Scala analysis: xen18-schulter-707-12
Temperament with fifth of 707.22045
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 150.543 cents 150.543150 2: 214.441 cents 214.440900 3: 278.339 cents 278.338650 4: 428.882 cents 428.881800 5: 492.780 cents 492.779550 6: 643.323 cents 643.322700 7: 707.220 cents 707.220450 8: 857.764 cents 857.763600 9: 921.661 cents 921.661350 10: 985.559 cents 985.559100 11: 1136.102 cents 1136.102250 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 63.8978 cents 63.8978 1: 150.5431 cents 150.5431 2: 63.8978 cents 63.8978 3: 63.8977 cents 63.8977 4: 150.5431 cents 150.5431 5: 63.8978 cents 63.8978 6: 150.5431 cents 150.5431 7: 63.8977 cents 63.8977 8: 150.5431 cents 150.5431 9: 63.8978 cents 63.8978 10: 63.8977 cents 63.8977 11: 150.5431 cents 150.5431 12: 63.8978 cents 63.8978
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 63.89775 cents 1: 5 150.54315 cents 2: 2 127.79550 cents 2: 10 214.44090 cents 3: 9 278.33865 cents 3: 3 364.98405 cents 4: 4 342.23640 cents 4: 8 428.88180 cents 5: 11 492.77955 cents 5: 1 579.42495 cents 6: 6 556.67730 cents 6: 6 643.32270 cents 7: 1 620.57505 cents 7: 11 707.22045 cents 8: 8 771.11820 cents 8: 4 857.76360 cents 9: 3 835.01595 cents 9: 9 921.66135 cents 10: 10 985.55910 cents 10: 2 1072.20450 cents 11: 5 1049.45685 cents 11: 7 1136.10225 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 0.0 : 150.5 214.4 278.3 428.9 492.8 643.3 707.2 857.8 921.7 985.6 1136.1 1200.0 150.5 : 63.9 127.8 278.3 342.2 492.8 556.7 707.2 771.1 835.0 985.6 1049.5 1200.0 214.4 : 63.9 214.4 278.3 428.9 492.8 643.3 707.2 771.1 921.7 985.6 1136.1 1200.0 278.3 : 150.5 214.4 365.0 428.9 579.4 643.3 707.2 857.8 921.7 1072.2 1136.1 1200.0 428.9 : 63.9 214.4 278.3 428.9 492.8 556.7 707.2 771.1 921.7 985.6 1049.5 1200.0 492.8 : 150.5 214.4 365.0 428.9 492.8 643.3 707.2 857.8 921.7 985.6 1136.1 1200.0 643.3 : 63.9 214.4 278.3 342.2 492.8 556.7 707.2 771.1 835.0 985.6 1049.5 1200.0 707.2 : 150.5 214.4 278.3 428.9 492.8 643.3 707.2 771.1 921.7 985.6 1136.1 1200.0 857.8 : 63.9 127.8 278.3 342.2 492.8 556.7 620.6 771.1 835.0 985.6 1049.5 1200.0 921.7 : 63.9 214.4 278.3 428.9 492.8 556.7 707.2 771.1 921.7 985.6 1136.1 1200.0 985.6 : 150.5 214.4 365.0 428.9 492.8 643.3 707.2 857.8 921.7 1072.2 1136.1 1200.0 1136.1: 63.9 214.4 278.3 342.2 492.8 556.7 707.2 771.1 921.7 985.6 1049.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 63.8978 .. 150.5431 cents 86.64540 cents 63.89775 cents 2: 127.7955 .. 214.4409 cents 86.64540 cents -22.74765 cents 3: 278.3386 .. 364.9841 cents 86.64540 cents 63.89775 cents 4: 342.2364 .. 428.8818 cents 86.64540 cents -22.74765 cents 5: 492.7796 .. 579.4249 cents 86.64540 cents 63.89775 cents 6: 556.6773 .. 643.3227 cents 86.64540 cents -22.74765 cents 7: 620.5751 .. 