Scala analysis: ozancirc
Circulating temperament in Ozan Yarman's 159-equal tuning
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 98.113 cents 98.113208 2: 196.226 cents 196.226415 3: 316.981 cents 316.981132 4: 384.906 cents 384.905660 5: 505.660 cents 505.660377 6: 588.679 cents 588.679245 7: 694.340 cents 694.339623 8: 807.547 cents 807.547170 9: 890.566 cents 890.566038 10: 1011.321 cents 1011.320755 11: 1079.245 cents 1079.245283 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 120.7547 cents 120.7547 1: 98.1132 cents 98.1132 2: 98.1132 cents 98.1132 3: 120.7547 cents 120.7547 4: 67.9245 cents 67.9245 5: 120.7547 cents 120.7547 6: 83.0189 cents 83.0189 7: 105.6604 cents 105.6604 8: 113.2075 cents 113.2075 9: 83.0189 cents 83.0189 10: 120.7547 cents 120.7547 11: 67.9245 cents 67.9245 12: 120.7547 cents 120.7547
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 67.92453 cents 1: 2 83.01887 cents 1: 2 98.11321 cents 1: 1 105.66038 cents 1: 1 113.20755 cents 1: 4 120.75472 cents 2: 5 188.67925 cents 2: 2 196.22642 cents 2: 2 203.77358 cents 2: 3 218.86792 cents 3: 2 271.69811 cents 3: 2 286.79245 cents 3: 2 301.88679 cents 3: 3 309.43396 cents 3: 3 316.98113 cents 4: 1 377.35849 cents 4: 4 384.90566 cents 4: 2 392.45283 cents 4: 2 407.54717 cents 4: 2 422.64151 cents 4: 1 437.73585 cents 5: 4 490.56604 cents 5: 1 498.11321 cents 5: 7 505.66038 cents 6: 3 573.58491 cents 6: 2 588.67925 cents 6: 1 596.22642 cents 6: 1 603.77358 cents 6: 2 611.32075 cents 6: 3 626.41509 cents 7: 7 694.33962 cents 7: 1 701.88679 cents 7: 4 709.43396 cents 8: 1 762.26415 cents 8: 2 777.35849 cents 8: 2 792.45283 cents 8: 2 807.54717 cents 8: 4 815.09434 cents 8: 1 822.64151 cents 9: 3 883.01887 cents 9: 3 890.56604 cents 9: 2 898.11321 cents 9: 2 913.20755 cents 9: 2 928.30189 cents 10: 3 981.13208 cents 10: 2 996.22642 cents 10: 2 1003.77358 cents 10: 5 1011.32075 cents 11: 4 1079.24528 cents 11: 1 1086.79245 cents 11: 1 1094.33962 cents 11: 2 1101.88679 cents 11: 2 1116.98113 cents 11: 2 1132.07547 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.90909 = 54/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 98.1 196.2 317.0 384.9 505.7 588.7 694.3 807.5 890.6 1011.3 1079.2 1200.0 98.1 : 98.1 218.9 286.8 407.5 490.6 596.2 709.4 792.5 913.2 981.1 1101.9 1200.0 196.2 : 120.8 188.7 309.4 392.5 498.1 611.3 694.3 815.1 883.0 1003.8 1101.9 1200.0 317.0 : 67.9 188.7 271.7 377.4 490.6 573.6 694.3 762.3 883.0 981.1 1079.2 1200.0 384.9 : 120.8 203.8 309.4 422.6 505.7 626.4 694.3 815.1 913.2 1011.3 1132.1 1200.0 505.7 : 83.0 188.7 301.9 384.9 505.7 573.6 694.3 792.5 890.6 1011.3 1079.2 1200.0 588.7 : 105.7 218.9 301.9 422.6 490.6 611.3 709.4 807.5 928.3 996.2 1117.0 1200.0 694.3 : 113.2 196.2 317.0 384.9 505.7 603.8 701.9 822.6 890.6 1011.3 1094.3 1200.0 807.5 : 83.0 203.8 271.7 392.5 490.6 588.7 709.4 777.4 898.1 981.1 1086.8 1200.0 890.6 : 120.8 188.7 309.4 407.5 505.7 626.4 694.3 815.1 898.1 1003.8 1117.0 1200.0 1011.3: 67.9 188.7 286.8 384.9 505.7 573.6 694.3 777.4 883.0 996.2 1079.2 1200.0 1079.2: 120.8 218.9 317.0 437.7 505.7 626.4 709.4 815.1 928.3 1011.3 1132.