Scala analysis: xen15-gilson-generalized-pythagorean-11-8-11
Generalized Pythagorean Scale, 11/8 stacked 11=5+6 times
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 161.861 cents 161.861481 2: 19487171/16777216 259.225597 3: 161051/131072 356.589712 4: 1331/1024 453.953827 5: 11/8 551.317942 undecimal semi-augmented fourth 6: 713.179 cents 713.179424 7: 214358881/134217728 810.543539 8: 1771561/1048576 907.907654 9: 14641/8192 1005.271769 10: 121/64 1102.635885 two (undecimal semi-augmented fourth) 11: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 128/121 97.3641 undecimal semitone 1: 161.8615 cents 161.8615 2: 97.3641 cents 97.3641 3: 128/121 97.3641 undecimal semitone 4: 128/121 97.3641 undecimal semitone 5: 128/121 97.3641 undecimal semitone 6: 161.8615 cents 161.8615 7: 97.3641 cents 97.3641 8: 128/121 97.3641 undecimal semitone 9: 128/121 97.3641 undecimal semitone 10: 128/121 97.3641 undecimal semitone 11: 128/121 97.3641 undecimal semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 9 97.36412 cents 1: 2 161.86148 cents 2: 7 194.72823 cents 2: 4 19487171/16777216 259.226 cents 3: 5 292.09235 cents 3: 6 161051/131072 356.590 cents 4: 3 389.45646 cents 4: 8 1331/1024 453.954 cents 5: 1 486.82058 cents 5: 10 11/8 551.318 cents undecimal semi-augmented fourth 6: 10 648.68206 cents 6: 1 713.17942 cents 7: 8 746.04617 cents 7: 3 214358881/134217728 810.544 cents 8: 6 843.41029 cents 8: 5 1771561/1048576 907.908 cents 9: 4 940.77440 cents 9: 7 14641/8192 1005.272 cents 10: 2 1038.13852 cents 10: 9 121/64 1102.636 cents two (undecimal semi-augmented fourth) 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 10 11 0.0 : 161.9 259.2 356.6 454.0 551.3 713.2 810.5 907.9 1005.3 1102.6 1200.0 161.9 : 97.4 194.7 292.1 389.5 551.3 648.7 746.0 843.4 940.8 1038.1 1200.0 259.2 : 97.4 194.7 292.1 454.0 551.3 648.7 746.0 843.4 940.8 1102.6 1200.0 356.6 : 97.4 194.7 356.6 454.0 551.3 648.7 746.0 843.4 1005.3 1102.6 1200.0 454.0 : 97.4 259.2 356.6 454.0 551.3 648.7 746.0 907.9 1005.3 1102.6 1200.0 551.3 : 161.9 259.2 356.6 454.0 551.3 648.7 810.5 907.9 1005.3 1102.6 1200.0 713.2 : 97.4 194.7 292.1 389.5 486.8 648.7 746.0 843.4 940.8 1038.1 1200.0 810.5 : 97.4 194.7 292.1 389.5 551.3 648.7 746.0 843.4 940.8 1102.6 1200.0 907.9 : 97.4 194.7 292.1 454.0 551.3 648.7 746.0 843.4 1005.3 1102.6 1200.0 1005.3: 97.4 194.7 356.6 454.0 551.3 648.7 746.0 907.9 1005.3 1102.6 1200.0 1102.6: 97.4 259.2 356.6 454.0 551.3 648.7 810.5 907.9 1005.3 1102.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 97.3641 .. 161.8615 cents 64.49737 cents 97.36412 cents 2: 194.7282 .. 259.2256 cents 64.49737 cents 32.86675 cents 3: 292.0923 .. 356.5897 cents 64.49737 cents 32.86675 cents 4: 389.4565 .. 453.9538 cents 64.49737 cents 32.86675 cents 5: 486.8206 .. 551.3179 cents 64.49737 cents 32.86675 cents 6: 648.6821 .. 713.1794 cents 64.49737 cents 97.36412 cents 7: 746.0462 .. 810.5435 cents 64.49737 cents 32.86675 cents 8: 843.4103 .. 907.9077 cents 64.49737 cents 32.86675 cents 9: 940.7744 .. 1005.2718 cents 64.49737 cents 32.86675 cents 10: 1038.1385 .. 