Scala analysis: 2011-may-31
May 31, 2011 scale -- based on 5.11.31 subgroup
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 125/121 56.305257 2: 33275/29791 191.474537 3: 34375/29791 247.779794 4: 31/25 372.408145 5: 155/121 428.713402 6: 1331/961 563.882682 7: 1375/961 620.187939 8: 961/625 744.816289 9: 961/605 801.121546 10: 1331/775 936.290827 11: 55/31 992.596084 12: 29791/15625 1117.224434
SHOW/INTERVAL
0: 923521/859375 124.6284 1: 125/121 56.3053 2: 161051/148955 135.1693 3: 125/121 56.3053 4: 923521/859375 124.6284 5: 125/121 56.3053 6: 161051/148955 135.1693 7: 125/121 56.3053 8: 923521/859375 124.6284 9: 125/121 56.3053 10: 161051/148955 135.1693 11: 125/121 56.3053 12: 923521/859375 124.6284
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 6 125/121 56.305 cents 1: 3 923521/859375 124.628 cents 1: 3 161051/148955 135.169 cents 2: 6 923521/831875 180.934 cents 2: 6 33275/29791 191.475 cents 3: 3 923521/805255 237.239 cents 3: 3 34375/29791 247.780 cents 3: 6 3751/3125 316.103 cents 4: 12 31/25 372.408 cents 5: 6 155/121 428.713 cents 5: 3 28629151/21484375 497.036 cents 5: 3 161051/120125 507.577 cents 6: 6 28629151/20796875 553.342 cents 6: 6 1331/961 563.883 cents 7: 3 28629151/20131375 609.647 cents 7: 3 1375/961 620.188 cents 7: 6 116281/78125 688.511 cents 8: 12 961/625 744.816 cents 9: 6 961/605 801.122 cents 9: 3 887503681/537109375 869.445 cents 9: 3 161051/96875 879.986 cents 10: 6 887503681/519921875 925.750 cents 10: 6 1331/775 936.291 cents 11: 3 887503681/503284375 982.055 cents 11: 3 55/31 992.596 cents 11: 6 3604711/1953125 1060.919 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 2.36364 = 26/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 56.3 191.5 247.8 372.4 428.7 563.9 620.2 744.8 801.1 936.3 992.6 1117.2 56.3 : 135.2 191.5 316.1 372.4 507.6 563.9 688.5 744.8 880.0 936.3 1060.9 1117.2 191.5 : 56.3 180.9 237.2 372.4 428.7 553.3 609.6 744.8 801.1 925.7 982.1 1117.2 247.8 : 124.6 180.9 316.1 372.4 497.0 553.3 688.5 744.8 869.4 925.7 1060.9 1117.2 372.4 : 56.3 191.5 247.8 372.4 428.7 563.9 620.2 744.8 801.1 936.3 992.6 1117.2 428.7 : 135.2 191.5 316.1 372.4 507.6 563.9 688.5 744.8 880.0 936.3 1060.9 1117.2 563.9 : 56.3 180.9 237.2 372.4 428.7 553.3 609.6 744.8 801.1 925.7 982.1 1117.2 620.2 : 124.6 180.9 316.1 372.4 497.0 553.3 688.5 744.8 869.4 925.7 1060.9 1117.2 744.8 : 56.3 191.5 247.8 372.4 428.7 563.9 620.2 744.8 801.1 936.3 992.6 1117.2 801.1 : 135.2 191.5 316.1 372.4 507.6 563.9 688.5 744.8 880.0 936.3 1060.9 1117.2 936.3 : 56.3 180.9 237.2 372.4 428.7 553.3 609.6 744.8 801.1 925.7 982.1 1117.2 992.6 : 124.6 180.9 316.1 372.4 497.0 553.3 688.5 744.8 869.4 925.7 1060.9 1117.2 1117.2
