Scala analysis: parapyth12-7
2.3.7 transversal of parapyth12
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: 9/8 203.910002 major whole tone 3: 7/6 266.870906 septimal minor third 4: 81/64 407.820003 Pythagorean major third 5: 21/16 470.780907 narrow fourth 6: 112/81 561.005903 7: 3/2 701.955001 perfect fifth 8: 14/9 764.915905 septimal minor sixth 9: 27/16 905.865003 Pythagorean major sixth 10: 7/4 968.825906 harmonic seventh 11: 243/128 1109.775004 Pythagorean major seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 256/243 90.2250 limma, Pythagorean minor second 1: 28/27 62.9609 Archytas' 1/3-tone 2: 243/224 140.9491 Archytas' 2/3-tone 3: 28/27 62.9609 Archytas' 1/3-tone 4: 243/224 140.9491 Archytas' 2/3-tone 5: 28/27 62.9609 Archytas' 1/3-tone 6: 256/243 90.2250 limma, Pythagorean minor second 7: 243/224 140.9491 Archytas' 2/3-tone 8: 28/27 62.9609 Archytas' 1/3-tone 9: 243/224 140.9491 Archytas' 2/3-tone 10: 28/27 62.9609 Archytas' 1/3-tone 11: 243/224 140.9491 Archytas' 2/3-tone 12: 256/243 90.2250 limma, Pythagorean minor second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 28/27 62.961 cents Archytas' 1/3-tone 1: 2 256/243 90.225 cents limma, Pythagorean minor second 1: 5 243/224 140.949 cents Archytas' 2/3-tone 2: 2 7168/6561 153.186 cents 2: 8 9/8 203.910 cents major whole tone 2: 2 8/7 231.174 cents septimal whole tone 3: 3 7/6 266.871 cents septimal minor third 3: 6 32/27 294.135 cents Pythagorean minor third 3: 3 2187/1792 344.859 cents 4: 4 896/729 357.096 cents 4: 4 81/64 407.820 cents Pythagorean major third 4: 4 9/7 435.084 cents septimal major third, BP third 5: 1 21/16 470.781 cents narrow fourth 5: 10 4/3 498.045 cents perfect fourth 5: 1 19683/14336 548.769 cents 6: 6 112/81 561.006 cents 6: 6 81/56 638.994 cents 7: 1 28672/19683 651.231 cents 7: 10 3/2 701.955 cents perfect fifth 7: 1 32/21 729.219 cents wide fifth 8: 4 14/9 764.916 cents septimal minor sixth 8: 4 128/81 792.180 cents Pythagorean minor sixth 8: 4 729/448 842.904 cents 9: 3 3584/2187 855.141 cents 9: 6 27/16 905.865 cents Pythagorean major sixth 9: 3 12/7 933.129 cents septimal major sixth 10: 2 7/4 968.826 cents harmonic seventh 10: 8 16/9 996.090 cents Pythagorean minor seventh 10: 2 6561/3584 1046.814 cents 11: 5 448/243 1059.051 cents 11: 2 243/128 1109.775 cents Pythagorean major seventh 11: 5 27/14 1137.039 cents septimal major seventh Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 2.90909 = 32/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 63.0 203.9 266.9 407.8 470.8 561.0 702.0 764.9 905.9 968.8 1109.8 1200.0 63.0 : 140.9 203.9 344.9 407.8 498.0 639.0 702.0 842.9 905.9 1046.8 1137.0 1200.0 203.9 : 63.0 203.9 266.9 357.1 498.0 561.0 702.0 764.9 905.9 996.1 1059.1 1200.0 266.9 : 140.9 203.9 294.1 435.1 498.0 639.0 702.0 842.9 933.1 996.1 1137.0 1200.0 407.8 : 63.0 153.2 294.1 357.1 