Scala analysis: tutone13
2.9.5.7.11 with {81/80, 126/125, 99/98} temperament in 16\99 tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 157.576 cents 157.575760 2: 193.939 cents 193.939390 3: 351.515 cents 351.515150 4: 387.879 cents 387.878790 5: 545.455 cents 545.454550 6: 581.818 cents 581.818180 7: 739.394 cents 739.393940 8: 775.758 cents 775.757580 9: 933.333 cents 933.333330 10: 969.697 cents 969.696970 11: 1127.273 cents 1127.272730 12: 1163.636 cents 1163.636360 13: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 36.3636 cents 36.3636 1: 157.5758 cents 157.5758 2: 36.3636 cents 36.3636 3: 157.5758 cents 157.5758 4: 36.3636 cents 36.3636 5: 157.5758 cents 157.5758 6: 36.3636 cents 36.3636 7: 157.5758 cents 157.5758 8: 36.3636 cents 36.3636 9: 157.5757 cents 157.5757 10: 36.3636 cents 36.3636 11: 157.5758 cents 157.5758 12: 36.3636 cents 36.3636 13: 36.3636 cents 36.3636
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 36.36363 cents 1: 6 157.57576 cents 2: 1 72.72727 cents 2: 12 193.93939 cents 3: 8 230.30303 cents 3: 5 351.51515 cents 4: 2 266.66667 cents 4: 11 387.87879 cents 5: 9 424.24242 cents 5: 4 545.45455 cents 6: 3 460.60606 cents 6: 10 581.81818 cents 7: 10 618.18182 cents 7: 3 739.39394 cents 8: 4 654.54545 cents 8: 9 775.75758 cents 9: 11 812.12121 cents 9: 2 933.33333 cents 10: 5 848.48485 cents 10: 8 969.69697 cents 11: 12 1006.06060 cents 11: 1 1127.27273 cents 12: 6 1042.42424 cents 12: 7 1163.63636 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 : 157.6 193.9 351.5 387.9 545.5 581.8 739.4 775.8 933.3 969.7 1127.3 1163.6 1200.0 157.6 : 36.4 193.9 230.3 387.9 424.2 581.8 618.2 775.8 812.1 969.7 1006.1 1042.4 1200.0 193.9 : 157.6 193.9 351.5 387.9 545.5 581.8 739.4 775.8 933.3 969.7 1006.1 1163.6 1200.0 351.5 : 36.4 193.9 230.3 387.9 424.2 581.8 618.2 775.8 812.1 848.5 1006.1 1042.4 1200.0 387.9 : 157.6 193.9 351.5 387.9 545.5 581.8 739.4 775.8 812.1 969.7 1006.1 1163.6 1200.0 545.5 : 36.4 193.9 230.3 387.9 424.2 581.8 618.2 654.5 812.1 848.5 1006.1 1042.4 1200.0 581.8 : 157.6 193.9 351.5 387.9 545.5 581.8 618.2 775.8 812.1 969.7 1006.1 1163.6 1200.0 739.4 : 36.4 193.9 230.3 387.9 424.2 460.6 618.2 654.5 812.1 848.5 1006.1 1042.4 1200.0 775.8 : 157.6 193.9 351.5 387.9 424.2 581.8 618.2 775.8 812.1 969.7 1006.1 1163.6 1200.0 933.3 : 36.4 193.9 230.3 266.7 424.2 460.6 618.2 654.5 812.1 848.5 1006.1 1042.4 1200.0 969.7 : 157.6 193.9 230.3 387.9 424.2 581.8 618.2 775.8 812.1 969.7 1006.1 1163.6 1200.0 1127.3: 36.4 72.7 230.3 266.7 424.2 460.6 618.2 654.5 812.1 848.5 1006.1 1042.4 1200.0 1163.6: 36.4 193.9 230.3 387.9 424.2 581.8 618.2 775.8 812.1 969.7 1006.1 1163.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 36.3636 .. 157.5758 cents 121.21213 cents 36.36363 cents 2: 72.7273 .. 193.9394 cents 121.21212 cents -84.84849 cents 3: 230.3030 .. 351.5152 cents 121.21212 cents 36.36364 cents 4: 266.6667 .. 387.8788 cents 121.21212 cents -84.84848 cents 5: 424.2424 .. 545.4546 cents 121.21213 cents 36.36363 cents 6: 460.6061 .. 581.8182 cents 121.21212 cents -84.84849 cents 7: 618.1818 .. 739.3939 cents 121.21212 cents 36.36364 cents 8: 654.5454 .. 775.7576 cents 121.21213 cents -84.84849 cents 9: 812.1212 .. 933.3333 cents 121.21212 cents 36.36363 cents 10: 848.4848 .. 969.6970 cents 121.21212 cents -84.84848 cents 11: 1006.0606 .. 1127.2727 cents 121.21213 cents 36.36363 cents 12: 1042.4242 .. 1163.6364 cents 121.21212 cents -84.84849 cents
