Scala analysis: xen11-chalmers-tetrachordal-06-06
Transposition by 2/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: 9/7 435.084095 septimal major third, BP third 5: 4/3 498.044999 perfect fourth 6: 27/14 1137.039096 septimal major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 28/27 62.9609 Archytas' 1/3-tone 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: 135/112 323.3528 septimal wide minor third 5: 28/27 62.9609 Archytas' 1/3-tone 6: 81/56 638.9941 7: 28/27 62.9609 Archytas' 1/3-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 245/243 14.191 cents minor BP diesis, Sensamagic comma 1: 2 36/35 48.770 cents septimal diesis, 1/4-tone 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 1 135/112 323.353 cents septimal wide minor third 1: 1 81/56 638.994 cents 2: 2 28/27 62.961 cents Archytas' 1/3-tone 2: 1 16/15 111.731 cents minor diatonic semitone 2: 1 243/196 372.123 cents 2: 1 5/4 386.314 cents major third 2: 2 3/2 701.955 cents perfect fifth 3: 1 16/15 111.731 cents minor diatonic semitone 3: 1 784/729 125.922 cents two (Archytas' 1/3-tone) 3: 1 5/4 386.314 cents major third 3: 1 9/7 435.084 cents septimal major third, BP third 3: 1 54/35 750.725 cents septimal semi-augmented fifth 3: 1 14/9 764.916 cents septimal minor sixth 3: 1 405/224 1025.308 cents 4: 1 448/405 174.692 cents 4: 1 9/7 435.084 cents septimal major third, BP third 4: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 4: 1 14/9 764.916 cents septimal minor sixth 4: 1 8/5 813.686 cents minor sixth 4: 1 729/392 1074.078 cents 4: 1 15/8 1088.269 cents classic major seventh 5: 2 4/3 498.045 cents perfect fourth 5: 1 8/5 813.686 cents minor sixth 5: 1 392/243 827.877 cents 5: 1 15/8 1088.269 cents classic major seventh 5: 2 27/14 1137.039 cents septimal major seventh 6: 1 112/81 561.006 cents 6: 1 224/135 876.647 cents narrow septimal major sixth 6: 2 27/14 1137.039 cents septimal major seventh 6: 2 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: 7 Average number of different intervals per interval class: 5.66667 = 17/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 48.8 63.0 111.7 435.1 498.0 1137.0 1200.0 48.8 : 14.2 63.0 386.3 449.3 1088.3 1151.2 1200.0 63.0 : 48.8 372.1 435.1 1074.1 1137.0 1185.8 1200.0 111.7 : 323.4 386.3 1025.3 1088.3 1137.0 1151.2 1200.0 435.1 : 63.0 702.0 764.9 813.7 827.9 876.6 1200.0 498.0 : 639.0 702.0 750.7 764.9 813.7 1137.0 1200.0 1137.0: 63.0 111.7 125.9 174.7 498.0 561.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 14.1905 .. 638.9941 cents 19683/13720, 624.8036 cents 245/243, 14.1905 cents 2: 62.9609 .. 701.9550 cents 81/56, 638.9941 cents 1568/2187,-576.0332 cents 3: 111.7313 .. 