Scala analysis: xen18-schulter-pure-11-14
Temperament with pure 11:14 major thirds, fifth of 704.377 cents
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 130.640 cents 130.640000 2: 208.750 cents 208.750000 3: 286.870 cents 286.870000 4: 417.510 cents 417.510000 5: 495.620 cents 495.620000 6: 626.260 cents 626.260000 7: 704.380 cents 704.380000 8: 835.020 cents 835.020000 9: 913.130 cents 913.130000 10: 991.250 cents 991.250000 11: 1121.880 cents 1121.880000 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 78.1200 cents 78.1200 1: 130.6400 cents 130.6400 2: 78.1100 cents 78.1100 3: 78.1200 cents 78.1200 4: 130.6400 cents 130.6400 5: 78.1100 cents 78.1100 6: 130.6400 cents 130.6400 7: 78.1200 cents 78.1200 8: 130.6400 cents 130.6400 9: 78.1100 cents 78.1100 10: 78.1200 cents 78.1200 11: 130.6300 cents 130.6300 12: 78.1200 cents 78.1200
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 78.11000 cents 1: 4 78.12000 cents 1: 1 130.63000 cents 1: 4 130.64000 cents 2: 2 156.23000 cents 2: 6 208.75000 cents 2: 4 208.76000 cents 3: 1 286.86000 cents 3: 8 286.87000 cents 3: 2 339.39000 cents 3: 1 339.40000 cents 4: 2 364.98000 cents 4: 2 364.99000 cents 4: 2 417.50000 cents 4: 6 417.51000 cents 5: 8 495.62000 cents 5: 3 495.63000 cents 5: 1 548.15000 cents 6: 1 573.73000 cents 6: 5 573.74000 cents 6: 5 626.26000 cents 6: 1 626.27000 cents 7: 1 651.85000 cents 7: 3 704.37000 cents 7: 8 704.38000 cents 8: 6 782.49000 cents 8: 2 782.50000 cents 8: 2 835.01000 cents 8: 2 835.02000 cents 9: 1 860.60000 cents 9: 2 860.61000 cents 9: 8 913.13000 cents 9: 1 913.14000 cents 10: 4 991.24000 cents 10: 6 991.25000 cents 10: 2 1043.77000 cents 11: 4 1069.36000 cents 11: 1 1069.37000 cents 11: 4 1121.88000 cents 11: 3 1121.89000 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.63636 = 40/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 130.6 208.8 286.9 417.5 495.6 626.3 704.4 835.0 913.1 991.3 1121.9 1200.0 130.6 : 78.1 156.2 286.9 365.0 495.6 573.7 704.4 782.5 860.6 991.2 1069.4 1200.0 208.8 : 78.1 208.8 286.9 417.5 495.6 626.3 704.4 782.5 913.1 991.2 1121.9 1200.0 286.9 : 130.6 208.7 339.4 417.5 548.1 626.3 704.4 835.0 913.1 1043.8 1121.9 1200.0 417.5 : 78.1 208.8 286.9 417.5 495.6 573.7 704.4 782.5 913.1 991.2 1069.4 1200.0 495.6 : 130.6 208.8 339.4 417.5 495.6 626.3 704.4 835.0 913.1 991.3 1121.9 1200.0 626.3 : 78.1 208.8 286.9 365.0 495.6 573.7 704.4 782.5 860.6 991.2 1069.4 1200.0 704.4 : 130.6 208.8 286.9 417.5 495.6 626.3 704.4 782.5 913.1 991.2 1121.9 1200.0 835.0 : 78.1 156.2 286.9 365.0 495.6 573.7 651.8 782.5 860.6 991.2 1069.4 1200.0 913.1 : 78.1 208.8 286.9 417.5 495.6 573.7 704.4 782.5 913.1 991.2 1121.9 1200.0 991.3 : 130.6 208.7 339.4 417.5 495.6 626.3 704.4 835.0 913.1 1043.8 1121.9 1200.0 1121.9: 78.1 208.8 286.9 365.0 495.6 573.7 704.4 782.5 913.1 991.2 1069.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 78.1100 .. 130.6400 cents 52.53000 cents 78.11000 cents 2: 156.2300 .. 208.7600 cents 52.53000 cents 25.59000 cents 3: 286.8600 .. 339.4000 cents 52.54000 cents 78.10000 cents 4: 364.9800 .. 