Scala analysis: 12edo
PIAGUI
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 99.020 cents 99.020000 2: 198.040 cents 198.040000 3: 297.070 cents 297.070000 4: 396.090 cents 396.090000 5: 498.040 cents 498.040000 6: 600.000 cents 600.000000 7: 699.020 cents 699.020000 8: 798.050 cents 798.050000 9: 897.070 cents 897.070000 10: 996.090 cents 996.090000 11: 1098.050 cents 1098.050000 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 101.9500 cents 101.9500 1: 99.0200 cents 99.0200 2: 99.0200 cents 99.0200 3: 99.0300 cents 99.0300 4: 99.0200 cents 99.0200 5: 101.9500 cents 101.9500 6: 101.9600 cents 101.9600 7: 99.0200 cents 99.0200 8: 99.0300 cents 99.0300 9: 99.0200 cents 99.0200 10: 99.0200 cents 99.0200 11: 101.9600 cents 101.9600 12: 101.9500 cents 101.9500
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 6 99.02000 cents 1: 2 99.03000 cents 1: 2 101.95000 cents 1: 2 101.96000 cents 2: 2 198.04000 cents 2: 4 198.05000 cents 2: 2 200.97000 cents 2: 2 200.98000 cents 2: 2 203.91000 cents 3: 4 297.07000 cents 3: 1 299.99000 cents 3: 2 300.00000 cents 3: 1 300.01000 cents 3: 4 302.93000 cents 4: 2 396.09000 cents 4: 2 399.02000 cents 4: 2 399.03000 cents 4: 4 401.95000 cents 4: 2 401.96000 cents 5: 2 498.04000 cents 5: 2 498.05000 cents 5: 2 500.97000 cents 5: 6 500.98000 cents 6: 2 599.99000 cents 6: 8 600.00000 cents 6: 2 600.01000 cents 7: 6 699.02000 cents 7: 2 699.03000 cents 7: 2 701.95000 cents 7: 2 701.96000 cents 8: 2 798.04000 cents 8: 4 798.05000 cents 8: 2 800.97000 cents 8: 2 800.98000 cents 8: 2 803.91000 cents 9: 4 897.07000 cents 9: 1 899.99000 cents 9: 2 900.00000 cents 9: 1 900.01000 cents 9: 4 902.93000 cents 10: 2 996.09000 cents 10: 2 999.02000 cents 10: 2 999.03000 cents 10: 4 1001.95000 cents 10: 2 1001.96000 cents 11: 2 1098.04000 cents 11: 2 1098.05000 cents 11: 2 1100.97000 cents 11: 6 1100.98000 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.45455 = 49/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 99.0 198.0 297.1 396.1 498.0 600.0 699.0 798.1 897.1 996.1 1098.0 1200.0 99.0 : 99.0 198.1 297.1 399.0 501.0 600.0 699.0 798.0 897.1 999.0 1101.0 1200.0 198.0 : 99.0 198.1 300.0 402.0 501.0 600.0 699.0 798.1 900.0 1002.0 1101.0 1200.0 297.1 : 99.0 201.0 302.9 402.0 501.0 600.0 699.0 801.0 902.9 1001.9 1101.0 1200.0 396.1 : 101.9 203.9 302.9 402.0 501.0 600.0 702.0 803.9 902.9 1001.9 1101.0 1200.0 498.0 : 102.0 201.0 300.0 399.0 498.1 600.0 702.0 801.0 900.0 999.0 1098.0 1200.0 600.0 : 99.0 198.1 297.1 396.1 498.1 600.0 699.0 798.0 897.1 996.1 1098.0 1200.0 699.0 : 99.0 198.0 297.1 399.0 501.0 600.0 699.0 798.1 897.1 999.0 1101.0 1200.0 798.1 : 99.0 198.0 300.0 402.0 501.0 600.0 699.0 798.0 900.0 1001.9 1101.0 1200.0 897.1 : 99.0 201.0 302.9 402.0 501.0 600.0 699.0 801.0 902.9 1002.0 1101.0 1200.0 996.1 : 102.0 203.9 302.9 402.0 501.0 600.0 702.0 803.9 902.9 1002.0 1101.0 1200.0 1098.0: 101.9 201.0 300.0 399.0 498.0 600.0 701.9 801.0 900.0 999.0 1098.