1102.6359 cents 64.49737 cents 32.86675 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 97.36411 cents, class 1 Average step (divided formal octave): 109.0909 cents Largest one step interval : 161.86148 cents Average / Smallest step : 1.120443 Largest / Average step : 1.483730 Largest / Smallest step : 1.662435 Median interval of one step : 97.36412 cents, amount: 9 Most common interval of one step : 97.36412 cents, amount: 9 Least squares average step : 112.27754 cents, oct.: 1235.05292 cents Scale is strictly proper Scale has Myhill's property chromas: 64.49737 cents and 32.86675 cents, ratio: 1.962390 generators: 5 of 551.31794 cents and 648.68206 cents ET pair of linear temperament : 11&13 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 986-tone equal temperament with octave 2/1 degrees: 133 213 293 373 453 586 666 746 826 906 986 generators: 453 and 533 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBBBABBBBB Step pattern size order : LSSSSLSSSSS Scale is a Constant Structure, by a margin of 32.86675 cents Scale diversity : 1.212316 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.462522 Rothenberg efficiency : 0.727273 redundancy: 0.272727 Efficiency x scale size : 8.000000 Number of different interval sizes : 20 = 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 : 32.86675 cents Most common intervals : 11/8, 551.3179 cents & inv., amount: 10 Scale is a chain of 5 triads 0.0 551.318 1102.636 cents Most common triad is 0.0 551.318 648.682 cents, amount: 9 Number of recognisable fifths : 1, average 713.1794 cents Scale contains two identical disjunct pentachords Best minor thirds form a closed circle Formal octave complements present : 1 = 9.0909% Limited inverse transpositions : 6 Inversional symmetry on degrees : 3 Inversional symmetry on intervals : 8-9 -- Rational properties -- Prime limit : 11 (not all pitches rational)
FIT/MODE
11: 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 34.6883 c. M: 58.6340 c. 13: 2 1 1 1 1 2 1 1 1 1 1 P M ME S SD: 14.9571 c. M:-25.2821 c. 22: 3 2 2 1 2 3 2 2 1 2 2 P T3 SD: 14.4706 c. M:-25.2285 c. 23: 3 2 2 2 2 3 2 1 2 2 2 P T3 SD: 14.8569 c. M:-24.2391 c. 24: 3 2 2 2 2 3 2 2 2 2 2 SP M ME S SD: 7.7971 c. M: 13.1794 c. Freivald-11 37: 5 3 3 3 3 5 3 3 3 3 3 SP M DE S SD: 0.1977 c. M:-0.3341 c. Freivald-11 505: 68 41 41 41 41 68 41 41 41 41 41 SP M DE S SD: 0.1823 c. M: 0.3081 c. 542: 73 44 44 44 44 73 44 44 44 44 44 SP M DE S SD: 0.1564 c. M: 0.2643 c. 579: 78 47 47 47 47 78 47 47 47 47 47 SP M DE S SD: 0.1337 c. M: 0.2261 c. 616: 83 50 50 50 50 83 50 50 50 50 50 SP M DE S SD: 0.1138 c. M: 0.1924 c. 653: 88 53 53 53 53 88 53 53 53 53 53 SP M DE S SD: 0.0962 c. M: 0.1626 c. 690: 93 56 56 56 56 93 56 56 56 56 56 SP M DE S SD: 0.0804 c. M: 0.1359 c. 727: 98 59 59 59 59 98 59 59 59 59 59 SP M DE S SD: 0.0663 c. M: 0.1120 c. 764: 103 62 62 62 62 103 62 62 62 62 62 SP M DE S SD: 0.0535 c. M: 0.0904 c. 801: 108 65 65 65 65 108 65 65 65 65 65 SP M DE S SD: 0.0419 c. M: 0.0708 c. 838: 113 68 68 68 68 113 68 68 68 68 68 SP M DE S SD: 0.0313 c. M: 0.0529 c. 875: 118 71 71 71 71 118 71 71 71 71 71 SP M DE S SD: 0.0216 c. M: 0.0366 c. 912: 123 74 74 74 74 123 74 74 74 74 74 SP M DE S SD: 0.0127 c. M: 0.0215 c. 949: 128 77 77 77 77 128 77 77 77 77 77 SP M DE S SD: 0.0045 c. M: 0.0077 c. 986: 133 80 80 80 80 133 80 80 80 80 80 SP M DE S SD: 0.0031 c. M:-0.0052 c. 1935: 261 157 157 157 157 261 157 157 157 157 157 SP M DE S SD: 0.0007 c. M: 0.0011 c.