SHOW DATA
Number of notes : 13 -- Interval properties -- Smallest interval : 36.36363 cents, class 1 Average step (divided formal octave): 92.3077 cents Largest one step interval : 157.57576 cents Average / Smallest step : 2.538462 Largest / Average step : 1.707071 Largest / Smallest step : 4.333334 Median interval of one step : 36.36363 cents, amount: 7 Most common interval of one step : 36.36363 cents, amount: 7 Least squares average step : 98.67170 cents, oct.: 1282.73208 cents Scale is not proper Scale has Myhill's property chromas: 121.21213 cents and 84.84850 cents, ratio: 1.428571 generators: 2 of 193.93939 cents and 1006.06061 cents ET pair of linear temperament : 31&99 Scale is distributional even Scale is a mode of a 99-tone equal temperament with octave 2/1 degrees: 13 16 29 32 45 48 61 64 77 80 93 96 99 generators: 16 and 83 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABABABABABB Step pattern size order : LSLSLSLSLSLSS Interval vector is [ 0 0 7 0 0 1 0 0 0 0 0 0 6 0 0 12 0 0 8 0 0 2 0 0 0 0 0 0 5 0 0 11 0 0 9 0 0 3 0 0 0 0 0 0 4 0 0 10 0 ] Scale is a Constant Structure, by a margin of 36.36363 cents Scale diversity : 1.188406 Lumma stability : 0.212121 Lumma impropriety factor : 0.424242 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 : 36.36363 cents Most common intervals : 193.93939 cents & inv., amount: 12 Scale is a chain of 6 triads 0.0 193.939 387.879 cents Most common triad is 0.0 193.939 1006.061 cents, amount: 11 Number of recognisable fifths : 0 Scale contains two identical disjunct hexachords Formal octave complements present : 1 = 7.6923% Limited inverse transpositions : 11 Inversional symmetry on degrees : 12 Inversional symmetry on intervals : 5-6 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
13: 2 0 2 0 2 0 2 0 2 1 1 1 0 N T3 SD: 24.2148 c. M:-45.6876 c. 14: 2 0 2 1 1 1 2 0 2 0 2 1 0 N T3 SD: 23.3347 c. M:-40.6926 c. 15: 2 0 2 1 2 0 2 1 2 0 2 1 0 N SD: 21.7143 c. M:-36.3636 c. 16: 2 1 2 0 2 1 2 0 2 1 2 1 0 N T3 SD: 20.9967 c. M:-36.3636 c. 17: 2 1 2 0 3 0 2 1 2 1 2 0 1 N SD: 20.3091 c. M: 34.9376 c. 18: 2 1 2 1 2 1 2 1 2 1 2 0 1 N T3 SD: 17.7095 c. M:-30.3030 c. 20: 3 0 3 0 3 1 2 1 3 0 3 0 1 N SD: 17.1568 c. M: 27.8788 c. 21: 3 0 3 1 3 0 3 1 2 1 3 0 1 N SD: 16.0367 c. M:-25.9740 c. 22: 3 1 2 1 3 1 3 0 3 1 3 0 1 N SD: 15.5881 c. M:-24.2424 c. 23: 3 1 3 0 3 1 3 1 3 1 3 0 1 N SD: 14.7939 c. M: 23.7154 c. 24: 3 1 3 1 3 1 3 1 3 1 3 0 1 N T3 SD: 15.6728 c. M:-30.3030 c. 25: 3 1 3 1 3 1 3 1 3 1 3 1 1 N M DE S SD: 13.7136 c. M: 23.2727 c. Hemithirds-13, Spell-13 29: 4 1 3 1 4 1 4 1 4 0 4 1 1 N SD: 12.0199 c. M: 20.4807 c. 30: 4 1 4 1 4 1 3 1 4 1 4 1 1 N SD: 11.6554 c. M: 19.3939 c. 31: 4 1 4 1 4 1 4 1 4 1 4 1 1 N M DE S SD: 2.7648 c. M: 4.6921 c. Hemithirds-13, Roulette-13 68: 9 2 9 2 9 2 9 2 9 2 9 2 2 N M DE S SD: 1.2604 c. M:-2.1390 c. Hemithirds-13 99: 13 3 13 3 13 3 13 3 13 3 13 3 3 N M DE S SD: 0.0000 c. M: 0.0000 c. Hemithirds-13