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 99.0200 .. 101.9600 cents 2.94000 cents 99.02000 cents 2: 198.0400 .. 203.9100 cents 5.87000 cents 96.08000 cents 3: 297.0700 .. 302.9300 cents 5.86000 cents 93.16000 cents 4: 396.0900 .. 401.9600 cents 5.87000 cents 93.16000 cents 5: 498.0400 .. 500.9800 cents 2.94000 cents 96.08000 cents 6: 599.9900 .. 600.0100 cents 0.02000 cents 99.01000 cents 7: 699.0200 .. 701.9600 cents 2.94000 cents 99.01000 cents 8: 798.0400 .. 803.9100 cents 5.87000 cents 96.08000 cents 9: 897.0700 .. 902.9300 cents 5.86000 cents 93.16000 cents 10: 996.0900 .. 1001.9600 cents 5.87000 cents 93.16000 cents 11: 1098.0400 .. 1100.9800 cents 2.94000 cents 96.08000 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 99.02000 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 101.96000 cents Average / Smallest step : 1.009897 Largest / Average step : 1.019600 Largest / Smallest step : 1.029691 Median interval of one step : 99.02500 cents, amount: 0 Most common interval of one step : 99.02000 cents, amount: 6 Least squares average step : 99.77152 cents, oct.: 1197.25828 cents Scale is strictly proper Scale is a mode of a 1636-tone equal temperament with octave 2/1 degrees: 135 270 405 540 679 818 953 1088 1223 1358 1497 1636 Least number of segments generator : 819 of 600.733 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 953 of 699.022 cents and inv. generated superset size: 1230 = 1218 more = 10250.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: AABACDABAADC Step pattern size order : AABACDABAADC Scale is a Constant Structure, by a margin of 93.16000 cents Scale diversity : 1.031399 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.960850 Rothenberg efficiency : 0.311851 redundancy: 0.688149 Efficiency x scale size : 3.742208 Number of different interval sizes : 49 = 4.45455 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 4.45455 = 49/11 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 0.01000 cents Most common intervals : 600.00000 cents & inv., amount: 8 Number of recognisable fifths : 12, average 700.0000 cents Best fifths form a closed circle Formal octave complements present : 2 = 16.6667% Limited transpositions : 6 Limited inverse transpositions : 4 10 Inversional symmetry on degrees : 2 5 8 11 -- 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: 2.3266 c. M:-3.9100 c. Twelve-tone Chromatic (1/11-comma) 122: 10 10 10 10 11 10 10 10 10 10 11 10 SP B ME SD: 2.0844 c. M:-3.5993 c. 134: 11 11 11 11 12 11 11 11 11 11 12 11 SP B ME SD: 1.8188 c. M:-3.4525 c. 146: 12 12 12 12 13 12 12 12 12 12 13 12 SP B ME SD: 1.6164 c. M:-3.3299 c. 154: 13 12 13 13 13 13 13 12 13 13 13 13 SP B ME SD: 1.7690 c. M: 3.2448 c. 158: 13 13 13 13 14 