Scala analysis: xen11-chalmers-tetrachordal-06-01
Transposition by A
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: 784/729 125.921808 two (Archytas' 1/3-tone) 4: 448/405 174.692189 5: 4/3 498.044999 perfect fourth 6: 112/81 561.005903 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 81/56 638.9941 1: 28/27 62.9609 Archytas' 1/3-tone 2: 36/35 48.7704 septimal diesis, 1/4-tone 3: 245/243 14.1905 minor BP diesis, Sensamagic comma 4: 36/35 48.7704 septimal diesis, 1/4-tone 5: 135/112 323.3528 septimal wide minor third 6: 28/27 62.9609 Archytas' 1/3-tone 7: 81/56 638.9941
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 : 63.0 111.7 125.9 174.7 498.0 561.0 1200.0 63.0 : 48.8 63.0 111.7 435.1 498.0 1137.0 1200.0 111.7 : 14.2 63.0 386.3 449.3 1088.3 1151.2 1200.0 125.9 : 48.8 372.1 435.1 1074.1 1137.0 1185.8 1200.0 174.7 : 323.4 386.3 1025.3 1088.3 1137.0 1151.2 1200.0 498.0 : 63.0 702.0 764.9 813.7 827.9 876.6 1200.0 561.0 : 639.0 702.0 750.7 764.9 813.7 1137.0 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 : 111.56584 cents, oct.: 780.96090 cents Scale is not proper Step pattern alph. order: ABCBDAE Step pattern size order : CBABDCE 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 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 : 729 (O: 729 U: 729) Highest odd numerator or denominator: 729 Scale harmonicity : 0.020420 Average absolute harmonicity : 0.204974 Specific harmonicity : 0.111685 Fundamental : 1/3645, -11.8317 octaves, 0.0718 Hz. Guide tone : 3136, 11.6147 octaves, 820457.773 Hz. Exponens Consonantiae : 1.143072E+07, 23.44641 octaves Euler's gradus suavitatis : 35 Sum of Mann's harmonic distance : 1327.5, average 189.64286 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.46324, average 1.49475 Sum of Tenney's harmonic distance : 21.61242, average 3.08749 Vogel's harmonic complexity : 21.71429 Wille's k value : 1822 Wilson's harmonic complexity : 37 Rectangular lattice diameter : 9 Triangular lattice diameter : 6 Lattice compactness : 111.20771, average 3.97170 Lattice compactness (without 2's) : 81.30139, average 2.90362 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 6 3.28571 23 1 3: -6 .. 0 -2.71429 19 1 5: -1 .. 0 -0.28571 2 1 7: 0 .. 