Scala analysis: parizekmic9
Parizekmic[9] (676/675 tempering), POTE tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 204.443 cents 204.443090 2: 248.889 cents 248.889230 3: 453.332 cents 453.332320 4: 497.778 cents 497.778450 5: 702.222 cents 702.221550 6: 746.668 cents 746.667680 7: 951.111 cents 951.110770 8: 995.557 cents 995.556910 9: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 204.4431 cents 204.4431 1: 204.4431 cents 204.4431 2: 44.4461 cents 44.4461 3: 204.4431 cents 204.4431 4: 44.4461 cents 44.4461 5: 204.4431 cents 204.4431 6: 44.4461 cents 44.4461 7: 204.4431 cents 204.4431 8: 44.4461 cents 44.4461 9: 204.4431 cents 204.4431
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 44.44614 cents 1: 5 204.44309 cents 2: 8 248.88923 cents 2: 1 408.88618 cents 3: 3 293.33536 cents 3: 6 453.33232 cents 4: 7 497.77845 cents 4: 2 657.77541 cents 5: 2 542.22459 cents 5: 7 702.22155 cents 6: 6 746.66768 cents 6: 3 906.66464 cents 7: 1 791.11382 cents 7: 8 951.11077 cents 8: 5 995.55691 cents 8: 4 1155.55386 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 0.0 : 204.4 248.9 453.3 497.8 702.2 746.7 951.1 995.6 1200.0 204.4 : 44.4 248.9 293.3 497.8 542.2 746.7 791.1 995.6 1200.0 248.9 : 204.4 248.9 453.3 497.8 702.2 746.7 951.1 1155.6 1200.0 453.3 : 44.4 248.9 293.3 497.8 542.2 746.7 951.1 995.6 1200.0 497.8 : 204.4 248.9 453.3 497.8 702.2 906.7 951.1 1155.6 1200.0 702.2 : 44.4 248.9 293.3 497.8 702.2 746.7 951.1 995.6 1200.0 746.7 : 204.4 248.9 453.3 657.8 702.2 906.7 951.1 1155.6 1200.0 951.1 : 44.4 248.9 453.3 497.8 702.2 746.7 951.1 995.6 1200.0 995.6 : 204.4 408.9 453.3 657.8 702.2 906.7 951.1 1155.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 44.4461 .. 204.4431 cents 159.99695 cents 44.44614 cents 2: 248.8892 .. 408.8862 cents 159.99695 cents 44.44614 cents 3: 293.3354 .. 453.3323 cents 159.99696 cents -115.55082 cents 4: 497.7785 .. 657.7754 cents 159.99696 cents 44.44613 cents 5: 542.2246 .. 702.2215 cents 159.99696 cents -115.55082 cents 6: 746.6677 .. 906.6646 cents 159.99696 cents 44.44613 cents 7: 791.1138 .. 951.1108 cents 159.99695 cents -115.55082 cents 8: 995.5569 .. 1155.5539 cents 159.99695 cents 44.44614 cents
SHOW DATA
Number of notes : 9 -- Interval properties -- Smallest interval : 44.44613 cents, class 1 Average step (divided formal octave): 133.3333 cents Largest one step interval : 204.44309 cents Average / Smallest step : 2.999886 Largest / Average step : 1.533323 Largest / Smallest step : 4.599795 Median interval of one step : 204.44309 cents, amount: 5 Most common interval of one step : 204.44309 cents, amount: 5 Least squares average step : 131.46202 cents, oct.: 1183.15822 cents Scale is not proper Scale has Myhill's property chromas: 159.99695 cents and 115.55081 cents, ratio: 1.384646 generators: 2 of 248.88923 cents and 7 of 951.11077 cents ET pair of linear temperament : 24&29 Scale is distributional even Scale is a mode of a 135-tone equal temperament with octave 2/1 degrees: 23 28 51 56 79 84 107 112 135 generators: 28 and 107 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABABABA Step pattern size order : LSLSLSLSL Interval vector is [ 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 8 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 6 0 0 0 0 7 0 0 0 0 2 0 0 0 0 0 0 ] Scale is a Constant Structure, by a margin of 44.44613 cents Scale diversity : 1.150460 Lumma stability : 0.222231 Lumma impropriety factor : 0.288877 Rothenberg efficiency : 0.740741 redundancy: 0.259259 Efficiency x scale size : 6.666667 Number of different interval sizes : 16 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 44.44613 cents Most common intervals : 248.88923 cents & inv., amount: 8 Scale is a chain of 4 triads 0.0 248.889 497.778 cents Most common triad is 0.0 248.889 951.111 cents, amount: 7 Number of recognisable fifths : 7, average 702.2215 cents Scale contains two identical conjunct pentachords Formal octave complements present : 9 = 100.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 4-5 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
9: 2 0 1 1 1 1 1 0 2 N T3 I SD: 42.9374 c. M: 62.2236 c. 10: 2 0 2 0 2 0 2 0 2 N M DE I SD: 22.9519 c. M: 35.5569 c. 14: 2 1 2 1 2 1 2 1 2 P M ME I SD: 21.3108 c. M: 33.0145 c. Semaphore-9 16: 3 0 3 1 2 1 3 0 3 N I SD: 19.6943 c. M: 27.2216 c. 18: 3 1 3 0 4 0 3 1 3 N I SD: 18.1446 c. M: 31.1118 c. 19: 3 1 3 1 3 1 3 1 3 N M DE I SD: 9.6627 c. M: 14.9694 c. Semaphore-9 24: 4 1 4 1 4 1 4 1 4 N M DE I SD: 2.8680 c. M: 4.4431 c. de Vries 9-tone, Semaphore-9 29: 5 1 5 1 5 1 5 1 5 N M DE I SD: 1.5837 c. M: 2.4535 c. Semaphore-9 53: 9 2 9 2 9 2 9 2 9 N M DE I SD: 0.4322 c. M: 0.6695 c. 82: 14 3 14 3 14 3 14 3 14 N M DE I SD: 0.2808 c. M: 0.4350 c. 135: 23 5 23 5 23 5 23 5 23 N M DE I SD: 0.0009 c. M: 0.0014 c.