13 13 13 13 13 14 13 SP B ME SD: 1.4646 c. M:-3.2258 c. 166: 14 13 14 14 14 14 14 13 14 14 14 14 SP B ME SD: 1.6462 c. M: 2.8693 c. 170: 14 14 14 14 15 14 14 14 14 14 15 14 SP B ME SD: 1.3538 c. M:-3.1365 c. 178: 15 14 15 15 15 15 15 14 15 15 15 15 SP B ME SD: 1.5559 c. M: 2.5444 c. 182: 15 15 15 15 16 15 15 15 15 15 16 15 SP B ME SD: 1.2760 c. M:-3.0589 c. 190: 16 15 16 16 16 16 16 15 16 16 16 16 SP B ME SD: 1.4912 c. M: 2.2605 c. 194: 16 16 16 16 17 16 16 16 16 16 17 16 SP B ME SD: 1.2249 c. M:-2.9909 c. 202: 17 16 17 17 17 17 17 16 17 17 17 17 SP B ME SD: 1.4468 c. M: 2.0104 c. 206: 17 17 17 17 17 18 17 17 17 17 17 18 SP B ME SD: 1.1838 c. M: 2.9044 c. 218: 18 18 18 18 18 19 18 18 18 18 18 19 SP B ME SD: 1.0829 c. M: 2.6372 c. 230: 19 19 19 19 19 20 19 19 19 19 19 20 SP B ME SD: 1.0062 c. M: 2.3978 c. 234: 19 20 19 19 20 20 19 20 19 19 20 20 SP B D3 SD: 1.1776 c. M:-1.9600 c. 242: 20 20 20 20 20 21 20 20 20 20 20 21 SP B ME SD: 0.9507 c. M: 2.1822 c. 254: 21 21 21 21 21 22 21 21 21 21 21 22 SP B ME SD: 0.9138 c. M: 1.9870 c. 258: 21 22 21 21 22 22 21 22 21 21 22 22 SP B D3 SD: 1.0555 c. M:-1.9600 c. 266: 22 22 22 22 22 23 22 22 22 22 22 23 SP B ME SD: 0.8926 c. M: 1.8094 c. 278: 23 23 23 23 23 24 23 23 23 23 23 24 SP B ME SD: 0.8843 c. M: 1.6471 c. 290: 24 24 24 24 24 25 24 24 24 24 24 25 SP B ME SD: 0.8863 c. M: 1.4983 c. 292: 24 24 24 24 25 25 24 24 24 24 25 25 SP B D3 S SD: 0.9344 c. M: 1.5695 c. 302: 25 25 25 25 25 26 25 25 25 25 25 26 SP B ME SD: 0.8961 c. M: 1.3613 c. 304: 25 25 25 25 26 26 25 25 25 25 26 26 SP B D3 S SD: 0.8056 c. M: 1.3532 c. 316: 26 26 26 26 27 27 26 26 26 26 27 27 SP B D3 S SD: 0.6867 c. M: 1.1533 c. 328: 27 27 27 27 28 28 27 27 27 27 28 28 SP B D3 S SD: 0.5765 c. M: 0.9680 c. 340: 28 28 28 28 29 29 28 28 28 28 29 29 SP B D3 S SD: 0.4740 c. M: 0.7959 c. 352: 29 29 29 29 30 30 29 29 29 29 30 30 SP B D3 S SD: 0.3785 c. M: 0.6355 c. 364: 30 30 30 30 31 31 30 30 30 30 31 31 SP B D3 S SD: 0.2894 c. M: 0.4856 c. 376: 31 31 31 31 32 32 31 31 31 31 32 32 SP B D3 S SD: 0.2059 c. M: 0.3453 c. 388: 32 32 32 32 33 33 32 32 32 32 33 33 SP B D3 S SD: 0.1276 c. M: 0.2137 c. 400: 33 33 33 33 34 34 33 33 33 33 34 34 SP B D3 S SD: 0.0540 c. M: 0.0900 c. 412: 34 34 34 34 35 35 34 34 34 34 35 35 SP B D3 S SD: 0.0158 c. M:-0.0265 c. 1224: 101 101 101 101 104 104 101 101 101 101 104 104 SP B D3 S SD: 0.0079 c. M: 0.0116 c. 1636: 135 135 135 135 139 139 135 135 135 135 139 139 SP B D3 S SD: 0.0036 c. M: 0.0060 c. 2048: 169 169 169 169 174 174 169 169 169 169 174 174 SP B D3 S SD: 0.0037 c. M:-0.0069 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: 1.4675 cents 3 x x x x 4 x x x 5 x x 6 S SD: 4.2371 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 7.2781 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.3695 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.7931 