Scala analysis: alternative12
Superset of Buzurg al-Erin with 13/11, 39/22
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 14/13 128.298245 2/3-tone 2: 8/7 231.174094 septimal whole tone 3: 13/11 289.209719 tridecimal minor third 4: 16/13 359.472338 tridecimal neutral third 5: 4/3 498.044999 perfect fourth 6: 63/44 621.417966 7: 3/2 701.955001 perfect fifth 8: 21/13 830.253246 9: 12/7 933.129094 septimal major sixth 10: 39/22 991.164720 11: 24/13 1061.427339 tridecimal neutral seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 13/12 138.5727 tridecimal 2/3-tone 1: 14/13 128.2982 2/3-tone 2: 52/49 102.8758 3: 91/88 58.0356 4: 176/169 70.2626 5: 13/12 138.5727 tridecimal 2/3-tone 6: 189/176 123.3730 7: 22/21 80.5370 undecimal minor semitone 8: 14/13 128.2982 2/3-tone 9: 52/49 102.8758 10: 91/88 58.0356 11: 176/169 70.2626 12: 13/12 138.5727 tridecimal 2/3-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 91/88 58.036 cents 1: 2 176/169 70.263 cents 1: 1 22/21 80.537 cents undecimal minor semitone 1: 2 52/49 102.876 cents 1: 1 189/176 123.373 cents 1: 2 14/13 128.298 cents 2/3-tone 1: 2 13/12 138.573 cents tridecimal 2/3-tone 2: 2 14/13 128.298 cents 2/3-tone 2: 2 169/154 160.911 cents 2: 1 9/8 203.910 cents major whole tone 2: 3 44/39 208.835 cents 2: 2 8/7 231.174 cents septimal whole tone 2: 1 819/704 261.946 cents 2: 1 7/6 266.871 cents septimal minor third 3: 2 8/7 231.174 cents septimal whole tone 3: 2 7/6 266.871 cents septimal minor third 3: 2 13/11 289.210 cents tridecimal minor third 3: 1 176/147 311.711 cents 3: 2 63/52 332.208 cents 3: 1 616/507 337.134 cents 3: 1 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 3: 1 26/21 369.747 cents 4: 2 16/13 359.472 cents tridecimal neutral third 4: 3 26/21 369.747 cents 4: 1 441/352 390.244 cents 4: 1 49/39 395.169 cents 4: 1 33/26 412.745 cents tridecimal major third 4: 1 169/132 427.782 cents 4: 1 9/7 435.084 cents septimal major third, BP third 4: 1 352/273 440.009 cents 4: 1 21/16 470.781 cents narrow fourth 5: 1 352/273 440.009 cents 5: 1 21/16 470.781 cents narrow fourth 5: 2 117/88 493.120 cents tridecimal gentle fourth 5: 6 4/3 498.045 cents perfect fourth 5: 1 231/169 541.044 cents 5: 1 39/28 573.657 cents 6: 1 91/66 556.081 cents 6: 1 18/13 563.382 cents tridecimal augmented fourth 6: 1 704/507 568.308 cents 6: 1 39/28 573.657 cents 6: 1 88/63 578.582 cents 6: 1 147/104 599.079 cents 6: 1 208/147 600.921 cents 6: 1 63/44 621.418 cents 6: 1 56/39 626.343 cents 6: 1 507/352 631.692 cents 6: 1 13/9 636.618 cents tridecimal diminished fifth 6: 1 132/91 643.919 cents 7: 1 56/39 626.343 cents 7: 1 338/231 658.956 cents 7: 6 3/2 701.955 cents perfect fifth 7: 2 176/117 706.880 cents 7: 1 32/21 729.219 cents wide