Scala analysis: meanqr
270-et Hahn reduced rational 6125/4096 Meantone[12]
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 16/15 111.731285 minor diatonic semitone 2: 28/25 196.198479 middle second 3: 448/375 307.929764 4: 784/625 392.396957 two (middle second) 5: 8192/6125 503.407045 6: 6144/4375 587.874239 7: 6125/4096 696.592955 8: 625/392 807.603043 9: 375/224 892.070236 10: 25/14 1003.801521 middle minor seventh 11: 15/8 1088.268715 classic major seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 16/15 111.7313 minor diatonic semitone 2: 21/20 84.4672 minor semitone 3: 16/15 111.7313 minor diatonic semitone 4: 21/20 84.4672 minor semitone 5: 2560/2401 111.0101 6: 21/20 84.4672 minor semitone 7: 26796875/25165824 108.7187 8: 2560/2401 111.0101 9: 21/20 84.4672 minor semitone 10: 16/15 111.7313 minor diatonic semitone 11: 21/20 84.4672 minor semitone 12: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 21/20 84.467 cents minor semitone 1: 1 26796875/25165824 108.719 cents 1: 2 2560/2401 111.010 cents 1: 4 16/15 111.731 cents minor diatonic semitone 2: 1 37515625/33554432 193.186 cents 2: 3 384/343 195.477 cents 2: 6 28/25 196.198 cents middle second 2: 1 390625/344064 219.729 cents 2: 1 256/225 223.463 cents Neapolitan diminished third 3: 1 288/245 279.944 cents 3: 2 147/125 280.666 cents 3: 3 78125/65536 304.196 cents 3: 2 2048/1715 307.209 cents 3: 4 448/375 307.930 cents 4: 2 328125/262144 388.663 cents 4: 3 1536/1225 391.676 cents 4: 3 784/625 392.397 cents two (middle second) 4: 1 390625/307328 415.206 cents 4: 1 15625/12288 415.927 cents 4: 2 7168/5625 419.661 cents 5: 1 1152/875 476.143 cents 5: 2 234375/175616 499.673 cents 5: 3 21875/16384 500.394 cents 5: 2 8192/6125 503.407 cents 5: 4 12544/9375 504.128 cents 6: 1 140625/100352 584.140 cents 6: 2 91875/65536 584.862 cents 6: 1 6144/4375 587.874 cents 6: 2 21952/15625 588.595 cents 6: 2 15625/10976 611.405 cents 6: 1 4375/3072 612.126 cents 6: 2 131072/91875 615.138 cents 6: 1 200704/140625 615.860 cents 7: 4 9375/6272 695.872 cents 7: 2 6125/4096 696.593 cents 7: 3 32768/21875 699.606 cents 7: 2 351232/234375 700.327 cents 7: 1 875/576 723.857 cents 8: 2 5625/3584 780.339 cents 8: 1 24576/15625 784.073 cents 8: 1 614656/390625 784.794 cents 8: 3 625/392 807.603 cents 8: 3 1225/768 808.324 cents 8: 2 524288/328125 811.337 cents 9: 4 375/224 892.070 cents 9: 2 1715/1024 892.791 cents 9: 3 131072/78125 895.804 cents 9: 2 250/147 919.334 cents 9: 1 245/144 920.056 cents 10: 1 225/128 976.537 cents augmented sixth 10: 1 688128/390625 980.271 cents 10: 6 25/14 1003.802 cents middle minor seventh 10: 3 343/192 1004.523 cents 10: 1 67108864/37515625 1006.814 cents 11: 4 15/8 1088.269 cents classic major seventh 11: 2 2401/1280 1088.990 cents 11: 1 50331648/26796875 1091.281 cents 11: 5 40/21 1115.533 cents acute major seventh Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 5.27273 = 58/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 111.7 196.2 307.9 392.4 503.4 587.9 696.6 807.6 892.1 1003.8 1088.3 1200.0 111.7 : 84.5 196.2 280.7 391.7 476.1 584.9 695.9 780.3 892.1 976.5 1088.3 1200.0 196.2 : 111.7 196.2 307.2 391.7 500.4 611.4 695.9 807.6 892.1 1003.8 1115.5 1200.0 307.9 : 84.5 195.5 279.9 388.7 499.7 584.1 695.9 780.3 892.1 1003.8 1088.3 1200.0 392.4 : 111.0 195.5 