707.2205 cents 86.64540 cents -22.74765 cents 8: 771.1182 .. 857.7636 cents 86.64540 cents 63.89775 cents 9: 835.0159 .. 921.6613 cents 86.64540 cents -22.74765 cents 10: 985.5591 .. 1072.2045 cents 86.64540 cents 63.89775 cents 11: 1049.4569 .. 1136.1022 cents 86.64540 cents -22.74765 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 63.89775 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 150.54315 cents Average / Smallest step : 1.565000 Largest / Average step : 1.505431 Largest / Smallest step : 2.356001 Median interval of one step : 63.89775 cents, amount: 7 Most common interval of one step : 63.89775 cents, amount: 7 Least squares average step : 102.02173 cents, oct.: 1224.26071 cents Scale is not proper Scale has Myhill's property chromas: 86.64540 cents and 22.74765 cents, ratio: 3.808982 generators: 5 of 492.77955 cents and 7 of 707.22045 cents ET pair of linear temperament : 17&39 Scale is distributional even Scale is a mode of a 1108-tone equal temperament with octave 1200.000 cents degrees: 139 198 257 396 455 594 653 792 851 910 1049 1108 generators: 455 and 653 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBABABABBAB Step pattern size order : LSSLSLSLSSLS Scale is a Constant Structure, by a margin of 22.74765 cents Ratio Whole / Half tone : 3.356001 Scale diversity : 1.216191 Lumma stability : 0.319489 Lumma impropriety factor : 0.113738 Rothenberg efficiency : 0.722222 redundancy: 0.277778 Efficiency x scale size : 8.666667 Number of different interval sizes : 22 = 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 : 22.74765 cents Most common intervals : 492.77955 cents & inv., amount: 11 Scale is a chain of 6 triads 0.0 63.898 707.220 cents Most common triad is 0.0 492.780 707.220 cents, amount: 10 Number of recognisable fifths : 11, average 707.2205 cents Scale contains two identical disjunct hexachords 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: 30.7753 c. M: 57.7636 c. Twelve-tone Chromatic (1/11-comma) 13: 2 0 1 2 0 2 1 1 1 1 1 1 N D3 SD: 25.0106 c. M:-34.0722 c. 17: 2 1 1 2 1 2 1 2 1 1 2 1 P M ME SD: 5.7033 c. M: 10.7048 c. Twelve-tone Chromatic (2/11-comma positive) 39: 5 2 2 5 2 5 2 5 2 2 5 2 N M DE SD: 2.0112 c. M:-3.7749 c. Twelve-tone Chromatic (1/4-comma positive) 56: 7 3 3 7 3 7 3 7 3 3 7 3 N M DE SD: 0.3307 c. M: 0.6207 c. 151: 19 8 8 19 8 19 8 19 8 8 19 8 N M DE SD: 0.2741 c. M:-0.5145 c. Reverse Meantone-12 207: 26 11 11 26 11 26 11 26 11 11 26 11 N M DE SD: 0.1105 c. M:-0.2074 c. 263: 33 14 14 33 14 33 14 33 14 14 33 14 N M DE SD: 0.0166 c. M:-0.0311 c. 845: 106 45 45 106 45 106 45 106 45 45 106 45 N M DE SD: 0.0065 c. M: 0.0121 c. 1108: 139 59 59 139 59 139 59 139 59 59 139 59 N M DE SD: 0.0010 c. M: 0.0019 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: 