fifth 7: 1 273/176 759.991 cents 8: 1 32/21 729.219 cents wide fifth 8: 1 273/176 759.991 cents 8: 1 14/9 764.916 cents septimal minor sixth 8: 1 264/169 772.218 cents 8: 1 52/33 787.255 cents tridecimal minor sixth 8: 1 78/49 804.831 cents 8: 1 704/441 809.756 cents 8: 3 21/13 830.253 cents 8: 2 13/8 840.528 cents tridecimal neutral sixth 9: 1 21/13 830.253 cents 9: 1 64/39 857.517 cents 39th subharmonic 9: 1 507/308 862.866 cents 9: 2 104/63 867.792 cents 9: 1 147/88 888.289 cents 9: 2 22/13 910.790 cents tridecimal major sixth 9: 2 12/7 933.129 cents septimal major sixth 9: 2 7/4 968.826 cents harmonic seventh 10: 1 12/7 933.129 cents septimal major sixth 10: 1 1408/819 938.054 cents 10: 2 7/4 968.826 cents harmonic seventh 10: 3 39/22 991.165 cents 10: 1 16/9 996.090 cents Pythagorean minor seventh 10: 2 308/169 1039.089 cents 10: 2 13/7 1071.702 cents 16/3-tone 11: 2 24/13 1061.427 cents tridecimal neutral seventh 11: 2 13/7 1071.702 cents 16/3-tone 11: 1 352/189 1076.627 cents 11: 2 49/26 1097.124 cents 11: 1 21/11 1119.463 cents undecimal major seventh 11: 2 169/88 1129.737 cents 11: 2 176/91 1141.964 cents Highest number of different intervals for one interval class: 12 Average number of different intervals per interval class: 7.81818 = 86/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 128.3 231.2 289.2 359.5 498.0 621.4 702.0 830.3 933.1 991.2 1061.4 1200.0 128.3 : 102.9 160.9 231.2 369.7 493.1 573.7 702.0 804.8 862.9 933.1 1071.7 1200.0 231.2 : 58.0 128.3 266.9 390.2 470.8 599.1 702.0 760.0 830.3 968.8 1097.1 1200.0 289.2 : 70.3 208.8 332.2 412.7 541.0 643.9 702.0 772.2 910.8 1039.1 1142.0 1200.0 359.5 : 138.6 261.9 342.5 470.8 573.7 631.7 702.0 840.5 968.8 1071.7 1129.7 1200.0 498.0 : 123.4 203.9 332.2 435.1 493.1 563.4 702.0 830.3 933.1 991.2 1061.4 1200.0 621.4 : 80.5 208.8 311.7 369.7 440.0 578.6 706.9 809.8 867.8 938.1 1076.6 1200.0 702.0 : 128.3 231.2 289.2 359.5 498.0 626.3 729.2 787.3 857.5 996.1 1119.5 1200.0 830.3 : 102.9 160.9 231.2 369.7 498.0 600.9 659.0 729.2 867.8 991.2 1071.7 1200.0 933.1 : 58.0 128.3 266.9 395.2 498.0 556.1 626.3 764.9 888.3 968.8 1097.1 1200.0 991.2 : 70.3 208.8 337.1 440.0 498.0 568.3 706.9 830.3 910.8 1039.1 1142.0 1200.0 1061.4: 138.6 266.9 369.7 427.8 498.0 636.6 760.0 840.5 968.8 1071.7 1129.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 58.0356 .. 138.5727 cents 22/21, 80.5370 cents 91/88, 58.0356 cents 2: 128.2982 .. 266.8709 cents 13/12, 138.5727 cents 168/169,-10.2744 cents 3: 231.1741 .. 369.7468 cents 13/12, 138.5727 cents 48/49,-35.6968 cents 4: 359.4723 .. 470.7809 cents 273/256, 111.3086 cents 168/169,-10.2744 cents 5: 440.0094 .. 573.6568 cents 1521/1408, 133.6474 cents 5632/5733,-30.7715 cents 6: 556.0806 .. 