Scala analysis: piaguilike2
Like Mario Pizarro's Piagui: steps of (9/8)^1/2 and (128/81)^1/8
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 99.023 cents 99.022500 2: 198.045 cents 198.045000 3: 297.067 cents 297.067500 4: 396.090 cents 396.090000 5: 4/3 498.044999 perfect fourth 6: 600.000 cents 600.000000 7: 699.023 cents 699.022500 8: 798.045 cents 798.045000 9: 897.067 cents 897.067500 10: 16/9 996.089998 Pythagorean minor seventh 11: 1098.045 cents 1098.045000 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 101.9550 cents 101.9550 1: 99.0225 cents 99.0225 2: 99.0225 cents 99.0225 3: 99.0225 cents 99.0225 4: 99.0225 cents 99.0225 5: 101.9550 cents 101.9550 6: 101.9550 cents 101.9550 7: 99.0225 cents 99.0225 8: 99.0225 cents 99.0225 9: 99.0225 cents 99.0225 10: 99.0225 cents 99.0225 11: 101.9550 cents 101.9550 12: 101.9550 cents 101.9550
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 8 99.02250 cents 1: 4 101.95500 cents 2: 6 198.04500 cents 2: 4 200.97750 cents 2: 2 203.91000 cents 3: 4 297.06750 cents 3: 4 300.00000 cents 3: 4 302.93250 cents 4: 2 396.09000 cents 4: 4 399.02250 cents 4: 6 401.95500 cents 5: 4 4/3 498.045 cents perfect fourth 5: 8 500.97750 cents 6: 12 600.00000 cents 7: 8 699.02250 cents 7: 4 701.95500 cents 8: 6 798.04500 cents 8: 4 800.97750 cents 8: 2 803.91000 cents 9: 4 897.06750 cents 9: 4 900.00000 cents 9: 4 902.93250 cents 10: 2 16/9 996.090 cents Pythagorean minor seventh 10: 4 999.02250 cents 10: 6 1001.95500 cents 11: 4 1098.04500 cents 11: 8 1100.97750 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 2.45455 = 27/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 99.0 198.0 297.1 396.1 498.0 600.0 699.0 798.0 897.1 996.1 1098.0 1200.0 99.0 : 99.0 198.0 297.1 399.0 501.0 600.0 699.0 798.0 897.1 999.0 1101.0 1200.0 198.0 : 99.0 198.0 300.0 402.0 501.0 600.0 699.0 798.0 900.0 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 1002.0 1101.0 1200.0 396.1 : 102.0 203.9 302.9 402.0 501.0 600.0 702.0 803.9 902.9 1002.0 1101.0 1200.0 498.0 : 102.0 201.0 300.0 399.0 498.0 600.0 702.0 801.0 900.0 999.0 1098.0 1200.0 600.0 : 99.0 198.0 297.1 396.1 498.0 600.0 699.0 798.0 897.1 996.1 1098.0 1200.0 699.0 : 99.0 198.0 297.1 399.0 501.0 600.0 699.0 798.0 897.1 999.0 1101.0 1200.0 798.0 : 99.0 198.0 300.0 402.0 501.0 600.0 699.0 798.0 900.0 1002.0 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: 102.0 201.0 300.0 399.0 498.0 600.0 702.0 801.0 900.0 999.0 1098.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 99.0225 .. 101.9550 cents 2.93250 cents 99.02250 cents 2: 198.0450 .. 203.9100 cents 5.86500 cents 96.09000 cents 3: 297.0675 .. 302.9325 cents 5.86500 cents 93.15750 cents 4: 396.0900 .. 401.9550 cents 5.86500 cents 93.15750 cents 5: 498.0450 .. 500.9775 cents 2.93250 cents 96.09000 cents 6: 600.0000 .. 600.0000 cents 1/1, 0.0000 cents 99.02250 cents 7: 699.0225 .. 701.9550 cents 2.93250 cents 99.02250 cents 8: 798.0450 .. 803.9100 cents 5.86500 cents 96.09000 cents 9: 897.0675 .. 902.9325 cents 5.86500 cents 93.15750 cents 10: 996.0900 .. 1001.9550 cents 5.86500 cents 93.15750 cents 11: 1098.0450 .. 