498.0 561.0 702.0 792.2 855.1 996.1 1059.1 1200.0 470.8 : 90.2 231.2 294.1 435.1 498.0 639.0 729.2 792.2 933.1 996.1 1137.0 1200.0 561.0 : 140.9 203.9 344.9 407.8 548.8 639.0 702.0 842.9 905.9 1046.8 1109.8 1200.0 702.0 : 63.0 203.9 266.9 407.8 498.0 561.0 702.0 764.9 905.9 968.8 1059.1 1200.0 764.9 : 140.9 203.9 344.9 435.1 498.0 639.0 702.0 842.9 905.9 996.1 1137.0 1200.0 905.9 : 63.0 203.9 294.1 357.1 498.0 561.0 702.0 764.9 855.1 996.1 1059.1 1200.0 968.8 : 140.9 231.2 294.1 435.1 498.0 639.0 702.0 792.2 933.1 996.1 1137.0 1200.0 1109.8: 90.2 153.2 294.1 357.1 498.0 561.0 651.2 792.2 855.1 996.1 1059.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 140.9491 cents 6561/6272, 77.9882 cents 28/27, 62.9609 cents 2: 153.1859 .. 231.1741 cents 6561/6272, 77.9882 cents 1605632/1594323, 12.2368 cents 3: 266.8709 .. 344.8591 cents 6561/6272, 77.9882 cents 49/48, 35.6968 cents 4: 357.0959 .. 435.0841 cents 6561/6272, 77.9882 cents 1605632/1594323, 12.2368 cents 5: 470.7809 .. 548.7691 cents 6561/6272, 77.9882 cents 49/48, 35.6968 cents 6: 561.0059 .. 638.9941 cents 6561/6272, 77.9882 cents 1605632/1594323, 12.2368 cents 7: 651.2309 .. 729.2191 cents 6561/6272, 77.9882 cents 1605632/1594323, 12.2368 cents 8: 764.9159 .. 842.9041 cents 6561/6272, 77.9882 cents 49/48, 35.6968 cents 9: 855.1409 .. 933.1291 cents 6561/6272, 77.9882 cents 1605632/1594323, 12.2368 cents 10: 968.8259 .. 1046.8141 cents 6561/6272, 77.9882 cents 49/48, 35.6968 cents 11: 1059.0509 .. 1137.0391 cents 6561/6272, 77.9882 cents 1605632/1594323, 12.2368 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 28/27, 62.9609 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 243/224, 140.9491 cents Average / Smallest step : 1.588287 Largest / Average step : 1.409491 Largest / Smallest step : 2.238677 Median interval of one step : 256/243, 90.2250 cents, amount: 2 Least squares average step : 98.62184 cents, oct.: 1183.46206 cents Scale is strictly proper Scale is 3-distributional even Step pattern alph. order: ABABACBABABC Step pattern size order : SLSLSMLSLSLM Scale is a Constant Structure, by a margin of 12.23680 cents Scale diversity : 1.327588 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.285108 Rothenberg efficiency : 0.514153 redundancy: 0.485847 Efficiency x scale size : 6.169841 Number of different interval sizes : 32 = 2.90909 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 2.90909 = 32/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 1605632/1594323, 12.2368 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 10 Most common triad is 0.0 498.045 701.955 cents, amount: 8 Number of recognisable fifths : 10, average 701.9550 cents Best fifths form a closed circle Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 8.3333% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 8-9 -- Rational properties -- Prime limit : 7 Odd number limit : 19683 (O: 19683 U: 19683) Highest odd numerator or denominator: 243 Scale harmonicity : 0.022082 Average absolute harmonicity : 0.162236 Specific harmonicity : 0.123058 Fundamental : 1/10368, -13.3399 octaves, 0.0252 Hz. Guide tone : 27216, 14.7322 octaves, 7120401.385 Hz. Exponens Consonantiae : 2.821755E+08, 28.07202 octaves Euler's gradus suavitatis : 36 Sum of Mann's harmonic distance : 458.0, average 38.16667 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 14.46333, average 1.20528 Sum of Tenney's harmonic distance : 28.31282, average 2.35940 Vogel's harmonic complexity : 22.33333 Wille's k value : 9841 Wilson's harmonic complexity : 34 Rectangular lattice diameter : 10 Triangular lattice diameter : 9 Lattice compactness : 396.96141, average 5.08925 Lattice compactness (without 2's) : 251.72028, average 3.22718 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -7 .. 4 -1.66667 36 1 3: -4 .. 5 0.50000 26 5 7: 0 .. 1 0.50000 6 6 Average exponent except 2's : 12 / 12 = 1.00000 Average absolute exponent except 2's: 32 / 12 = 2.66667 Scale is JI-epimorphic with val: <12 19 34| = patent
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 24.5911 c. M:-38.9941 c. Twelve-tone Chromatic (1/11-comma) 15: 1 2 0 2 1 1 2 1 1 1 2 1 P D3 SD: 20.1453 c. M:-36.0900 c. 17: 1 2 1 2 1 1 2 1 2 1 2 1 P M ME SD: 13.5853 c. M:-23.3367 c. Supra-12 24: 1 3 1 3 1 2 3 1 3 1 3 2 P D3 SD: 12.2226 c. M: 20.7809 c. 26: 1 3 2 3 1 2 3 2 3 1 3 2 N SD: 12.0125 c. M:-19.6995 c. 27: 1 4 1 3 2 2 3 1 3 2 3 2 N SD: 12.5504 c. M: 18.5165 c. 28: 1 4 1 4 1 2 3 2 3 2 3 2 N SD: 11.8973 c. M:-20.7514 c. 30: 2 3 2 3 2 2 4 1 4 1 4 2 P SD: 10.6348 c. M:-18.0450 c. 32: 2 3 2 4 2 2 4 1 4 2 4 2 N SD: 10.7043 c. M:-16.7191 c. 33: 2 4 1 4 2 2 4 2 4 2 4 2 N SD: 10.6724 c. M:-17.4977 c. 35: 2 4 2 4 2 2 4 2 4 2 4 3 P SD: 9.8530 c. M: 16.2407 c. 36: 2 4 2 4 2 3 4 2 4 2 4 3 SP D3 SD: 4.8364 c. M: 9.7750 c. 41: 2 5 2 5 2 3 5 2 5 2 5 3 P D3 SD: 2.8730 c. M: 4.9083 c. 53: 3 6 3 6 3 4 6 3 6 3 6 4 SP D3 SD: 3.4416 c. M:-5.0318 c. 77: 4 9 4 9 4 6 9 4 9 4 9 6 SP D3 SD: 1.9735 c. M: 3.2815 c. 94: 5 11 5 11 5 7 11 5 11 5 11 7 SP D3 SD: 0.9034 c. M:-1.5595 c. 135: 7 16 7 16 7 10 16 7 16 7 16 10 SP D3 SD: 0.6989 c. M:-1.3361 c. 171: 9 20 9 20 9 13 20 9 20 9 20 13 SP D3 SD: 0.4986 c. M: 1.0031 c. 212: 11 25 11 25 11 16 25 11 25 11 25 16 SP D3 SD: 0.5894 c. M: 0.9696 c. 265: 14 31 14 31 14 20 31 14 31 14 31 20 SP D3 SD: 0.2891 c. M:-0.5035 c. 306: 16 36 16 36 16 23 36 16 36 16 36 23 SP D3 SD: 0.1472 c. M: 0.2216 c. 400: 21 47 21 47 21 30 47 21 47 21 47 30 SP D3 SD: 0.1338 c. M:-0.2250 c. 571: 30 67 30 67 30 43 67 30 67 30 67 43 SP D3 SD: 0.0766 c. M: 0.1428 c. 706: 37 83 37 83 37 53 83 37 83 37 83 53 SP D3 SD: 0.0719 c. M:-0.1400 c. 877: 46 103 46 103 46 66 103 46 103 46 103 66 SP D3 SD: 0.0512 c. M: 0.0854 c. 971: 51 114 51 114 51 73 114 51 