643.9194 cents 8712/8281, 87.8387 cents 98/99,-17.5761 cents 7: 626.3432 .. 759.9906 cents 1521/1408, 133.6474 cents 98/99,-17.5761 cents 8: 729.2191 .. 840.5277 cents 273/256, 111.3086 cents 5632/5733,-30.7715 cents 9: 830.2532 .. 968.8259 cents 13/12, 138.5727 cents 168/169,-10.2744 cents 10: 933.1291 .. 1071.7018 cents 13/12, 138.5727 cents 48/49,-35.6968 cents 11: 1061.4273 .. 1141.9644 cents 22/21, 80.5370 cents 168/169,-10.2744 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 91/88, 58.0356 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 13/12, 138.5727 cents Average / Smallest step : 1.723080 Largest / Average step : 1.385727 Largest / Smallest step : 2.387717 Median interval of one step : 52/49, 102.8758 cents, amount: 2 Least squares average step : 100.08634 cents, oct.: 1201.03603 cents Scale is not proper Step pattern alph. order: ABCDEFGABCDE Step pattern size order : FDABGECFDABG Scale is not a Constant Structure Scale diversity : 1.543615 Lumma stability : 0.096726 Lumma impropriety factor : 0.174322 Rothenberg efficiency : 0.258261 redundancy: 0.741739 Efficiency x scale size : 3.099134 Number of different interval sizes : 72 = 6.54545 / class Number of one step interval sizes : 7 Highest interval variety : 12 Mean interval variety : 7.81818 = 86/11 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 21632/21609, 1.8417 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 6 Number of recognisable fifths : 8, average 703.1863 cents Scale contains two identical disjunct hexachords Scale contains a complete diamond : 1 3 Length of longest harmonic part : 2 at degree 11 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 25.0000% -- Rational properties -- Prime limit : 13 Odd number limit : 819 (O: 819 U: 819) Highest odd numerator or denominator: 63 Scale harmonicity : 0.010303 Average absolute harmonicity : 0.153098 Specific harmonicity : 0.062425 Fundamental : 1/12012, -13.5522 octaves, 0.0218 Hz. Guide tone : 13104, 13.6777 octaves, 3428341.408 Hz. Exponens Consonantiae : 1.574052E+08, 27.22991 octaves Euler's gradus suavitatis : 59 Sum of Mann's harmonic distance : 184.0, average 15.33333 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 11.81284, average 0.98440 Sum of Tenney's harmonic distance : 23.87090, average 1.98924 Vogel's harmonic complexity : 34.16667 Wille's k value : 8599 Wilson's harmonic complexity : 60 Rectangular lattice diameter : 8 Triangular lattice diameter : 4 Lattice compactness : 225.77125, average 2.89450 Lattice compactness (without 2's) : 134.95026, average 1.73013 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 4 1.00000 20 1 3: -1 .. 2 0.50000 8 2 7: -1 .. 1 0.08333 5 2 11: -1 .. 0 -0.25000 3 1 13: -1 .. 1 -0.16667 6 6 Average exponent except 2's : 2 / 12 = 0.16667 Average absolute exponent except 2's: 22 / 12 = 1.83333 Scale is weakly epimorphic with val: <12 19 34 44 47|