1100.9775 cents 2.93250 cents 96.09000 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 99.02250 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 101.95500 cents Average / Smallest step : 1.009872 Largest / Average step : 1.019550 Largest / Smallest step : 1.029614 Median interval of one step : 99.02250 cents, amount: 8 Most common interval of one step : 99.02250 cents, amount: 8 Least squares average step : 99.77142 cents, oct.: 1197.25698 cents Scale is strictly proper Scale has 2 repeating blocks of 6 notes Scale is 3-distributional even 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: AAAABBAAAABB Step pattern size order : SSSSLLSSSSLL Scale is a Constant Structure, by a margin of 93.15750 cents Scale diversity : 1.031353 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.960900 Rothenberg efficiency (ambiguous key): 0.327393 redundancy: 0.672607 Efficiency x scale size : 3.928716 Number of different interval sizes : 27 = 2.45455 / class Number of one step interval sizes : 2 Highest interval variety : 3 Mean interval variety : 2.45455 = 27/11 Median interval variety : 3 Lowest interval variety : 1 Smallest interval difference : 2.93250 cents Most common intervals : 600.00000 cents & inv., amount: 12 Number of recognisable fifths : 12, average 700.0000 cents Scale contains two identical disjunct hexachords Scale is a well-temperament. It has 2 different sizes of fifth 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 : 3 (not all pitches rational)
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 2.3269 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: 2.0841 c. M:-3.5943 c. 134: 11 11 11 11 12 11 11 11 11 11 12 11 SP B ME SD: 1.8186 c. M:-3.4475 c. 146: 12 12 12 12 13 12 12 12 12 12 13 12 SP B ME SD: 1.6162 c. M:-3.3249 c. 154: 13 12 13 13 13 13 13 12 13 13 13 13 SP B ME SD: 1.7682 c. M: 3.2398 c. 158: 13 13 13 13 14 13 13 13 13 13 14 13 SP B ME SD: 1.4644 c. M:-3.2208 c. 160: 13 13 14 13 13 14 13 13 14 13 13 14 SP B ME S SD: 2.2895 c. M: 3.0450 c. 164: 14 13 14 13 14 14 14 13 14 13 14 14 SP B D3 SD: 1.9008 c. M:-3.4165 c. 166: 14 13 14 14 14 14 14 13 14 14 14 14 SP B ME SD: 1.6455 c. M: 2.8643 c. 170: 14 14 14 14 15 14 14 14 14 14 15 14 SP B ME SD: 1.3536 c. M:-3.1315 c. 178: 15 14 15 15 15 15 15 14 15 15 15 15 SP B ME SD: 1.5552 c. M: 2.5394 c. 182: 15 15 15 15 16 15 15 15 15 15 16 15 SP B ME SD: 1.2760 c. M:-3.0539 c. 190: 16 15 16 16 16 16 16 15 16 16 16 16 SP B ME SD: 1.4906 c. M: 2.2555 c. 194: 16 16 16 16 17 16 16 16 16 16 17 16 SP B ME SD: 1.2248 c. M:-2.9859 c. 202: 17 16 17 17 17 17 17 16 17 17 17 17 SP B ME SD: 1.4462 c. M: 2.0054 c. 206: 17 17 17 17 17 18 17 17 17 17 17 18 SP B ME SD: 1.1838 c. M: 2.8994 c. 218: 18 18 18 18 18 19 18 18 18 18 18 19 SP B ME SD: 1.0829 c. M: 2.6322 c. 230: 19 19 19 19 19 20 19 19 19 19 19 20 SP B ME SD: 1.0062 c. M: 2.3928 c. 234: 19 20 19 19 20 20 19 20 19 19 20 20 SP B D3 SD: 1.1783 c. M:-1.9550 c. 242: 20 20 20 20 20 21 20 20 20 20 20 21 SP B ME SD: 0.9509 c. M: 2.1772 c. 254: 21 21 21 21 21 22 21 21 21 21 21 22 SP B ME SD: 0.9140 c. M: 1.9820 c. 258: 21 22 21 21 22 22 21 22 21 21 22 22 SP B D3 SD: 1.0563 c. M:-1.9550 c. 266: 22 22 22 22 22 23 22 22 22 22 22 23 SP B ME SD: 0.8928 c. M: 1.8044 c. 278: 23 23 23 23 23 24 23 23 23 23 23 24 SP B ME SD: 0.8846 c. M: 1.6421 c. 290: 24 24 24 24 24 25 24 24 24 24 24 25 SP B ME SD: 0.8865 c. M: 1.4933 c. 292: 24 24 24 24 25 25 24 24 24 24 25 25 SP B D3 S SD: 0.9340 c. M: 1.5695 c. 302: 25 25 25 25 25 26 25 25 25 25 25 26 SP B ME SD: 0.8964 c. M: 1.3563 c. 304: 25 25 25 25 26 26 25 25 25 25 26 26 SP B D3 S SD: 0.8053 c. M: 1.3532 c. 316: 26 26 26 26 27 27 26 26 26 26 27 27 SP B D3 S SD: 0.6863 c. M: 1.1533 c. 328: 27 27 27 27 28 28 27 27 27 27 28 28 SP B D3 S SD: 0.5761 c. M: 0.9680 