Scala analysis: xen11-chalmers-tetrachordal-06-10
Transposition by A/B
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 245/243 14.190522 minor BP diesis, Sensamagic comma 2: 28/27 62.960904 Archytas' 1/3-tone 3: 16/15 111.731285 minor diatonic semitone 4: 35/27 449.274618 septimal semi-diminished fourth, 9/4-tone 5: 4/3 498.044999 perfect fourth 6: 35/18 1151.229619 septimal semi-diminished octave 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 36/35 48.7704 septimal diesis, 1/4-tone 1: 245/243 14.1905 minor BP diesis, Sensamagic comma 2: 36/35 48.7704 septimal diesis, 1/4-tone 3: 36/35 48.7704 septimal diesis, 1/4-tone 4: 175/144 337.5433 5: 36/35 48.7704 septimal diesis, 1/4-tone 6: 35/24 653.1846 septimal semi-diminished fifth 7: 36/35 48.7704 septimal diesis, 1/4-tone
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 : 14.2 63.0 111.7 449.3 498.0 1151.2 1200.0 14.2 : 48.8 97.5 435.1 483.9 1137.0 1185.8 1200.0 63.0 : 48.8 386.3 435.1 1088.3 1137.0 1151.2 1200.0 111.7 : 337.5 386.3 1039.5 1088.3 1102.5 1151.2 1200.0 449.3 : 48.8 702.0 750.7 764.9 813.7 862.5 1200.0 498.0 : 653.2 702.0 716.1 764.9 813.7 1151.2 1200.0 1151.2: 48.8 63.0 111.7 160.5 498.0 546.8 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 : 143.35720 cents, oct.: 1003.50037 cents Scale is not proper Step pattern alph. order: ABBCBDB Step pattern size order : ABBCBDB Scale is sum-free (all different intervals) 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 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: 245 Scale harmonicity : 0.019341 Average absolute harmonicity : 0.206982 Specific harmonicity : 0.110084 Fundamental : 1/2430, -11.2467 octaves, 0.1077 Hz. Guide tone : 3920, 11.9366 octaves, 1025572.216 Hz. Exponens Consonantiae : 9.525600E+06, 23.18338 octaves Euler's gradus suavitatis : 36 Sum of Mann's harmonic distance : 349.5, average 49.92857 Mersenne's string divisions : 926060520 Sum of van Prooijen's expressibility: 8.56188, average 1.22313 Sum of Tenney's harmonic distance : 17.18849, average 2.45550 Vogel's harmonic complexity : 22.14286 Wille's k value : 2362 Wilson's harmonic complexity : 39 Rectangular lattice diameter : 9 Triangular lattice diameter : 5 Lattice compactness : 94.73656, average 3.38345 Lattice compactness (without 2's) : 69.69985, average 2.48928 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 4 1.14286 10 1 3: -5 .. 0 -2.14286 15 1 5: -1 .. 1 0.28571 4 1 7: 0 .. 