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 25.1274 c. M:-40.5277 c. Twelve-tone Chromatic (1/11-comma) 16: 2 1 1 1 2 1 1 2 1 1 1 2 N D3 I SD: 18.9198 c. M: 33.1291 c. 17: 2 1 1 1 2 2 1 2 1 1 1 2 N D3 SD: 10.7747 c. M: 19.4094 c. 27: 3 2 2 1 3 3 2 3 2 1 2 3 N SD: 9.9033 c. M:-21.9014 c. 29: 3 3 1 2 3 3 2 3 3 1 2 3 N SD: 9.3428 c. M:-18.5950 c. 32: 3 3 2 2 3 4 2 3 3 1 2 4 N SD: 11.4195 c. M: 16.1647 c. 33: 4 2 2 2 4 3 2 4 3 1 2 4 N SD: 9.4067 c. M:-17.1563 c. 36: 4 3 2 2 4 4 2 4 3 2 2 4 N SD: 6.2106 c. M:-11.9154 c. 41: 4 4 2 2 5 4 3 4 4 2 2 5 N SD: 6.2238 c. M: 11.2251 c. 46: 5 4 2 3 5 5 3 5 4 2 3 5 N SD: 4.2002 c. M:-8.1379 c. 58: 6 5 3 3 7 6 4 6 5 3 3 7 N SD: 3.5330 c. M: 7.7482 c. 67: 7 6 3 4 8 7 4 7 6 3 4 8 N SD: 3.8344 c. M: 6.3726 c. 77: 8 7 4 4 9 8 5 8 7 4 4 9 N SD: 3.3783 c. M:-6.8942 c. 84: 9 7 4 5 10 8 6 9 7 4 5 10 N SD: 3.5902 c. M: 7.1323 c. 87: 9 8 4 5 10 9 6 9 8 4 5 10 N SD: 2.3894 c. M:-4.8019 c. 94: 10 8 5 5 11 10 6 10 8 5 5 11 N SD: 2.3969 c. M:-4.5800 c. 103: 11 9 5 6 12 10 7 11 9 5 6 12 N SD: 2.1606 c. M: 3.9422 c. 104: 11 9 5 6 12 11 7 11 9 5 6 12 N SD: 1.2742 c. M:-1.8912 c. 166: 18 14 8 10 19 17 11 18 14 8 10 19 N SD: 1.0037 c. M:-1.9734 c. 207: 22 18 10 12 24 21 14 22 18 10 12 24 N SD: 0.6625 c. M: 1.2677 c. 224: 24 19 11 13 26 23 15 24 19 11 13 26 N SD: 0.4656 c. M: 0.9862 c. 270: 29 23 13 16 31 28 18 29 23 13 16 31 N SD: 0.4947 c. M:-0.8579 c. 311: 33 27 15 18 36 32 21 33 27 15 18 36 N SD: 0.4899 c. M: 0.9671 c. 328: 35 28 16 19 38 34 22 35 28 16 19 38 N SD: 0.4642 c. M: 0.9358 c. 373: 40 32 18 22 43 38 25 40 32 18 22 43 N SD: 0.4488 c. M:-0.8494 c. 431: 46 37 21 25 50 44 29 46 37 21 25 50 N SD: 0.3728 c. M: 0.6385 c. 477: 51 41 23 28 55 49 32 51 41 23 28 55 N SD: 0.1474 c. M:-0.2761 c. 701: 75 60 34 41 81 72 47 75 60 34 41 81 N SD: 0.0825 c. M: 0.1762 c. 1178: 126 101 57 69 136 121 79 126 101 57 69 136 N SD: 0.0640 c. M:-0.1202 c. 1282: 137 110 62 75 148 132 86 137 110 62 75 148 N SD: 0.0651 c. M:-0.1109 c. 1506: 161 129 73 88 174 155 101 161 129 73 88 174 N SD: 0.0643 c. M: 0.1098 c. 1759: 188 151 85 103 203 181 118 188 151 85 103 203 N SD: 0.0665 c. M:-0.1284 c. 1879: 201 161 91 110 217 193 126 201 161 91 110 217 N SD: 0.0610 c. M:-0.0931 c. 1983: 212 170 96 116 229 204 133 212 170 96 116 229 N SD: 0.0303 c. M:-0.0646 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: 16.2568 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 8.7303 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 11.2878 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.1638 cents 7 x 8 x x 9:10 x 11:12 x 13:14 S SD: 