c. 340: 28 28 28 28 29 29 28 28 28 28 29 29 SP B D3 S SD: 0.4736 c. M: 0.7959 c. 352: 29 29 29 29 30 30 29 29 29 29 30 30 SP B D3 S SD: 0.3782 c. M: 0.6355 c. 364: 30 30 30 30 31 31 30 30 30 30 31 31 SP B D3 S SD: 0.2890 c. M: 0.4856 c. 376: 31 31 31 31 32 32 31 31 31 31 32 32 SP B D3 S SD: 0.2055 c. M: 0.3453 c. 388: 32 32 32 32 33 33 32 32 32 32 33 33 SP B D3 S SD: 0.1272 c. M: 0.2137 c. 400: 33 33 33 33 34 34 33 33 33 33 34 34 SP B D3 S SD: 0.0536 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: 0.0069 c. M: 0.0116 c. 1636: 135 135 135 135 139 139 135 135 135 135 139 139 SP B D3 S SD: 0.0012 c. M: 0.0020 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: 1.4663 cents 3 x x x x 4 x x x 5 x x 6 S SD: 4.2363 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 7.2780 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.3702 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.7921 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 10.2621 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.9724 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 8.0304 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.0837 cents 11 x 12:13:14:15:16 x 17:18:20:21:22 S SD: 11.2134 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 5.9611 cents 13:14 x 15:16:17:18:19:21:22:23:25:26 SD: 9.6741 cents 14:15:16:17:18:19:20:21:22:24:25:26:28 S SD: 7.5046 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: 4.7719 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 4.1388 cents 24:25:27:28:30:32:34:36:38:40:43:45:48 SD: 4.0034 cents 26:28:29:31:33:35:37:39:41:44:46:49:52 SD: 3.7454 cents 27:29:30:32:34:36:38:40:43:45:48:51:54 SD: 3.2435 cents 31:33:35:37:39:41:44:46:49:52:55:58:62 SD: 2.6734 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.2268 cents 36:38:40:43:45:48:51:54:57:60:64:68:72 SD: 2.1651 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: 1.5299 cents 58:61:65:69:73:77:82:87:92:97:103:109:116 SD: 1.4508 cents 63:67:71:75:79:84:89:94:100:106:112:119:126 SD: 1.3079 cents 66:70:74:78:83:88:93:99:105:111:117:124:132 SD: 1.2478 cents 75:79:84:89:94:100:106:112:119:126:133:141:150 SD: 1.1331 cents 81:86:91:96:102:108:115:121:128:136:144:153:162 SD: 1.0493 cents 82:87:92:97:103:109:116:123:130:138:146:155:164 SD: 0.9595 cents 85:90:95:101:107:113:120:127:135:143:151:160:170 SD: 0.9102 cents 90:95:101:107:113:120:127:135:143:151:160:170:180 SD: 0.7848 cents 106:112:119:126:133:141:150:159:168:178:188:200:212 SD: 0.7406 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: 0.6300 cents 133:141:149:158:167:177:188:199:211:223:236:251:266 SD: 0.5520 cents 140:148:157:166:176:187:198:210:222:235:249:264:280 SD: 0.4689 cents 167:177:187:198:210:223:236:250:265:280:297:315:334 SD: 0.4559 cents 171:181:192:203:215:228:242:256:271:287:304:322:342 SD: 0.3240 cents 225:238:252:267:283:300:318:337:357:378:400:424:450 SD: 0.3012 cents 237:251:266:281:298:316:335:355:376:398:421:447:474 SD: 0.2975 cents 256:271:287:304:322:341:362:383:406:430:455:483:512 SD: 0.2465 cents 273:289:306:324:343:364:386:409:433:458:485:515:546 SD: 0.2108 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: 0.1448 cents 471:499:528:559:592:628:666:705:747:791:837:888:942 SD: 0.1410 cents 495:524:555:588:622:660:700:741:785:831:880:933:990 SD: 0.1353 cents 545:577:611:647:685:727:771:816:864:915:969:1028:1090 SD: 0.1067 cents 577:611:647:685:725:769:816:864:915:969:1026:1088:1154 SD: 0.1063 cents