Scala analysis: qcmqd8_4
F-C# in 1/4-comma meantone, other 5ths ~4.888 cents wide or (2048/2025)^(1/4)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 76.049 cents 76.049000 2: 193.157 cents 193.156860 3: 289.735 cents 289.735290 4: 5/4 386.313714 major third 5: 503.422 cents 503.421570 6: 579.471 cents 579.470570 7: 696.578 cents 696.578430 8: 782.892 cents 782.892140 9: 889.735 cents 889.735290 10: 996.578 cents 996.578430 11: 1082.892 cents 1082.892140 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 117.1079 cents 117.1079 1: 76.0490 cents 76.0490 2: 117.1079 cents 117.1079 3: 96.5784 cents 96.5784 4: 96.5784 cents 96.5784 5: 117.1079 cents 117.1079 6: 76.0490 cents 76.0490 7: 117.1079 cents 117.1079 8: 86.3137 cents 86.3137 9: 106.8431 cents 106.8431 10: 106.8431 cents 106.8431 11: 86.3137 cents 86.3137 12: 117.1079 cents 117.1079
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 76.04900 cents 1: 2 86.31371 cents 1: 2 96.57843 cents 1: 2 106.84315 cents 1: 4 117.10786 cents 2: 7 193.15686 cents 2: 2 203.42157 cents 2: 3 213.68629 cents 3: 2 279.47057 cents 3: 2 289.73529 cents 3: 2 300.00000 cents 3: 6 310.26471 cents 4: 5 5/4 386.314 cents major third 4: 2 396.57843 cents 4: 2 406.84314 cents 4: 2 417.10786 cents 4: 1 427.37257 cents 5: 4 493.15685 cents 5: 8 503.42157 cents 6: 3 579.47057 cents 6: 2 589.73528 cents 6: 2 600.00000 cents 6: 2 610.26472 cents 6: 3 620.52943 cents 7: 8 696.57843 cents 7: 4 706.84314 cents 8: 1 772.62743 cents 8: 2 782.89214 cents 8: 2 793.15685 cents 8: 2 803.42157 cents 8: 5 813.68629 cents 9: 6 889.73529 cents 9: 2 900.00000 cents 9: 2 910.26471 cents 9: 2 920.52943 cents 10: 3 986.31371 cents 10: 2 996.57843 cents 10: 7 1006.84314 cents 11: 4 1082.89214 cents 11: 2 1093.15685 cents 11: 2 1103.42157 cents 11: 2 1113.68629 cents 11: 2 1123.95100 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 3.90909 = 43/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 76.0 193.2 289.7 386.3 503.4 579.5 696.6 782.9 889.7 996.6 1082.9 1200.0 76.0 : 117.1 213.7 310.3 427.4 503.4 620.5 706.8 813.7 920.5 1006.8 1124.0 1200.0 193.2 : 96.6 193.2 310.3 386.3 503.4 589.7 696.6 803.4 889.7 1006.8 1082.9 1200.0 289.7 : 96.6 213.7 289.7 406.8 493.2 600.0 706.8 793.2 910.3 986.3 1103.4 1200.0 386.3 : 117.1 193.2 310.3 396.6 503.4 610.3 696.6 813.7 889.7 1006.8 1103.4 1200.0 503.4 : 76.0 193.2 279.5 386.3 493.2 579.5 696.6 772.6 889.7 986.3 1082.9 1200.0 579.5 : 117.1 203.4 310.3 417.1 503.4 620.5 696.6 813.7 910.3 1006.8 1124.0 1200.0 696.6 : 86.3 193.2 300.0 386.3 503.4 579.5 696.6 793.2 889.7 1006.8 1082.9 1200.0 782.9 : 106.8 213.7 300.0 417.1 493.2 610.3 706.8 803.4 920.5 996.6 1113.7 1200.0 889.7 : 106.8 193.2 310.3 386.3 503.4 600.0 696.6 813.7 889.7 1006.8 1093.2 1200.0 996.6 : 86.3 203.4 279.5 396.6 493.2 589.7 706.8 782.9 900.0 986.3 1093.2 1200.0 1082.9: 117.1 193.2 310.3 406.8 503.4 620.5 696.6 813.7 900.0 1006.8 1113.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 76.0490 .. 117.1079 cents 41.05886 cents 76.04900 cents 2: 193.1569 .. 213.6863 cents 20.52943 cents 76.04900 cents 3: 279.4706 .. 310.2647 cents 30.79414 cents 65.78428 cents 4: 386.3137 .. 427.3726 cents 41.05886 cents 76.04900 cents 5: 493.1568 .. 503.4216 cents 10.26472 cents 65.78428 cents 6: 579.4706 .. 620.5294 cents 41.05886 cents 76.04900 cents 7: 696.5784 .. 706.8431 cents 10.26471 cents 76.04900 cents 8: 772.6274 .. 