2.6327 cents 3 x x x x 4 x x 5 x x x 6 S SD: 9.0371 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 11.5102 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 17.9539 cents 6 x x 7 x 8 x 9:10 x 11 x 12 S SD: 11.7440 cents 7 x 8 x 9 x 10 x 11:12 x x 14 S SD: 13.7267 cents 8 x 9 x 10:11 x 12:13 x 14:15:16 S SD: 11.3486 cents 9:10 x 11 x 12:13:14:15 x 16:17:18 S SD: 11.7769 cents 10:11 x 12:13 x x 15:16:17:18:19:20 SD: 8.5118 cents 11:12 x 13:14:15:16:17:18:19 x 21:22 SD: 7.2715 cents 12:13 x 14:15:16:17:18:20 x 21:23:24 SD: 6.9650 cents 13:14 x 15 x 17:19:20:21:22:23:25:26 SD: 6.9316 cents 14:15:16 x 18:19:20:21:23:24:25:27:28 SD: 5.5583 cents 16:17:18:19 x 21:23:24:26:27:28:31:32 SD: 5.8925 cents 17 x 19:20:22:23:25:26:28:29:30:33:34 SD: 5.2407 cents 18:20 x 21:23:24:26:27:30:31:32:35:36 SD: 4.7179 cents 19:21 x 22:24:25:28:29:31:32:34:37:38 SD: 6.2285 cents 20:22:23 x 26:27:29:30:33:34:35:39:40 SD: 5.0852 cents 21:23:24:25:27:28:30:32:34:36:37:40:42 SD: 4.7394 cents 22:24:25:26:28:29:32:33:36:37:39:42:44 SD: 3.0790 cents 30:33:34:35:38:40:44:45:49:51:53:58:60 SD: 2.9843 cents 31:34:35:36:40:41:45:47:51:53:55:60:62 SD: 2.7113 cents 33:36:37:39:42:44:48:50:54:56:58:64:66 SD: 2.6111 cents 36:39:41:42:46:48:52:54:59:61:64:69:72 SD: 2.3551 cents 40:44:45:47:51:53:58:60:66:68:71:77:80 SD: 2.0555 cents 45:49:51:53:58:60:65:68:74:77:80:87:90 SD: 1.8548 cents 46:50:52:54:59:61:67:69:75:78:81:89:92 SD: 1.7028 cents 53:58:60:62:68:70:77:80:87:90:94:102:106 SD: 1.4985 cents 64:70:72:75:82:85:93:96:105:109:113:123:128 SD: 1.2297 cents 67:73:76:79:86:89:97:101:110:114:118:129:134 SD: 0.9709 cents 85:93:96:100:109:113:123:128:140:145:150:164:170 SD: 0.9200 cents 91:99:103:107:117:121:132:137:149:155:161:175:182 SD: 0.8504 cents 97:106:110:114:124:129:141:146:159:165:171:187:194 SD: 0.7450 cents 107:117:121:126:137:142:155:161:176:182:189:206:214 SD: 0.7287 cents 121:132:137:142:155:161:175:182:199:206:214:233:242 SD: 0.5503 cents 142:155:161:167:182:189:206:214:233:242:251:274:284 SD: 0.4971 cents 167:182:189:196:214:222:242:251:274:284:295:322:334 SD: 0.3277 cents 189:206:214:222:242:251:274:284:310:322:334:364:378 SD: 0.3223 cents 206:225:233:242:264:274:299:310:338:351:364:397:412 SD: 0.2906 cents 242:264:274:284:310:322:351:364:397:412:428:466:484 SD: 0.2832 cents 264:288:299:310:338:351:383:397:433:450:466:509:528 SD: 0.2828 cents 274:299:310:322:351:364:397:412:450:467:484:528:548 SD: 0.2661 cents 309:337:350:363:396:411:448:465:507:526:546:596:618 SD: 0.1987 cents 349:381:395:410:447:464:506:525:573:594:617:673:698 SD: 0.1897 cents 373:407:422:438:478:496:541:561:612:635:659:719:746 SD: 0.1384 cents 516:563:584:606:661:686:748:776:847:879:912:995:1032 SD: 0.1217 cents 562:613:636:660:720:747:815:846:922:957:993:1083:1124 SD: 0.1081 cents