Scala analysis: parizek_syndiat
Petr Parizek, diatonic scale with syntonic alternatives
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 10/9 182.403712 minor whole tone 2: 9/8 203.910002 major whole tone 3: 5/4 386.313714 major third 4: 4/3 498.044999 perfect fourth 5: 27/20 519.551289 acute fourth 6: 40/27 680.448711 grave fifth 7: 3/2 701.955001 perfect fifth 8: 5/3 884.358713 major sixth, BP sixth 9: 27/16 905.865003 Pythagorean major sixth 10: 50/27 1066.762425 grave major seventh 11: 15/8 1088.268715 classic major seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 10/9 182.4037 minor whole tone 2: 81/80 21.5063 syntonic comma, Didymus comma 3: 10/9 182.4037 minor whole tone 4: 16/15 111.7313 minor diatonic semitone 5: 81/80 21.5063 syntonic comma, Didymus comma 6: 800/729 160.8974 grave whole tone 7: 81/80 21.5063 syntonic comma, Didymus comma 8: 10/9 182.4037 minor whole tone 9: 81/80 21.5063 syntonic comma, Didymus comma 10: 800/729 160.8974 grave whole tone 11: 81/80 21.5063 syntonic comma, Didymus comma 12: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 81/80 21.506 cents syntonic comma, Didymus comma 1: 2 16/15 111.731 cents minor diatonic semitone 1: 2 800/729 160.897 cents grave whole tone 1: 3 10/9 182.404 cents minor whole tone 2: 2 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 2: 4 10/9 182.404 cents minor whole tone 2: 4 9/8 203.910 cents major whole tone 2: 2 32/27 294.135 cents Pythagorean minor third 3: 2 9/8 203.910 cents major whole tone 3: 1 729/640 225.416 cents acute major second 3: 2 32/27 294.135 cents Pythagorean minor third 3: 4 6/5 315.641 cents minor third 3: 2 100/81 364.807 cents grave major third 3: 1 5/4 386.314 cents major third 4: 2 6/5 315.641 cents minor third 4: 2 243/200 337.148 cents acute minor third 4: 4 5/4 386.314 cents major third 4: 2 320/243 476.539 cents grave fourth 4: 2 4/3 498.045 cents perfect fourth 5: 2 81/64 407.820 cents Pythagorean major third 5: 6 4/3 498.045 cents perfect fourth 5: 2 27/20 519.551 cents acute fourth 5: 1 1000/729 547.211 cents 5: 1 64/45 609.776 cents 2nd tritone 6: 4 27/20 519.551 cents acute fourth 6: 2 25/18 568.717 cents classic augmented fourth 6: 2 36/25 631.283 cents classic diminished fifth 6: 4 40/27 680.449 cents grave fifth 7: 1 45/32 590.224 cents diatonic tritone 7: 1 729/500 652.789 cents 7: 2 40/27 680.449 cents grave fifth 7: 6 3/2 701.955 cents perfect fifth 7: 2 128/81 792.180 cents Pythagorean minor sixth 8: 2 3/2 701.955 cents perfect fifth 8: 2 243/160 723.461 cents acute fifth 8: 4 8/5 813.686 cents minor sixth 8: 2 400/243 862.852 cents grave major sixth 8: 2 5/3 884.359 cents major sixth, BP sixth 9: 1 8/5 813.686 cents minor sixth 9: 2 81/50 835.193 cents acute minor sixth 9: 4 5/3 884.359 cents major sixth, BP sixth 9: 2 27/16 905.865 cents Pythagorean major sixth 9: 1 1280/729 974.584 cents grave minor seventh 9: 2 16/9 996.090 cents Pythagorean minor seventh 10: 2 27/16 905.865 cents Pythagorean major sixth 10: 4 16/9 996.090 cents Pythagorean minor seventh 10: 4 9/5 1017.596 cents just minor seventh, BP seventh 10: 2 50/27 1066.762 cents grave major seventh 11: 3 9/5 1017.596 cents just minor seventh, BP seventh 11: 2 729/400 1039.103 cents acute minor seventh 11: 2 15/8 1088.269 cents classic major seventh 11: 5 