Scala analysis: xen15-gilson-generalized-pythagorean-11-8-13
Generalized Pythagorean Scale, 11/8 stacked 13=6+7 times
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 64.497 cents 64.497366 2: 161.861 cents 161.861481 3: 19487171/16777216 259.225597 4: 161051/131072 356.589712 5: 1331/1024 453.953827 6: 11/8 551.317942 undecimal semi-augmented fourth 7: 615.815 cents 615.815308 8: 713.179 cents 713.179424 9: 214358881/134217728 810.543539 10: 1771561/1048576 907.907654 11: 14641/8192 1005.271769 12: 121/64 1102.635885 two (undecimal semi-augmented fourth) 13: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 128/121 97.3641 undecimal semitone 1: 64.4974 cents 64.4974 2: 97.3641 cents 97.3641 3: 97.3641 cents 97.3641 4: 128/121 97.3641 undecimal semitone 5: 128/121 97.3641 undecimal semitone 6: 128/121 97.3641 undecimal semitone 7: 64.4974 cents 64.4974 8: 97.3641 cents 97.3641 9: 97.3641 cents 97.3641 10: 128/121 97.3641 undecimal semitone 11: 128/121 97.3641 undecimal semitone 12: 128/121 97.3641 undecimal semitone 13: 128/121 97.3641 undecimal semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 64.49737 cents 1: 11 97.36412 cents 2: 4 161.86148 cents 2: 9 194.72823 cents 3: 6 19487171/16777216 259.226 cents 3: 7 292.09235 cents 4: 8 161051/131072 356.590 cents 4: 5 389.45646 cents 5: 10 1331/1024 453.954 cents 5: 3 486.82058 cents 6: 12 11/8 551.318 cents undecimal semi-augmented fourth 6: 1 584.18469 cents 7: 1 615.81531 cents 7: 12 648.68206 cents 8: 3 713.17942 cents 8: 10 746.04617 cents 9: 5 214358881/134217728 810.544 cents 9: 8 843.41029 cents 10: 7 1771561/1048576 907.908 cents 10: 6 940.77440 cents 11: 9 14641/8192 1005.272 cents 11: 4 1038.13852 cents 12: 11 121/64 1102.636 cents two (undecimal semi-augmented fourth) 12: 2 1135.50263 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 10 11 12 13 0.0 : 64.5 161.9 259.2 356.6 454.0 551.3 615.8 713.2 810.5 907.9 1005.3 1102.6 1200.0 64.5 : 97.4 194.7 292.1 389.5 486.8 551.3 648.7 746.0 843.4 940.8 1038.1 1135.5 1200.0 161.9 : 97.4 194.7 292.1 389.5 454.0 551.3 648.7 746.0 843.4 940.8 1038.1 1102.6 1200.0 259.2 : 97.4 194.7 292.1 356.6 454.0 551.3 648.7 746.0 843.4 940.8 1005.3 1102.6 1200.0 356.6 : 97.4 194.7 259.2 356.6 454.0 551.3 648.7 746.0 843.4 907.9 1005.3 1102.6 1200.0 454.0 : 97.4 161.9 259.2 356.6 454.0 551.3 648.7 746.0 810.5 907.9 1005.3 1102.6 1200.0 551.3 : 64.5 161.9 259.2 356.6 454.0 551.3 648.7 713.2 810.5 907.9 1005.3 1102.6 1200.0 615.8 : 97.4 194.7 292.1 389.5 486.8 584.2 648.7 746.0 843.4 940.8 1038.1 1135.5 1200.0 713.2 : 97.4 194.7 292.1 389.5 486.8 551.3 648.7 746.0 843.4 940.8 1038.1 1102.6 1200.0 810.5 : 97.4 194.7 292.1 389.5 454.0 551.3 648.7 746.0 843.4 940.8 1005.3 1102.6 1200.0 907.9 : 97.4 194.7 292.1 356.6 454.0 551.3 648.7 746.0 843.4 907.9 1005.3 1102.6 1200.0 1005.3: 97.4 194.7 259.2 356.6 454.0 551.3 648.7 746.0 810.5 907.9 1005.3 1102.6 1200.0 1102.6: 97.4 161.9 259.2 356.6 454.0 551.3 648.7 713.2 810.5 907.9 1005.3 1102.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 64.4974 .. 97.3641 cents 32.86675 cents 64.49737 cents 2: 161.8615 .. 194.7282 cents 32.86675 cents 64.49737 cents 3: 259.2256 .. 292.0923 cents 32.86675 cents 64.49737 cents 4: 356.5897 .. 389.4565 cents 32.86675 cents 64.49737 cents 5: 453.9538 .. 486.8206 cents 32.86675 cents 64.49737 cents 6: 551.3179 .. 584.1847 cents 32.86675 cents 64.49737 cents 7: 615.8153 .. 648.6821 cents 32.86675 cents 31.63062 cents 8: 713.1794 .. 746.0462 cents 32.86675 cents 64.49737 cents 9: 810.5435 .. 843.4103 cents 32.86675 cents 64.49737 cents 10: 907.9077 .. 940.7744 cents 32.86675 cents 64.49737 cents 11: 1005.2718 .. 1038.1385 cents 32.86675 cents 64.49737 cents 12: 1102.6359 .. 1135.5026 cents 32.86675 cents 64.49737 cents