1025.3078 cents 6075/3584, 913.5765 cents 32/45,-590.2237 cents 4: 174.6922 .. 1088.2687 cents 6075/3584, 913.5765 cents 100352/164025,-850.6156 cents 5: 498.0450 .. 1137.0391 cents 81/56, 638.9941 cents 32/45,-590.2237 cents 6: 561.0059 .. 1185.8095 cents 19683/13720, 624.8036 cents 1568/2187,-576.0332 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 : 81/56, 638.9941 cents Average / Smallest step : 12.080498 Largest / Average step : 3.727466 Largest / Smallest step : 45.029638 Median interval of one step : 28/27, 62.9609 cents, amount: 2 Least squares average step : 142.59059 cents, oct.: 998.13410 cents Scale is not proper Step pattern alph. order: ABACDED Step pattern size order : BABDCEC Scale is not a Constant Structure Scale diversity : 1.445801 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 : 5 Highest interval variety : 7 Mean interval variety : 5.66667 = 17/3 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 245/243, 14.1905 cents Most common intervals : 28/27, 62.9609 cents & inv., amount: 4 Number of recognisable fifths : 2, average 701.9550 cents Scale contains a complete diamond : 7 27 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 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 : 729 (O: 729 U: 729) Highest odd numerator or denominator: 35 Scale harmonicity : 0.020846 Average absolute harmonicity : 0.213946 Specific harmonicity : 0.120507 Fundamental : 1/1890, -10.8842 octaves, 0.1384 Hz. Guide tone : 3024, 11.5622 octaves, 791155.709 Hz. Exponens Consonantiae : 5.715360E+06, 22.44641 octaves Euler's gradus suavitatis : 34 Sum of Mann's harmonic distance : 112.0, average 16.00000 Mersenne's string divisions : 1667653680 Sum of van Prooijen's expressibility: 7.01425, average 1.00204 Sum of Tenney's harmonic distance : 14.11615, average 2.01659 Vogel's harmonic complexity : 20.85714 Wille's k value : 1822 Wilson's harmonic complexity : 37 Rectangular lattice diameter : 9 Triangular lattice diameter : 6 Lattice compactness : 97.29536, average 3.47483 Lattice compactness (without 2's) : 74.45892, average 2.65925 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 4 1.42857 12 1 3: -3 .. 3 0.28571 12 1 5: -1 .. 0 -0.28571 2 1 7: -1 .. 1 -0.28571 4 4 Average exponent except 2's :-2 / 7 =-0.28571 Average absolute exponent except 2's: 18 / 7 = 2.57143 Scale is weakly epimorphic with val: <7 10 16 22| Scale is weakly epimorphic with val: <7 10 17 21| Scale is weakly epimorphic with val: <7 11 18 21| Scale is weakly epimorphic with val: <7 12 15 18|
FIT/MODE
