Scala analysis: or7r6
Octave-reduced 2d tuning with 6^(1/7) as generator
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 129.409 cents 129.409290 2: 258.819 cents 258.818570 3: 313.727 cents 313.727140 4: 388.228 cents 388.227860 5: 443.136 cents 443.136430 6: 572.546 cents 572.545710 7: 3/2 701.955001 perfect fifth 8: 756.864 cents 756.863570 9: 886.273 cents 886.272860 10: 1015.682 cents 1015.682140 11: 1145.091 cents 1145.091430 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 54.9086 cents 54.9086 1: 129.4093 cents 129.4093 2: 129.4093 cents 129.4093 3: 54.9086 cents 54.9086 4: 74.5007 cents 74.5007 5: 54.9086 cents 54.9086 6: 129.4093 cents 129.4093 7: 129.4093 cents 129.4093 8: 54.9086 cents 54.9086 9: 129.4093 cents 129.4093 10: 129.4093 cents 129.4093 11: 129.4093 cents 129.4093 12: 54.9086 cents 54.9086
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 54.90857 cents 1: 1 74.50072 cents 1: 7 129.40929 cents 2: 2 129.40929 cents 2: 6 184.31785 cents 2: 4 258.81857 cents 3: 1 184.31786 cents 3: 2 258.81857 cents 3: 8 313.72714 cents 3: 1 388.22786 cents 4: 2 313.72714 cents 4: 2 368.63571 cents 4: 2 388.22786 cents 4: 6 443.13643 cents 5: 5 443.13643 cents 5: 3 498.04500 cents 5: 4 572.54571 cents 6: 2 498.04500 cents 6: 4 572.54571 cents 6: 4 627.45428 cents 6: 2 701.95500 cents 7: 4 627.45428 cents 7: 3 3/2 701.955 cents perfect fifth 7: 5 756.86357 cents 8: 6 756.86357 cents 8: 2 811.77214 cents 8: 2 831.36429 cents 8: 2 886.27286 cents 9: 1 811.77214 cents 9: 8 886.27286 cents 9: 2 941.18143 cents 9: 1 1015.68214 cents 10: 4 941.18143 cents 10: 6 1015.68214 cents 10: 2 1070.59071 cents 11: 7 1070.59071 cents 11: 1 1125.49928 cents 11: 4 1145.09143 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.45455 = 38/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 129.4 258.8 313.7 388.2 443.1 572.5 702.0 756.9 886.3 1015.7 1145.1 1200.0 129.4 : 129.4 184.3 258.8 313.7 443.1 572.5 627.5 756.9 886.3 1015.7 1070.6 1200.0 258.8 : 54.9 129.4 184.3 313.7 443.1 498.0 627.5 756.9 886.3 941.2 1070.6 1200.0 313.7 : 74.5 129.4 258.8 388.2 443.1 572.5 702.0 831.4 886.3 1015.7 1145.1 1200.0 388.2 : 54.9 184.3 313.7 368.6 498.0 627.5 756.9 811.8 941.2 1070.6 1125.5 1200.0 443.1 : 129.4 258.8 313.7 443.1 572.5 702.0 756.9 886.3 1015.7 1070.6 1145.1 1200.0 572.5 : 129.4 184.3 313.7 443.1 572.5 627.5 756.9 886.3 941.2 1015.7 1070.6 1200.0 702.0 : 54.9 184.3 313.7 443.1 498.0 627.5 756.9 811.8 886.3 941.2 1070.6 1200.0 756.9 : 129.4 258.8 388.2 443.1 572.5 702.0 756.9 831.4 886.3 1015.7 1145.1 1200.0 886.3 : 129.4 258.8 313.7 443.1 572.5 627.5 702.0 756.9 886.3 1015.7 1070.6 1200.0 1015.7: 129.4 184.3 313.7 443.1 498.0 572.5 627.5 756.9 886.3 941.2 1070.6 1200.0 1145.1: 54.9 184.3 313.7 368.6 443.1 498.0 627.5 756.9 811.8 941.2 1070.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 54.9086 .. 129.4093 cents 74.50072 cents 54.90857 cents 2: 129.4093 .. 258.8186 cents 129.40928 cents 1/1, 0.0000 cents 3: 184.3179 .. 388.2279 cents 203.91000 cents -74.50071 cents 4: 313.7271 .. 443.1364 cents 129.40929 cents -74.50072 cents 5: 443.1364 .. 