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 56.3053 .. 135.1693 cents 19487171/18619375, 78.8640 cents 125/121, 56.3053 cents 2: 180.9336 .. 191.4745 cents 10.54093 cents 45.76433 cents 3: 237.2389 .. 316.1029 cents 19487171/18619375, 78.8640 cents 45.76433 cents 4: 372.4081 .. 372.4081 cents 1/1, 0.0000 cents 125/121, 56.3053 cents 5: 428.7134 .. 507.5774 cents 19487171/18619375, 78.8640 cents 125/121, 56.3053 cents 6: 553.3418 .. 563.8827 cents 10.54093 cents 45.76433 cents 7: 609.6470 .. 688.5110 cents 19487171/18619375, 78.8640 cents 45.76433 cents 8: 744.8163 .. 744.8163 cents 1/1, 0.0000 cents 125/121, 56.3053 cents 9: 801.1215 .. 879.9856 cents 19487171/18619375, 78.8640 cents 125/121, 56.3053 cents 10: 925.7499 .. 936.2908 cents 10.54093 cents 45.76433 cents 11: 982.0552 .. 1060.9192 cents 19487171/18619375, 78.8640 cents 45.76433 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 125/121, 56.3053 cents, class 1 Average step (divided formal octave): 93.1020 cents Largest one step interval : 161051/148955, 135.1693 cents Average / Smallest step : 1.653523 Largest / Average step : 1.451840 Largest / Smallest step : 2.400651 Median interval of one step : 90.46680 cents, amount: 0 Most common interval of one step : 125/121, 56.3053 cents, amount: 6 Least squares average step : 91.38029 cents, oct.: 1096.56346 cents Scale is strictly proper Scale has 3 repeating blocks of 4 notes Scale is 3-distributional even Step pattern alph. order: ABACABACABAC Step pattern size order : SLSMSLSMSLSM Scale is a Constant Structure, by a margin of 45.76433 cents Scale diversity : 1.236053 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.548160 Rothenberg efficiency (ambiguous key): 0.269048 redundancy: 0.730952 Efficiency x scale size : 3.228571 Number of different interval sizes : 26 = 2.36364 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 2.36364 = 26/11 Median interval variety : 3 Lowest interval variety : 1 Smallest interval difference : 10.54093 cents Most common intervals : 31/25, 372.4081 cents & inv., amount: 12 Most common triad is 0.0 372.408 744.816 cents, amount: 12 Number of recognisable fifths : 6, average 688.5110 cents Number of appreciable fifths : 0 Number of recognisable fourths : 6, average 502.3070 cents Formal octave complements present : 3 = 25.0000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 4 8 Limited inverse transpositions : 3 7 11 Inversional symmetry on intervals : 1-2 3-4 5-6 7-8 9-10 11-12 -- Rational properties -- Prime limit : 31 Odd number limit : 887503681 (O: 887503681 U: 537109375) Highest odd numerator or denominator: 34375 Scale harmonicity : 0.006199 Fundamental : too low to compute Guide tone : too high to compute Exponens Consonantiae : 6.979168E+21, 72.56354 octaves Euler's gradus suavitatis : 275 Sum of Mann's harmonic distance : 91599.0, average 7633.25000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 36.40352, average 3.03363 Sum of Tenney's harmonic distance : 71.03276, average 5.91940 Vogel's harmonic complexity : too high to compute Wille's k value : too high to compute Wilson's harmonic complexity : 296 Rectangular lattice diameter : 22 Triangular lattice diameter : 12 Lattice compactness : 355.01262, average 4.55144 Lattice compactness (without 2's) : 355.01262, average 4.55144 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 5: -6 .. 