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 67.9245 .. 120.7547 cents 52.83019 cents 67.92453 cents 2: 188.6792 .. 218.8679 cents 30.18868 cents 67.92453 cents 3: 271.6981 .. 316.9811 cents 45.28302 cents 52.83019 cents 4: 377.3585 .. 437.7358 cents 60.37736 cents 60.37736 cents 5: 490.5660 .. 505.6604 cents 15.09434 cents 52.83019 cents 6: 573.5849 .. 626.4151 cents 52.83019 cents 67.92453 cents 7: 694.3396 .. 709.4340 cents 15.09434 cents 67.92453 cents 8: 762.2642 .. 822.6415 cents 60.37736 cents 52.83019 cents 9: 883.0189 .. 928.3019 cents 45.28302 cents 60.37736 cents 10: 981.1321 .. 1011.3208 cents 30.18868 cents 52.83019 cents 11: 1079.2453 .. 1132.0755 cents 52.83019 cents 67.92453 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 67.92453 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 120.75472 cents Average / Smallest step : 1.472222 Largest / Average step : 1.207547 Largest / Smallest step : 1.777778 Median interval of one step : 101.88679 cents, amount: 0 Most common interval of one step : 120.75472 cents, amount: 4 Least squares average step : 99.63425 cents, oct.: 1195.61103 cents Scale is strictly proper Scale is a mode of a 159-tone equal temperament with octave 1200.000 cents degrees: 13 26 42 51 67 78 92 107 118 134 143 159 Least number of segments generator : 80 of 603.774 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 136 of 1026.415 cents and inv. generated superset size: 73 = 61 more = 608.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: AABCBDEFDBCB Step pattern size order : CCFAFBDEBFAF Interval vector is [ 0 0 0 0 0 0 0 0 2 0 2 0 2 1 1 4 0 0 0 0 0 0 0 0 5 2 2 0 3 0 0 0 0 0 0 2 0 2 0 2 3 3 0 0 0 0 0 0 0 1 4 2 0 2 0 2 0 1 0 0 0 0 0 0 4 1 7 0 0 0 0 0 0 0 0 3 0 2 1 ] Scale is a Constant Structure, by a margin of 52.83019 cents Scale diversity : 1.339151 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.616352 Rothenberg efficiency : 0.285795 redundancy: 0.714205 Efficiency x scale size : 3.429545 Number of different interval sizes : 54 = 4.90909 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 4.90909 = 54/11 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 7.54717 cents Most common intervals : 505.66038 cents & inv., amount: 7 Most common triad is 0.0 505.660 694.340 cents, amount: 5 Number of recognisable fifths : 12, average 700.0000 cents Best fifths form a closed circle Formal octave complements present : 3 = 25.0000% Limited transpositions with margin 52.8302 cents: 5 7 Limited inverse transpositions