SHOW DATA
Number of notes : 13 -- Interval properties -- Smallest interval : 64.49737 cents, class 1 Average step (divided formal octave): 92.3077 cents Largest one step interval : 97.36412 cents Average / Smallest step : 1.431185 Largest / Average step : 1.054778 Largest / Smallest step : 1.509583 Median interval of one step : 97.36412 cents, amount: 11 Most common interval of one step : 97.36412 cents, amount: 11 Least squares average step : 90.90313 cents, oct.: 1181.74069 cents Scale is strictly proper Scale has Myhill's property chromas: 32.86675 cents and 31.63062 cents, ratio: 1.039080 generators: 6 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 1935-tone equal temperament with octave 2/1 degrees: 104 261 418 575 732 889 993 1150 1307 1464 1621 1778 1935 generators: 889 and 1046 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBBBBABBBBBB Step pattern size order : SLLLLLSLLLLLL Scale is a Constant Structure, by a margin of 31.63062 cents Scale diversity : 1.214589 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.671333 Rothenberg efficiency : 0.717949 redundancy: 0.282051 Efficiency x scale size : 9.333333 Number of different interval sizes : 24 = 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 : 31.63062 cents Most common intervals : 11/8, 551.3179 cents & inv., amount: 12 Scale is a chain of 6 triads 0.0 551.318 1102.636 cents Most common triad is 0.0 551.318 648.682 cents, amount: 11 Number of recognisable fifths : 3, average 713.1794 cents Scale contains two identical disjunct hexachords Best fifths form a closed circle Best major thirds form a closed circle Formal octave complements present : 1 = 7.6923% Limited inverse transpositions : 7 Inversional symmetry on degrees : 10 Inversional symmetry on intervals : 3-4 -- Rational properties -- Prime limit : 11 (not all pitches rational)
FIT/MODE
13: 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 17.8772 c. M:-30.3385 c. 19: 1 2 1 2 1 2 1 1 2 1 2 1 2 P M ME S SD: 17.2469 c. M: 28.9517 c. Unsmate-13 20: 1 2 1 2 2 1 1 2 2 1 2 1 2 P D3 S SD: 16.3922 c. M:-29.4565 c. 21: 1 2 2 1 2 2 1 2 1 2 2 1 2 P M ME S SD: 16.3496 c. M:-29.6777 c. 22: 1 2 2 1 2 2 1 2 2 2 1 2 2 P M ME S SD: 14.8726 c. M: 29.3170 c. 23: 1 2 2 2 2 2 1 2 2 1 2 2 2 P D3 SD: 14.3724 c. M:-24.2391 c. 24: 1 2 2 2 2 2 1 2 2 2 2 2 2 P M ME S SD: 9.3193 c. M: 15.8153 c. Freivald-13, Diatonicized Chromatic 37: 2 3 3 3 3 3 2 3 3 3 3 3 3 SP M ME S SD: 0.2362 c. M:-0.4009 c. Freivald-13 505: 27 41 41 41 41 41 27 41 41 41 41 41 41 SP M DE S SD: 0.2179 c. M: 0.3698 c. 542: 29 44 44 44 44 44 29 44 44 44 44 44 44 SP M DE S SD: 0.1869 c. M: 0.3172 c. 579: 31 47 47 47 47 47 31 47 47 47 47 47 47 SP M DE S SD: 0.1598 c. M: 0.2713 c. 616: 33 50 50 50 50 50 33 50 50 50 50 50 50 SP M DE S SD: 0.1361 c. M: 0.2309 c. 653: 35 53 53 53 53 53 35 53 53 53 53 53 53 SP M DE S SD: 0.1150 c. M: 0.1951 c. 690: 37 56 56 56 56 56 37 56 56 56 56 56 56 SP M DE S SD: 0.0961 c. M: 0.1631 c. 727: 39 59 59 59 59 59 39 59 59 59 59 59 59 SP M DE S SD: 0.0792 c. M: 0.1344 c. 764: 41 62 62 62 62 62 41 62 62 62 62 62 62 SP M DE S SD: 0.0639 c. M: 0.1085 c. 801: 43 65 65 65 65 65 43 65 65 65 65 65 65 SP M DE S SD: 0.0501 c. M: 0.0850 c. 838: 45 68 68 68 68 68 45 68 68 68 68 68 68 SP M DE S SD: 0.0374 c. M: 0.0635 c. 875: 47 71 71 71 71 71 47 71 71 71 71 71 71 SP M DE S SD: 0.0259 c. M: 0.0439 c. 912: 49 74 74 74 74 74 49 74 74 74 74 74 74 SP M DE S SD: 0.0152 c. M: 0.0258 c. 949: 51 77 77 77 77 77 51 77 77 77 77 77 77 SP M DE S SD: 0.0054 c. M: 0.0092 c. 986: 53 80 80 80 80 80 53 80 80 80 80 80 80 SP M DE S SD: 0.0036 c. M:-0.0062 c. 1935: 104 157 157 157 157 157 104 157 157 157 157 157 157 SP M DE S SD: 0.0008 c. M: 0.0014 c.