FIT/HARMONIC
1 x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x x x x 4 S SD: 5.6122 cents 3 x x x 4 x x x 5 x x 6 S SD: 16.6619 cents 4 x x 5 x x 6 x x 7 x 8 S SD: 12.0877 cents 5 x x 6 x 7 x 8 x 9 x 10 S SD: 10.6050 cents 6 x 7 x 8 x 9 x 10:11 x 12 S SD: 11.3371 cents 7 x 8 x 9:10 x 11:12 x 13:14 S SD: 12.6985 cents 8:9 x 10 x 11:12:13 x 14:15:16 S SD: 9.0237 cents 9:10 x 11:12 x x 14:15:16:17:18 S SD: 8.9910 cents 10:11 x 12:13:14:15:16:17:18:19:20 S SD: 5.6001 cents 11:12:13 x 14:15:17:18:19:20:21:22 SD: 9.2721 cents 12:13:14:15:16:17:18:19:20:21:23:24 SD: 8.5733 cents 13:14:15:16:17:18:20:21:22:23:25:26 SD: 5.8615 cents 17:19:20:21:22:23:26:27:29:30:32:34 SD: 5.5836 cents 18:20:21:22:23:25:27:29:30:32:34:36 SD: 4.7579 cents 19:21:22:23:25:26:29:30:32:34:36:38 SD: 4.2052 cents 23:25:27:28:30:32:35:37:39:41:43:46 SD: 4.1996 cents 26:29:30:32:34:36:39:42:44:46:49:52 SD: 4.0604 cents 27:30:31:33:35:37:41:43:46:48:51:54 SD: 3.3843 cents 29:32:34:36:38:40:44:46:49:52:55:58 SD: 3.0817 cents 30:33:35:37:39:41:45:48:51:54:57:60 SD: 2.4010 cents 39:43:45:48:51:54:59:62:66:70:74:78 SD: 2.2722 cents 43:47:50:53:56:59:65:69:73:77:81:86 SD: 1.6057 cents 57:63:66:70:74:78:86:91:96:102:108:114 SD: 1.5308 cents 61:67:71:75:79:84:92:97:103:109:115:122 SD: 1.0990 cents 74:81:86:91:96:102:112:118:125:132:140:148 SD: 0.9075 cents 80:88:93:98:104:110:121:128:135:143:151:160 SD: 0.7705 cents 104:114:121:128:135:143:157:166:176:186:197:208 SD: 0.6564 cents 123:135:143:151:160:169:186:196:208:220:233:246 SD: 0.6274 cents 131:144:152:161:170:180:198:209:221:234:248:262 SD: 0.5463 cents 136:149:158:167:177:187:205:217:230:243:257:272 SD: 0.5377 cents 144:158:167:177:187:198:217:230:243:257:272:288 SD: 0.5358 cents 154:169:179:189:200:212:233:246:260:275:291:308 SD: 0.5075 cents 161:177:187:198:209:221:243:257:272:288:304:322 SD: 0.4894 cents 173:190:201:213:225:238:261:276:292:309:327:346 SD: 0.4430 cents 174:191:202:214:226:239:263:278:294:311:329:348 SD: 0.3288 cents 184:202:214:226:239:253:278:294:311:329:348:368 SD: 0.2992 cents 253:278:294:311:329:348:382:404:427:452:478:506 SD: 0.2718 cents 267:293:310:328:347:367:403:426:451:477:505:534 SD: 0.2282 cents 310:340:360:381:403:426:468:495:524:554:586:620 SD: 0.2251 cents 328:360:381:403:426:451:495:524:554:586:620:656 SD: 0.1785 cents 347:381:403:426:451:477:524:554:586:620:656:694 SD: 0.1770 cents 367:403:426:451:477:505:554:586:620:656:694:734 SD: 0.1686 cents 390:428:453:479:507:536:589:623:659:697:737:780 SD: 0.1636 cents 447:491:519:549:581:615:675:714:755:799:845:894 SD: 0.1600 cents 451:495:524:554:586:620:681:720:762:806:853:902 SD: 0.1437 cents 477:524:554:586:620:656:720:762:806:853:902:954 SD: 0.1403 cents 541:594:628:665:703:744:817:864:914:967:1023:1082 SD: 0.1366 cents 551:605:640:677:716:758:832:880:931:985:1042:1102 SD: 0.1081 cents