2 0.71429 5 4 Average exponent except 2's :-16 / 7 =-2.28571 Average absolute exponent except 2's: 26 / 7 = 3.71429 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 1 0 0 2 0 4 N SD: 41.5002 c. M: 62.9609 c. 8: 0 1 0 0 2 1 4 N SD: 38.6318 c. M: 62.9609 c. 9: 0 1 0 0 3 0 5 N SD: 34.2413 c. M: 62.9609 c. 10: 1 0 0 0 3 1 5 N SD: 34.2142 c. M:-57.0391 c. 12: 1 0 0 1 3 1 6 N SD: 24.9179 c. M:-38.9941 c. 13: 1 0 0 1 3 1 7 N SD: 23.4548 c. M: 36.5065 c. 15: 1 0 1 0 4 1 8 N SD: 20.7055 c. M:-34.0782 c. 17: 1 1 0 1 4 1 9 N SD: 19.1288 c. M:-37.0725 c. 19: 1 1 0 1 5 1 10 N SD: 8.7707 c. M:-14.7815 c. 32: 2 1 0 2 8 2 17 N SD: 9.2824 c. M: 13.4218 c. 34: 2 1 1 1 9 2 18 N SD: 7.1451 c. M:-15.2547 c. 36: 2 1 1 1 10 2 19 N SD: 6.6177 c. M: 11.7313 c. 39: 2 2 0 2 10 2 21 N SD: 6.7769 c. M:-11.3456 c. 41: 2 2 0 2 11 2 22 N SD: 4.6534 c. M: 8.8486 c. 53: 3 2 1 2 14 3 28 N SD: 5.2395 c. M:-9.9272 c. 54: 3 2 1 2 14 3 29 N SD: 5.2387 c. M: 9.1561 c. 55: 3 2 1 2 15 3 29 N SD: 3.6173 c. M:-6.2668 c. 56: 3 2 1 2 15 3 30 N SD: 3.4292 c. M: 5.1879 c. 74: 4 3 1 3 20 4 39 N SD: 3.7728 c. M:-6.5617 c. 75: 4 3 1 3 20 4 40 N SD: 1.3296 c. M:-2.0782 c. 96: 5 4 1 4 26 5 51 N SD: 1.0557 c. M:-1.9550 c. 152: 8 6 2 6 41 8 81 N SD: 0.6918 c. M: 1.2050 c. 171: 9 7 2 7 46 9 91 N SD: 0.4228 c. M:-0.7464 c. 248: 13 10 3 10 67 13 132 N SD: 0.3065 c. M: 0.4986 c. 323: 17 13 4 13 87 17 172 N SD: 0.2144 c. M:-0.3940 c. 419: 22 17 5 17 113 22 223 N SD: 0.1700 c. M:-0.3306 c. 667: 35 27 8 27 180 35 355 N SD: 0.1924 c. M:-0.3134 c. 687: 36 28 8 28 185 36 366 N SD: 0.1610 c. M: 0.3072 c. 742: 39 30 9 30 200 39 395 N SD: 0.1311 c. M:-0.2237 c. 783: 41 32 9 32 211 41 417 N SD: 0.1252 c. M: 0.2513 c. 858: 45 35 10 35 231 45 457 N SD: 0.1155 c. M: 0.1667 c. 935: 49 38 11 38 252 49 498 N SD: 0.1084 c. M: 0.1503 c. 1106: 58 45 13 45 298 58 589 N SD: 0.0396 c. M: 0.0656 c. 1525: 80 62 18 62 411 80 812 N SD: 0.0275 c. M:-0.0534 c. 1848: 97 75 22 75 498 97 984 N SD: 0.0309 c. M:-0.0522 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: 70.4745 cents 3 x x x x 4 x 6 S SD: 0.0000 cents 4 x x x x 5:6:8 S SD: 59.9542 cents 5 x x x 6 x 7:10 SD: 47.5268 cents 6 x x x 7:8 x 12 S SD: 30.7262 cents 7 x x x 8:9:10:14 SD: 25.4270 cents 8 x x x 9 x 11:16 SD: 10.2607 cents 9 x x x 10:12 x 18 S SD: 2.5705 cents 10 x x x 11:13:14:20 SD: 12.4437 cents 11 x x x 12 x 15:22 SD: 11.3397 cents 12 x x 13 x 16:17:24 SD: 10.9647 cents 13 x x 14 x 17:18:26 SD: 8.4462 cents 14 x x 15 x 19 x 28 SD: 10.4399 cents 15 x 16 x 17:20:21:30 SD: 9.4362 cents 16 x 17 x 18:21:22:32 SD: 8.3349 cents 17 x 18 x 19:23:24:34 SD: 9.8321 cents 18 x 19 x 20:24:25:36 SD: 4.2312 cents 19 x 20 x 21:25:26:38 SD: 7.4225 cents 20:21 x x 22:27:28:40 SD: 7.6978 cents 21:22 x x 23:28:29:42 SD: 4.9380 cents 22:23 x x 24:29:30:44 SD: 8.3538 cents 23:24 x 25 x 31:32:46 SD: 6.0658 cents 24:25 x 26:27:32:33:48 SD: 5.6937 cents 25:26 x 27:28:33:35:50 SD: 6.0224 cents 26:27 x 28:29:35:36:52 SD: 3.7176 cents 27:28 x 29:30:36:37:54 SD: 2.9128 