Scala analysis: butterfly2
"Butterfly II" well-temperament
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 96.094 cents 96.093750 2: 196.875 cents 196.875000 3: 297.656 cents 297.656250 4: 392.578 cents 392.578130 5: 499.219 cents 499.218750 6: 594.141 cents 594.140630 7: 700.781 cents 700.781250 8: 795.703 cents 795.703130 9: 896.484 cents 896.484380 10: 997.266 cents 997.265650 11: 1093.359 cents 1093.359350 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 106.6407 cents 106.6407 1: 96.0937 cents 96.0937 2: 100.7813 cents 100.7813 3: 100.7812 cents 100.7812 4: 94.9219 cents 94.9219 5: 106.6406 cents 106.6406 6: 94.9219 cents 94.9219 7: 106.6406 cents 106.6406 8: 94.9219 cents 94.9219 9: 100.7813 cents 100.7813 10: 100.7813 cents 100.7813 11: 96.0937 cents 96.0937 12: 106.6407 cents 106.6407
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 94.92188 cents 1: 2 96.09375 cents 1: 4 100.78125 cents 1: 3 106.64062 cents 2: 2 195.70313 cents 2: 2 196.87500 cents 2: 6 201.56250 cents 2: 2 202.73435 cents 3: 4 296.48438 cents 3: 2 297.65625 cents 3: 1 298.82810 cents 3: 2 302.34375 cents 3: 2 303.51562 cents 3: 1 308.20312 cents 4: 2 392.57813 cents 4: 2 397.26563 cents 4: 2 399.60937 cents 4: 4 403.12500 cents 4: 2 404.29687 cents 5: 3 498.04688 cents 5: 4 499.21875 cents 5: 3 500.39062 cents 5: 2 503.90625 cents 6: 2 594.14063 cents 6: 2 595.31250 cents 6: 2 598.82813 cents 6: 2 601.17187 cents 6: 2 604.68750 cents 6: 2 605.85937 cents 7: 2 696.09375 cents 7: 3 699.60938 cents 7: 4 700.78125 cents 7: 3 701.95312 cents 8: 2 795.70313 cents 8: 4 796.87500 cents 8: 2 800.39063 cents 8: 2 802.73437 cents 8: 2 807.42187 cents 9: 1 891.79688 cents 9: 2 896.48438 cents 9: 2 897.65625 cents 9: 1 901.17190 cents 9: 2 902.34375 cents 9: 4 903.51562 cents 10: 2 997.26565 cents 10: 6 998.43750 cents 10: 2 1003.12500 cents 10: 2 1004.29687 cents 11: 3 1093.35935 cents 11: 4 1099.21875 cents 11: 2 1103.90625 cents 11: 3 1105.07812 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.72727 = 52/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 96.1 196.9 297.7 392.6 499.2 594.1 700.8 795.7 896.5 997.3 1093.4 1200.0 96.1 : 100.8 201.6 296.5 403.1 498.0 604.7 699.6 800.4 901.2 997.3 1103.9 1200.0 196.9 : 100.8 195.7 302.3 397.3 503.9 598.8 699.6 800.4 896.5 1003.1 1099.2 1200.0 297.7 : 94.9 201.6 296.5 403.1 498.0 598.8 699.6 795.7 902.3 998.4 1099.2 1200.0 392.6 : 106.6 201.6 308.2 403.1 503.9 604.7 700.8 807.4 903.5 1004.3 1105.1 1200.0 499.2 : 94.9 201.6 296.5 397.3 498.0 594.1 700.8 796.9 897.7 998.4 1093.4 1200.0 594.1 : 106.6 201.6 302.3 403.1 499.2 605.9 702.0 802.7 903.5 998.4 1105.1 1200.0 700.8 : 94.9 195.7 296.5 392.6 499.2 595.3 696.1 796.9 891.8 998.4 1093.4 1200.0 795.7 : 100.8 201.6 297.7 404.3 500.4 601.2 702.0 796.9 903.5 998.4 1105.1 1200.0 896.5 : 100.8 196.9 303.5 399.6 500.4 601.2 696.1 802.7 897.7 1004.3 1099.2 1200.0 997.3 : 96.1 202.7 298.8 399.6 500.4 595.3 702.0 796.9 903.5 998.4 1099.2 1200.0 1093.4: 106.6 202.7 303.5 404.3 499.2 605.9 700.8 807.4 902.3 1003.1 1103.