Scala analysis: star11a
Star11a hobbit block = prehobbit11
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 25/24 70.672427 classic chromatic semitone, minor chroma 2: 144/125 244.968860 classic diminished third 3: 6/5 315.641287 minor third 4: 5/4 386.313714 major third 5: 25/18 568.717426 classic augmented fourth 6: 36/25 631.282574 classic diminished fifth 7: 8/5 813.686286 minor sixth 8: 5/3 884.358713 major sixth, BP sixth 9: 125/72 955.031140 classic augmented sixth 10: 48/25 1129.327573 classic diminished octave 11: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 25/24 70.6724 classic chromatic semitone, minor chroma 1: 25/24 70.6724 classic chromatic semitone, minor chroma 2: 3456/3125 174.2964 3: 25/24 70.6724 classic chromatic semitone, minor chroma 4: 25/24 70.6724 classic chromatic semitone, minor chroma 5: 10/9 182.4037 minor whole tone 6: 648/625 62.5651 major diesis 7: 10/9 182.4037 minor whole tone 8: 25/24 70.6724 classic chromatic semitone, minor chroma 9: 25/24 70.6724 classic chromatic semitone, minor chroma 10: 3456/3125 174.2964 11: 25/24 70.6724 classic chromatic semitone, minor chroma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 648/625 62.565 cents major diesis 1: 6 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 2 3456/3125 174.296 cents 1: 2 10/9 182.404 cents minor whole tone 2: 3 625/576 141.345 cents two (classic chromatic semitone, minor chroma) 2: 6 144/125 244.969 cents classic diminished third 2: 2 125/108 253.076 cents semi-augmented whole tone 3: 8 6/5 315.641 cents minor third 3: 2 3125/2592 323.749 cents 3: 1 32/25 427.373 cents classic diminished fourth 4: 6 5/4 386.314 cents major third 4: 1 20736/15625 489.938 cents two (classic diminished third) 4: 4 4/3 498.045 cents perfect fourth 5: 2 125/96 456.986 cents classic augmented third 5: 4 864/625 560.610 cents 5: 5 25/18 568.717 cents classic augmented fourth 6: 5 36/25 631.283 cents classic diminished fifth 6: 4 625/432 639.390 cents 6: 2 192/125 743.014 cents classic diminished sixth 7: 4 3/2 701.955 cents perfect fifth 7: 1 15625/10368 710.062 cents 7: 6 8/5 813.686 cents minor sixth 8: 1 25/16 772.627 cents classic augmented fifth 8: 2 5184/3125 876.251 cents 8: 8 5/3 884.359 cents major sixth, BP sixth 9: 2 216/125 946.924 cents semi-augmented sixth 9: 6 125/72 955.031 cents classic augmented sixth 9: 3 1152/625 1058.655 cents 10: 2 9/5 1017.596 cents just minor seventh, BP seventh 10: 2 3125/1728 1025.704 cents 10: 6 48/25 1129.328 cents classic diminished octave 10: 1 625/324 1137.435 cents octave - major diesis Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.20000 = 16/5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 0.0 : 70.7 245.0 315.6 386.3 568.7 631.3 813.7 884.4 955.0 1129.3 1200.0 70.7 : 174.3 245.0 315.6 498.0 560.6 743.0 813.7 884.4 