160/81 1178.494 cents octave - syntonic comma Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.72727 = 52/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 182.4 203.9 386.3 498.0 519.6 680.4 702.0 884.4 905.9 1066.8 1088.3 1200.0 182.4 : 21.5 203.9 315.6 337.1 498.0 519.6 702.0 723.5 884.4 905.9 1017.6 1200.0 203.9 : 182.4 294.1 315.6 476.5 498.0 680.4 702.0 862.9 884.4 996.1 1178.5 1200.0 386.3 : 111.7 133.2 294.1 315.6 498.0 519.6 680.4 702.0 813.7 996.1 1017.6 1200.0 498.0 : 21.5 182.4 203.9 386.3 407.8 568.7 590.2 702.0 884.4 905.9 1088.3 1200.0 519.6 : 160.9 182.4 364.8 386.3 547.2 568.7 680.4 862.9 884.4 1066.8 1178.5 1200.0 680.4 : 21.5 203.9 225.4 386.3 407.8 519.6 702.0 723.5 905.9 1017.6 1039.1 1200.0 702.0 : 182.4 203.9 364.8 386.3 498.0 680.4 702.0 884.4 996.1 1017.6 1178.5 1200.0 884.4 : 21.5 182.4 203.9 315.6 498.0 519.6 702.0 813.7 835.2 996.1 1017.6 1200.0 905.9 : 160.9 182.4 294.1 476.5 498.0 680.4 792.2 813.7 974.6 996.1 1178.5 1200.0 1066.8: 21.5 133.2 315.6 337.1 519.6 631.3 652.8 813.7 835.2 1017.6 1039.1 1200.0 1088.3: 111.7 294.1 315.6 498.0 609.8 631.3 792.2 813.7 996.1 1017.6 1178.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 21.5063 .. 182.4037 cents 800/729, 160.8974 cents 81/80, 21.5063 cents 2: 133.2376 .. 294.1350 cents 800/729, 160.8974 cents 243/250,-49.1661 cents 3: 203.9100 .. 386.3137 cents 10/9, 182.4037 cents 243/256,-90.2250 cents 4: 315.6413 .. 498.0450 cents 10/9, 182.4037 cents 24/25,-70.6724 cents 5: 407.8200 .. 609.7763 cents 4096/3645, 201.9563 cents 243/256,-90.2250 cents 6: 519.5513 .. 680.4487 cents 800/729, 160.8974 cents 243/256,-90.2250 cents 7: 590.2237 .. 792.1800 cents 4096/3645, 201.9563 cents 243/256,-90.2250 cents 8: 701.9550 .. 884.3587 cents 10/9, 182.4037 cents 243/256,-90.2250 cents 9: 813.6863 .. 996.0900 cents 10/9, 182.4037 cents 24/25,-70.6724 cents 10: 905.8650 .. 1066.7624 cents 800/729, 160.8974 cents 243/256,-90.2250 cents 11: 1017.5963 .. 1178.4937 cents 800/729, 160.8974 cents 243/250,-49.1661 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 81/80, 21.5063 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 10/9, 182.4037 cents Average / Smallest step : 4.649803 Largest / Average step : 1.824037 Largest / Smallest step : 8.481412 Median interval of one step : 16/15, 111.7313 cents, amount: 2 Most common interval of one step : 81/80, 21.5063 cents, amount: 5 Least squares average step : 104.00264 cents, oct.: 1248.03163 cents Scale is not proper Step pattern alph. order: ABACBDBABDBC Step pattern size order : DADBACADACAB Scale is not a Constant Structure Scale diversity : 1.335230 Lumma stability : 0.035844 Lumma impropriety factor : 0.634562 Rothenberg efficiency : 0.367989 redundancy: 0.632011 Efficiency x scale size : 4.415873 Number of different interval sizes : 38 = 3.45455 / class Number of one step interval sizes : 4 Highest interval variety : 6 Mean interval variety : 4.72727 = 52/11 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 2048/2025, 19.5526 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 8 Most common triad is 0.0 498.045 701.955 cents, amount: 6 Number of recognisable fifths : 8, average 701.9550 cents Scale is fully connected 5-limit major-minor triadic Scale contains a complete diamond : 1 3 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 