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 94.9219 .. 106.6406 cents 11.71874 cents 94.92188 cents 2: 195.7031 .. 202.7344 cents 7.03122 cents 89.06251 cents 3: 296.4844 .. 308.2031 cents 11.71874 cents 93.75003 cents 4: 392.5781 .. 404.2969 cents 11.71874 cents 84.37501 cents 5: 498.0469 .. 503.9062 cents 5.85937 cents 93.75001 cents 6: 594.1406 .. 605.8594 cents 11.71874 cents 90.23438 cents 7: 696.0938 .. 701.9531 cents 5.85937 cents 90.23438 cents 8: 795.7031 .. 807.4219 cents 11.71874 cents 93.75001 cents 9: 891.7969 .. 903.5156 cents 11.71874 cents 84.37501 cents 10: 997.2656 .. 1004.2969 cents 7.03122 cents 93.75003 cents 11: 1093.3593 .. 1105.0781 cents 11.71877 cents 89.06248 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 94.92188 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 106.64062 cents Average / Smallest step : 1.053498 Largest / Average step : 1.066406 Largest / Smallest step : 1.123457 Median interval of one step : 100.78125 cents, amount: 4 Most common interval of one step : 100.78125 cents, amount: 4 Least squares average step : 99.62019 cents, oct.: 1195.44231 cents Scale is strictly proper Scale is a mode of a 1024-tone equal temperament with octave 2/1 degrees: 82 168 254 335 426 507 598 679 765 851 933 1024 Least number of segments generator : 513 of 601.172 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 957 of 1121.484 cents and inv. generated superset size: 532 = 520 more = 4433.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBCDCDCBBAD Step pattern size order : BCCADADACCBD Scale is a Constant Structure, by a margin of 84.37501 cents Scale diversity : 1.073569 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.910156 Rothenberg efficiency : 0.277537 redundancy: 0.722463 Efficiency x scale size : 3.330447 Number of different interval sizes : 52 = 4.72727 / class Number of one step interval sizes : 4 Highest interval variety : 6 Mean interval variety : 4.72727 = 52/11 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 1.17185 cents Most common intervals : 201.56250 cents & inv., amount: 6 Most common triad is 0.0 201.562 998.438 cents, amount: 4 Number of recognisable fifths : 12, average 700.0000 cents Scale is a well-temperament. It has 4 different sizes of fifth Best fifths form a closed