813.6863 cents 41.05886 cents 65.78429 cents 9: 889.7353 .. 920.5294 cents 30.79414 cents 76.04900 cents 10: 986.3137 .. 1006.8431 cents 20.52943 cents 65.78428 cents 11: 1082.8921 .. 1123.9510 cents 41.05886 cents 76.04900 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 76.04900 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 117.10786 cents Average / Smallest step : 1.314942 Largest / Average step : 1.171079 Largest / Smallest step : 1.539900 Median interval of one step : 101.71079 cents, amount: 0 Most common interval of one step : 117.10786 cents, amount: 4 Least squares average step : 98.91563 cents, oct.: 1186.98750 cents Scale is strictly proper Step pattern alph. order: ABCCBABDEEDB Step pattern size order : AECCEAEBDDBE Scale is a Constant Structure, by a margin of 65.78428 cents Scale diversity : 1.234839 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.726274 Rothenberg efficiency : 0.314478 redundancy: 0.685522 Efficiency x scale size : 3.773737 Number of different interval sizes : 43 = 3.90909 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 3.90909 = 43/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 10.26471 cents Most common intervals : 503.42157 cents & inv., amount: 8 Most common triad is 0.0 503.422 696.578 cents, amount: 7 Number of recognisable fifths : 12, average 700.0000 cents Best fifths form a closed circle Formal octave complements present : 3 = 25.0000% Limited transpositions with margin 41.0589 cents: 5 7 10 Limited inverse transpositions : 6 Inversional symmetry on degrees : 3 9 -- Rational properties -- Prime limit : 5 (not all pitches rational)
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 13.1036 c. M:-23.9510 c. Twelve-tone Chromatic (1/11-comma) 29: 2 3 2 2 3 2 3 2 3 2 2 3 SP M ME SD: 9.2135 c. M:-20.6095 c. 30: 2 3 2 3 3 1 3 3 2 3 2 3 SP D3 SD: 11.8351 c. M: 19.4706 c. 31: 2 3 2 3 3 2 3 2 3 3 2 3 SP M ME SD: 6.6506 c. M: 18.7675 c. 35: 2 4 2 3 4 2 3 3 3 3 3 3 SP D3 SD: 9.2529 c. M: 15.4496 c. 38: 2 4 3 3 4 2 4 3 3 3 3 4 SP D3 S SD: 8.4798 c. M: 17.6311 c. 40: 3 3 4 3 4 2 4 3 4 3 3 4 SP D3 SD: 8.3081 c. M:-13.9510 c. 41: 3 4 3 3 4 3 4 3 3 4 3 4 SP M ME SD: 7.1555 c. M:-11.7559 c. Schismic-12 43: 3 4 3 4 4 3 4 3 4 4 3 4 SP M ME SD: 5.4047 c. M: 10.6655 c. 50: 3 5 4 4 5 3 5 4 4 5 3 5 SP D3 SD: 4.6868 c. M:-11.4216 c. 52: 3 5 5 4 5 3 5 4 5 4 4 5 SP SD: 6.0087 c. M:-10.2647 c. 54: 3 6 4 4 6 3 5 4 5 5 4 5 SP S SD: 5.8030 c. M: 9.3823 c. 58: 4 5 5 5 5 4 6 4 5 5 4 6 SP D3 S SD: 5.0525 c. M: 7.0301 c. 62: 4 6 5 5 6 4 6 4 6 5 5 6 SP D3 SD: 3.7784 c. M: 9.4817 c. 74: 5 7 6 6 7 5 7 5 7 7 5 7 SP D3 S SD: 3.8276 c. M:-8.8270 c. 78: 5 8 6 6 8 5 7 6 7 7 5 8 SP SD: 3.8402 c. M:-6.8431 c. 81: 5 8 7 6 8 5 8 6 7 7 6 8 SP SD: 2.5069 c. M:-6.5610 c. 91: 6 9 7 7 9 6 9 6 8 9 6 9 SP SD: 3.5839 c. M: 6.2188 c. 93: 6 9 7 8 9 6 9 7 8 8 7 9 SP SD: 2.3568 c. M: 5.8643 c. 95: 6 9 8 8 9 6 9 7 8 9 7 9 SP SD: 2.8183 c. M: 5.5248 c. 98: 6 10 8 8 9 6 10 7 9 8 7 10 SP SD: 3.5381 c. M:-5.5230 c. 100: 6 10 8 8 10 6 10 7 9 9 7 10 SP S SD: 2.2152 c. M: 4.0490 c. 112: 7 11 9 9 11 7 11 8 10 10 8 11 SP S SD: 0.5739 c. M: 1.0490 c. 236: 15 23 19 19 23 15 23 17 21 21 17 23 SP S SD: 0.1216 c. M:-0.2222 c. 348: 22 34 28 28 34 22 34 25 31 31 25 34 SP S SD: 0.1023 c. M: 0.1869 c. 584: 37 57 47 47 57 37 57 42 52 52 42 57 SP S SD: 0.0118 c. M: 0.0216 c. 1404: 89 137 113 113 137 89 137 101 