5 = 41.6667% Scale is differentially coherent in interval classes 1 and 2 combined Scale is differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined Limited inverse transpositions : 3 Inversional symmetry on intervals : 1-2 7-8 -- Rational properties -- Prime limit : 5 Odd number limit : 729 (O: 729 U: 729) Highest odd numerator or denominator: 27 Scale harmonicity : 0.023697 Average absolute harmonicity : 0.187117 Specific harmonicity : 0.152106 Fundamental : 1/2160, -11.0768 octaves, 0.1211 Hz. Guide tone : 5400, 12.3987 octaves, 1412778.053 Hz. Exponens Consonantiae : 1.166400E+07, 23.47556 octaves Euler's gradus suavitatis : 32 Sum of Mann's harmonic distance : 162.5, average 13.54167 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 11.16221, average 0.93018 Sum of Tenney's harmonic distance : 22.05788, average 1.83816 Vogel's harmonic complexity : 19.91667 Wille's k value : 1822 Wilson's harmonic complexity : 33 Rectangular lattice diameter : 9 Triangular lattice diameter : 6 Lattice compactness : 297.95742, average 3.81997 Lattice compactness (without 2's) : 205.00672, average 2.62829 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 3 -0.58333 23 1 3: -3 .. 3 0.00000 20 4 5: -1 .. 2 0.50000 8 7 Average exponent except 2's : 6 / 12 = 0.50000 Average absolute exponent except 2's: 28 / 12 = 2.33333
FIT/MODE
12: 2 0 2 1 0 2 0 2 0 2 0 1 N T3 SD: 15.2910 c. M:-33.2376 c. 18: 3 0 3 1 1 2 1 2 1 2 0 2 N SD: 19.1387 c. M: 31.3783 c. 19: 3 0 3 2 0 3 0 3 0 3 0 2 N SD: 11.3824 c. M: 21.6545 c. 24: 4 0 4 2 0 4 0 4 0 3 1 2 N SD: 12.8518 c. M: 19.5513 c. 25: 4 0 4 2 1 3 1 3 1 3 1 2 N SD: 12.4121 c. M: 20.3587 c. 26: 4 0 4 3 0 4 0 4 1 3 1 2 N SD: 12.5583 c. M:-19.4236 c. 27: 4 1 4 2 1 3 1 4 0 4 0 3 N SD: 12.4732 c. M: 21.6020 c. 28: 4 1 4 3 0 4 0 5 0 4 0 3 N SD: 10.7852 c. M: 16.8401 c. 29: 4 1 4 3 0 4 1 4 1 4 0 3 N SD: 12.4240 c. M: 22.9996 c. 30: 5 0 5 3 0 4 1 4 1 4 0 3 N SD: 12.1884 c. M:-21.9550 c. 31: 5 0 5 3 0 5 0 5 0 5 0 3 N SD: 10.8324 c. M:-17.1085 c. 33: 5 1 5 3 0 5 0 5 1 4 1 3 N SD: 9.8155 c. M:-14.2718 c. 34: 5 1 5 3 1 4 1 5 1 4 1 3 N SD: 6.8676 c. M:-11.7821 c. 41: 6 1 6 4 1 5 1 6 1 5 1 4 N SD: 5.9834 c. M: 13.1039 c. 46: 7 1 7 4 1 6 1 7 1 6 1 4 N SD: 3.9741 c. M:-7.3835 c. 53: 8 1 8 5 1 7 1 8 1 7 1 5 N SD: 1.2028 c. M: 2.6115 c. 118: 18 2 18 11 2 16 2 18 2 16 2 11 N SD: 0.6009 c. M:-1.0342 c. 171: 26 3 26 16 3 23 3 26 3 23 3 16 N SD: 0.3148 c. M: 0.6018 c. 388: 59 7 59 36 7 52 7 59 7 52 7 36 N SD: 0.2052 c. M:-0.3911 c. 441: 67 8 67 41 8 59 8 67 8 59 8 41 N SD: 0.1368 c. M:-0.2574 c. 559: 85 10 85 52 10 75 10 85 10 75 10 52 N SD: 0.0692 c. M:-0.1428 c. 612: 93 11 93 57 11 82 11 93 11 82 11 57 N SD: 0.0441 c. M: 0.0958 c. 1171: 178 21 178 109 21 157 21 178 21 157 21 109 N SD: 0.0167 c. M:-0.0319 c. 1783: 271 32 271 166 32 239 32 271 32 239 32 166 N SD: 0.0151 c. M:-0.0239 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 4 x x x 5 x x x 6 S SD: 0.0000 cents 4 x x 5 x x x 6 x 7 x x 8 S SD: 15.7402 cents 5 x x 6 x 7 x x 8 x 9 x 10 S SD: 25.5895 cents 6 x 7 x 8 x x 9:10 x 11 x 12 S SD: 10.8868 cents 7 x 8:9 x x 10:11 x 12:13 x 14 S SD: 17.1070 cents 8 x 9:10 x 11 x 12:13:14 x 15:16 S SD: 10.3790 cents 9:10 x 11:12 x 13:14:15 x x 17:18 SD: 10.8701 cents 10:11 x x 13:14 x 15 x 17 x 19:20 SD: 11.8468 