1058.7 1129.3 1200.0 245.0 : 70.7 141.3 323.7 386.3 568.7 639.4 710.1 884.4 955.0 1025.7 1200.0 315.6 : 70.7 253.1 315.6 498.0 568.7 639.4 813.7 884.4 955.0 1129.3 1200.0 386.3 : 182.4 245.0 427.4 498.0 568.7 743.0 813.7 884.4 1058.7 1129.3 1200.0 568.7 : 62.6 245.0 315.6 386.3 560.6 631.3 702.0 876.3 946.9 1017.6 1200.0 631.3 : 182.4 253.1 323.7 498.0 568.7 639.4 813.7 884.4 955.0 1137.4 1200.0 813.7 : 70.7 141.3 315.6 386.3 457.0 631.3 702.0 772.6 955.0 1017.6 1200.0 884.4 : 70.7 245.0 315.6 386.3 560.6 631.3 702.0 884.4 946.9 1129.3 1200.0 955.0 : 174.3 245.0 315.6 489.9 560.6 631.3 813.7 876.3 1058.7 1129.3 1200.0 1129.3: 70.7 141.3 315.6 386.3 457.0 639.4 702.0 884.4 955.0 1025.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.5651 .. 182.4037 cents 3125/2916, 119.8386 cents 648/625, 62.5651 cents 2: 141.3449 .. 253.0761 cents 16/15, 111.7313 cents 125/128,-41.0589 cents 3: 315.6413 .. 427.3726 cents 16/15, 111.7313 cents 648/625, 62.5651 cents 4: 386.3137 .. 498.0450 cents 16/15, 111.7313 cents 125/128,-41.0589 cents 5: 456.9861 .. 568.7174 cents 16/15, 111.7313 cents 125/128,-41.0589 cents 6: 631.2826 .. 743.0139 cents 16/15, 111.7313 cents 648/625, 62.5651 cents 7: 701.9550 .. 813.6863 cents 16/15, 111.7313 cents 125/128,-41.0589 cents 8: 772.6274 .. 884.3587 cents 16/15, 111.7313 cents 125/128,-41.0589 cents 9: 946.9239 .. 1058.6551 cents 16/15, 111.7313 cents 648/625, 62.5651 cents 10: 1017.5963 .. 1137.4349 cents 3125/2916, 119.8386 cents 125/128,-41.0589 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 648/625, 62.5651 cents, class 1 Average step (divided formal octave): 109.0909 cents Largest one step interval : 10/9, 182.4037 cents Average / Smallest step : 1.743637 Largest / Average step : 1.672034 Largest / Smallest step : 2.915420 Median interval of one step : 25/24, 70.6724 cents, amount: 6 Most common interval of one step : 25/24, 70.6724 cents, amount: 6 Least squares average step : 109.76937 cents, oct.: 1207.46307 cents Scale is not proper Step pattern alph. order: ABAACDCAABA Step pattern size order : BCBBDADBBCB Scale is a Constant Structure, by a margin of 29.61357 cents Scale diversity : 1.302990 Lumma stability : 0.260688 Lumma impropriety factor : 0.205294 Rothenberg efficiency : 0.428571 redundancy: 0.571429 Efficiency x scale size : 4.714286 Number of different interval sizes : 32 = 3.20000 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.20000 = 16/5 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 15625/15552, 8.1073 cents Most common intervals : 6/5, 315.6413 cents & inv., amount: 8 Most common triad is 0.0 315.641 884.359 cents, amount: 5 Number of recognisable fifths : 5, average 703.5765 cents Scale is fully connected 5-limit major-minor triadic Scale contains a complete diamond : 3 5 25 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 