304.2 415.2 499.7 611.4 695.9 807.6 919.3 1003.8 1115.5 1200.0 503.4 : 84.5 193.2 304.2 388.7 500.4 584.9 696.6 808.3 892.8 1004.5 1089.0 1200.0 587.9 : 108.7 219.7 304.2 415.9 500.4 612.1 723.9 808.3 920.1 1004.5 1115.5 1200.0 696.6 : 111.0 195.5 307.2 391.7 503.4 615.1 699.6 811.3 895.8 1006.8 1091.3 1200.0 807.6 : 84.5 196.2 280.7 392.4 504.1 588.6 700.3 784.8 895.8 980.3 1089.0 1200.0 892.1 : 111.7 196.2 307.9 419.7 504.1 615.9 700.3 811.3 895.8 1004.5 1115.5 1200.0 1003.8: 84.5 196.2 307.9 392.4 504.1 588.6 699.6 784.1 892.8 1003.8 1088.3 1200.0 1088.3: 111.7 223.5 307.9 419.7 504.1 615.1 699.6 808.3 919.3 1003.8 1115.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 84.4672 .. 111.7313 cents 64/63, 27.2641 cents 21/20, 84.4672 cents 2: 193.1859 .. 223.4626 cents 30.27666 cents 562734375/536870912, 81.4546 cents 3: 279.9445 .. 307.9298 cents 686/675, 27.9853 cents 405/392, 56.4819 cents 4: 388.6632 .. 419.6610 cents 268435456/263671875, 30.9979 cents 17578125/16777216, 80.7334 cents 5: 476.1430 .. 504.1282 cents 686/675, 27.9853 cents 405/392, 56.4819 cents 6: 584.1405 .. 615.8595 cents 31.71906 cents 1318359375/1258815488, 80.0122 cents 7: 695.8718 .. 723.8570 cents 686/675, 27.9853 cents 1318359375/1258815488, 80.0122 cents 8: 780.3390 .. 811.3368 cents 268435456/263671875, 30.9979 cents 405/392, 56.4819 cents 9: 892.0702 .. 920.0555 cents 686/675, 27.9853 cents 17578125/16777216, 80.7334 cents 10: 976.5374 .. 1006.8141 cents 30.27666 cents 405/392, 56.4819 cents 11: 1088.2687 .. 1115.5328 cents 64/63, 27.2641 cents 562734375/536870912, 81.4546 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 21/20, 84.4672 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 16/15, 111.7313 cents Average / Smallest step : 1.183892 Largest / Average step : 1.117313 Largest / Smallest step : 1.322777 Median interval of one step : 109.86440 cents, amount: 0 Most common interval of one step : 21/20, 84.4672 cents, amount: 5 Least squares average step : 99.71748 cents, oct.: 1196.60980 cents Scale is strictly proper Step pattern alph. order: ABABCBDCBABA Step pattern size order : DADACABCADAD Scale is a Constant Structure, by a margin of 56.48190 cents Scale diversity : 1.203573 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.732719 Rothenberg efficiency : 0.274423 redundancy: 0.725577 Efficiency x scale size : 3.293074 Number of different interval sizes : 58 = 5.27273 / class Number of one step interval sizes : 4 Highest interval variety : 8 Mean interval variety : 5.27273 = 58/11 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 2401/2400, 0.7212 cents Most common intervals : 28/25, 196.1985 cents & inv., amount: 6 Most common triad is 0.0 196.198 1003.802 cents, amount: 3 Number of recognisable fifths : 11, average 697.8312 cents Best fifths form a closed circle Scale contains a complete diamond : 7 25 375 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 11 = 91.6667% Limited inverse transpositions with margin 27.9853 cents: 7 -- Rational properties -- Prime limit : 7 Odd number limit : 37515625 (O: 37515625 U: 37515625) Highest odd numerator or denominator: 6125 Scale harmonicity : 0.008152 Average absolute harmonicity : 0.116052 Specific harmonicity : 0.046657 Fundamental : 1/376320000, -28.4874 octaves, 0.0000 Hz. Guide tone : 