Scala analysis: parapyth12trans
A JI transversal of parapyth17.scl for use in calculations. If you temper out 352/351 and 364/363 it becomes parapyth17.
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: 14/11 417.507964 undecimal diminished fourth or major third 5: 21/16 470.780907 narrow fourth 6: 11/8 551.317942 undecimal semi-augmented fourth 7: 3/2 701.955001 perfect fifth 8: 14/9 764.915905 septimal minor sixth 9: 22/13 910.790281 tridecimal major sixth 10: 7/4 968.825906 harmonic seventh 11: 21/11 1119.462965 undecimal major seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 22/21 80.5370 undecimal minor semitone 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: 12/11 150.6371 undecimal neutral second, 3/4-tone 5: 33/32 53.2729 undecimal comma, al-Farabi's 1/4-tone 6: 22/21 80.5370 undecimal minor semitone 7: 12/11 150.6371 undecimal neutral second, 3/4-tone 8: 28/27 62.9609 Archytas' 1/3-tone 9: 99/91 145.8744 10: 91/88 58.0356 11: 12/11 150.6371 undecimal neutral second, 3/4-tone 12: 22/21 80.5370 undecimal minor semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 33/32 53.273 cents undecimal comma, al-Farabi's 1/4-tone 1: 1 91/88 58.036 cents 1: 3 28/27 62.961 cents Archytas' 1/3-tone 1: 2 22/21 80.537 cents undecimal minor semitone 1: 1 243/224 140.949 cents Archytas' 2/3-tone 1: 1 99/91 145.874 cents 1: 3 12/11 150.637 cents undecimal neutral second, 3/4-tone 2: 1 121/112 133.810 cents 2: 1 88/81 143.498 cents 2nd undecimal neutral second 2: 4 9/8 203.910 cents major whole tone 2: 1 273/242 208.673 cents 2: 1 44/39 208.835 cents 2: 2 112/99 213.598 cents 2: 2 8/7 231.174 cents septimal whole tone 3: 3 7/6 266.871 cents septimal minor third 3: 3 33/28 284.447 cents undecimal minor third 3: 1 13/11 289.210 cents tridecimal minor third 3: 2 32/27 294.135 cents Pythagorean minor third 3: 2 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 3: 1 16/13 359.472 cents tridecimal neutral third 4: 3 11/9 347.408 cents undecimal neutral third 4: 1 364/297 352.171 cents 4: 1 81/64 407.820 cents Pythagorean major third 4: 3 14/11 417.508 cents undecimal diminished fourth or major third 4: 3 9/7 435.084 cents septimal major third, BP third 4: 1 352/273 440.009 cents 5: 1 21/16 470.781 cents narrow fourth 5: 1 297/224 488.357 cents 5: 1 117/88 493.120 cents tridecimal gentle fourth 5: 1 121/91 493.282 cents 5: 7 4/3 498.045 cents perfect fourth 5: 1 168/121 568.145 cents 6: 3 11/8 551.318 cents undecimal semi-augmented fourth 6: 1 91/66 556.081 cents 6: 2 112/81 561.006 cents 6: 2 81/56 638.994 cents 6: 1 132/91 643.919 cents 6: 3 16/11 648.682 cents undecimal semi-diminished fifth 7: 1 121/84 631.855 cents 7: 7 3/2 701.955 cents perfect fifth 7: 1 182/121 706.718 cents 7: 1 176/117 