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 3 x x x x x 4 S SD: 18.7195 cents 3 x x x x 4 x x x 5 x x x 6 S SD: 22.7210 cents 4 x x x 5 x x 6 x x 7 x x 8 S SD: 9.3704 cents 5 x x 6 x x 7 x 8 x 9 x x 10 S SD: 14.1709 cents 6 x 7 x x 8 x 9 x 10 x x x 12 S SD: 21.3231 cents 7 x 8 x 9 x 10 x 11:12 x 13 x 14 S SD: 12.7940 cents 8 x 9 x 10:11 x 12:13 x 14:15 x 16 S SD: 10.6471 cents 9 x 10:11 x 12:13 x 14:15:16:17 x 18 S SD: 10.7158 cents 10:11 x 12:13 x 14:15:16:17:18:19 x 20 S SD: 10.6545 cents 11:12 x 13:14:15 x 17 x 19 x 21 x 22 SD: 9.1084 cents 12:13 x x 15:16:17:18:19 x 21:23 x 24 SD: 7.7422 cents 13:14:15:16 x 18 x 20 x 22:23:25 x 26 SD: 7.8839 cents 14:15:16:17:18:19:20:21:22:24:25:27 x 28 SD: 8.1499 cents 15:16:17:18:19 x 21:23 x x 26:29 x 30 SD: 7.7496 cents 16 x 18 x 20:22 x x 25:27:28:31 x 32 SD: 4.3604 cents 17 x 19:21 x 23:24:26:27:29:30 x 33:34 SD: 4.5501 cents 18 x 20:22:23 x 25 x 28:31:32 x 35:36 SD: 5.7537 cents 19:21 x 23:24:26:27:29:30 x 33:36:37:38 SD: 4.6941 cents 20:22 x x 25:27:28 x 31:34:35:38:39:40 SD: 3.9370 cents 21:23 x x 26:29 x 32:33:36:37:40:41:42 SD: 3.0664 cents 22:24:25:27:28:30:31:34 x 38:39:42:43:44 SD: 4.4098 cents 23:25:26:28:29 x 32:35:36:39:40:44:45:46 SD: 3.3249 cents 25:27:28 x 31:34:35:38:39:43:44:48:49:50 SD: 3.0876 cents 26:28:29:32:33:36 x 40:41:45:46:50:51:52 SD: 4.3402 cents 27 x 30:33:34:37:38:41:42:46:47:52:53:54 SD: 2.6916 cents 28 x 31:34:35:38:39:43:44:48:49:54:55:56 SD: 2.7391 cents 29:32 x x 36:40:41:44:45:50:51:56:57:58 SD: 3.7075 cents 30:33:34:37:38:41:42:46:47:51:53:58:59:60 SD: 3.3482 cents 32:35:36:39:40:44:45:49:50:55:56:61:63:64 SD: 1.7494 cents 37 x 41:45:46:51:52:57:58:63:65:71:72:74 SD: 2.7404 cents 39:43:44:48:49:53:55:60:61:67:68:75:76:78 SD: 2.5046 cents 40:44:45:49:50:55:56:61:63:69:70:77:78:80 SD: 1.8764 cents 43:47:48:53:54:59:60:66:67:74:75:82:84:86 SD: 1.6785 cents 49:54:55:60:61:67:69:75:77:84:86:94:96:98 SD: 1.5859 cents 52:57:58:64:65:71:73:80:81:89:91:100:102:104 SD: 1.3624 cents 60:66:67:74:75:82:84:92:94:103:105:115:118:120 SD: 1.2958 cents 67:73:75:82:84:92:94:103:105:115:117:128:131:134 SD: 1.1871 cents 73:80:82:89:91:100:102:112:114:125:128:140:143:146 SD: 1.0981 cents 75:82:84:92:94:103:105:115:117:129:131:144:147:150 SD: 0.8871 cents 84:92:94:103:105:115:118:129:131:144:147:161:165:168 SD: 0.8835 cents 92:101:103:113:115:126:129:141:144:158:161:176:180:184 SD: 0.7013 cents 116:127:130:142:145:159:162:178:182:199:203:222:227:232 SD: 0.6203 cents 124:136:139:152:155:170:174:190:194:213:217:238:243:248 SD: 0.6035 cents 135:148:151:165:169:185:189:207:211:231:236:259:264:270 SD: 0.5655 cents 143:157:160:175:179:196:200:219:224:245:250:274:280:286 SD: 0.4687 cents 160:175:179:196:200:219:224:245:250:274:280:307:313:320 SD: 0.4570 cents 168:184:188:206:210:230:235:258:263:288:294:322:329:336 SD: 0.3548 cents 210:230:235:257:263:288:294:322:329:360:368:403:411:420 SD: 0.3166 cents 218:239:244:267:273:299:305:334:341:374:382:418:427:436 SD: 0.2955 cents 253:277:283:310:317:347:354:388:396:434:443:485:495:506 SD: 0.2908 cents 262:287:293:321:328:359:367:402:410:449:459:502:513:524 SD: 0.2602 cents 270:296:302:331:338:370:378:414:423:463:473:518:529:540 SD: 0.2425 cents 294:322:329:360:368:403:411:451:460:504:515:564:576:588 SD: 0.2389 cents 306:335:342:375:383:419:428:469:479:525:536:587:599:612 SD: 0.2304 cents 315:345:352:386:394:432:441:483:493:540:552:604:617:630 SD: 0.2218 cents 338:370:378:414:423:463:473:518:529:579:592:648:662:676 SD: 0.1694 cents 378:414:423:463:473:518:529:579:592:648:662:725:740:756 SD: 0.1493 cents 430:471:481:527:538:589:602:659:673:737:753:825:842:860 SD: 0.1253 cents 533:584:596:653:667:730:746:817:834:914:933:1022:1044:1066 SD: 0.1241 cents 546:598:611:669:683:748:764:837:855:936:956:1047:1069:1092 SD: 0.1041 cents