Scala analysis: parapyth12
A triple Fokker block of the 2.3.7.11.13 temperament called "parapyth" (TOP tuning)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 58.236 cents 58.236040 2: 206.959 cents 206.958660 3: 265.195 cents 265.194710 4: 413.917 cents 413.917330 5: 472.153 cents 472.153370 6: 554.510 cents 554.509650 7: 703.232 cents 703.232270 8: 761.468 cents 761.468320 9: 910.191 cents 910.190940 10: 968.427 cents 968.426980 11: 1117.150 cents 1117.149600 12: 1199.506 cents 1199.505880
SHOW/INTERVAL
0: 82.3563 cents 82.3563 1: 58.2360 cents 58.2360 2: 148.7226 cents 148.7226 3: 58.2361 cents 58.2361 4: 148.7226 cents 148.7226 5: 58.2360 cents 58.2360 6: 82.3563 cents 82.3563 7: 148.7226 cents 148.7226 8: 58.2361 cents 58.2361 9: 148.7226 cents 148.7226 10: 58.2360 cents 58.2360 11: 148.7226 cents 148.7226 12: 82.3563 cents 82.3563
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 58.23604 cents 1: 2 82.35628 cents 1: 5 148.72262 cents 2: 2 140.59232 cents 2: 8 206.95866 cents 2: 2 231.07890 cents 3: 3 265.19471 cents 3: 6 289.31494 cents 3: 3 355.68129 cents 4: 4 347.55099 cents 4: 4 413.91733 cents 4: 4 438.03756 cents 5: 1 472.15337 cents 5: 10 496.27361 cents 5: 1 562.63995 cents 6: 6 554.50965 cents 6: 6 644.99623 cents 7: 1 636.86593 cents 7: 10 703.23227 cents 7: 1 727.35251 cents 8: 4 761.46832 cents 8: 4 785.58855 cents 8: 4 851.95490 cents 9: 3 843.82459 cents 9: 6 910.19094 cents 9: 3 934.31117 cents 10: 2 968.42698 cents 10: 8 992.54722 cents 10: 2 1058.91356 cents 11: 5 1050.78326 cents 11: 2 1117.14960 cents 11: 5 1141.26984 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 2.90909 = 32/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 58.2 207.0 265.2 413.9 472.2 554.5 703.2 761.5 910.2 968.4 1117.1 1199.5 58.2 : 148.7 207.0 355.7 413.9 496.3 645.0 703.2 852.0 910.2 1058.9 1141.3 1199.5 207.0 : 58.2 207.0 265.2 347.6 496.3 554.5 703.2 761.5 910.2 992.5 1050.8 1199.5 265.2 : 148.7 207.0 289.3 438.0 496.3 645.0 703.2 852.0 934.3 992.5 1141.3 1199.5 413.9 : 58.2 140.6 289.3 347.6 496.3 554.5 703.2 785.6 843.8 992.5 1050.8 1199.5 472.2 : 82.4 231.1 289.3 438.0 496.3 645.0 727.4 785.6 934.3 992.5 1141.3 1199.5 554.5 : 148.7 207.0 355.7 413.9 562.6 645.0 703.2 852.0 910.2 1058.9 1117.1 1199.5 703.2 : 58.2 207.0 265.2 413.9 496.3 554.5 703.2 761.5 910.2 968.4 1050.8 1199.5 761.5 : 148.7 207.0 355.7 438.0 496.3 645.0 703.2 852.0 910.2 992.5 1141.3 1199.5 910.2 : 58.2 207.0 289.3 347.6 496.3 554.5 703.2 761.5 843.8 992.5 1050.8 1199.5 968.4 : 148.7 231.1 289.3 438.0 496.3 645.0 703.2 785.6 934.3 992.5 1141.3 1199.5 1117.1: 82.4 140.6 289.3 347.6 496.3 554.5 636.9 785.6 843.8 992.5 1050.8 1199.5 1199.5
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 58.2360 .. 148.7226 cents 90.48658 cents 58.23604 cents 2: 140.5923 .. 231.0789 cents 90.48658 cents -8.13030 cents 3: 265.1947 .. 355.6813 cents 90.48658 cents 34.11581 cents 4: 347.5510 .. 438.0376 cents 90.48657 cents -8.13030 cents 5: 472.1534 .. 562.6399 cents 90.48658 cents 34.11581 cents 6: 554.5096 .. 644.9962 cents 90.48658 cents -8.13030 cents 7: 636.8659 .. 727.3525 cents 90.48658 cents -8.13030 cents 8: 761.4683 .. 851.9549 cents 90.48658 cents 34.11581 cents 9: 843.8246 .. 