706.880 cents 7: 1 448/297 711.643 cents 7: 1 32/21 729.219 cents wide fifth 8: 1 273/176 759.991 cents 8: 3 14/9 764.916 cents septimal minor sixth 8: 3 11/7 782.492 cents undecimal augmented fifth 8: 1 128/81 792.180 cents Pythagorean minor sixth 8: 1 297/182 847.829 cents 8: 3 18/11 852.592 cents undecimal neutral sixth 9: 1 13/8 840.528 cents tridecimal neutral sixth 9: 2 44/27 845.453 cents neutral sixth 9: 2 27/16 905.865 cents Pythagorean major sixth 9: 1 22/13 910.790 cents tridecimal major sixth 9: 3 56/33 915.553 cents 9: 3 12/7 933.129 cents septimal major sixth 10: 2 7/4 968.826 cents harmonic seventh 10: 2 99/56 986.402 cents 10: 1 39/22 991.165 cents 10: 1 484/273 991.327 cents 10: 4 16/9 996.090 cents Pythagorean minor seventh 10: 1 81/44 1056.502 cents 2nd undecimal neutral seventh 10: 1 224/121 1066.190 cents 11: 3 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 11: 1 182/99 1054.126 cents 11: 1 448/243 1059.051 cents 11: 2 21/11 1119.463 cents undecimal major seventh 11: 3 27/14 1137.039 cents septimal major seventh 11: 1 176/91 1141.964 cents 11: 1 64/33 1146.727 cents 33rd subharmonic Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 6.36364 = 70/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 63.0 203.9 266.9 417.5 470.8 551.3 702.0 764.9 910.8 968.8 1119.5 1200.0 63.0 : 140.9 203.9 354.5 407.8 488.4 639.0 702.0 847.8 905.9 1056.5 1137.0 1200.0 203.9 : 63.0 213.6 266.9 347.4 498.0 561.0 706.9 764.9 915.6 996.1 1059.1 1200.0 266.9 : 150.6 203.9 284.4 435.1 498.0 643.9 702.0 852.6 933.1 996.1 1137.0 1200.0 417.5 : 53.3 133.8 284.4 347.4 493.3 551.3 702.0 782.5 845.5 986.4 1049.4 1200.0 470.8 : 80.5 231.2 294.1 440.0 498.0 648.7 729.2 792.2 933.1 996.1 1146.7 1200.0 551.3 : 150.6 213.6 359.5 417.5 568.1 648.7 711.6 852.6 915.6 1066.2 1119.5 1200.0 702.0 : 63.0 208.8 266.9 417.5 498.0 561.0 702.0 764.9 915.6 968.8 1049.4 1200.0 764.9 : 145.9 203.9 354.5 435.1 498.0 639.0 702.0 852.6 905.9 986.4 1137.0 1200.0 910.8 : 58.0 208.7 289.2 352.2 493.1 556.1 706.7 760.0 840.5 991.2 1054.1 1200.0 968.8 : 150.6 231.2 294.1 435.1 498.0 648.7 702.0 782.5 933.1 996.1 1142.0 1200.0 1119.5: 80.5 143.5 284.4 347.4 498.0 551.3 631.9 782.5 845.5 991.3 1049.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 53.2729 .. 150.6371 cents 128/121, 97.3641 cents 33/32, 53.2729 cents 2: 133.8100 .. 231.1741 cents 128/121, 97.3641 cents 1331/1344,-16.8271 cents 3: 266.8709 .. 359.4723 cents 96/91, 92.6014 cents 49/48, 35.6968 cents 4: 347.4079 .. 440.0094 cents 96/91, 92.6014 cents 143/144,-12.0644 cents 5: 470.7809 .. 568.1450 cents 128/121, 97.3641 cents 5733/5632, 30.7715 cents 6: 551.3179 .. 648.6821 cents 128/121, 97.3641 cents 1331/1344,-16.8271 cents 7: 631.8550 .. 