circle Formal octave complements present : 3 = 25.0000% Limited transpositions with margin 11.7188 cents: 1 2 3 4 5 6 7 8 9 10 11 Limited inverse transpositions : 11 Inversional symmetry on intervals : 5-6 11-12 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 4.1186 c. M:-7.4219 c. Twelve-tone Chromatic (1/11-comma) 76: 6 6 7 6 7 6 6 6 7 6 6 7 SP D3 SD: 4.5354 c. M: 7.4013 c. 77: 6 7 6 6 7 6 7 6 7 6 6 7 SP M ME SD: 3.1184 c. M:-7.4117 c. 79: 6 7 7 6 7 6 7 6 7 7 6 7 SP M ME SD: 3.4334 c. M:-6.1412 c. Meantone Chromatic (3/20-comma) 88: 7 7 8 7 8 7 7 7 8 7 7 8 SP D3 SD: 3.9314 c. M: 5.9659 c. 89: 7 8 7 7 8 7 8 7 7 8 7 8 SP M ME SD: 2.6078 c. M: 6.5967 c. 90: 7 8 7 7 8 8 8 7 7 8 7 8 SP D3 SD: 4.1882 c. M: 5.9115 c. 91: 7 8 8 7 8 7 8 7 8 8 7 8 SP M ME SD: 3.0230 c. M:-5.6405 c. Meantone Chromatic (1/7-comma), Romieu-12 99: 8 8 9 7 9 8 9 8 8 8 8 9 SP D3 SD: 2.9759 c. M:-5.3741 c. 101: 8 9 8 8 9 8 9 8 8 9 8 9 SP M ME SD: 2.1940 c. M: 5.3953 c. 103: 8 9 9 8 9 8 9 8 9 9 8 9 SP M ME SD: 2.7914 c. M:-5.2564 c. Meantone Chromatic (3/22-comma) 109: 9 9 9 9 9 9 10 8 9 10 8 10 SP D3 SD: 3.1420 c. M: 4.7413 c. 110: 9 9 9 9 10 8 10 9 9 9 9 10 SP D3 SD: 2.6478 c. M: 5.0497 c. 111: 9 9 10 8 10 9 10 9 9 9 9 10 SP D3 SD: 2.5756 c. M:-5.0465 c. 113: 9 10 9 9 10 9 10 9 9 10 9 10 SP M ME SD: 1.9635 c. M:-4.8949 c. 114: 9 10 9 9 10 9 11 9 9 10 9 10 SP D3 SD: 3.1965 c. M: 4.6669 c. 115: 9 10 10 9 10 9 10 9 10 10 9 10 SP M ME SD: 2.6737 c. M:-4.9524 c. Meantone Chromatic (3/23-comma), Preston-12 116: 9 10 10 9 10 9 11 9 10 9 10 10 SP D3 SD: 2.7349 c. M: 4.4855 c. 121: 10 10 10 10 10 10 11 9 10 11 9 11 SP D3 SD: 2.8559 c. M:-4.3872 c. 122: 10 10 10 10 11 9 11 10 10 10 10 11 SP D3 SD: 2.2381 c. M: 3.9767 c. 125: 10 11 10 10 11 10 11 10 10 11 10 11 SP M ME SD: 1.8631 c. M:-4.7250 c. 128: 10 11 11 10 11 10 12 10 11 10 11 11 SP D3 SD: 2.4859 c. M:-3.5157 c. 130: 10 11 11 10 12 10 12 10 11 11 10 12 SP D3 SD: 2.6906 c. M: 4.8858 c. 134: 11 11 11 11 12 10 12 11 11 11 11 12 SP D3 SD: 1.9626 c. M: 3.2358 c. 137: 11 11 12 11 12 11 12 11 11 12 11 12 SP M ME SD: 1.7655 c. M: 4.1743 c. 146: 12 12 12 12 13 11 13 12 12 12 12 13 SP D3 SD: 1.7947 c. M: 2.7451 c. 149: 12 12 13 12 13 12 13 12 12 13 12 13 SP M ME SD: 1.7213 c. M: 3.5864 c. 154: 12 13 13 12 14 12 14 12 13 13 12 14 SP D3 SD: 1.6693 c. M: 2.9677 c. 158: 13 13 13 13 14 12 14 13 13 13 13 14 SP D3 SD: 1.7105 c. M:-2.6404 c. 166: 13 14 14 13 15 13 15 13 14 14 13 15 SP D3 SD: 1.2820 c. M: 2.2167 c. 178: 14 15 15 14 16 14 16 14 15 15 14 16 SP D3 SD: 0.9628 c. M: 1.7117 c. 190: 15 16 16 15 17 15 17 15 16 16 15 17 SP D3 SD: 0.7128 c. M: 1.3569 c. 202: 16 17 17 16 18 16 18 16 17 17 16 18 SP D3 SD: 0.5467 c. M: 