5 0.00000 30 11: -2 .. 3 0.50000 18 1 31: -3 .. 3 -0.25000 21 11 Average exponent except 2's : 3 / 12 = 0.25000 Average absolute exponent except 2's: 69 / 12 = 5.75000 Scale is weakly epimorphic with val: <29 42 62| Scale is weakly epimorphic with val: <29 46 62| Scale is weakly epimorphic with val: <31 42 66| Scale is JI-epimorphic with val: <31 46 66|
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 24.3705 c. M:-36.7968 c. Twelve-tone Chromatic (1/11-comma) 13: 1 1 1 1 1 2 0 2 0 2 1 1 N D3 SD: 24.3522 c. M:-38.6880 c. 14: 1 1 1 2 0 2 1 1 1 2 0 2 P B D3 SD: 22.3297 c. M: 34.9751 c. 16: 1 2 1 1 1 2 1 2 0 2 1 2 N D3 SD: 20.2217 c. M: 33.0297 c. 18: 1 2 1 2 1 2 1 2 1 2 1 2 SP B ME SD: 3.9125 c. M:-5.7628 c. 57: 3 7 3 6 3 7 3 6 3 7 3 6 SP B D3 SD: 4.3621 c. M:-7.0258 c. 60: 3 7 3 7 3 7 3 7 3 7 3 7 SP B DE SD: 3.8933 c. M: 5.7145 c. 63: 3 8 3 7 3 8 3 7 3 8 3 7 SP B D3 SD: 2.3881 c. M:-3.5964 c. 81: 4 10 4 9 4 10 4 9 4 10 4 9 SP B D3 SD: 1.0212 c. M:-1.6260 c. 99: 5 12 5 11 5 12 5 11 5 12 5 11 SP B D3 SD: 0.3143 c. M:-0.4923 c. 414: 21 50 21 46 21 50 21 46 21 50 21 46 SP B D3 SD: 0.3131 c. M:-0.4923 c. 420: 21 51 21 47 21 51 21 47 21 51 21 47 SP B D3 SD: 0.2980 c. M: 0.4440 c. 438: 22 53 22 49 22 53 22 49 22 53 22 49 SP B D3 SD: 0.2193 c. M: 0.3579 c. 519: 26 63 26 58 26 63 26 58 26 63 26 58 SP B D3 SD: 0.2099 c. M: 0.3364 c. 537: 27 65 27 60 27 65 27 60 27 65 27 60 SP B D3 SD: 0.1252 c. M: 0.2012 c. 636: 32 77 32 71 32 77 32 71 32 77 32 71 SP B D3 SD: 0.0657 c. M: 0.0932 c. 735: 37 89 37 82 37 89 37 82 37 89 37 82 SP B D3 SD: 0.0411 c. M: 0.0640 c. 1389: 70 168 70 155 70 168 70 155 70 168 70 155 SP B D3 SD: 0.0305 c. M: 0.0439 c. 1488: 75 180 75 166 75 180 75 166 75 180 75 166 SP B D3 SD: 0.0090 c. M: 0.0147 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 82.7756 cents 2 x x x x x x x 3 x x x 4 S SD: 46.6071 cents 3 x x x x x 4 x x x 5 x 6 S SD: 39.2759 cents 4 x x x 5 x x x 6 x x 7:8 S SD: 24.2993 cents 5 x x x 6 x 7 x x 8 x 9:10 S SD: 21.1700 cents 6 x x 7 x x 8 x 9 x 10:11 x S SD: 22.3209 cents 7 x x 8 x 9 x 10 x 11:12 x 13 S SD: 8.7448 cents 8 x 9 x 10 x 11 x 12:13 x 14:15 S SD: 10.3994 cents 9 x 10 x 11 x 12:13:14 x 15:16:17 S SD: 11.6503 cents 10 x 11 x 12:13:14 x 15:16:17:18:19 S SD: 9.8684 cents 11 x 12:13 x 14:15:16:17 x 19:20:21 SD: 9.3132 cents 12 x 13:14:15 x x 17:18:19 x 21:23 SD: 9.8168 cents 13 x x 15:16:17:18:19:20:21:22:23:25 SD: 6.7393 cents 14:15 x 16:17:18:19:20 x 22:24:25:27 SD: 8.7978 cents 15:16:17 x x 19:21 x 23:24:26:27:29 SD: 8.6601 cents 16:17:18 x 20:21:22:23:25 x 27:28:31 SD: 8.8008 cents 17:18:19:20:21:22 x 24:26:27:29:30:32 SD: 6.1925 cents 18:19:20:21:22:23:25:26:28:29:31:32:34 