11.3984 cents 8 x 9 x 10:11 x 12:13 x 14:15:16 S SD: 9.3765 cents 9 x 10 x 11:12:13:14 x 15:16:17:18 S SD: 11.4889 cents 10:11 x 12 x 13:14:15:16:17:18 x 20 S SD: 9.0702 cents 11:12 x 13:14:15:16:17:18:19 x 20:22 S SD: 10.0815 cents 12:13 x 14:15:16:17:18:19 x 21:22:24 SD: 5.9267 cents 13:14:15 x 16:17:19:20:21:22:23:24:26 SD: 6.4932 cents 14:15:16 x 17:19:20:21:23:24:25:26:28 SD: 4.7197 cents 15:16:17:18 x 20:21:23:24:26:27:28:30 SD: 6.9529 cents 16:17:18:19:20:21:23:24:26:27:28:30:32 SD: 5.8549 cents 18:19 x 21:22:24:26:27:29:31:32:33:36 SD: 4.3921 cents 19:20:22 x 23:25:27:29:31:33:34:35:38 SD: 6.7966 cents 20:22:23:24:25:27:29:30:32:34:35:37:40 SD: 5.7848 cents 21:23:24:25:26:28:30:32:34:36:37:39:42 SD: 3.8276 cents 26:28:30:31:32:35:37:39:42:45:46:48:52 SD: 2.8644 cents 34:37:39:40:42:45:49:51:55:58:60:63:68 SD: 2.5554 cents 38:41:43:45:47:51:54:57:61:65:67:70:76 SD: 2.5344 cents 39:42:45:46:48:52:56:59:63:67:69:72:78 SD: 1.9594 cents 44:47:50:52:54:59:63:66:71:75:78:81:88 SD: 1.9400 cents 48:52:55:57:59:64:69:72:78:82:85:89:96 SD: 1.7645 cents 54:58:62:64:66:72:77:81:87:93:96:100:108 SD: 1.7548 cents 56:60:64:66:69:75:80:84:90:96:99:103:112 SD: 1.4965 cents 60:65:69:71:74:80:86:90:97:103:106:111:120 SD: 1.4409 cents 62:67:71:73:76:83:89:93:100:106:110:114:124 SD: 1.4102 cents 65:70:74:77:80:87:93:98:105:111:115:120:130 SD: 1.2954 cents 70:75:80:83:86:93:100:105:113:120:124:129:140 SD: 1.1391 cents 78:84:89:92:96:104:112:117:126:134:138:144:156 SD: 0.6922 cents 104:112:119:123:128:139:149:156:168:178:184:192:208 SD: 0.5512 cents 132:142:151:156:162:176:189:198:213:226:234:244:264 SD: 0.5498 cents 156:168:178:184:192:208:223:234:252:267:277:288:312 SD: 0.5474 cents 168:181:192:199:207:224:241:252:271:288:298:310:336 SD: 0.5171 cents 169:182:193:200:208:225:242:254:273:290:300:312:338 SD: 0.4855 cents 181:195:207:214:223:241:259:272:292:310:321:334:362 SD: 0.4682 cents 182:196:208:215:224:243:261:273:294:312:323:336:364 SD: 0.3472 cents 234:252:267:277:288:312:335:351:378:401:415:432:468 SD: 0.3416 cents 246:265:281:291:303:328:352:369:397:422:436:454:492 SD: 0.2803 cents 252:271:288:298:310:336:361:378:407:432:447:465:504 SD: 0.2714 cents 260:280:297:307:320:347:372:390:420:446:461:480:520 SD: 0.2470 cents 273:294:312:323:336:364:391:410:441:468:484:504:546 SD: 0.2436 cents 286:308:327:338:352:381:410:429:462:490:507:528:572 SD: 0.2407 cents 312:336:357:369:384:416:447:468:504:535:553:576:624 SD: 0.2263 cents 336:362:384:397:414:448:481:504:543:576:596:620:672 SD: 0.2194 cents 364:392:416:430:448:485:521:546:588:624:645:672:728 SD: 0.1407 cents 468:504:535:553:576:624:670:702:756:802:830:864:936 SD: 0.0952 cents 546:588:624:645:672:728:782:819:882:936:968:1008:1092 SD: 0.0752 cents