x x x 7:8 x 12 S SD: 35.4564 cents 7 x x x 8:9:10:14 SD: 29.5310 cents 8 x x x 9 x 11:16 SD: 14.5471 cents 9 x x x 10:12 x 18 S SD: 7.3007 cents 10 x x x 11:13:14:20 SD: 14.1768 cents 11 x x x 12 x 15:22 SD: 4.6502 cents 12 x x x 13:16 x 24 SD: 7.3097 cents 13 x x 14 x 17:18:26 SD: 10.2440 cents 14 x x 15 x x 19:28 SD: 6.5668 cents 15 x x 16 x 20:21:30 SD: 8.9242 cents 16 x x 17:18:21:22:32 SD: 10.3804 cents 17 x x 18:19 x 23:34 SD: 10.4370 cents 18 x x 19:20:24:25:36 SD: 7.1778 cents 19 x x 20:21:25:26:38 SD: 7.0115 cents 20 x 21 x 22:27 x 40 SD: 7.6865 cents 21 x 22 x 23:28:29:42 SD: 4.2966 cents 22 x 23 x 24:29:30:44 SD: 5.5927 cents 23 x 24 x 25:31:32:46 SD: 7.3390 cents 24 x 25 x 26:32:33:48 SD: 4.7355 cents 25 x 26:27 x 33:34:50 SD: 6.3231 cents 26 x 27:28:29:35:36:52 SD: 6.7578 cents 27 x 28:29:30:36:37:54 SD: 4.1668 cents 28 x 29:30:31:37:38:56 SD: 4.9464 cents 29 x 30:31:32:39:40:58 SD: 3.5348 cents 30 x 31:32:33:40:41:60 SD: 1.6236 cents 31:32 x 33:34:41:43:62 SD: 4.1972 cents 32:33 x 34:35:43:44:64 SD: 2.8709 cents 33:34 x 35:36:44:45:66 SD: 2.8887 cents 34:35 x 36:37:45:47:68 SD: 4.4607 cents 35:36 x 37:38:47:48:70 SD: 4.4769 cents 36:37 x 38:40:48:49:72 SD: 5.2203 cents 37:38 x 39:41:49:51:74 SD: 5.1142 cents 38:39 x 41:42:51:52:76 SD: 4.4519 cents 39:40 x 42:43:52:53:78 SD: 4.1537 cents 40:41 x 43:44:53:55:80 SD: 3.2324 cents 43:44:45:46:47:57:59:86 SD: 3.1901 cents 48:49:50:51:53:64:66:96 SD: 2.9229 cents 51:52:53:54:56:68:70:102 SD: 2.8928 cents 53 x 55:57:58:71:73:106 SD: 3.0988 cents 54 x 56:58:59:72:74:108 SD: 2.3398 cents 55 x 57:59:60:73:75:110 SD: 3.1372 cents 56 x 58:60:61:75:77:112 SD: 2.8815 cents 57 x 59:61:63:76:78:114 SD: 2.4741 cents 58 x 60:62:64:77:80:116 SD: 2.8132 cents 59 x 61:63:65:79:81:118 SD: 1.9666 cents 60 x 62:64:66:80:82:120 SD: 1.6236 cents 61:63 x 65:67:81:84:122 SD: 2.0927 cents 62:64 x 66:68:83:85:124 SD: 1.6649 cents 63:65 x 67:69:84:86:126 SD: 1.8906 cents 64:66 x 68:70:85:88:128 SD: 2.1156 cents 65:67 x 69:71:87:89:130 SD: 2.3191 cents 66:68 x 70:72:88:91:132 SD: 2.8331 cents 67:69 x 71:74:89:92:134 SD: 2.9479 cents 68:70:71:73:75:91:93:136 SD: 2.8945 cents 69:71:72:74:76:92:95:138 SD: 2.4555 cents 70:72:73:75:77:93:96:140 SD: 2.0799 cents 71:73:74:76:78:95:97:142 SD: 2.0151 cents 72:74:75:77:79:96:99:144 SD: 1.4415 cents 73:75:76:78:80:97:100:146 SD: 1.4393 cents 75:77:78:80:82:100:103:150 SD: 1.2514 cents 88 x 91:94:97:117:121:176 SD: 1.9724 cents 89 x 92:95:98:119:122:178 SD: 1.6331 cents 90 x 93:96:99:120:123:180 SD: 1.6236 cents 91 x 94:97:100:121:125:182 SD: 1.5439 cents 92:95 x 98:101:123:126:184 SD: 1.4936 cents 93:96 x 99:102:124:128:186 SD: 1.5748 cents 94:97 x 100:103:125:129:188 SD: 1.4933 cents 100:103:104:107:110:133:137:200 SD: 1.4404 cents 102:105:106:109:112:136:140:204 SD: 0.7734 cents 105:108:109:112:115:140:144:210 SD: 0.4983 cents 135:139:140:144:148:180:185:270 SD: 0.3709 cents 240:247:249:256:263:320:329:480 SD: 0.3625 cents 317:326:329:338:348:423:435:634 SD: 0.3608 cents 318:327:330:339:349:424:436:636 SD: 0.2517 cents 348:358:361:371:382:464:477:696 SD: 0.2423 cents 423:435:439:451:464:564:580:846 SD: 0.2333 cents 452:465:469:482:496:603:620:904 SD: 0.2198 cents 453:466:470:483:497:604:621:906 SD: 0.1886 cents 495:509:513:528:543:660:679:990 SD: 0.1867 cents 566:582:587:604:621:755:776:1132 SD: 0.1864 cents 567:583:588:605:622:756:778:1134 SD: 0.1763 cents 568:584:589:606:623:757:779:1136 SD: 0.1716 cents 597:614:619:637:655:796:819:1194 SD: 0.1207 cents