with margin 52.8302 cents: 2 7 9 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 10.9206 c. M:-20.7547 c. Twelve-tone Chromatic (1/11-comma) 26: 2 2 3 1 3 2 2 2 2 3 1 3 P D3 S SD: 11.6542 c. M: 22.9318 c. 28: 2 3 2 2 3 2 2 3 2 3 1 3 SP D3 SD: 11.3245 c. M:-18.0593 c. 30: 2 3 3 2 3 2 2 3 2 3 2 3 SP D3 SD: 10.8629 c. M: 18.1132 c. 31: 3 2 3 2 3 2 3 3 2 3 2 3 SP M ME SD: 6.7091 c. M:-18.0158 c. Genus diatonico-chromaticum 34: 3 3 3 2 3 3 3 3 2 4 2 3 SP D3 SD: 9.8465 c. M:-15.5383 c. 36: 3 3 4 2 3 3 3 3 3 3 2 4 P T3 S SD: 9.7366 c. M:-16.3522 c. 37: 3 3 4 2 3 3 3 4 2 4 2 4 SP SD: 9.0871 c. M: 19.1739 c. 38: 3 3 4 2 4 3 3 4 2 4 2 4 SP D3 SD: 6.3031 c. M:-13.5055 c. 43: 4 3 4 3 4 3 4 4 3 4 3 4 SP M ME SD: 6.3451 c. M:-13.5147 c. Genus diatonico-chromaticum 47: 4 4 4 3 5 3 4 5 3 5 2 5 SP SD: 6.4169 c. M: 10.5982 c. 49: 4 4 5 3 5 3 4 5 3 5 3 5 SP SD: 5.2851 c. M: 8.9334 c. 50: 4 4 5 3 5 4 4 5 3 5 3 5 SP D3 SD: 4.7545 c. M:-11.3208 c. 53: 4 5 5 3 5 4 5 5 3 6 3 5 SP SD: 6.1622 c. M: 7.5472 c. 57: 5 4 6 3 6 4 5 5 4 6 3 6 SP SD: 4.6860 c. M: 7.5472 c. 59: 5 5 6 3 6 4 5 6 4 6 3 6 SP SD: 4.5029 c. M:-8.4426 c. 62: 5 5 6 4 6 4 6 6 4 6 4 6 SP D3 S SD: 4.2560 c. M: 8.0341 c. 69: 6 5 7 4 7 5 6 6 5 7 4 7 SP SD: 3.7866 c. M: 7.5472 c. 71: 6 6 7 4 7 5 6 7 5 7 4 7 SP SD: 3.5680 c. M:-6.5905 c. 82: 7 6 9 4 9 5 7 8 6 8 5 8 SP SD: 4.3081 c. M:-6.5347 c. 83: 7 7 8 5 8 6 7 8 6 8 5 8 SP SD: 3.6567 c. M:-6.1832 c. 86: 7 7 9 5 8 6 8 8 6 8 5 9 SP S SD: 3.6076 c. M: 6.6696 c. 88: 7 7 9 5 9 6 8 8 6 9 5 9 SP S SD: 2.8787 c. M: 5.3173 c. 97: 8 8 10 5 10 7 8 9 7 10 5 10 SP SD: 2.7203 c. M:-5.1352 c. 100: 8 8 10 6 10 7 9 9 7 10 6 10 SP S SD: 2.6567 c. M: 4.9811 c. 102: 8 9 10 6 10 7 9 10 7 10 6 10 SP SD: 2.6186 c. M:-4.2175 c. 109: 9 9 11 6 11 7 10 10 8 11 6 11 SP SD: 2.1810 c. M: 5.1930 c. 110: 9 9 11 6 11 8 10 10 8 11 6 11 SP S SD: 2.3543 c. M:-3.9794 c. 116: 9 10 12 6 12 8 10 11 8 12 6 12 SP SD: 2.3521 c. M: 5.0098 c. 121: 10 10 12 7 12 8 11 11 9 12 7 12 SP SD: 1.9795 c. M: 4.2414 c. 128: 10 11 13 7 13 9 11 12 9 13 7 13 SP SD: 1.6249 c. M: 4.3632 c. 131: 11 10 14 7 13 9 12 12 9 13 8 13 SP SD: 2.4205 c. M: 3.8600 c. 132: 11 11 13 7 14 9 11 13 9 13 8 13 SP SD: 2.4389 c. M:-3.7736 c. 133: 11 11 13 8 13 9 12 13 9 13 8 13 SP SD: 2.2783 c. M:-4.4829 c. 135: 11 11 14 7 14 9 12 13 9 14 7 14 SP SD: 1.9414 c. M: 3.6897 c. 140: 11 12 14 8 14 10 12 13 10 14 8 14 SP SD: 1.5389 c. M: 3.8275 c. 147: 12 12 15 8 15 10 13 14 10 15 8 15 SP SD: 0.8915 c. M: 1.6943 c. 159: 13 13 16 9 16 11 14 15 11 16 9 16 SP SD: 0.0000 c. M:-0.0000 c. Yarman-12