125 125 101 137 SP S SD: 0.0106 c. M:-0.0194 c. 1988: 126 194 160 160 194 126 194 143 177 177 143 194 SP S SD: 0.0040 c. M:-0.0073 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: 2.6883 cents 3 x x x x 4 x x x 5 x x 6 S SD: 2.5345 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 7.0671 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 9.1003 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 6.9396 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 12.1870 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 8.0599 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 8.3191 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 8.3368 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 10.6058 cents 12 x 13:14:15:16:17:18:19:20:21:22:24 S SD: 7.1567 cents 13:14 x 15:16:17:18:19:20:22:23:24:26 S SD: 9.4998 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 8.7665 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 6.2420 cents 16:17:18:19:20:21:22:24:25:27:28:30:32 SD: 5.3120 cents 17:18:19:20:21:23:24:25:27:28:30:32:34 SD: 5.1848 cents 18:19:20:21:23:24:25:27:28:30:32:34:36 SD: 4.7505 cents 21:22:23:25:26:28:29:31:33:35:37:39:42 SD: 4.6238 cents 23:24:26:27:29:31:32:34:36:38:41:43:46 SD: 3.6006 cents 24:25:27:28:30:32:34:36:38:40:43:45:48 SD: 3.4010 cents 27:28:30:32:34:36:38:40:42:45:48:50:54 SD: 3.2482 cents 28:29:31:33:35:37:39:42:44:47:50:52:56 SD: 2.9752 cents 33:34:37:39:41:44:46:49:52:55:59:62:66 SD: 2.8138 cents 39:41:44:46:49:52:55:58:61:65:69:73:78 SD: 2.6354 cents 40:42:45:47:50:54:56:60:63:67:71:75:80 SD: 2.1379 cents 44:46:49:52:55:59:61:66:69:74:78:82:88 SD: 1.8010 cents 45:47:50:53:56:60:63:67:71:75:80:84:90 SD: 1.6448 cents 59:62:66:70:74:79:82:88:93:99:105:110:118 SD: 1.6057 cents 60:63:67:71:75:80:84:90:94:100:107:112:120 SD: 1.2795 cents 67:70:75:79:84:90:94:100:105:112:119:125:134 SD: 1.1922 cents 68:71:76:80:85:91:95:102:107:114:121:127:136 SD: 0.9581 cents 91:95:102:108:114:122:127:136:143:152:162:170:182 SD: 0.8858 cents 93:97:104:110:116:124:130:139:146:155:165:174:186 SD: 0.8595 cents 103:108:115:122:129:138:144:154:162:172:183:193:206 SD: 0.8318 cents 109:114:122:129:136:146:152:163:171:182:194:204:218 SD: 0.6640 cents 128:134:143:151:160:171:179:191:201:214:228:239:256 SD: 0.6387 cents 131:137:146:155:164:175:183:196:206:219:233:245:262 SD: 0.5827 cents 136:142:152:161:170:182:190:203:214:227:242:254:272 SD: 0.4853 cents 159:166:178:188:199:213:222:238:250:266:283:297:318 SD: 0.4632 cents 176:184:197:208:220:235:246:263:277:294:313:329:352 SD: 0.3942 cents 196:205:219:232:245:262:274:293:308:328:349:366:392 SD: 0.3840 cents 204:213:228:241:255:273:285:305:321:341:363:381:408 SD: 0.2868 cents 252:263:282:298:315:337:352:377:396:421:448:471:504 SD: 0.2706 cents 269:281:301:318:336:360:376:402:423:450:478:503:538 SD: 0.2643 cents 287:300:321:339:359:384:401:429:451:480:510:536:574 SD: 0.2602 cents 311:325:348:368:389:416:435:465:489:520:553:581:622 SD: 0.2565 cents 313:327:350:370:391:419:437:468:492:523:557:585:626 SD: 0.2520 cents 329:344:368:389:411:440:460:492:517:550:585:615:658 SD: 0.1656 cents 400:418:447:473:500:535:559:598:629:669:711:748:800 SD: 0.1514 cents 488:510:546:577:610:653:682:730:767:816:868:912:976 SD: 0.1491 cents 509:532:569:602:636:681:711:761:800:851:905:951:1018 SD: 0.1477 cents 533:557:596:630:666:713:745:797:838:891:948:996:1066 SD: 0.0974 cents