729.2191 cents 128/121, 97.3641 cents 1331/1344,-16.8271 cents 8: 759.9906 .. 852.5921 cents 96/91, 92.6014 cents 5733/5632, 30.7715 cents 9: 840.5277 .. 933.1291 cents 96/91, 92.6014 cents 143/144,-12.0644 cents 10: 968.8259 .. 1066.1900 cents 128/121, 97.3641 cents 49/48, 35.6968 cents 11: 1049.3629 .. 1146.7271 cents 128/121, 97.3641 cents 1331/1344,-16.8271 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 33/32, 53.2729 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 12/11, 150.6371 cents Average / Smallest step : 1.877125 Largest / Average step : 1.506371 Largest / Smallest step : 2.827647 Median interval of one step : 22/21, 80.5370 cents, amount: 2 Least squares average step : 98.82418 cents, oct.: 1185.89011 cents Scale is not proper Step pattern alph. order: ABACDECAFGCE Step pattern size order : CECGADGCFBGD Scale is a Constant Structure, by a margin of 2.37644 cents Scale diversity : 1.388295 Lumma stability : 0.199569 Lumma impropriety factor : 0.076198 Rothenberg efficiency : 0.272685 redundancy: 0.727315 Efficiency x scale size : 3.272222 Number of different interval sizes : 70 = 6.36364 / class Number of one step interval sizes : 7 Highest interval variety : 7 Mean interval variety : 6.36364 = 70/11 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 10648/10647, 0.1626 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 7 Most common triad is 0.0 498.045 701.955 cents, amount: 4 Number of recognisable fifths : 10, average 703.8926 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 with margin 97.3641 cents: 5 -- Rational properties -- Prime limit : 13 Odd number limit : 297 (O: 297 U: 297) Highest odd numerator or denominator: 27 Scale harmonicity : 0.011346 Average absolute harmonicity : 0.154309 Specific harmonicity : 0.085851 Fundamental : 1/61776, -15.9148 octaves, 0.0042 Hz. Guide tone : 2772, 11.4367 octaves, 725226.067 Hz. Exponens Consonantiae : 1.712431E+08, 27.35147 octaves Euler's gradus suavitatis : 55 Sum of Mann's harmonic distance : 137.5, average 11.45833 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 11.34833, average 0.94569 Sum of Tenney's harmonic distance : 22.46413, average 1.87201 Vogel's harmonic complexity : 39.08333 Wille's k value : 40540 Wilson's harmonic complexity : 57 Rectangular lattice diameter : 9 Triangular lattice diameter : 5 Lattice compactness : 248.08000, average 3.18051 Lattice compactness (without 2's) : 155.13405, average 1.98890 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -0.66667 20 1 3: -3 .. 2 -0.08333 11 2 7: 0 .. 1 0.58333 7 5 11: -1 .. 1 0.00000 4 3 13: -1 .. 0 -0.08333 1 1 Average exponent except 2's : 5 / 12 = 0.41667 Average absolute exponent except 2's: 23 / 12 = 1.91667 Scale is JI-epimorphic with val: <12 19 34 42 45| Scale is weakly epimorphic with val: <12 19 37 39 42|