7: 0 0 0 2 0 4 1 N SD: 95.0044 c. M: 155.1879 c. 8: 0 0 1 2 0 5 0 N SD: 45.2011 c. M:-62.9609 c. 10: 0 1 0 3 0 5 1 N SD: 40.1727 c. M:-57.0391 c. 11: 0 1 0 3 1 5 1 N SD: 35.6386 c. M: 48.7704 c. 12: 0 0 1 3 1 6 1 N SD: 36.0295 c. M: 62.9609 c. 14: 1 0 0 4 1 7 1 N SD: 21.9849 c. M:-36.9439 c. 16: 1 0 1 4 1 8 1 N SD: 22.0111 c. M:-38.2687 c. 17: 1 0 1 4 1 9 1 N SD: 15.1579 c. M:-29.4452 c. 19: 1 0 1 5 1 10 1 N SD: 8.6287 c. M:-14.5845 c. 22: 1 0 1 6 1 12 1 N SD: 5.7882 c. M:-8.4154 c. 41: 2 0 2 11 2 22 2 N SD: 5.0543 c. M:-9.7662 c. 53: 2 1 2 14 3 28 3 N SD: 3.5373 c. M:-4.9636 c. 55: 2 1 2 15 3 29 3 N SD: 2.9675 c. M: 5.1340 c. 72: 3 1 3 19 4 38 4 N SD: 2.9331 c. M:-4.9354 c. 74: 3 1 3 20 4 39 4 N SD: 2.3820 c. M:-4.6577 c. 75: 3 1 3 20 4 40 4 N SD: 1.5362 c. M: 3.0841 c. 77: 3 1 3 21 4 41 4 N SD: 1.4084 c. M: 2.6404 c. 96: 4 1 4 26 5 51 5 N SD: 1.3194 c. M:-2.4159 c. 118: 5 1 5 32 6 63 6 N SD: 1.5499 c. M:-2.2040 c. 130: 5 2 5 35 7 69 7 N SD: 1.4615 c. M: 2.6165 c. 149: 6 2 6 40 8 79 8 N SD: 1.0169 c. M: 1.4686 c. 152: 6 2 6 41 8 81 8 N SD: 0.8208 c. M: 1.4020 c. 171: 7 2 7 46 9 91 9 N SD: 0.2788 c. M:-0.5494 c. 248: 10 3 10 67 13 132 13 N SD: 0.2988 c. M: 0.4410 c. 323: 13 4 13 87 17 172 17 N SD: 0.2904 c. M: 0.4732 c. 419: 17 5 17 113 22 223 22 N SD: 0.1464 c. M:-0.2844 c. 494: 20 6 20 133 26 263 26 N SD: 0.1641 c. M: 0.2663 c. 590: 24 7 24 159 31 314 31 N SD: 0.1375 c. M:-0.2601 c. 612: 25 7 25 165 32 326 32 N SD: 0.1692 c. M:-0.2492 c. 665: 27 8 27 179 35 354 35 N SD: 0.1418 c. M:-0.1970 c. 687: 28 8 28 185 36 366 36 N SD: 0.1251 c. M: 0.2284 c. 764: 31 9 31 206 40 407 40 N SD: 0.1235 c. M: 0.2130 c. 858: 35 10 35 231 45 457 45 N SD: 0.1152 c. M:-0.1807 c. 913: 37 11 37 246 48 486 48 N SD: 0.0942 c. M: 0.1395 c. 935: 38 11 38 252 49 498 49 N SD: 0.0562 c. M: 0.0771 c. 1106: 45 13 45 298 58 589 58 N SD: 0.0307 c. M:-0.0542 c. 1525: 62 18 62 411 80 812 80 N SD: 0.0325 c. M:-0.0634 c. 2019: 82 24 82 544 106 1075 106 N SD: 0.0275 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 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: 24.3852 cents 5 x x x 6:7 x 10 SD: 48.7639 cents 6 x x 7 x 8 x 12 S SD: 51.7132 cents 7 x x 8:9 x x 14 SD: 39.8143 cents 8 x x 9:10:11:15:16 SD: 25.3709 cents 9 x x 10 x 12:17:18 SD: 19.8276 cents 10 x x 11:13 x 19:20 SD: 15.5557 cents 11 x x 12:14:15:21:22 SD: 12.0750 cents 12 x x 13:15:16:23:24 SD: 11.3383 cents 13 x x 14:17 x 25:26 SD: 8.5144 cents 14 x x 15:18:19:27:28 SD: 6.3195 cents 15 x x 16:19:20:29:30 SD: 5.2380 cents 16 x x 17 x 21:31:32 SD: 7.3023 cents 17 x x 18:22:23:33:34 SD: 6.5005 cents 18 x x 19:23:24:35:36 SD: 5.0790 cents 19 x x 20:24:25:37:38 SD: 9.5342 cents 20 x 21 x 26:27:39:40 SD: 8.1411 cents 21 x 22 x 27:28:41:42 SD: 5.5142 cents 22 x 23 x 28:29:42:44 SD: 6.9432 cents 23 x 24:25:30:31:44:46 SD: 8.0722 cents 24 x 25:26:31:32:46:48 SD: 5.1607 cents 25 x 