SD: 5.3222 cents 19:20:21:22 x 24:26:27:29:30:33:34:36 SD: 5.4357 cents 21:22:23:24:26:27:29:30:32:33:36:37:40 SD: 4.4460 cents 22:23 x 25:27:28:30:31:34:35:38:39:42 SD: 5.1329 cents 23:24:26:27 x 29:32:33:35:37:40:41:44 SD: 5.6307 cents 24:25:27:28:30:31:33:34:37:38:41:43:46 SD: 3.8055 cents 25:26:28:29:31:32:35:36:38:40:43:44:48 SD: 3.3484 cents 26:27:29:30:32:33:36:37:40:41:45:46:50 SD: 2.8647 cents 32:33:36:37:40:41:44:46:49:51:55:57:61 SD: 2.2473 cents 46:48:51:53:57:59:64:66:71:73:79:82:88 SD: 2.2225 cents 49:51:55:57:61:63:68:70:75:78:84:87:93 SD: 2.1939 cents 50:52:56:58:62:64:69:72:77:79:86:89:95 SD: 1.9937 cents 53:55:59:61:66:68:73:76:81:84:91:94:101 SD: 1.6853 cents 54:56:60:62:67:69:75:77:83:86:93:96:103 SD: 1.5275 cents 58:60:65:67:72:74:80:83:89:92:100:103:111 SD: 1.3305 cents 63:65:70:73:78:81:87:90:97:100:108:112:120 SD: 1.3253 cents 67:69:75:77:83:86:93:96:103:106:115:119:128 SD: 1.1540 cents 78:81:87:90:97:100:108:112:120:124:134:138:149 SD: 1.1497 cents 84:87:94:97:104:108:116:120:129:133:144:149:160 SD: 1.0587 cents 85:88:95:98:105:109:118:122:131:135:146:151:162 SD: 0.9543 cents 93:96:104:107:115:119:129:133:143:148:160:165:177 SD: 0.8107 cents 117:121:131:135:145:150:162:167:180:186:201:208:223 SD: 0.6330 cents 128:132:143:148:159:164:177:183:197:203:220:227:244 SD: 0.6092 cents 149:154:166:172:185:191:206:213:229:237:256:264:284 SD: 0.5988 cents 151:156:169:174:187:193:209:216:232:240:259:268:288 SD: 0.5737 cents 153:158:171:177:190:196:212:219:235:243:263:271:292 SD: 0.5672 cents 156:161:174:180:193:200:216:223:240:248:268:277:297 SD: 0.5319 cents 163:168:182:188:202:209:226:233:251:259:280:289:311 SD: 0.5047 cents 181:187:202:209:224:232:251:259:278:288:311:321:345 SD: 0.4915 cents 182:188:203:210:226:233:252:260:280:289:313:323:347 SD: 0.4389 cents 195:201:218:225:242:250:270:279:300:310:335:346:372 SD: 0.4228 cents 213:220:238:246:264:273:295:305:328:338:366:378:406 SD: 0.3468 cents 216:223:241:249:268:277:299:309:332:343:371:383:412 SD: 0.3264 cents 267:276:298:308:331:342:370:382:411:424:459:474:509 SD: 0.2914 cents 299:309:334:345:371:383:414:428:460:475:514:530:570 SD: 0.2478 cents 325:336:363:375:403:416:450:465:500:516:558:577:620 SD: 0.2346 cents 359:371:401:414:445:460:497:514:552:570:617:637:684 SD: 0.2288 cents 392:405:438:452:486:502:543:561:603:623:673:695:747 SD: 0.2127 cents 395:408:441:456:490:506:547:565:607:627:678:701:753 SD: 0.2012 cents 420:434:469:485:521:538:582:601:646:667:721:745:801 SD: 0.1827 cents 428:442:478:494:531:548:593:612:658:680:735:759:816 SD: 0.1789 cents 462:477:516:533:573:592:640:661:710:734:793:820:881 SD: 0.1674 cents 480:496:536:554:595:615:665:687:738:762:824:852:915 SD: 0.1657 cents 488:504:545:563:605:625:676:698:750:775:838:866:930 SD: 0.1340 cents 513:530:573:592:636:657:711:734:789:815:881:910:978 SD: 0.1221 cents 545:563:609:629:676:698:755:780:838:866:936:967:1039 SD: 0.1144 cents