752640000, 29.4874 octaves, 196909865468.145 Hz. Exponens Consonantiae : 2.832335E+17, 57.97477 octaves Euler's gradus suavitatis : 86 Sum of Mann's harmonic distance : 19527.0, average 1627.25000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 27.10308, average 2.25859 Sum of Tenney's harmonic distance : 53.90793, average 4.49233 Vogel's harmonic complexity : 48.41667 Wille's k value : 281367187 Wilson's harmonic complexity : 74 Rectangular lattice diameter : 14 Triangular lattice diameter : 10 Lattice compactness : 692.97899, average 8.88435 Lattice compactness (without 2's) : 312.63335, average 4.00812 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -12 .. 13 1.41667 65 1 3: -1 .. 1 0.08333 5 5: -4 .. 4 -0.33333 30 2 7: -2 .. 2 -0.08333 13 9 Average exponent except 2's :-4 / 12 =-0.33333 Average absolute exponent except 2's: 48 / 12 = 4.00000 Scale is weakly epimorphic with val: <12 19 25 33|
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 7.7232 c. M:-12.1258 c. Twelve-tone Chromatic (1/11-comma) 31: 3 2 3 2 3 2 3 3 2 3 2 3 SP M ME SD: 3.7343 c. M: 7.2291 c. Genus diatonico-chromaticum 43: 4 3 4 3 4 3 4 4 3 4 3 4 SP M ME SD: 1.1082 c. M: 1.8277 c. Genus diatonico-chromaticum 98: 9 7 9 7 9 7 9 9 7 9 7 9 SP M DE SD: 1.1449 c. M: 1.8073 c. 141: 13 10 13 10 13 10 13 13 10 13 10 13 SP M DE SD: 1.0375 c. M: 1.5468 c. 171: 16 12 16 12 16 12 15 16 12 16 12 16 SP SD: 1.0136 c. M:-1.8561 c. 184: 17 13 17 13 17 13 17 17 13 17 13 17 SP M DE SD: 1.0132 c. M: 1.4080 c. 202: 19 14 19 14 19 14 18 19 14 19 14 19 SP SD: 0.8945 c. M: 1.5434 c. 214: 20 15 20 15 20 15 19 20 15 20 15 20 SP SD: 0.6382 c. M: 1.2659 c. 245: 23 17 23 17 23 17 22 23 17 23 17 23 SP SD: 0.6872 c. M:-1.0828 c. 257: 24 18 24 18 24 18 23 24 18 24 18 24 SP SD: 0.4228 c. M:-0.8731 c. 269: 25 19 25 19 25 19 24 25 19 25 19 25 SP SD: 0.4148 c. M:-0.9733 c. 288: 27 20 27 20 27 20 26 27 20 27 20 27 SP SD: 0.5870 c. M:-0.7687 c. 300: 28 21 28 21 28 21 27 28 21 28 21 28 SP SD: 0.3250 c. M:-0.5930 c. 312: 29 22 29 22 29 22 28 29 22 29 22 29 SP SD: 0.2795 c. M:-0.5873 c. 343: 32 24 32 24 32 24 31 32 24 32 24 32 SP SD: 0.3159 c. M: 0.5602 c. 355: 33 25 33 25 33 25 32 33 25 33 25 33 SP SD: 0.2407 c. M: 0.3241 c. 868: 81 61 81 61 80 61 79 80 61 81 61 81 SP SD: 0.2398 c. M: 0.3652 c. 880: 82 62 82 62 81 62 80 81 62 82 62 82 SP SD: 0.2117 c. M: 0.3303 c. 923: 86 65 86 65 85 65 84 85 65 86 65 86 SP SD: 0.1869 c. M: 0.2651 c. 966: 90 68 90 68 89 68 88 89 68 90 68 90 SP SD: 0.1773 c. M:-0.3015 c. 1137: 106 80 106 80 105 80 103 105 80 106 80 106 SP SD: 0.1533 c. M: 0.2497 c. 1149: 107 81 107 81 106 81 104 106 81 107 81 107 SP SD: 0.1533 c. M: 0.2923 c. 1180: 110 83 110 83 109 83 107 109 83 110 83 110 SP SD: 0.1224 c. M: 0.2058 c. 1192: 111 84 111 84 110 84 108 110 84 111 84 111 SP SD: 0.1155 c. M: 0.2205 c. 1223: 114 86 114 86 113 86 111 113 86 114 86 114 SP SD: 0.1030 c. M: 0.1651 c. 1235: 115 87 115 87 114 87 112 114 87 115 87 115 SP SD: 0.0865 c. M: 0.1536 c. 1278: 119 90 119 90 118 90 116 118 90 119 90 119 SP SD: 0.0718 c. M:-0.1207 c. 1492: 139 105 139 105 138 105 135 138 105 139 105 139 SP SD: 0.0781 c. M: 0.1131 c. 1535: 143 108 143 108 142 108 139 142 108 143 108 143 SP SD: 0.0506 c. M: 0.0833 c. 1578: 147 111 147 111 146 111 143 146 111 147 111 147 SP SD: 0.0347 c. M: 0.0558 c. 1590: 148 