FIT/HARMONIC
1 x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x x x 4 S SD: 0.1333 cents 3 x x x 4 x x 5 x 6 S SD: 22.2509 cents 4 x x 5 x 6 x 7 x 8 S SD: 17.3302 cents 5 x 6 x 7 x 8 x 9:10 S SD: 25.7782 cents 6 x 7 x 8:9 x 10:11:12 S SD: 14.6006 cents 7 x 8:9 x x 11:12 x 14 SD: 9.4943 cents 8:9 x 10:11:12 x 14 x 16 S SD: 14.5985 cents 9:10 x x 12 x 14 x 16:18 S SD: 5.7239 cents 10:11:12:13 x 15 x 17:18:20 SD: 12.4147 cents 11:12:13:14:15 x 17:19:20:22 SD: 11.8367 cents 12 x 14 x 16:18 x 21 x 24 S SD: 5.0490 cents 13 x 15:17 x x 20 x 23:26 SD: 2.7291 cents 14 x 16:18:19:21:22:24:25:28 SD: 7.1556 cents 15:17 x 19:20 x 23:26:27:30 SD: 7.3195 cents 16:18 x 21 x 24:25:28 x 32 SD: 5.9920 cents 17:19:20:22:23 x 26:29:30:34 SD: 6.6978 cents 18:20:21:23:24:27:28:31:32:36 SD: 5.0691 cents 19:21:22:25 x x 29:33:34:38 SD: 6.1390 cents 20 x 23:26:27:30:31:35:36:40 SD: 4.7889 cents 21 x 24:27:28 x 32:36:37:42 SD: 5.5319 cents 22:25 x x 29:33:34:38:39:44 SD: 3.9320 cents 23:26:27:30:31 x 35:40:41:46 SD: 5.2396 cents 24:27:28:31:32:36:37:42:43:48 SD: 3.4179 cents 25:28:29:32:33 x 38:43:44:50 SD: 5.6023 cents 26:29:30:34:35:39:40:45:46:52 SD: 2.9577 cents 28 x 32:36:37:42:43:49:50:56 SD: 4.4676 cents 29:33 x 38:39:44:45:50:52:58 SD: 5.1404 cents 30:34:35:39:40:45:46:52:53:60 SD: 2.7809 cents 33:37:38:43:44:50:51:57:59:66 SD: 2.6286 cents 39:44:45:51:52:59:60:68:69:78 SD: 2.5915 cents 40:45:46:52:53:60:62:69:71:80 SD: 2.1171 cents 46:52:53:60:61:69:71:80:82:92 SD: 1.9273 cents 50:56:58:65:67:75:77:87:89:100 SD: 1.8651 cents 54:61:62:70:72:81:83:94:96:108 SD: 1.6980 cents 57:64:66:74:76:86:88:99:101:114 SD: 1.6233 cents 63:71:73:82:84:95:97:109:112:126 SD: 1.2989 cents 70:79:81:91:93:105:108:121:124:140 SD: 1.2980 cents 72:81:83:94:96:108:111:125:128:144 SD: 1.1075 cents 78:88:90:101:104:117:120:135:139:156 SD: 1.0004 cents 90:101:104:117:120:135:139:156:160:180 SD: 0.8733 cents 96:108:111:125:128:144:148:166:171:192 SD: 0.7983 cents 104:117:120:135:139:156:160:180:185:208 SD: 0.6016 cents 130:146:150:169:173:195:200:225:231:260 SD: 0.5736 cents 144:162:166:187:192:216:222:249:256:288 SD: 0.5637 cents 150:169:173:195:200:225:231:260:267:300 SD: 0.4717 cents 174:196:201:226:232:261:268:301:309:348 SD: 0.3908 cents 234:263:270:304:312:351:360:405:416:468 SD: 0.3394 cents 246:277:284:320:328:369:379:426:437:492 SD: 0.3229 cents 264:297:305:343:352:396:406:457:469:528 SD: 0.2636 cents 304:342:351:395:405:456:468:527:540:608 SD: 0.2337 cents 310:349:358:403:413:465:477:537:551:620 SD: 0.1970 cents 400:450:462:520:533:600:616:693:711:800 SD: 0.1933 cents 408:459:471:530:544:612:628:707:725:816 SD: 0.1217 cents 414:466:478:538:552:621:637:717:736:828 SD: 0.1209 cents 504:567:582:655:672:756:776:873:896:1008 SD: 0.1181 cents 582:655:672:756:776:873:896:1008:1034:1164 SD: 0.1047 cents