FIT/HARMONIC
1 x x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x x 3 x x x x 4 S SD: 5.6122 cents 3 x x x x 4 x x x x 5 x x 6 S SD: 16.6619 cents 4 x x x 5 x x x 6 x x 7 x 8 S SD: 12.0877 cents 5 x x x 6 x 7 x x 8 x 9 x 10 S SD: 10.6050 cents 6 x x 7 x 8 x x 9 x 10:11 x 12 S SD: 11.3371 cents 7 x x 8 x 9 x 10 x 11:12 x 13:14 S SD: 8.4825 cents 8 x 9 x 10 x 11 x 12:13 x 14:15:16 S SD: 9.0237 cents 9 x 10 x 11:12 x 13 x 14:15:16:17:18 S SD: 8.3195 cents 10 x 11 x 12:13:14 x 15:16:17:18:19:20 S SD: 5.6001 cents 11 x 12:13 x 14:15:16:17:18:19:20:21:22 S SD: 8.9431 cents 12 x 13:14:15:16 x 17:18:19:20:21:23:24 SD: 7.2653 cents 13 x 14:15:16:17:18:19:20:21:22:23:25:26 SD: 6.3749 cents 14 x 15:16:17:18:19:20:21:22:24:25:26:28 S SD: 6.6583 cents 15:16 x 17:18:20:21 x 23:24:25:27:28:30 SD: 9.3411 cents 16:17:18:19:20:21:22:23:24:26:27:29:30:32 SD: 6.8884 cents 17:18:19:20:21:22:23:24:26:27:29:30:32:34 SD: 5.6073 cents 18:19:20:21:22:23:25:26:27:29:30:32:34:36 SD: 4.8766 cents 19:20:21:22:23:25:26:27:29:30:32:34:36:38 SD: 4.0603 cents 23:24:25:27:28:30:32:33:35:37:39:41:43:46 SD: 3.6913 cents 26:27:29:30:32:34:36:37:39:42:44:46:49:52 SD: 3.4578 cents 27:28:30:31:33:35:37:39:41:43:46:48:51:54 SD: 3.2825 cents 29:30:32:34:36:38:40:41:44:46:49:52:55:58 SD: 2.9287 cents 30:31:33:35:37:39:41:43:45:48:51:54:57:60 SD: 2.1927 cents 43:45:47:50:53:56:59:61:65:69:73:77:81:86 SD: 1.9200 cents 49:51:54:57:60:64:67:70:74:78:83:88:93:98 SD: 1.6144 cents 51:53:56:59:63:66:70:73:77:81:86:91:96:102 SD: 1.5391 cents 57:59:63:66:70:74:78:81:86:91:96:102:108:114 SD: 1.4640 cents 61:63:67:71:75:79:84:87:92:97:103:109:115:122 SD: 1.1468 cents 70:73:77:81:86:91:96:100:106:112:118:125:132:140 SD: 1.1321 cents 74:77:81:86:91:96:102:106:112:118:125:132:140:148 SD: 0.9682 cents 80:83:88:93:98:104:110:114:121:128:135:143:151:160 SD: 0.6858 cents 104:108:114:121:128:135:143:148:157:166:176:186:197:208 SD: 0.6786 cents 110:114:121:128:135:143:151:157:166:176:186:197:208:220 SD: 0.6182 cents 131:136:144:152:161:170:180:187:198:209:221:234:248:262 SD: 0.4639 cents 161:167:177:187:198:209:221:230:243:257:272:288:304:322 SD: 0.4426 cents 174:181:191:202:214:226:239:248:263:278:294:311:329:348 SD: 0.4403 cents 183:190:201:213:225:238:252:261:276:292:309:327:346:366 SD: 0.4246 cents 184:191:202:214:226:239:253:263:278:294:311:329:348:368 SD: 0.3234 cents 236:245:259:274:290:307:325:337:356:377:399:422:446:472 SD: 0.3118 cents 253:263:278:294:311:329:348:361:382:404:427:452:478:506 SD: 0.3069 cents 266:276:292:309:327:346:366:380:402:425:449:475:503:532 SD: 0.3010 cents 267:277:293:310:328:347:367:381:403:426:451:477:505:534 SD: 0.2048 cents 347:360:381:403:426:451:477:495:524:554:586:620:656:694 SD: 0.1745 cents 367:381:403:426:451:477:505:524:554:586:620:656:694:734 SD: 0.1552 cents 447:464:491:519:549:581:615:638:675:714:755:799:845:894 SD: 0.1360 cents 477:495:524:554:586:620:656:681:720:762:806:853:902:954 SD: 0.1301 cents 550:571:604:639:676:715:756:785:830:878:929:983:1040:1100 SD: 0.1226 cents 551:572:605:640:677:716:758:786:832:880:931:985:1042:1102 SD: 0.1139 cents