112 148 112 147 112 144 147 112 148 112 148 SP SD: 0.0327 c. M: 0.0559 c. 1633: 152 115 152 115 151 115 148 151 115 152 115 152 SP SD: 0.0251 c. M: 0.0390 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: 2.6810 cents 3 x x x x 4 x x x 5 x x 6 S SD: 3.1308 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 8.9758 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 3.5526 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.5981 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 11.5293 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 7.6739 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.7896 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.0492 cents 11:12 x 13:14:15 x 16 x 18:20:21:22 S SD: 10.7841 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.8062 cents 13:14:15 x 16:17:18:19:21:22:23:24:26 SD: 8.8816 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 7.1755 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 3.9896 cents 24:26:27:29:30:32:34:36:38:40:43:45:48 SD: 3.4649 cents 27:29:30:32:34:36:38:40:43:45:48:51:54 SD: 2.8365 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 1.9729 cents 42:45:47:50:53:56:59:63:67:70:75:79:84 SD: 1.5668 cents 47:50:53:56:59:63:66:70:75:79:84:88:94 SD: 1.4559 cents 59:63:66:70:74:79:83:88:94:99:105:111:118 SD: 1.3690 cents 62:66:69:74:78:83:87:93:99:104:111:116:124 SD: 1.3094 cents 71:76:80:85:89:95:100:106:113:119:127:133:142 SD: 1.2330 cents 74:79:83:88:93:99:104:111:118:124:132:139:148 SD: 0.9460 cents 89:95:100:106:112:119:125:133:142:149:159:167:178 SD: 0.8188 cents 101:108:113:121:127:135:142:151:161:169:180:189:202 SD: 0.8004 cents 107:114:120:128:134:143:150:160:171:179:191:201:214 SD: 0.6608 cents 119:127:133:142:149:159:167:178:190:199:213:223:238 SD: 0.6456 cents 133:142:149:159:167:178:187:199:212:223:238:249:266 SD: 0.5345 cents 149:159:167:178:187:199:209:223:238:249:266:279:298 SD: 0.5298 cents 150:160:168:179:188:201:211:224:239:251:268:281:300 SD: 0.4965 cents 165:176:185:197:207:221:232:247:263:276:295:309:330 SD: 0.4555 cents 166:177:186:198:208:222:233:248:265:278:296:311:332 SD: 0.4480 cents 168:179:188:201:211:225:236:251:268:281:300:315:336 SD: 0.4435 cents 181:193:203:216:227:242:254:271:289:303:323:339:362 SD: 0.4377 cents 190:203:213:227:238:254:267:284:303:318:339:356:380 SD: 0.4007 cents 200:213:224:239:251:267:281:299:319:335:357:375:400 SD: 0.3827 cents 210:224:235:251:263:281:295:314:335:352:375:394:420 SD: 0.3562 cents 225:240:252:269:282:301:316:336:359:377:402:422:450 SD: 0.3172 cents 240:256:269:287:301:321:337:359:383:402:429:450:480 SD: 0.2798 cents 252:269:282:301:316:337:354:377:402:422:450:473:504 SD: 0.2591 cents 267:285:299:319:335:357:375:399:426:447:477:501:534 SD: 0.2211 cents 299:319:335:357:375:400:420:447:477:501:534:561:598 SD: 0.2187 cents 358:382:401:428:449:479:503:535:571:599:639:671:716 SD: 0.2164 cents 359:383:402:429:450:480:504:537:572:601:641:673:718 SD: 0.1750 cents 374:399:419:447:469:500:525:559:596:626:668:701:748 SD: 0.1736 cents 406:433:455:485:509:543:570:607:647:680:725:761:812 SD: 0.1713 cents 432:461:484:516:542:578:607:646:689:723:771:810:864 SD: 0.1638 cents 448:478:502:535:562:599:629:670:714:750:800:840:896 SD: 0.1281 cents 569:607:637:680:714:761:799:851:907:953:1016:1067:1138 SD: 0.1254 cents