Scala analysis: xen12-chalmers-tritriadic-mt-5-9-11
Tritriadic M->T scale built from 5:9:11
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 11/10 165.004228 Ptolemy's second, 4/5-tone 2: 10/9 182.403712 minor whole tone 3: 11/9 347.407941 undecimal neutral third 4: 81/50 835.192576 acute minor sixth 5: 9/5 1017.596288 just minor seventh, BP seventh 6: 99/50 1182.600516 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 100/99 17.3995 Ptolemy's comma 1: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 100/99 17.3995 Ptolemy's comma 3: 11/10 165.0042 Ptolemy's second, 4/5-tone 4: 729/550 487.7846 5: 10/9 182.4037 minor whole tone 6: 11/10 165.0042 Ptolemy's second, 4/5-tone 7: 100/99 17.3995 Ptolemy's comma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 100/99 17.399 cents Ptolemy's comma 1: 3 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 10/9 182.404 cents minor whole tone 1: 1 729/550 487.785 cents 2: 4 10/9 182.404 cents minor whole tone 2: 1 11/9 347.408 cents undecimal neutral third 2: 1 729/500 652.789 cents 2: 1 81/55 670.188 cents 3: 1 1000/891 199.803 cents 3: 2 11/9 347.408 cents undecimal neutral third 3: 1 100/81 364.807 cents grave major third 3: 1 81/55 670.188 cents 3: 2 81/50 835.193 cents acute minor sixth 4: 2 100/81 364.807 cents grave major third 4: 1 110/81 529.812 cents 4: 1 81/50 835.193 cents acute minor sixth 4: 2 18/11 852.592 cents undecimal neutral sixth 4: 1 891/500 1000.197 cents 5: 1 110/81 529.812 cents 5: 1 1000/729 547.211 cents 5: 1 18/11 852.592 cents undecimal neutral sixth 5: 4 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 1100/729 712.215 cents 6: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 3 20/11 1034.996 cents large minor seventh 6: 2 99/50 1182.601 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 : 165.0 182.4 347.4 835.2 1017.6 1182.6 1200.0 165.0 : 17.4 182.4 670.2 852.6 1017.6 1035.0 1200.0 182.4 : 165.0 652.8 835.2 1000.2 1017.6 1182.6 1200.0 347.4 : 487.8 670.2 835.2 852.6 1017.6 1035.0 1200.0 835.2 : 182.4 347.4 364.8 529.8 547.2 712.2 1200.0 1017.6: 165.0 182.4 347.4 364.8 529.8 1017.6 1200.0 1182.6: 17.4 182.4 199.8 364.8 852.6 1035.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 17.3995 .. 487.7846 cents 6561/5000, 470.3852 cents 100/99, 17.3995 cents 2: 182.4037 .. 670.1883 cents 729/550, 487.7846 cents 5500/6561,-305.3809 cents 3: 199.8032 .. 835.1926 cents 72171/50000, 635.3894 cents 5000/6561,-470.3852 cents 4: 364.8074 .. 1000.1968 cents 72171/50000, 635.3894 cents 5000/6561,-470.3852 cents 5: 529.8117 .. 1017.5963 cents 729/550, 487.7846 cents 5000/6561,-470.3852 cents 6: 712.2154 .. 1182.6005 cents 6561/5000, 470.3852 cents 5500/6561,-305.3809 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 100/99, 17.3995 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 729/550, 487.7846 cents Average / Smallest step : 9.852509 Largest / Average step : 2.845410 Largest / Smallest step : 28.034432 Median interval of one step : 11/10, 165.0042 cents, amount: 3 Most common interval of one step : 11/10, 165.0042 cents, amount: 3 Least squares average step : 182.11707 