934.3112 cents 90.48658 cents -8.13031 cents 10: 968.4270 .. 1058.9136 cents 90.48658 cents 34.11581 cents 11: 1050.7833 .. 1141.2698 cents 90.48658 cents -8.13030 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 58.23604 cents, class 1 Average step (divided formal octave): 99.9588 cents Largest one step interval : 148.72262 cents Average / Smallest step : 1.716443 Largest / Average step : 1.487839 Largest / Smallest step : 2.553790 Median interval of one step : 82.35628 cents, amount: 2 Least squares average step : 98.74509 cents, oct.: 1184.94108 cents Scale is not proper Scale is 3-distributional even Step pattern alph. order: ABABACBABABC Step pattern size order : SLSLSMLSLSLM Scale is a Constant Structure, by a margin of 8.13030 cents Scale diversity : 1.299116 Lumma stability : 0.210866 Lumma impropriety factor : 0.040668 Rothenberg efficiency : 0.514153 redundancy: 0.485847 Efficiency x scale size : 6.169841 Number of different interval sizes : 32 = 2.90909 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 2.90909 = 32/11 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 8.13030 cents Most common intervals : 496.27361 cents & inv., amount: 10 Most common triad is 0.0 496.274 703.232 cents, amount: 8 Number of recognisable fifths : 10, average 703.2323 cents Number of recognisable fourths : 10, average 496.2736 cents Best fifths form a closed circle Formal octave complements present : 1 = 8.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 8-9 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 27.1825 c. M:-45.2433 c. Twelve-tone Chromatic (1/11-comma) 15: 1 2 0 2 1 1 2 1 1 1 2 1 P D3 SD: 20.8755 c. M:-38.2023 c. 16: 1 2 1 2 0 1 2 1 2 1 2 1 N T3 SD: 21.6641 c. M:-35.8974 c. 17: 1 2 1 2 1 1 2 1 2 1 2 1 P M ME SD: 12.6269 c. M:-21.7608 c. Supra-12 26: 1 3 2 3 1 2 3 1 4 1 3 2 N SD: 12.3392 c. M: 23.3109 c. 28: 1 4 1 4 1 2 3 2 3 2 3 2 N SD: 10.7611 c. M: 17.8003 c. 29: 1 4 1 4 1 2 4 1 4 1 4 2 N D3 SD: 12.0110 c. M: 17.1684 c. 30: 1 4 2 3 2 2 4 1 4 1 4 2 N SD: 10.5275 c. M: 18.2525 c. 32: 2 4 1 4 2 2 4 1 4 2 4 2 N SD: 10.5102 c. M:-17.9487 c. 33: 2 4 1 4 2 2 4 2 4 2 4 2 N SD: 9.8311 c. M:-14.4613 c. 35: 2 4 2 4 2 2 5 1 5 1 5 2 N SD: 9.6503 c. M:-16.4713 c. 36: 2 4 2 4 2 3 4 2 4 2 4 3 SP D3 SD: 8.9306 c. M: 17.6025 c. 38: 2 5 1 5 2 3 4 2 5 2 4 3 P SD: 8.9265 c. M:-14.0029 c. 40: 2 5 2 5 2 2 5 2 5 2 5 3 N SD: 8.7220 c. M: 14.7320 c. 41: 2 5 2 5 2 3 5 2 5 2 5 3 P D3 SD: 2.8261 c. M: 5.4124 c. 58: 3 7 3 7 3 4 7 3 7 3 7 4 P D3 SD: 2.6204 c. M:-3.8810 c. 87: 4 11 4 11 4 6 11 4 11 4 11 6 N D3 SD: 2.2677 c. M: 3.3810 c. 99: 5 12 5 12 5 7 12 5 12 5 12 7 P D3 SD: 1.6589 c. M:-2.8365 c. 104: 5 13 5 13 5 7 13 5 13 5 13 7 N D3 SD: 0.7986 c. M:-1.6203 c. 145: 7 18 7 18 7 10 18 7 18 7 18 10 N D3 SD: 0.3596 c. M: 0.6235 c. 249: 12 31 12 31 12 17 31 12 31 12 31 17 N D3 SD: 0.3060 c. M: 0.5210 c. 348: 17 43 17 43 17 24 43 17 43 17 43 24 N D3 SD: 0.2530 c. M:-0.4342 c. 394: 19 49 19 49 19 27 49 19 49 19 49 27 N D3 SD: 0.2557 c. M: 0.4232 c. 452: 22 56 22 56 22 31 56 22 56 22 56 31 N D3 SD: 0.1305 c. M:-0.2184 c. 597: 29 74 29 74 29 41 74 29 74 29 74 41 N D3 SD: 0.0206 c. M:-0.0358 c. 1936: 94 240 94 240 94 133 240 94 240 94 240 133 