Scala analysis: Golden_MOS_02
period Phi, generator second successive golden section of Phi, Bobro
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 69.097 cents 69.097000 2: 168.368 cents 168.367900 3: 267.639 cents 267.638800 4: 366.910 cents 366.909700 5: 436.007 cents 436.006700 6: 535.278 cents 535.277600 7: 634.549 cents 634.548500 8: 733.819 cents 733.819400 9: 833.090 cents 833.090300
SHOW/INTERVAL
0: 99.2709 cents 99.2709 1: 69.0970 cents 69.0970 2: 99.2709 cents 99.2709 3: 99.2709 cents 99.2709 4: 99.2709 cents 99.2709 5: 69.0970 cents 69.0970 6: 99.2709 cents 99.2709 7: 99.2709 cents 99.2709 8: 99.2709 cents 99.2709 9: 99.2709 cents 99.2709
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 69.09700 cents 1: 7 99.27090 cents 2: 4 168.36790 cents 2: 5 198.54180 cents 3: 6 267.63880 cents 3: 3 297.81270 cents 4: 8 366.90970 cents 4: 1 397.08360 cents 5: 1 436.00670 cents 5: 8 466.18060 cents 6: 3 535.27760 cents 6: 6 565.45150 cents 7: 5 634.54850 cents 7: 4 664.72240 cents 8: 7 733.81940 cents 8: 2 763.99330 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 0.0 : 69.1 168.4 267.6 366.9 436.0 535.3 634.5 733.8 833.1 69.1 : 99.3 198.5 297.8 366.9 466.2 565.5 664.7 764.0 833.1 168.4: 99.3 198.5 267.6 366.9 466.2 565.5 664.7 733.8 833.1 267.6: 99.3 168.4 267.6 366.9 466.2 565.5 634.5 733.8 833.1 366.9: 69.1 168.4 267.6 366.9 466.2 535.3 634.5 733.8 833.1 436.0: 99.3 198.5 297.8 397.1 466.2 565.5 664.7 764.0 833.1 535.3: 99.3 198.5 297.8 366.9 466.2 565.5 664.7 733.8 833.1 634.5: 99.3 198.5 267.6 366.9 466.2 565.5 634.5 733.8 833.1 733.8: 99.3 168.4 267.6 366.9 466.2 535.3 634.5 733.8 833.1 833.1
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 69.0970 .. 99.2709 cents 30.17390 cents 69.09700 cents 2: 168.3679 .. 198.5418 cents 30.17390 cents 69.09700 cents 3: 267.6388 .. 297.8127 cents 30.17390 cents 69.09700 cents 4: 366.9097 .. 397.0836 cents 30.17390 cents 69.09700 cents 5: 436.0067 .. 466.1806 cents 30.17390 cents 38.92310 cents 6: 535.2776 .. 565.4515 cents 30.17390 cents 69.09700 cents 7: 634.5485 .. 664.7224 cents 30.17390 cents 69.09700 cents 8: 733.8194 .. 763.9933 cents 30.17390 cents 69.09700 cents
SHOW DATA
Number of notes : 9 -- Interval properties -- Smallest interval : 69.09700 cents, class 1 Average step (divided formal octave): 92.5656 cents Largest one step interval : 99.27090 cents Average / Smallest step : 1.339647 Largest / Average step : 1.072438 Largest / Smallest step : 1.436689 Median interval of one step : 99.27090 cents, amount: 7 Most common interval of one step : 99.27090 cents, amount: 7 Least squares average step : 90.80103 cents, oct.: 817.20930 cents Scale is strictly proper Scale has Myhill's property chromas: 30.17390 cents and 38.92310 cents, ratio: 1.289959 generators: 4 of 366.90970 cents and 466.18060 cents ET pair of linear temperament : 25&84 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 856-tone equal temperament with octave 833.090 cents degrees: 71 173 275 377 448 550 652 754 856 generators: 377 and 479 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBBABBBB Step pattern size order : SLLLSLLLL Scale is a Constant Structure, by a margin of 38.92310 cents Scale diversity : 1.002596 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.710246 Rothenberg efficiency : 0.740741 redundancy: 0.259259 Efficiency x scale size : 6.666667 Number of different interval sizes : 16 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 30.17390 cents Most common intervals : 366.90970 cents & inv., amount: 8 Scale is a chain of 4 triads 0.0 366.910 733.819 cents Most common triad is 0.0 366.910 466.181 cents, amount: 7 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best major thirds form a closed circle Formal octave complements present : 1 = 11.1111% 2/1 octave complements present : 1 = 11.1111% Scale is n-1 differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval class 4 Scale is n-1 differentially coherent in interval class 5 Limited inverse transpositions : 5 Inversional symmetry on degrees : 7 Inversional symmetry on intervals : 2-3 -- Rational properties --