cents, oct.: 1274.81952 cents Scale is not proper Step pattern alph. order: ABACDAB Step pattern size order : BABDCBA Scale is not a Constant Structure Scale diversity : 1.216073 Lumma stability : 0.028999 Lumma impropriety factor : 0.695994 Rothenberg efficiency : 0.544218 redundancy: 0.455782 Efficiency x scale size : 3.809524 Number of different interval sizes : 18 = 3.00000 / 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 : 100/99, 17.3995 cents Most common intervals : 10/9, 182.4037 cents & inv., amount: 5 Most common triad is 0.0 182.404 1017.596 cents, amount: 3 Number of recognisable fifths : 1, average 712.2154 cents Scale contains a complete diamond : 5 9 Length of longest harmonic part : 2 at degree 4 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 42.8571% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 11 Odd number limit : 891 (O: 891 U: 891) Highest odd numerator or denominator: 99 Scale harmonicity : 0.018056 Average absolute harmonicity : 0.187578 Specific harmonicity : 0.090772 Fundamental : 1/450, -8.8138 octaves, 0.5814 Hz. Guide tone : 8910, 13.1212 octaves, 2331083.787 Hz. Exponens Consonantiae : 4.009500E+06, 21.93499 octaves Euler's gradus suavitatis : 37 Sum of Mann's harmonic distance : 178.5, average 25.50000 Mersenne's string divisions : 155761620 Sum of van Prooijen's expressibility: 7.89539, average 1.12791 Sum of Tenney's harmonic distance : 15.24757, average 2.17822 Vogel's harmonic complexity : 19.71429 Wille's k value : 445 Wilson's harmonic complexity : 44 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 90.98625, average 3.24951 Lattice compactness (without 2's) : 83.83777, average 2.99421 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 1 -0.14286 5 1 3: -2 .. 4 0.57143 12 5: -2 .. 1 -0.71429 7 3 11: 0 .. 1 0.42857 3 3 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 22 / 7 = 3.14286 Scale is weakly epimorphic with val: <7 10 16 25| Scale is weakly epimorphic with val: <7 10 17 22| Scale is weakly epimorphic with val: <7 10 18 26| Scale is weakly epimorphic with val: <7 11 16 26| Scale is weakly epimorphic with val: <7 11 17 23| Scale is weakly epimorphic with val: <7 12 15 23|
FIT/MODE
7: 1 0 1 3 1 1 0 N SD: 12.4639 c. M:-21.9503 c. 13: 2 0 2 5 2 2 0 N SD: 13.0544 c. M:-21.8228 c. 14: 2 0 2 6 2 2 0 N SD: 12.4639 c. M:-21.9503 c. 20: 3 0 3 8 3 3 0 N SD: 10.1478 c. M:-17.3995 c. 27: 4 0 4 11 4 4 0 N SD: 9.7151 c. M:-17.3995 c. 38: 5 1 5 15 6 5 1 N SD: 8.8762 c. M: 14.1795 c. 39: 5 1 5 16 6 5 1 N SD: 7.6778 c. M: 13.3697 c. 44: 6 1 6 18 6 6 1 N SD: 7.5620 c. M:-10.2620 c. 45: 6 1 6 18 7 6 1 N SD: 5.6126 c. M: 9.2672 c. 46: 6 1 6 19 7 6 1 N SD: 5.5574 c. M: 8.6875 c. 52: 7 1 7 21 8 7 1 N SD: 3.2769 c. M: 5.6774 c. 59: 8 1 8 24 9 8 1 N SD: 1.6525 c. M: 2.9395 c. 66: 9 1 9 27 10 9 1 N SD: 1.0926 c. M: 1.9534 c. 125: 17 2 17 51 19 17 2 N SD: 1.1812 c. M: 1.8079 c. 131: 18 2 18 53 20 18 2 N SD: 0.8613 c. M: 1.6048 c. 138: 19 2 19 56 21 19 2 N SD: 0.2598 c. M:-0.4181 c. 204: 28 3 28 83 31 28 3 N SD: 0.2027 c. M: 0.3491 c. 342: 47 5 47 139 52 47 5 N SD: 0.0822 c. M: 0.1444 c. 625: 86 9 86 254 95 86 9 N SD: 0.0759 