2 0.71429 5 4 Average exponent except 2's :-8 / 7 =-1.14286 Average absolute exponent except 2's: 24 / 7 = 3.42857 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 2 0 4 0 N SD: 45.6664 c. M:-65.0111 c. 8: 0 0 1 2 0 5 0 N SD: 38.3915 c. M: 62.9609 c. 10: 0 1 0 3 0 6 0 N SD: 32.0076 c. M:-57.0391 c. 12: 0 0 1 3 1 6 1 N SD: 36.5657 c. M: 62.9609 c. 13: 0 0 1 4 0 7 1 N G SD: 33.6396 c. M: 62.9609 c. 14: 0 1 0 4 1 7 1 N SD: 22.2107 c. M: 36.9439 c. 16: 0 1 0 5 0 9 1 N G SD: 25.8908 c. M: 48.0450 c. 17: 0 1 0 5 1 9 1 N SD: 21.0664 c. M: 41.1430 c. 18: 0 1 1 5 0 10 1 N SD: 18.0836 c. M: 31.3783 c. 19: 0 1 1 5 1 10 1 N SD: 10.1743 c. M:-14.5845 c. 21: 0 1 1 6 1 11 1 N SD: 9.5432 c. M:-16.2407 c. 22: 0 1 1 6 1 12 1 N SD: 8.7024 c. M: 14.1905 c. 24: 0 1 1 7 1 13 1 N SD: 8.5594 c. M: 14.1905 c. 41: 0 2 2 11 2 22 2 N SD: 8.0193 c. M: 14.1905 c. 43: 1 1 2 12 2 23 2 N SD: 6.7061 c. M:-13.7165 c. 45: 1 1 2 13 2 24 2 N SD: 7.4222 c. M:-12.4761 c. 46: 0 2 2 13 2 25 2 N SD: 7.7750 c. M: 14.1905 c. 51: 1 2 2 14 2 28 2 N SD: 5.3938 c. M:-9.3389 c. 53: 1 2 2 15 2 29 2 N SD: 4.1926 c. M:-8.4510 c. 56: 1 2 2 16 2 31 2 N SD: 4.4337 c. M:-7.2380 c. 57: 1 2 2 16 3 31 2 N SD: 5.8173 c. M:-7.2182 c. 58: 1 2 2 17 2 32 2 N SD: 5.3889 c. M: 8.2830 c. 62: 1 2 3 17 3 33 3 N SD: 5.3469 c. M: 9.2941 c. 64: 1 2 3 18 3 34 3 N SD: 5.2127 c. M:-8.2050 c. 65: 1 2 3 18 3 35 3 N SD: 4.7645 c. M: 7.5763 c. 67: 1 3 2 19 3 36 3 N SD: 4.5701 c. M:-8.6809 c. 70: 1 3 3 19 3 38 3 N SD: 4.2949 c. M:-8.2687 c. 72: 1 3 3 20 3 39 3 N SD: 2.6748 c. M:-4.9354 c. 74: 1 3 3 21 3 40 3 N SD: 2.8147 c. M:-4.7794 c. 75: 1 3 3 21 3 41 3 N SD: 1.2436 c. M: 2.0450 c. 96: 1 4 4 27 4 52 4 N SD: 1.1663 c. M:-1.9550 c. 149: 2 6 6 42 6 81 6 N SD: 1.2940 c. M:-1.9169 c. 152: 2 6 6 43 6 83 6 N SD: 0.9998 c. M:-1.5990 c. 171: 2 7 7 48 7 93 7 N SD: 0.2809 c. M:-0.5494 c. 246: 3 10 10 69 10 134 10 N SD: 0.3958 c. M: 0.4941 c. 248: 3 10 10 70 10 135 10 N SD: 0.3953 c. M:-0.7254 c. 323: 4 13 13 91 13 176 13 N SD: 0.3588 c. M:-0.6702 c. 345: 4 14 14 97 14 188 14 N SD: 0.4056 c. M: 0.6537 c. 417: 5 17 17 117 17 227 17 N SD: 0.2924 c. M:-0.4989 c. 419: 5 17 17 118 17 228 17 N SD: 0.1863 c. M:-0.3674 c. 494: 6 20 20 139 20 269 20 N SD: 0.1854 c. M:-0.3844 c. 590: 7 24 24 166 24 321 24 N SD: 0.1437 c. M:-0.2601 c. 665: 8 27 27 187 27 362 27 N SD: 0.1341 c. M:-0.2456 c. 764: 9 31 31 215 31 416 31 N SD: 0.1168 c. M: 0.2130 c. 935: 11 38 38 263 38 509 38 N SD: 0.0631 c. M: 0.0771 c. 1106: 13 45 45 311 45 602 45 N SD: 0.0545 c. M: 0.0884 c. 1354: 16 55 55 381 55 737 55 N SD: 0.0394 c. M: 0.0622 c. 1525: 18 62 62 429 62 830 62 N SD: 0.0276 c. M:-0.0534 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: 