26:27:32:33:48:50 SD: 5.0238 cents 26 x 27:28:33:35:50:52 SD: 5.4721 cents 27 x 28:29:35:36:52:54 SD: 3.1205 cents 28 x 29:30:36:37:54:56 SD: 2.9128 cents 29 x 30:31:37:39:56:58 SD: 3.4768 cents 30 x 31:32:39:40:58:60 SD: 3.4260 cents 31:32 x 33:40:41:60:62 SD: 2.9991 cents 32:33 x 34:41:43:62:64 SD: 3.1087 cents 33:34 x 35:42:44:64:66 SD: 3.7586 cents 34:35 x 36:44:45:66:68 SD: 4.0239 cents 35:36 x 37:45:47:68:70 SD: 3.9305 cents 36:37 x 38:46:48:69:72 SD: 3.9449 cents 37:38 x 39:48:49:71:74 SD: 4.9585 cents 38:39 x 41:49:51:73:76 SD: 4.1075 cents 39:40 x 42:50:52:75:78 SD: 3.1076 cents 40:41 x 43:51:53:77:80 SD: 3.9291 cents 41:42:43:44:53:55:79:82 SD: 3.8895 cents 42:43:44:45:54:56:81:84 SD: 2.9724 cents 45:46:47:48:58:60:87:90 SD: 2.4875 cents 53 x 55:57:68:71:102:106 SD: 2.8708 cents 54 x 56:58:69:72:104:108 SD: 2.7085 cents 55 x 57:59:71:73:106:110 SD: 2.4139 cents 56 x 58:60:72:75:108:112 SD: 1.8546 cents 57 x 59:61:73:76:110:114 SD: 1.5805 cents 58 x 60:62:75:77:112:116 SD: 2.3055 cents 59 x 61:63:76:79:114:118 SD: 1.7135 cents 60 x 62:64:77:80:116:120 SD: 1.3631 cents 61:63 x 65:78:81:118:122 SD: 2.4797 cents 62:64 x 66:80:83:120:124 SD: 2.2101 cents 63:65 x 67:81:84:122:126 SD: 1.7130 cents 64:66 x 68:82:85:123:128 SD: 2.2646 cents 65:67 x 69:84:87:125:130 SD: 2.5290 cents 66:68 x 70:85:88:127:132 SD: 1.8959 cents 67:69 x 71:86:89:129:134 SD: 2.3074 cents 69:71:72:74:89:92:133:138 SD: 2.1914 cents 70:72:73:75:90:93:135:140 SD: 1.9780 cents 71:73:74:76:91:95:137:142 SD: 1.9179 cents 72:74:75:77:93:96:139:144 SD: 1.7417 cents 73:75:76:78:94:97:141:146 SD: 1.4816 cents 74:76:77:79:95:99:143:148 SD: 1.3986 cents 88 x 91:94:113:117:170:176 SD: 1.3725 cents 89 x 92:95:114:119:172:178 SD: 1.7575 cents 90 x 93:96:116:120:174:180 SD: 1.4417 cents 91 x 94:97:117:121:176:182 SD: 1.6219 cents 92:95 x 98:118:123:177:184 SD: 1.7374 cents 93:96 x 99:120:124:179:186 SD: 1.6737 cents 94:97 x 100:121:125:181:188 SD: 1.5431 cents 99:102:103:106:127:132:191:198 SD: 1.4169 cents 101:104:105:108:130:135:195:202 SD: 1.1590 cents 102:105:106:109:131:136:197:204 SD: 0.8474 cents 105:108:109:112:135:140:203:210 SD: 0.6600 cents 108:111:112:115:139:144:208:216 SD: 0.6333 cents 136:140:141:145:175:181:262:272 SD: 0.6152 cents 137:141:142:146:176:183:264:274 SD: 0.6116 cents 165:170:171:176:212:220:318:330 SD: 0.5044 cents 207:213:215:221:266:276:399:414 SD: 0.4925 cents 210:216:218:224:270:280:405:420 SD: 0.2522 cents 375:386:389:400:482:500:723:750 SD: 0.2220 cents 378:389:392:403:486:504:729:756 SD: 0.1767 cents 462:475:479:493:594:616:891:924 SD: 0.1556 cents 570:586:591:608:733:760:1099:1140 SD: 0.1522 cents 588:605:610:627:756:784:1134:1176 SD: 0.1450 cents