c. M:-0.1195 c. 691: 95 10 95 281 105 95 10 N SD: 0.0656 c. M:-0.1186 c. 829: 114 12 114 337 126 114 12 N SD: 0.0187 c. M:-0.0306 c. 1171: 161 17 161 476 178 161 17 N SD: 0.0121 c. M: 0.0215 c. 2000: 275 29 275 813 304 275 29 N SD: 0.0048 c. M: 0.0079 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 66.6188 cents 3 x x 4:5 x x 6 S SD: 52.8192 cents 4 x x 5:6:7 x 8 S SD: 36.7801 cents 5 x x 6:8:9 x 10 S SD: 9.5905 cents 6 x x 7:10:11 x 12 SD: 24.8906 cents 7 x 8:9:11:13 x 14 SD: 25.1161 cents 8 x 9:10:13:14 x 16 SD: 13.2411 cents 9 x 10:11:15:16 x 18 SD: 10.7328 cents 10:11 x 12:16:18 x 20 S SD: 7.6724 cents 11:12 x 13:18:20 x 22 SD: 12.9598 cents 12:13 x 15:19:22 x 24 SD: 13.8453 cents 13:14 x 16:21:23 x 26 SD: 9.8148 cents 14:15:16:17:23:25 x 28 SD: 12.2023 cents 15 x 17:18:24:27 x 30 SD: 10.2897 cents 16 x 18:20:26:29 x 32 SD: 9.2697 cents 17 x 19:21:28:31 x 34 SD: 8.4149 cents 18 x 20:22:29:32 x 36 SD: 4.7043 cents 19:21 x 23:31:34 x 38 SD: 4.9011 cents 20:22 x 24:32:36 x 40 S SD: 7.6724 cents 21:23 x 26:34:38 x 42 SD: 5.0594 cents 22:24 x 27:36:40 x 44 S SD: 5.8749 cents 23:25:26:28:37:41 x 46 SD: 7.0592 cents 24:26:27:29:39:43 x 48 SD: 6.7611 cents 25 x 28:31:41:45 x 50 SD: 7.1177 cents 26 x 29:32:42:47:51:52 SD: 3.8429 cents 27 x 30:33:44:49:53:54 SD: 3.8387 cents 28 x 31:34:45:50:55:56 SD: 4.5230 cents 29:32 x 35:47:52:57:58 SD: 4.4498 cents 30:33 x 37:49:54:59:60 SD: 4.0265 cents 31:34 x 38:50:56:61:62 SD: 2.7043 cents 35 x 39:43:57:63:69:70 SD: 2.6073 cents 36 x 40:44:58:65:71:72 SD: 2.1449 cents 37 x 41:45:60:67:73:74 SD: 2.5983 cents 38:42 x 46:62:68:75:76 SD: 4.1870 cents 39:43 x 48:63:70:77:78 SD: 2.5549 cents 40:44 x 49:65:72:79:80 SD: 1.3236 cents 45 x 50:55:73:81:89:90 SD: 0.5113 cents 46 x 51:56:75:83:91:92 SD: 2.3835 cents 47 x 52:57:76:85:93:94 SD: 2.9505 cents 48:53 x 59:78:86:95:96 SD: 2.5418 cents 49:54 x 60:79:88:97:98 SD: 1.7093 cents 55 x 61:67:89:99:109:110 SD: 1.1678 cents 56 x 62:68:91:101:111:112 SD: 2.4113 cents 57:63 x 70:92:103:113:114 SD: 2.5130 cents 58:64 x 71:94:104:115:116 SD: 1.5566 cents 63:69:70:77:102:113:125:126 SD: 1.4837 cents 65 x 72:79:105:117:129:130 SD: 2.1307 cents 66 x 73:81:107:119:131:132 SD: 1.9809 cents 67:74 x 82:109:121:133:134 SD: 2.1153 cents 68:75:76:83:110:122:135:136 SD: 1.9673 cents 69:76:77:84:112:124:137:138 SD: 1.7561 cents 71:78:79:87:115:128:141:142 SD: 1.1478 cents 75 x 83:92:122:135:149:150 SD: 2.1861 cents 76:84 x 93:123:137:150:152 SD: 1.7671 cents 79:87:88:97:128:142:156:158 SD: 1.5254 cents 80:88:89:98:130:144:158:160 SD: 1.1758 cents 81:89:90:99:131:146:160:162 SD: 0.8417 cents 85 x 94:104:138:153:168:170 SD: 1.6146 cents 87:96:97:106:141:157:172:174 SD: 1.5734 cents 89:98:99:109:144:160:176:178 SD: 0.8258 cents 90:99:100:110:146:162:178:180 SD: 0.4383 cents 171:188:190:209:277:308:339:342 SD: 0.3707 cents 189:208:210:231:306:340:374:378 SD: 0.2786 cents 260:286:289:318:421:468:515:520 SD: 0.2489 cents 261:287:290:319:423:470:517:522 SD: 0.2017 cents 350:385:389:428:567:630:693:700 SD: 0.1466 cents 360:396:400:440:583:648:713:720 SD: 0.1096 cents 450:495:500:550:729:810:891:900 SD: 0.0000 cents