cents 11:12 x 14 x 15:16:17:18:19:20:21:22 S SD: 10.2874 cents 12:13:14:15:16 x x 18:20 x 22:23:24 S SD: 9.7092 cents 13:14:15:16:17:18:19:20 x 22:24 x 26 S SD: 10.5569 cents 14 x 16:18 x 19 x 21:23:24:26 x 28 SD: 8.4720 cents 15 x 17:19:20 x 22:23:25 x x 28:30 SD: 6.2489 cents 16 x 18:20:21:22 x 24 x 27 x 30:32 S SD: 5.2328 cents 17:19 x 21 x 23:25:26:28:29:31:32:34 SD: 5.7964 cents 18:20 x 23:24 x x 27:30 x 33:34:36 SD: 5.4684 cents 19:21 x 24:25:26:28:29 x 32:35:36:38 SD: 5.3870 cents 20:22:23:25 x 27 x 30:33:34:37:38:40 SD: 5.2396 cents 21:23:24:26:28 x 31:32:35 x 39 x 42 SD: 5.4934 cents 22:24:25:28:29:30 x 33 x 37 x 41:44 SD: 6.2103 cents 23 x 26:29 x 31:34:35:38:39 x 43:46 SD: 3.9445 cents 24 x 27:30:32 x x 36:40:41:44:45:48 SD: 3.0510 cents 25 x 28:31:33:34:37:38 x 42:46:47:50 SD: 3.8104 cents 26:29 x 33 x 35 x 39:43:44:48:49:52 SD: 3.6465 cents 27:30 x 34:36 x 40:41:45:46:50:51:54 SD: 3.2426 cents 28:31:32:35:37:38:41:42 x 47:52:53:56 SD: 3.9551 cents 29:32:33:36 x 39:43:44:48:49:54 x 58 SD: 3.6818 cents 30:33:34:38:40:41:44:45:50:51 x 56:60 SD: 4.0334 cents 31:34:35:39:41:42:46:47 x 52:57:58:62 SD: 3.5523 cents 32 x 36:40 x 43:47:48:53:54:59:60:64 SD: 2.1523 cents 33 x 37:41:44:45:49:50:55:56:61:62:66 SD: 2.6995 cents 34:38 x 43:45:46:50:51:57 x 63:64:68 SD: 3.1683 cents 35:39 x 44 x 47:52:53:58:59:65:66:70 SD: 2.6893 cents 37:41:42:46:49:50:55:56:62 x x 69:74 SD: 3.0695 cents 38:42:43:48 x 51:56:57:63:64:70:71:76 SD: 2.7513 cents 39:43:44:49:52:53:58:59:65:66:72:73:78 SD: 2.2604 cents 40:44:45:50:53:54:59:60:67:68:74:75:80 SD: 2.2345 cents 41 x 46:51:55 x 61:62:68:69:76:77:82 SD: 2.3662 cents 42 x 47:53:56:57:62:63:70:71:78:79:84 SD: 2.1111 cents 43:48 x 54:57:58:64:65:72:73:80:81:86 SD: 2.5363 cents 44:49:50:55:59 x 65:66:73:74:81:83:88 SD: 2.4891 cents 45:50:51:56:60:61:67:68:75:76:83:84:90 SD: 2.0762 cents 46:51:52:58:61:62:68:69:77:78:85:86:92 SD: 2.0155 cents 47:52:53:59:63 x 70:71:78:79:87:88:94 SD: 2.1348 cents 48:53:54:60:64:65:71:72:80:81:89:90:96 SD: 1.0484 cents 50 x 56:63:67:68:74:75:83:84:93:94:100 SD: 2.3657 cents 51:57 x 64:68:69:76:77:85:86:94:96:102 SD: 2.0484 cents 52:58:59:65:69:70:77:78:87:88:96:98:104 SD: 1.9208 cents 54:60:61:68:72:73:80:81:90:91:100:101:108 SD: 1.3001 cents 59 x 66:74:79:80:87:89:98:100:109:111:118 SD: 2.1237 cents 60:67:68:75:80:81:89:90:100:101:111:113:120 SD: 1.4971 cents 63:70:71:79:84:85:93:95:105:106:117:118:126 SD: 1.2248 cents 64:71:72:80:85:86:95:96:107:108:119:120:128 SD: 1.2008 cents 72:80:81:90:96:97:107:108:120:122:133:135:144 SD: 0.8788 cents 80:89:90:100:107:108:119:120:133:135:148:150:160 SD: 0.8535 cents 96:107:108:120:128:130:142:144:160:162:178:180:192 SD: 0.6955 cents 120:133:135:150:160:162:178:180:200:203:222:225:240 SD: 0.5571 cents 128:142:144:160:171:173:190:192:213:216:237:240:256 SD: 0.5372 cents 135:150:152:169:180:182:200:203:225:228:250:253:270 SD: 0.4946 cents 144:160:162:180:192:194:213:216:240:243:267:270:288 SD: 0.4143 cents 160:178:180:200:213:216:237:240:267:270:296:300:320 SD: 0.3704 cents 208:231:234:260:277:281:308:312:347:351:385:390:416 SD: 0.2726 cents 272:302:306:340:363:367:403:408:453:459:504:510:544 SD: 0.2316 cents 288:320:324:360:384:389:427:432:480:486:533:540:576 SD: 0.1623 cents 432:480:486:540:576:583:640:648:720:729:800:810:864 SD: 0.0495 cents