cents 28:29 x 30:31:37:39:56 SD: 3.5367 cents 29:30:31 x 32:39:40:58 SD: 2.8353 cents 30:31:32 x 33:40:41:60 SD: 3.8757 cents 31:32:33 x 34:41:43:62 SD: 3.8038 cents 32:33:34 x 35:43:44:64 SD: 4.7065 cents 33:34:35 x 37:44:46:66 SD: 5.1827 cents 34:35:36:37:38:45:47:68 SD: 5.0061 cents 35:36:37:38:39:47:48:70 SD: 5.0028 cents 36:37:38:39:40:48:50:72 SD: 4.1618 cents 38:39 x 41:42:51:53:76 SD: 4.4436 cents 39:40 x 42:43:52:54:78 SD: 3.3717 cents 40:41 x 43:44:53:55:80 SD: 4.4553 cents 41:43 x 44:45:55:57:82 SD: 4.6418 cents 42:44 x 45:46:56:58:84 SD: 4.2543 cents 43:45:46 x 48:57:59:86 SD: 4.7177 cents 44:46:47 x 49:59:61:88 SD: 3.5530 cents 45:47:48 x 50:60:62:90 SD: 2.6335 cents 46:48:49 x 51:61:64:92 SD: 3.0729 cents 47:49:50:51:52:63:65:94 SD: 2.9619 cents 48:50:51:52:53:64:66:96 SD: 2.7448 cents 53:55 x 57:59:71:73:106 SD: 2.5460 cents 54:56 x 58:60:72:75:108 SD: 1.8546 cents 55:57 x 59:61:73:76:110 SD: 1.7057 cents 56:58 x 60:62:75:77:112 SD: 2.3716 cents 57:59:61 x 63:76:79:114 SD: 1.3067 cents 58:60:62 x 64:77:80:116 SD: 1.8597 cents 59:61:63 x 65:79:82:118 SD: 2.4309 cents 63:65:67:68:70:84:87:126 SD: 2.0655 cents 68:71 x 73:75:91:94:136 SD: 2.4412 cents 69:72 x 74:76:92:95:138 SD: 2.6236 cents 70:73 x 75:77:93:97:140 SD: 2.7995 cents 71:74:76 x 79:95:98:142 SD: 2.6967 cents 72:75:77 x 80:96:100:144 SD: 2.3492 cents 73:76:78:79:81:97:101:146 SD: 2.1974 cents 74:77:79:80:82:99:102:148 SD: 1.9740 cents 75:78:80:81:83:100:104:150 SD: 1.4492 cents 76:79:81:82:84:101:105:152 SD: 1.3310 cents 78:81:83:84:86:104:108:156 SD: 1.1633 cents 83:86 x 89:92:111:115:166 SD: 1.4928 cents 84:87 x 90:93:112:116:168 SD: 1.2253 cents 85:88:91 x 94:113:118:170 SD: 1.8455 cents 86:89:92 x 95:115:119:172 SD: 1.4016 cents 98:102 x 105:108:131:136:196 SD: 2.2530 cents 99:103:106 x 110:132:137:198 SD: 1.9420 cents 100:104:107:108:111:133:138:200 SD: 1.8802 cents 101:105:108:109:112:135:140:202 SD: 1.6171 cents 102:106:109:110:113:136:141:204 SD: 1.0437 cents 104:108:111:112:115:139:144:208 SD: 0.8536 cents 105:109:112:113:116:140:145:210 SD: 0.5406 cents 162:168:173:174:179:216:224:324 SD: 0.5077 cents 225:233:240:242:249:300:311:450 SD: 0.3816 cents 300:311:320:323:332:400:415:600 SD: 0.3330 cents 303:314:323:326:335:404:419:606 SD: 0.2857 cents 329:341:351:354:364:439:455:658 SD: 0.2747 cents 330:342:352:355:365:440:456:660 SD: 0.2396 cents 423:439:451:455:468:564:585:846 SD: 0.2322 cents 434:450:463:467:480:579:600:868 SD: 0.2121 cents 452:469:482:486:500:603:625:904 SD: 0.2117 cents 462:479:493:497:511:616:639:924 SD: 0.1558 cents 567:588:605:610:627:756:784:1134 SD: 0.1450 cents