FIT/MODE
9: 1 1 1 1 1 1 1 1 1 SP B ME I SD: 15.9618 c. M:-26.8212 c. Pelog Nawanada: Sunda 15: 1 2 2 2 1 2 1 2 2 P D3 SD: 14.6702 c. M: 23.6156 c. 16: 1 2 2 2 1 2 2 2 2 P M ME S SD: 11.5819 c. M: 19.4616 c. Superlocrian 20: 2 2 2 3 1 3 2 3 2 P D3 SD: 12.2451 c. M: 19.4616 c. 21: 2 2 3 2 2 2 3 2 3 SP D3 SD: 11.4001 c. M: 19.7420 c. 23: 2 3 2 3 2 3 3 2 3 SP M ME S SD: 9.7340 c. M:-17.4352 c. 24: 2 3 3 3 2 2 3 3 3 SP D3 S SD: 10.0826 c. M:-15.2505 c. 25: 2 3 3 3 2 3 3 3 3 SP M ME S SD: 1.6662 c. M: 2.7997 c. Superlocrian 59: 5 7 7 7 5 7 7 7 7 SP M DE S SD: 1.0228 c. M:-1.7187 c. 84: 7 10 10 10 7 10 10 10 10 SP M DE S SD: 0.2225 c. M:-0.3739 c. 109: 9 13 13 13 9 13 13 13 13 SP M DE S SD: 0.2107 c. M: 0.3540 c. 193: 16 23 23 23 16 23 23 23 23 SP M DE S SD: 0.0221 c. M: 0.0372 c. 470: 39 56 56 56 39 56 56 56 56 SP M DE S SD: 0.0216 c. M:-0.0363 c. 663: 55 79 79 79 55 79 79 79 79 SP M DE S SD: 0.0089 c. M:-0.0149 c. 856: 71 102 102 102 71 102 102 102 102 SP M DE S SD: 0.0019 c. M:-0.0032 c. 1905: 158 227 227 227 158 227 227 227 227 SP M DE S SD: 0.0005 c. M: 0.0009 c.
FIT/HARMONIC
1 x x x x x x x x 2 S SD: 366.9097 cents 2 x x x x x x x 3 x S SD: 31.8644 cents 3 x x x x x 4 x x 5 S SD: 31.6809 cents 4 x x x 5 x x x 6 x S SD: 18.6538 cents 5 x x 6 x x 7 x x 8 S SD: 23.3616 cents 6 x x 7 x x 8 x 9:10 S SD: 17.7318 cents 7 x x 8 x 9 x 10:11 x S SD: 15.7928 cents 8 x 9 x 10 x 11 x 12:13 S SD: 10.8953 cents 9 x 10 x 11 x 12:13:14:15 S SD: 12.4313 cents 10 x 11:12 x 13:14 x 15:16 S SD: 13.1972 cents 11 x 12:13 x 14:15:16:17:18 S SD: 6.5427 cents 12 x 13:14:15 x 16:17:18:19 S SD: 11.1304 cents 13 x 14:15:16:17:18:19:20:21 S SD: 8.2055 cents 14 x 15:16:17:18:19:20:21:23 SD: 10.2441 cents 15:16:17:18 x 19:20:22:23:24 S SD: 12.3657 cents 16:17:18:19:20:21:22:23:24:26 S SD: 8.8851 cents 17:18:19:20:21:22:23:25:26:28 SD: 6.9955 cents 18:19:20:21:22:23:25:26:28:29 SD: 6.5344 cents 20:21:22:23:25:26:27:29:31:32 SD: 6.0194 cents 21:22:23:25:26:27:29:30:32:34 SD: 5.3226 cents 24:25:26:28:30:31:33:35:37:39 SD: 5.2349 cents 25:26:28:29:31:32:34:36:38:40 SD: 4.2611 cents 28:29:31:33:35:36:38:40:43:45 SD: 4.0688 cents 29:30:32:34:36:37:40:42:44:47 SD: 3.6667 cents 30:31:33:35:37:39:41:43:46:49 SD: 3.4641 cents 38:40:42:44:47:49:52:55:58:61 SD: 3.3408 cents 41:43:45:48:51:53:56:59:63:66 SD: 2.8644 cents 42:44:46:49:52:54:57:61:64:68 SD: 2.3777 cents 47:49:52:55:58:60:64:68:72:76 SD: 1.9372 cents 55:57:61:64:68:71:75:79:84:89 SD: 1.9166 cents 66:69:73:77:82:85:90:95:101:107 SD: 1.6514 cents 70:73:77:82:87:90:95:101:107:113 SD: 1.6270 cents 72:75:79:84:89:93:98:104:110:116 SD: 1.4690 cents 76:79:84:89:94:98:104:110:116:123 SD: 1.4636 cents 77:80:85:90:95:99:105:111:118:125 SD: 1.0990 cents 97:101:107:113:120:125:132:140:148:157 SD: 0.6612 cents 144:150:159:168:178:185:196:208:220:233 SD: 0.5550 cents 174:181:192:203:215:224:237:251:266:282 SD: 0.4540 cents 199:207:219:232:246:256:271:287:304:322 SD: 0.3896 cents 246:256:271:287:304:316:335:355:376:398 SD: 0.3284 cents 275:286:303:321:340:354:375:397:420:445 SD: 0.3091 cents 293:305:323:342:362:377:399:423:448:474 SD: 0.2413 cents 343:357:378:400:424:441:467:495:524:555 SD: 0.2351 cents 364:379:401:425:450:468:496:525:556:589 SD: 0.1971 cents 461:480:508:538:570:593:628:665:704:746 SD: 0.1543 cents 538:560:593:628:665:692:733:776:822:871 SD: 0.1288 cents