417.5100 cents 52.53000 cents 25.58000 cents 5: 495.6200 .. 548.1500 cents 52.53000 cents 78.11000 cents 6: 573.7300 .. 626.2700 cents 52.54000 cents 25.58000 cents 7: 651.8500 .. 704.3800 cents 52.53000 cents 25.58000 cents 8: 782.4900 .. 835.0200 cents 52.53000 cents 78.11000 cents 9: 860.6000 .. 913.1400 cents 52.54000 cents 25.58000 cents 10: 991.2400 .. 1043.7700 cents 52.53000 cents 78.10000 cents 11: 1069.3600 .. 1121.8900 cents 52.53000 cents 25.59000 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 78.11000 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 130.64000 cents Average / Smallest step : 1.280246 Largest / Average step : 1.306400 Largest / Smallest step : 1.672513 Median interval of one step : 78.12000 cents, amount: 4 Least squares average step : 101.22557 cents, oct.: 1214.70683 cents Scale is strictly proper Scale is a mode of a 891-tone equal temperament with octave 1200.000 cents degrees: 97 155 213 310 368 465 523 620 678 736 833 891 Least number of segments generator : 446 of 600.673 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 523 of 704.377 cents and inv. generated superset size: 12 = 0 more = 100.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCABACABCDC Step pattern size order : DABDADBDABCB Scale is a Constant Structure, by a margin of 25.58000 cents Scale diversity : 1.211945 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.518450 Rothenberg efficiency : 0.379597 redundancy: 0.620403 Efficiency x scale size : 4.555159 Number of different interval sizes : 40 = 3.63636 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.63636 = 40/11 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 0.01000 cents Number of recognisable fifths : 11, average 704.3773 cents Best fifths form a closed circle Formal octave complements present : 7 = 58.3333% Limited inverse transpositions : 11 Inversional symmetry on intervals : 5-6 11-12 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 18.6557 c. M: 35.0200 c. Twelve-tone Chromatic (1/11-comma) 16: 2 1 1 2 1 1 1 2 1 1 2 1 P D3 SD: 20.0612 c. M:-32.4900 c. 17: 2 1 1 2 1 2 1 2 1 1 2 1 P M ME SD: 6.4163 c. M:-12.0388 c. Twelve-tone Chromatic (2/11-comma positive) 29: 3 2 2 3 2 3 2 3 2 2 3 2 SP M ME SD: 3.9583 c. M: 7.4338 c. Twelve-tone Chromatic (1/14-comma positive) 46: 5 3 3 5 3 5 3 5 3 3 5 3 SP M DE SD: 0.1243 c. M: 0.2374 c. Twelve-tone Chromatic (1/9-comma positive) 477: 52 31 31 52 31 52 31 52 31 31 52 31 SP M DE SD: 0.1089 c. M:-0.2001 c. 523: 57 34 34 57 34 57 34 57 34 34 57 34 SP M DE SD: 0.0884 c. M:-0.1616 c. 569: 62 37 37 62 37 62 37 62 37 37 62 37 SP M DE SD: 0.0712 c. M:-0.1294 c. 615: 67 40 40 67 40 67 40 67 40 40 67 40 SP M DE SD: 0.0566 c. M:-0.1020 c. 661: 72 43 43 72 43 72 43 72 43 43 72 43 SP M DE SD: 0.0441 c. M:-0.0783 c. 707: 77 46 46 77 46 77 46 77 46 46 77 46 SP M DE SD: 0.0332 c. M:-0.0578 c. 753: 82 49 49 82 49 82 49 82 49 49 82 49 SP M DE SD: 0.0236 c. M:-0.0398 c. 799: 87 52 52 87 52 87 52 87 52 52 87 52 SP M DE SD: 0.0152 c. M:-0.0238 c. 845: 92 55 55 92 55 92 