114 51 114 73 SP D3 SD: 0.0493 c. M:-0.0739 c. 1277: 67 150 67 150 67 96 150 67 150 67 150 96 SP D3 SD: 0.0070 c. M:-0.0136 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x x x x 4 S SD: 0.0000 cents 3 x x x x 4 x x x 5 x x 6 S SD: 11.5751 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 5.3766 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 17.4335 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 11.6135 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 12.1039 cents 8 x 9 x 10 x 11:12 x x 14:15:16 S SD: 4.5600 cents 9 x 10 x 11:12 x x 14:15:16:17:18 S SD: 9.7928 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 9.7732 cents 11 x 12:13:14 x 15 x 17 x 19:21:22 SD: 8.6085 cents 12 x x 14:15:16:17:18:19:20:21:23:24 SD: 6.8151 cents 13:14 x 15:16:17:18 x 20:22:23:25:26 SD: 9.0912 cents 14:15:16 x 18 x 19:21:22:24:25:27:28 SD: 9.3489 cents 15:16:17:18:19:20:21 x 23:25:26:28:30 SD: 8.3019 cents 16:17:18:19:20:21:22:24:25:27:28:30:32 SD: 5.1240 cents 17:18:19:20 x 22:24 x 26:29:30:32:34 SD: 7.1874 cents 18:19:20:21:23:24:25:27:28:30:32:34:36 SD: 5.1099 cents 20:21 x 23:25:26:28:30:31:34:35:38:40 SD: 4.5329 cents 22:23:25:26:28:29:30:33:34:37:39:42:44 SD: 4.1502 cents 23:24:26:27:29:30:32:35:36:39:40:44:46 SD: 3.4061 cents 26:27:29:30:33:34:36:39:40:44:46:49:52 SD: 3.3029 cents 29:30:33:34:37:38:40:44:45:49:51:55:58 SD: 2.8781 cents 31:32:35:36:39:41:43:47:48:52:54:59:62 SD: 2.7344 cents 32:33:36:37:41:42:44:48:50:54:56:61:64 SD: 2.6221 cents 41:43:46:48:52:54:57:62:64:69:72:78:82 SD: 2.4730 cents 42:44:47:49:53:55:58:63:65:71:74:80:84 SD: 2.2020 cents 47:49:53:55:59:62:65:71:73:79:82:89:94 SD: 2.1346 cents 48:50:54:56:61:63:66:72:75:81:84:91:96 SD: 1.3667 cents 71:74:80:83:90:93:98:107:110:120:124:135:142 SD: 1.3565 cents 76:79:86:89:96:100:105:114:118:128:133:144:152 SD: 1.2535 cents 78:81:88:91:99:102:108:117:121:132:137:148:156 SD: 1.1427 cents 79:82:89:92:100:104:109:119:123:133:138:150:158 SD: 0.9904 cents 80:83:90:93:101:105:111:120:124:135:140:152:160 SD: 0.9626 cents 86:89:97:100:109:113:119:129:134:145:151:163:172 SD: 0.9462 cents 102:106:115:119:129:134:141:153:159:172:179:194:204 SD: 0.7469 cents 112:116:126:131:142:147:155:168:174:189:196:213:224 SD: 0.5901 cents 128:133:144:149:162:168:177:192:199:216:224:243:256 SD: 0.4356 cents 144:149:162:168:182:189:199:216:224:243:252:273:288 SD: 0.4346 cents 185:192:208:216:234:243:256:278:288:312:324:351:370 SD: 0.4146 cents 192:199:216:224:243:252:265:288:299:324:336:365:384 SD: 0.3743 cents 214:222:241:250:271:281:296:321:333:361:375:406:428 SD: 0.3549 cents 240:249:270:280:304:315:332:360:373:405:420:456:480 SD: 0.2304 cents 272:282:306:317:344:357:376:408:423:459:476:516:544 SD: 0.2220 cents 384:398:432:448:486:504:531:576:597:648:672:729:768 SD: 0.1143 cents 432:448:486:504:547:567:597:648:672:729:756:820:864 SD: 0.1064 cents