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: 3.8077 cents 3 x x x x 4 x x x 5 x x 6 S SD: 3.2749 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 10.7987 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 2.1624 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.9422 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 12.0080 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.3758 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.6325 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.4872 cents 11 x 12:13:14:15 x 16 x 18:20:21:22 S SD: 11.4376 cents 12:13 x 14:15:16:17:18:19:20 x 22:24 S SD: 7.4473 cents 13:14:15 x 16:17:18:19:21:22:23:24:26 SD: 8.9742 cents 14:15:16:17 x 19:20:21:22:23:25:26:28 SD: 6.5370 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 4.0745 cents 18:19:20:22 x 24:25:27:29:30:32:34:36 SD: 4.7462 cents 20:21:22:24:25:27:28:30:32:33:36:37:40 SD: 3.9880 cents 24:25:27:29:30:32:34:36:38:40:43:45:48 SD: 3.2437 cents 30:32:34:36:37:40:42:45:48:50:54:56:60 SD: 3.0661 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.6847 cents 35:37:39:42:44:47:49:52:56:59:63:65:70 SD: 2.1523 cents 44:47:49:53:55:59:62:66:70:74:79:82:88 SD: 2.0117 cents 49:52:55:59:61:66:69:73:78:82:88:91:98 SD: 1.4243 cents 59:62:66:71:74:79:83:88:94:99:106:110:118 SD: 1.3717 cents 64:68:72:77:80:86:90:96:102:107:115:119:128 SD: 1.3284 cents 65:69:73:78:81:87:91:97:104:109:117:121:130 SD: 1.2259 cents 67:71:75:80:84:90:94:100:107:112:120:125:134 SD: 1.1749 cents 69:73:77:83:86:92:97:103:110:115:124:129:138 SD: 1.1412 cents 83:88:93:100:104:111:117:124:132:139:149:155:166 SD: 0.9923 cents 89:94:100:107:111:119:125:133:142:149:160:166:178 SD: 0.7575 cents 101:107:113:121:126:135:142:151:161:169:181:188:202 SD: 0.6440 cents 116:123:130:139:145:155:163:173:185:194:208:216:232 SD: 0.6388 cents 124:131:139:149:155:166:174:185:198:207:222:231:248 SD: 0.6195 cents 136:144:152:163:170:182:191:203:217:227:244:254:272 SD: 0.5987 cents 140:148:157:168:175:187:197:209:223:234:251:261:280 SD: 0.5617 cents 141:149:158:169:176:189:198:211:225:236:253:263:282 SD: 0.5263 cents 150:159:168:180:187:201:211:224:239:251:269:280:300 SD: 0.4447 cents 168:178:188:202:210:225:236:251:268:281:301:313:336 SD: 0.3841 cents 209:221:234:251:261:280:294:312:333:350:375:390:418 SD: 0.3166 cents 257:272:288:309:321:344:361:384:410:430:461:479:514 SD: 0.2634 cents 274:290:307:329:342:367:385:409:437:458:491:511:548 SD: 0.2122 cents 357:378:400:429:446:478:502:533:569:597:640:666:714 SD: 0.2045 cents 358:379:401:430:447:479:503:535:571:599:642:668:716 SD: 0.1996 cents 377:399:422:453:471:505:530:563:601:631:676:703:754 SD: 0.1881 cents 393:416:440:472:491:526:552:587:627:657:705:733:786 SD: 0.1793 cents 407:431:456:489:508:545:572:608:649:681:730:759:814 SD: 0.1776 cents 442:468:495:531:552:592:621:660:705:739:793:824:884 SD: 0.1573 cents 474:502:531:569:592:635:666:708:756:793:850:884:948 SD: 0.1520 cents 483:511:541:580:603:647:679:721:770:808:866:901:966 SD: 0.1443 cents 498:527:558:598:622:667:700:744:794:833:893:929:996 SD: 0.1102 cents