55 92 55 55 92 55 SP M DE SD: 0.0079 c. M:-0.0135 c. 891: 97 58 58 97 58 97 58 97 58 58 97 58 SP M DE SD: 0.0030 c. M:-0.0055 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: 1.2125 cents 3 x x x x 4 x x x 5 x x 6 S SD: 9.6244 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 9.6240 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 12.4754 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 11.3243 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 11.5755 cents 8 x 9 x 10:11 x 12:13 x 14:15:16 S SD: 9.4931 cents 9 x 10:11 x 12:13:14 x 15:16:17:18 S SD: 10.7852 cents 10:11 x 12:13 x 14:15:16:17:18:19:20 S SD: 8.1051 cents 11:12 x 13:14:15:16:17:18:19:20:21:22 S SD: 8.3142 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.3613 cents 13:14:15 x x 17:19:20:21:22:23:25:26 SD: 7.2816 cents 14:15:16:17:18:19:20:21:23:24:25:27:28 SD: 6.4139 cents 16:17:18:19:20:21:23:24:26:27:28:31:32 SD: 4.9432 cents 21:23:24:25:27:28:30:32:34:36:37:40:42 SD: 4.5735 cents 22:24:25:26:28:29:32:33:36:37:39:42:44 SD: 3.5935 cents 23:25:26:27:29:31:33:35:37:39:41:44:46 SD: 3.4756 cents 26:28:29:31:33:35:37:39:42:44:46:50:52 SD: 3.2031 cents 30:32:34:35:38:40:43:45:49:51:53:57:60 SD: 3.0007 cents 34:37:38:40:43:45:49:51:55:58:60:65:68 SD: 2.6555 cents 37:40:42:44:47:49:53:56:60:63:66:71:74 SD: 2.3847 cents 39:42:44:46:50:52:56:59:63:66:69:75:78 SD: 1.8039 cents 48:52:54:57:61:64:69:72:78:81:85:92:96 SD: 1.5108 cents 55:59:62:65:70:73:79:83:89:93:98:105:110 SD: 1.4069 cents 62:67:70:73:79:83:89:93:100:105:110:119:124 SD: 1.2787 cents 66:71:74:78:84:88:95:99:107:112:117:126:132 SD: 1.1223 cents 76:82:86:90:97:101:109:114:123:129:135:145:152 SD: 0.9894 cents 78:84:88:92:99:104:112:117:126:132:138:149:156 SD: 0.7612 cents 111:120:125:131:141:148:159:167:180:188:197:212:222 SD: 0.7495 cents 115:124:130:136:146:153:165:173:186:195:204:220:230 SD: 0.6651 cents 117:126:132:138:149:156:168:176:190:198:207:224:234 SD: 0.6616 cents 124:134:140:146:158:165:178:186:201:210:220:237:248 SD: 0.5757 cents 139:150:157:164:177:185:200:209:225:236:246:266:278 SD: 0.5755 cents 140:151:158:165:178:186:201:210:227:237:248:268:280 SD: 0.5447 cents 150:162:169:177:191:200:215:225:243:254:266:287:300 SD: 0.5105 cents 154:166:174:182:196:205:221:231:249:261:273:294:308 SD: 0.4982 cents 166:179:187:196:211:221:238:249:269:281:294:317:332 SD: 0.4911 cents 177:191:200:209:225:236:254:266:287:300:314:338:354 SD: 0.4549 cents 179:193:202:211:228:238:257:269:290:303:317:342:358 SD: 0.3852 cents 193:208:218:228:246:257:277:290:313:327:342:369:386 SD: 0.3791 cents 205:221:231:242:261:273:294:308:332:347:363:392:410 SD: 0.3488 cents 227:245:256:268:289:302:326:341:368:385:402:434:454 SD: 0.2977 cents 271:292:306:320:345:361:389:407:439:459:480:518:542 SD: 0.2593 cents 305:329:344:360:388:406:438:458:494:517:541:583:610 SD: 0.1411 cents 422:455:476:498:537:562:606:634:684:715:748:807:844 SD: 0.1231 cents 498:537:562:588:634:663:715:748:807:844:883:952:996 SD: 0.1104 cents 576:621:650:680:733:767:827:865:933:976:1021:1101:1152 SD: 0.0862 cents