11 = 100.0000% Scale is 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 classes 7 and 8 combined Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 5-6 -- Rational properties -- Prime limit : 5 Odd number limit : 15625 (O: 15625 U: 15625) Highest odd numerator or denominator: 125 Scale harmonicity : 0.017836 Average absolute harmonicity : 0.155807 Specific harmonicity : 0.102437 Fundamental : 1/9000, -13.1357 octaves, 0.0291 Hz. Guide tone : 18000, 14.1357 octaves, 4709260.175 Hz. Exponens Consonantiae : 1.620000E+08, 27.27142 octaves Euler's gradus suavitatis : 40 Sum of Mann's harmonic distance : 368.0, average 33.45455 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 12.58146, average 1.14377 Sum of Tenney's harmonic distance : 25.53164, average 2.32106 Vogel's harmonic complexity : 24.54545 Wille's k value : 7812 Wilson's harmonic complexity : 42 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 277.19515, average 4.19993 Lattice compactness (without 2's) : 184.70857, average 2.79861 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 4 0.54545 24 1 3: -2 .. 2 0.00000 12 5: -3 .. 3 0.00000 18 10 Average exponent except 2's : 0 / 11 = 0.00000 Average absolute exponent except 2's: 30 / 11 = 2.72727 Scale is weakly epimorphic with val: <11 15 28| Scale is weakly epimorphic with val: <11 15 29| Scale is weakly epimorphic with val: <11 16 24| Scale is weakly epimorphic with val: <11 16 28| Scale is weakly epimorphic with val: <11 17 27| Scale is JI-epimorphic with val: <11 18 26| Scale is weakly epimorphic with val: <11 18 27| Scale is weakly epimorphic with val: <11 19 25|
FIT/MODE
11: 0 2 0 1 2 0 2 1 0 2 1 N T3 SD: 58.3828 c. M: 97.4595 c. 12: 1 1 1 1 2 0 2 1 1 1 1 P D3 I SD: 27.9378 c. M: 44.9689 c. 13: 1 2 0 1 2 1 2 1 0 2 1 N T3 I SD: 25.2307 c. M:-38.7182 c. 15: 1 2 1 1 2 1 2 1 1 2 1 P M ME I SD: 8.4638 c. M: 13.6863 c. 19: 1 3 1 1 3 1 3 1 1 3 1 N M DE I SD: 5.5524 c. M:-7.6627 c. 34: 2 5 2 2 5 2 5 2 2 5 2 N M DE I SD: 2.2637 c. M:-4.0115 c. 84: 5 12 5 5 13 4 13 5 5 12 5 N I SD: 1.6281 c. M:-2.7111 c. 99: 6 14 6 6 15 5 15 6 6 14 6 N I SD: 1.6151 c. M:-2.5446 c. 103: 6 15 6 6 16 5 16 6 6 15 6 N I SD: 1.3426 c. M:-2.1564 c. 118: 7 17 7 7 18 6 18 7 7 17 7 N I SD: 0.5786 c. M:-0.9011 c. 137: 8 20 8 8 21 7 21 8 8 20 8 N I SD: 0.5662 c. M: 0.9123 c. 152: 9 22 9 9 23 8 23 9 9 22 9 N I SD: 0.3268 c. M: 0.5284 c. 270: 16 39 16 16 41 14 41 16 16 39 16 N I SD: 0.3381 c. M:-0.5244 c. 289: 17 42 17 17 44 15 44 17 17 42 17 N I SD: 0.1008 c. M: 0.1545 c. 441: 26 64 26 26 67 23 67 26 26 64 26 N I SD: 0.0563 c. M:-0.0808 c. 730: 43 106 43 43 111 38 111 43 43 106 43 N I SD: 0.0295 c. M:-0.0497 c. 1342: 79 195 79 79 204 70 204 79 79 195 79 N I SD: 0.0246 c. M:-0.0386 c. 1783: 105 259 105 105 271 93 271 105 105 259 105 N I SD: 0.0082 c. M:-0.0130 c.