1.0442 c. 214: 17 18 18 17 19 17 19 17 18 18 17 19 SP D3 SD: 0.4887 c. M:-0.8652 c. 226: 18 19 19 18 20 18 20 18 19 19 18 20 SP D3 SD: 0.5340 c. M:-0.9644 c. 416: 33 35 35 33 37 33 37 33 35 35 33 37 SP D3 SD: 0.5032 c. M: 0.9014 c. 440: 35 37 37 35 39 35 39 35 37 37 35 39 SP D3 SD: 0.5008 c. M:-0.9162 c. 495: 40 41 42 39 44 39 44 39 42 41 40 44 SP SD: 0.4816 c. M: 0.9020 c. 507: 41 42 43 40 45 40 45 40 43 42 41 45 SP SD: 0.4800 c. M:-0.9477 c. 517: 41 44 43 41 46 41 46 41 43 44 41 46 SP SD: 0.4707 c. M: 0.9293 c. 529: 42 45 44 42 47 42 47 42 44 45 42 47 SP SD: 0.4506 c. M:-0.8440 c. 541: 43 46 45 43 48 43 48 43 45 46 43 48 SP SD: 0.4502 c. M:-0.8859 c. 553: 44 47 46 44 49 44 49 44 46 47 44 49 SP SD: 0.4670 c. M:-0.9260 c. 560: 45 47 47 44 50 44 50 44 47 47 45 50 SP SD: 0.4819 c. M: 0.8371 c. 562: 45 47 47 45 50 44 50 45 47 47 45 50 SP SD: 0.4425 c. M: 0.8591 c. 572: 46 48 48 45 51 45 51 45 48 48 46 51 SP SD: 0.4220 c. M: 0.7622 c. 584: 47 49 49 46 52 46 52 46 49 49 47 52 SP SD: 0.3773 c. M: 0.6903 c. 596: 48 50 50 47 53 47 53 47 50 50 48 53 SP SD: 0.3510 c. M: 0.6214 c. 608: 49 51 51 48 54 48 54 48 51 51 49 54 SP SD: 0.3443 c. M:-0.6168 c. 652: 52 55 55 51 58 52 58 51 55 55 52 58 SP SD: 0.3782 c. M: 0.6111 c. 664: 53 56 56 52 59 53 59 52 56 56 53 59 SP SD: 0.3540 c. M:-0.5365 c. 673: 54 56 57 53 60 53 60 53 57 56 54 60 SP SD: 0.3658 c. M: 0.7383 c. 676: 54 57 57 53 60 54 60 53 57 57 54 60 SP SD: 0.3455 c. M:-0.5686 c. 685: 55 57 58 54 61 54 61 54 58 57 55 61 SP SD: 0.3249 c. M: 0.6706 c. 697: 56 58 59 55 62 55 62 55 59 58 56 62 SP SD: 0.2987 c. M: 0.6053 c. 709: 57 59 60 56 63 56 63 56 60 59 57 63 SP SD: 0.2892 c. M:-0.5537 c. 762: 61 64 64 60 68 60 68 60 64 64 61 68 SP SD: 0.3071 c. M: 0.4521 c. 774: 62 65 65 61 69 61 69 61 65 65 62 69 SP SD: 0.2467 c. M: 0.3664 c. 786: 63 66 66 62 70 62 70 62 66 66 63 70 SP SD: 0.1933 c. M: 0.3191 c. 798: 64 67 67 63 71 63 71 63 67 67 64 71 SP SD: 0.1512 c. M: 0.2732 c. 810: 65 68 68 64 72 64 72 64 68 68 65 72 SP SD: 0.1291 c. M: 0.2286 c. 988: 79 83 83 78 88 78 88 78 83 83 79 88 SP SD: 0.1501 c. M: 0.2704 c. 1000: 80 84 84 79 89 79 89 79 84 84 80 89 SP SD: 0.0988 c. M: 0.1781 c. 1012: 81 85 85 80 90 80 90 80 85 85 81 90 SP SD: 0.0488 c. M: 0.0880 c. 1024: 82 86 86 81 91 81 91 81 86 86 82 91 SP SD: 0.0000 c. M:-0.0000 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: 0.5869 cents 3 x x x x 4 x x x 5 x x 6 S SD: 4.0608 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 7.2863 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 6.9149 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.1791 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 10.6087 