101.9550 cents 3 x x x x 4 x 6 S SD: 0.0000 cents 4 x x x 5 x x 8 SD: 31.4805 cents 5 x x x x 7 x 10 SD: 42.2336 cents 6 x x 7 x 8 x 12 S SD: 51.7132 cents 7 x x 8:9 x x 14 SD: 40.0943 cents 8 x x 9:10:11 x 16 SD: 30.9223 cents 9 x x 10 x 12 x 18 S SD: 23.5575 cents 10 x x 11:13 x 19:20 SD: 16.7048 cents 11 x x 12:14:15:21:22 SD: 14.2064 cents 12 x x 13 x 16:23:24 SD: 9.1549 cents 13 x x 14:17 x 25:26 SD: 7.3741 cents 14 x x 15:18:19:27:28 SD: 7.4864 cents 15 x x 16:19:20:29:30 SD: 8.2483 cents 16 x x 17:21 x 31:32 SD: 5.8459 cents 17 x x 18:22:23:33:34 SD: 5.7236 cents 18 x x 19:23:24:35:36 SD: 6.1617 cents 19 x x 20 x 25:37:38 SD: 8.1332 cents 20 x 21 x 26:27:39:40 SD: 6.2413 cents 21 x 22 x 27:28:41:42 SD: 4.7329 cents 22 x 23 x x 29:43:44 SD: 6.4605 cents 23 x 24:25:30:31:45:46 SD: 6.9905 cents 24 x 25:26:31:32:47:48 SD: 5.1911 cents 25 x 26:27:32:33:49:50 SD: 6.3676 cents 26 x 27:28:34:35:51:52 SD: 5.3067 cents 27 x 28:29:35:36:53:54 SD: 3.3864 cents 28 x 29:30:36:37:54:56 SD: 4.4353 cents 29 x 30:31:38:39:56:58 SD: 4.5483 cents 30 x 31:32:39:40:58:60 SD: 2.1160 cents 31 x 32:33:40:41:60:62 SD: 3.3356 cents 32 x 33:34:41:43:62:64 SD: 4.6194 cents 33 x 34:35:43:44:64:66 SD: 3.0058 cents 34 x 35:36:44:45:66:68 SD: 3.7516 cents 35 x 36:37:45:47:68:70 SD: 4.7071 cents 36 x 37:38:47:48:70:72 SD: 4.4769 cents 37 x 38:39:48:49:72:74 SD: 4.8516 cents 38 x 39:41:49:51:74:76 SD: 5.0978 cents 39 x 40:42:51:52:76:78 SD: 4.9567 cents 40 x 41:43:52:53:78:80 SD: 4.5846 cents 41 x 43:44:53:55:80:82 SD: 4.2855 cents 42 x 44:45:54:56:82:84 SD: 4.1483 cents 43 x 45:46:56:57:84:86 SD: 3.7422 cents 44 x 46:47:57:59:86:88 SD: 3.2483 cents 54:55:56:58:70:72:105:108 SD: 3.0387 cents 57:58:59:61:74:76:111:114 SD: 2.5147 cents 60:61:62:64:78:80:117:120 SD: 2.4547 cents 71:72:74:76:92:95:138:142 SD: 2.2630 cents 72:73:75:77:93:96:140:144 SD: 2.0799 cents 74:75:77:79:96:99:144:148 SD: 1.7829 cents 75:76:78:80:97:100:146:150 SD: 1.5675 cents 78:79:81:83:101:104:152:156 SD: 1.4492 cents 87:88:90:93:113:116:169:174 SD: 1.2613 cents 101:102:105:108:131:135:196:202 SD: 1.2446 cents 102:103:106:109:132:136:198:204 SD: 0.9852 cents 104:105:108:111:135:139:202:208 SD: 0.8913 cents 105:106:109:112:136:140:204:210 SD: 0.4957 cents 213:215:221:227:276:284:414:426 SD: 0.4043 cents 237:239:246:253:307:316:461:474 SD: 0.3617 cents 240:242:249:256:311:320:467:480 SD: 0.2276 cents 270:272:280:288:350:360:525:540 SD: 0.2020 cents 375:378:389:400:486:500:729:750 SD: 0.1208 cents 597:602:619:637:774:796:1161:1194 SD: 0.1086 cents