FIT/HARMONIC
1 x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x x x x 4 S SD: 35.3362 cents 3 x x x x 4 x x 5 x x 6 S SD: 23.5575 cents 4 x x x 5 x 6 x x 7 x 8 S SD: 18.0015 cents 5 x x 6 x 7 x 8 x 9 x 10 S SD: 12.8136 cents 6 x 7 x x 8:9 x 10 x x 12 S SD: 20.4635 cents 7 x 8 x 9 x 10:11 x 12:13:14 S SD: 12.3987 cents 8 x 9 x 10:11:12:13 x 14:15:16 S SD: 12.2345 cents 9 x 10:11 x x 13:14:15:16:17:18 SD: 12.3846 cents 10 x x 12:13:14 x 16:17 x 19:20 SD: 11.3432 cents 11:12 x 13:14:15:16 x 18:19:21:22 SD: 11.4193 cents 12:13:14 x 15 x 17:19:20:21:23:24 SD: 8.9014 cents 13:14:15 x 16:18:19:21:22:23:25:26 SD: 8.2396 cents 15:16:17:18:19:21:22:24:25:26:29:30 SD: 6.0042 cents 17:18 x 20:21:24 x 27:28:30:33:34 S SD: 7.8082 cents 18:19:21:22:23:25:26:29:30:31:35:36 SD: 5.9665 cents 19:20:22:23:24:26:27:30:32:33:36:38 S SD: 5.4022 cents 20:21:23:24:25:28:29:32:33:35:38:40 SD: 3.3462 cents 25:26:29:30:31:35:36:40:42:43:48:50 SD: 2.8542 cents 39:41:45:47:49:54:56:62:65:68:75:78 SD: 2.2882 cents 41:43:47:49:51:57:59:66:68:71:79:82 SD: 2.1831 cents 45:47:52:54:56:63:65:72:75:78:86:90 SD: 1.8186 cents 48:50:55:58:60:67:69:77:80:83:92:96 SD: 1.7975 cents 52:54:60:62:65:72:75:83:87:90:100:104 SD: 1.5586 cents 64:67:74:77:80:89:92:102:107:111:123:128 SD: 1.3791 cents 65:68:75:78:81:90:94:104:108:113:125:130 SD: 1.3365 cents 71:74:82:85:89:99:102:114:118:123:136:142 SD: 1.3322 cents 72:75:83:86:90:100:104:115:120:125:138:144 SD: 0.9641 cents 75:78:86:90:94:104:108:120:125:130:144:150 SD: 0.9485 cents 95:99:109:114:119:132:137:152:158:165:182:190 SD: 0.8983 cents 100:104:115:120:125:139:144:160:167:174:192:200 SD: 0.6140 cents 120:125:138:144:150:167:173:192:200:208:230:240 SD: 0.5875 cents 125:130:144:150:156:174:180:200:208:217:240:250 SD: 0.5609 cents 144:150:166:173:180:200:207:230:240:250:276:288 SD: 0.5185 cents 164:171:189:197:205:228:236:262:273:285:315:328 SD: 0.4575 cents 185:193:213:222:231:257:266:296:308:321:355:370 SD: 0.4419 cents 195:203:225:234:244:271:281:312:325:339:374:390 SD: 0.4410 cents 196:204:226:235:245:272:282:314:327:340:376:392 SD: 0.4363 cents 200:208:230:240:250:278:288:320:333:347:384:400 SD: 0.4348 cents 211:220:243:253:264:293:304:338:352:366:405:422 SD: 0.3845 cents 216:225:249:259:270:300:311:346:360:375:415:432 SD: 0.2662 cents 288:300:332:346:360:400:415:461:480:500:553:576 SD: 0.2460 cents 316:329:364:379:395:439:455:506:527:549:607:632 SD: 0.2415 cents 336:350:387:403:420:467:484:538:560:583:645:672 SD: 0.2120 cents 355:370:409:426:444:493:511:568:592:616:682:710 SD: 0.2076 cents 360:375:415:432:450:500:518:576:600:625:691:720 SD: 0.1677 cents 435:453:501:522:544:604:626:696:725:755:835:870 SD: 0.1544 cents 455:474:524:546:569:632:655:728:758:790:874:910 SD: 0.1413 cents 480:500:553:576:600:667:691:768:800:833:922:960 SD: 0.1305 cents 500:521:576:600:625:694:720:800:833:868:960:1000 SD: 0.1294 cents 525:547:605:630:656:729:756:840:875:911:1008:1050 SD: 0.1231 cents 600:625:691:720:750:833:864:960:1000:1042:1152:1200 SD: 0.0926 cents