N D3 SD: 0.0245 c. M: 0.0478 c. 2040: 99 253 99 253 99 140 253 99 253 99 253 140 N D3 SD: 0.0207 c. M:-0.0372 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.4941 cents 2 x x x x x x 3 x x x x 4 S SD: 0.6848 cents 3 x x x x 4 x x x 5 x x 6 S SD: 12.1926 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 6.9101 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 18.4104 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 12.8424 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 12.8051 cents 8 x 9 x 10 x 11:12 x x 14:15:16 S SD: 5.7456 cents 9 x 10 x 11:12 x x 14:15:16:17:18 S SD: 10.7535 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 10.3267 cents 11 x 12:13:14 x 15 x 17 x 19:21:22 SD: 8.5066 cents 12 x x 14:15:16:17:18:19:20:21:23:24 SD: 7.5512 cents 13:14 x 15 x 17:18 x 20:22:23:25:26 SD: 8.7454 cents 14:15:16 x 18 x 19:21:22:24 x 27:28 SD: 9.1713 cents 15:16:17 x 19:20:21 x 23:25:26:29:30 SD: 8.0037 cents 16:17:18:19:20:21:22:24:25:27:28:31:32 SD: 5.8532 cents 17:18:19:20 x 22:23 x 26:29:30:32:34 SD: 7.3171 cents 18:19:20:21:23:24:25:27:28:30:31:34:36 SD: 5.6049 cents 19:20:21:22:24:25:26:29:30:32:33:36:38 SD: 5.5618 cents 20:21 x 23:25:26:28:30:31:34:35:38:40 SD: 5.1524 cents 21:22:24 x 27:28:29:32:33:36:37:40:42 SD: 5.7597 cents 22:23:25:26:28:29:30:33:34:37:38:42:44 SD: 3.8710 cents 23:24:26:27:29:30:32:35:36:39:40:44:46 SD: 3.6722 cents 26:27:29:30:33:34:36:39:40:44:45:50:52 SD: 3.3728 cents 29:30:33:34:37:38:40:44:45:49:51:55:58 SD: 2.6066 cents 32:33:36:37:41:42:44:48:50:54:56:61:64 SD: 2.0625 cents 48:50:54:56:61:63:66:72:75:81:84:92:96 SD: 1.6858 cents 54:56:61:63:69:71:74:81:84:91:94:103:108 SD: 1.6065 cents 55:57:62:64:70:72:76:83:85:93:96:105:110 SD: 1.3596 cents 56:58:63:65:71:74:77:84:87:95:98:107:112 SD: 1.2777 cents 64:66:72:75:81:84:88:96:99:108:112:122:128 SD: 1.2667 cents 78:81:88:91:99:102:107:117:121:132:136:149:156 SD: 1.2385 cents 79:82:89:92:100:104:109:119:123:134:138:151:158 SD: 1.2011 cents 80:83:90:93:102:105:110:120:124:135:140:153:160 SD: 1.0995 cents 84:87:95:98:107:110:116:126:130:142:147:160:168 SD: 1.0336 cents 85:88:96:99:108:112:117:128:132:144:149:162:170 SD: 0.8259 cents 96:99:108:112:122:126:132:144:149:162:168:183:192 SD: 0.7013 cents 116:120:131:135:147:152:160:174:180:196:203:221:232 SD: 0.6785 cents 119:123:134:139:151:156:164:179:185:201:208:227:238 SD: 0.6564 cents 127:131:143:148:161:167:175:191:197:215:222:242:254 SD: 0.6184 cents 140:145:158:163:178:184:193:210:217:237:245:267:280 SD: 0.4782 cents 156:161:176:182:198:205:215:234:242:264:273:297:312 SD: 0.4727 cents 175:181:197:204:222:230:241:263:272:296:306:334:350 SD: 0.3940 cents 181:187:204:211:230:238:249:272:281:306:317:345:362 SD: 0.3834 cents 204:211:230:238:259:268:281:306:317:345:357:389:408 SD: 0.2492 cents 259:268:292:302:329:340:357:389:402:438:453:494:518 SD: 0.2133 cents 315:326:355:367:400:414:434:473:489:533:551:601:630 SD: 0.1950 cents 355:367:400:414:451:466:489:533:551:601:621:677:710 SD: 0.1948 cents 411:425:463:479:522:540:566:617:638:695:719:784:822 SD: 0.1379 cents 471:487:531:549:598:619:649:707:731:797:824:898:942 SD: 0.1364 cents 503:520:567:586:639:661:693:755:781:851:880:959:1006 SD: 0.1286 cents