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 26.9517 c. M:-48.6821 c. Twelve-tone Chromatic (1/11-comma) 13: 1 1 1 2 0 1 2 0 2 1 1 1 N D3 SD: 25.5846 c. M:-46.5587 c. 15: 1 2 0 2 1 1 2 1 1 1 2 1 P D3 SD: 21.1434 c. M:-36.0900 c. 16: 1 2 1 2 0 1 2 1 2 1 2 1 N T3 SD: 20.4160 c. M:-33.1291 c. 17: 1 2 1 2 1 1 2 1 2 1 2 1 P M ME SD: 12.2179 c. M:-23.3367 c. Supra-12 24: 1 3 1 3 1 2 3 1 3 1 3 2 P D3 SD: 13.7960 c. M: 20.7809 c. 26: 1 3 2 3 1 2 3 1 4 1 3 2 N SD: 12.6975 c. M: 26.4544 c. 28: 1 4 1 4 1 2 3 2 3 2 3 2 N SD: 11.1722 c. M: 20.1038 c. 31: 2 3 2 4 1 2 4 2 4 1 4 2 N SD: 9.0642 c. M:-18.2420 c. 33: 2 4 1 4 2 2 4 2 4 2 4 2 N SD: 9.7980 c. M: 17.5080 c. 35: 2 4 2 4 2 2 4 2 5 1 5 2 N SD: 9.3085 c. M: 16.2407 c. 36: 2 4 2 5 1 3 4 2 4 2 5 2 N SD: 8.4280 c. M:-15.8254 c. 37: 2 4 2 5 2 2 5 2 4 2 5 2 N SD: 9.1002 c. M:-15.7056 c. 41: 2 5 2 5 2 3 5 2 5 2 5 3 P D3 SD: 4.1939 c. M: 7.7519 c. 57: 3 7 3 7 2 4 7 3 7 3 7 4 N SD: 5.1810 c. M: 7.6230 c. 58: 3 7 3 7 3 4 7 3 7 3 7 4 P D3 SD: 3.2615 c. M:-7.3027 c. 63: 3 8 3 8 3 4 8 3 8 3 8 4 N D3 SD: 3.5707 c. M: 5.8180 c. 72: 4 8 4 9 3 5 9 4 9 3 9 5 N SD: 2.9203 c. M:-5.8764 c. 77: 4 9 4 10 3 5 10 4 9 4 10 5 N SD: 3.2229 c. M: 6.8942 c. 89: 5 10 5 11 4 6 11 5 11 4 11 6 N SD: 2.7186 c. M:-6.0637 c. 94: 5 11 5 12 4 6 12 5 11 5 12 6 N SD: 2.2850 c. M: 4.4073 c. 113: 6 13 6 14 5 8 14 6 14 5 14 8 N SD: 2.3178 c. M: 4.4187 c. 118: 6 14 6 15 5 8 15 6 14 6 15 8 N SD: 2.4083 c. M: 5.7055 c. 129: 7 15 7 16 6 8 16 7 16 6 16 9 N SD: 2.4112 c. M: 4.2806 c. 130: 7 15 7 16 6 9 16 7 16 6 16 9 N SD: 1.6499 c. M:-3.0559 c. 135: 7 16 7 17 6 9 17 7 16 7 17 9 N SD: 1.2479 c. M: 4.1236 c. 152: 8 18 8 19 7 10 19 8 18 8 19 10 N SD: 1.6419 c. M:-2.9033 c. 166: 9 19 9 21 7 11 21 9 20 8 21 11 N SD: 1.2279 c. M:-2.0993 c. 207: 11 24 11 26 9 14 26 11 25 10 26 14 N SD: 0.6592 c. M: 1.2157 c. 224: 12 26 12 28 10 15 28 12 27 11 28 15 N SD: 0.6875 c. M:-1.3248 c. 265: 14 31 14 33 12 18 33 14 32 13 33 18 N SD: 0.5722 c. M:-1.1349 c. 270: 14 32 14 34 12 18 34 14 33 13 34 18 N SD: 0.3859 c. M: 0.7387 c. 477: 25 56 25 60 21 32 60 25 58 23 60 32 N SD: 0.1915 c. M: 0.3745 c. 701: 37 82 37 88 31 47 88 37 85 34 88 47 N SD: 0.1745 c. M:-0.3772 c. 742: 39 87 39 93 33 50 93 39 90 36 93 50 N SD: 0.1706 c. M: 0.3255 c. 747: 39 88 39 94 33 50 94 39 91 36 94 50 N SD: 0.1882 c. M: 0.3139 c. 877: 46 103 46 110 39 59 110 46 107 42 110 59 N SD: 0.1697 c. M:-0.4982 c. 971: 51 114 51 122 43 65 122 51 118 47 122 65 N SD: 0.1035 c. M:-0.2075 c. 1012: 53 119 53 127 45 68 127 53 123 49 127 68 N SD: 0.0786 c. M: 0.1183 c. 1489: 78 175 78 187 66 100 187 78 181 72 187 100 N SD: 0.0866 c. M: 0.1295 c. 1506: 79 177 79 189 67 101 189 79 183 73 189 101 N SD: 0.0648 c. M:-0.1354 