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 10.2626 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.9721 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 8.0306 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.0828 cents 11 x 12:13:14:15:16 x 17:18:20:21:22 S SD: 11.2136 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 5.9612 cents 13:14 x 15:16:17:18:19:21:22:23:25:26 SD: 9.6737 cents 14:15:16:17:18:19:20:21:22:24:25:26:28 S SD: 7.5050 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 5.1380 cents 16:17:18:19:20:21:23:24:25:27:28:30:32 SD: 4.7720 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 4.1389 cents 24:25:27:28:30:32:34:36:38:40:43:45:48 SD: 4.0036 cents 26:28:29:31:33:35:37:39:41:44:46:49:52 SD: 3.7456 cents 27:29:30:32:34:36:38:40:43:45:48:51:54 SD: 3.2434 cents 31:33:35:37:39:41:44:46:49:52:55:58:62 SD: 2.6735 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.2271 cents 36:38:40:43:45:48:51:54:57:60:64:68:72 SD: 2.1648 cents 46:49:52:55:58:61:65:69:73:77:82:87:92 SD: 2.1496 cents 48:51:54:57:60:64:68:72:76:81:85:91:96 SD: 1.6666 cents 50:53:56:59:63:67:71:75:79:84:89:94:100 SD: 1.5305 cents 58:61:65:69:73:77:82:87:92:97:103:109:116 SD: 1.4507 cents 63:67:71:75:79:84:89:94:100:106:112:119:126 SD: 1.3080 cents 66:70:74:78:83:88:93:99:105:111:117:124:132 SD: 1.2480 cents 75:79:84:89:94:100:106:112:119:126:133:141:150 SD: 1.1330 cents 81:86:91:96:102:108:115:121:128:136:144:153:162 SD: 1.0495 cents 82:87:92:97:103:109:116:123:130:138:146:155:164 SD: 0.9594 cents 85:90:95:101:107:113:120:127:135:143:151:160:170 SD: 0.9097 cents 90:95:101:107:113:120:127:135:143:151:160:170:180 SD: 0.7845 cents 106:112:119:126:133:141:150:159:168:178:188:200:212 SD: 0.7405 cents 116:123:130:138:146:155:164:174:184:195:206:219:232 SD: 0.6434 cents 123:130:138:146:155:164:174:184:195:207:219:232:246 SD: 0.6298 cents 133:141:149:158:167:177:188:199:211:223:236:251:266 SD: 0.5516 cents 140:148:157:166:176:187:198:210:222:235:249:264:280 SD: 0.4692 cents 167:177:187:198:210:223:236:250:265:280:297:315:334 SD: 0.4560 cents 171:181:192:203:215:228:242:256:271:287:304:322:342 SD: 0.3246 cents 225:238:252:267:283:300:318:337:357:378:400:424:450 SD: 0.3008 cents 237:251:266:281:298:316:335:355:376:398:421:447:474 SD: 0.2977 cents 256:271:287:304:322:341:362:383:406:430:455:483:512 SD: 0.2458 cents 273:289:306:324:343:364:386:409:433:458:485:515:546 SD: 0.2107 cents 374:396:419:444:470:499:529:560:593:628:665:705:748 SD: 0.1664 cents 396:419:444:470:498:528:560:593:628:665:704:747:792 SD: 0.1444 cents 471:499:528:559:592:628:666:705:747:791:837:888:942 SD: 0.1409 cents 495:524:555:588:622:660:700:741:785:831:880:933:990 SD: 0.1352 cents 545:577:611:647:685:727:771:816:864:915:969:1028:1090 SD: 0.1068 cents 577:611:647:685:725:769:816:864:915:969:1026:1088:1154 SD: 0.1060 cents