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.6312 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 8.0206 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.1043 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 11.3004 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.3733 cents 13:14 x 15:16:17:18:19:21:22:23:24:26 SD: 9.6243 cents 14:15:16:17:18:19:20:21:22:24:25:26:28 S SD: 7.6615 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 5.1682 cents 16:17:18:19:20:21:23:24:25:27:28:30:32 SD: 4.9984 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 4.1302 cents 24:25:27:29:30:32:34:36:38:40:43:45:48 SD: 3.7624 cents 27:29:30:32:34:36:38:40:43:45:48:51:54 SD: 3.4906 cents 31:33:35:37:39:41:44:46:49:52:55:58:62 SD: 2.9072 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.0063 cents 48:51:54:57:60:64:68:72:76:81:85:90:96 SD: 1.7194 cents 50:53:56:59:63:67:70:75:79:84:89:94:100 SD: 1.6959 cents 58:61:65:69:73:77:82:87:92:97:103:109:116 SD: 1.3953 cents 66:70:74:78:83:88:93:99:105:111:117:124:132 SD: 1.3040 cents 68:72:76:81:85:91:96:102:108:114:121:128:136 SD: 1.0658 cents 74:78:83:88:93:99:104:111:117:124:132:139:148 SD: 0.9525 cents 86:91:96:102:108:115:121:129:136:144:153:162:172 SD: 0.8685 cents 90:95:101:107:113:120:127:135:143:151:160:169:180 SD: 0.6947 cents 117:124:131:139:147:156:165:175:185:196:208:220:234 SD: 0.6651 cents 118:125:132:140:148:157:166:177:187:198:210:222:236 SD: 0.6609 cents 122:129:137:145:153:163:172:183:193:205:217:229:244 SD: 0.5384 cents 156:165:175:185:196:208:220:234:247:262:278:293:312 SD: 0.5056 cents 158:167:177:188:198:211:223:237:250:265:281:297:316 SD: 0.4420 cents 176:186:197:209:221:235:248:264:279:295:313:331:352 SD: 0.3567 cents 192:203:215:228:241:256:271:288:304:322:342:361:384 SD: 0.3504 cents 208:220:233:247:261:278:293:312:329:349:370:391:416 SD: 0.3420 cents 224:237:251:266:281:299:316:336:355:376:398:421:448 SD: 0.3196 cents 240:254:269:285:301:320:338:360:380:403:427:451:480 SD: 0.2855 cents 266:281:298:316:334:355:375:399:421:446:473:500:532 SD: 0.2711 cents 267:282:299:317:335:356:376:400:423:448:475:502:534 SD: 0.2487 cents 283:299:317:336:355:378:399:424:448:475:503:532:566 SD: 0.2481 cents 298:315:334:354:374:398:420:447:472:500:530:560:596 SD: 0.2298 cents 315:333:353:374:395:420:444:472:499:529:560:592:630 SD: 0.2171 cents 367:388:411:436:460:490:517:550:581:616:653:690:734 SD: 0.2088 cents 389:411:436:462:488:519:548:583:616:653:692:732:778 SD: 0.1511 cents 491:519:550:583:616:655:692:736:777:824:873:923:982 SD: 0.1416 cents 523:553:586:621:656:698:737:784:828:878:930:984:1046 SD: 0.1275 cents 581:614:651:690:729:775:819:871:920:975:1034:1093:1162 SD: 0.1032 cents