c. 1713: 90 201 90 215 76 115 215 90 208 83 215 115 N SD: 0.0488 c. M: 0.1073 c. 1983: 104 233 104 249 88 133 249 104 241 96 249 133 N SD: 0.0289 c. M:-0.0529 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: 12.6577 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 7.7986 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 18.0097 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 13.2874 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 13.1861 cents 8 x 9 x 10 x 11:12 x x 14:15:16 S SD: 6.3022 cents 9 x 10 x 11:12 x x 14:15:16:17:18 S SD: 11.1110 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 10.0134 cents 11 x 12:13:14 x 15 x 17 x 19:21:22 SD: 8.0843 cents 12 x x 14:15:16:17:18:19:20:21:23:24 SD: 7.7923 cents 13:14 x 15 x 17:18 x 20:22:23:25:26 SD: 8.3920 cents 14:15:16 x 18 x 19:21:22:24:25:27:28 SD: 8.4230 cents 15:16:17:18:19:20:21 x 23:25:26:29:30 SD: 8.5163 cents 16:17:18:19:20:21:22:24:25:27:28:31:32 SD: 5.5360 cents 17:18:19:20 x 22:23 x 26:29:30:32:34 SD: 6.9807 cents 18:19:20:21:23:24:25:27:28:30:32:34:36 SD: 5.4491 cents 19:20:21:22:24:25:26:29:30:32:33:36:38 SD: 5.2839 cents 20:21 x 23:25:26:28:30:31:34:35:38:40 SD: 5.3567 cents 22:23:25:26:28:29:30:33:34:37:39:42:44 SD: 3.7287 cents 23:24:26:27:29:30:32:35:36:39:40:44:46 SD: 3.6998 cents 25:26:28:29:32:33:34:38:39:42:44:48:50 SD: 3.3769 cents 29:30:33:34:37:38:40:44:45:49:51:55:58 SD: 2.8349 cents 32:33:36:37:41:42:44:48:50:54:56:61:64 SD: 1.9699 cents 48:50:54:56:61:63:66:72:75:81:84:92:96 SD: 1.1692 cents 77:80:87:90:98:101:106:116:120:130:135:147:154 SD: 1.1027 cents 78:81:88:91:99:102:107:117:121:132:137:149:156 SD: 1.0965 cents 80:83:90:93:102:105:110:120:124:135:140:153:160 SD: 0.9154 cents 88:91:99:103:112:116:121:132:137:149:154:168:176 SD: 0.8915 cents 96:100:108:112:122:126:132:144:149:162:168:183:192 SD: 0.8819 cents 102:106:115:119:130:134:140:153:159:173:179:195:204 SD: 0.8449 cents 106:110:119:124:135:139:146:159:165:179:186:202:212 SD: 0.8141 cents 110:114:124:128:140:144:151:165:171:186:193:210:220 SD: 0.7715 cents 112:116:126:131:143:147:154:168:174:190:196:214:224 SD: 0.7430 cents 128:133:144:149:163:168:176:192:199:217:224:244:256 SD: 0.5548 cents 144:149:162:168:183:189:198:216:224:244:252:275:288 SD: 0.4307 cents 186:193:209:217:237:244:256:279:289:315:326:355:372 SD: 0.4229 cents 192:199:216:224:244:252:264:288:299:325:336:367:384 SD: 0.3342 cents 240:249:270:280:305:315:330:360:373:406:420:458:480 SD: 0.2705 cents 272:282:306:317:346:357:374:408:423:460:476:519:544 SD: 0.2160 cents 352:365:396:411:448:462:484:528:548:596:616:672:704 SD: 0.1821 cents 384:398:432:448:489:504:528:576:597:650:672:733:768 SD: 0.1447 cents 432:448:486:504:550:567:594:648:672:731:756:825:864 SD: 0.0691 cents