572.5457 cents 129.40928 cents 1/1, 0.0000 cents 6: 498.0450 .. 701.9550 cents 203.91000 cents -74.50071 cents 7: 627.4543 .. 756.8636 cents 129.40929 cents -74.50072 cents 8: 756.8636 .. 886.2729 cents 129.40929 cents 1/1, 0.0000 cents 9: 811.7721 .. 1015.6821 cents 203.91000 cents -74.50072 cents 10: 941.1814 .. 1070.5907 cents 129.40928 cents -74.50071 cents 11: 1070.5907 .. 1145.0914 cents 74.50072 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 54.90857 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 129.40929 cents Average / Smallest step : 1.821209 Largest / Average step : 1.294093 Largest / Smallest step : 2.356814 Median interval of one step : 129.40929 cents, amount: 7 Most common interval of one step : 129.40929 cents, amount: 7 Least squares average step : 99.83073 cents, oct.: 1197.96872 cents Scale is not proper Step pattern alph. order: AABCBAABAAAB Step pattern size order : LLSMSLLSLLLS Scale is not a Constant Structure Scale diversity : 1.222926 Lumma stability : 0.091514 Lumma impropriety factor : 0.372504 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 : 3 Highest interval variety : 4 Mean interval variety : 3.45455 = 38/11 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 19.59215 cents Most common intervals : 443.13643 cents & inv., amount: 11 Scale has Generated (pseudo-Myhill) property, generator: 756.864 cents and inv. Scale is a chain of 6 triads 0.0 184.318 443.136 cents Most common triad is 0.0 443.136 756.864 cents, amount: 10 Number of recognisable fifths : 5, average 701.9550 cents Formal octave complements present : 5 = 41.6667% Limited inverse transpositions : 7 Inversional symmetry on intervals : 3-4 9-10 -- Rational properties -- Prime limit : 3 (not all pitches rational)
FIT/MODE
12: 1 1 1 1 0 1 2 0 2 1 1 1 N T3 SD: 38.1664 c. M: 72.5457 c. 13: 1 2 0 1 1 1 1 1 1 2 1 1 N SD: 31.6753 c. M: 55.8012 c. 15: 2 1 1 1 1 1 2 0 2 2 1 1 N SD: 22.2280 c. M:-36.8636 c. 18: 2 2 1 1 1 2 2 0 2 2 2 1 N SD: 18.7400 c. M:-31.3783 c. 19: 2 2 1 1 1 2 2 1 2 2 2 1 N SD: 5.0692 c. M: 9.2805 c. 46: 5 5 2 3 2 5 5 2 5 5 5 2 N G SD: 1.6804 c. M:-3.0765 c. 65: 7 7 3 4 3 7 7 3 7 7 7 3 N G SD: 0.2925 c. M: 0.5356 c. 176: 19 19 8 11 8 19 19 8 19 19 19 8 N G SD: 0.2231 c. M:-0.4085 c. 241: 26 26 11 15 11 26 26 11 26 26 26 11 N G SD: 0.0841 c. M:-0.1539 c. 306: 33 33 14 19 14 33 33 14 33 33 33 14 N G SD: 0.0041 c. M:-0.0074 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: 0.0000 cents 3 x x x x 4 x x x 5 x x 6 S SD: 18.3140 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 11.7238 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 11.5507 cents 6 x 7 x x 8 x 9 x 10:11 x 12 S SD: 10.8242 cents 7 x 8 x x 9:10 x 11:12:13 x 14 S SD: 13.4311 cents 8 x 9 x 10 x 11:12 x 13:14 x 16 S SD: 12.5823 cents 9:10 x 11 x 12:13 x 14:15:16:17:18 S SD: 12.8886 cents 10:11 x 12 x 13:14:15 x 17:18:19:20 SD: 6.7520 cents 11:12 x 13 x 14:15 x 17:18:20:21:22 SD: 7.9739 cents 12:13:14 x 15:16:17:18:19:20:22:23:24 S SD: 7.6508 cents 13:14:15 x 16:17:18 x 20:22:23:25:26 SD: 5.6224 cents 14:15:16:17 x 18:19:21:22:23:25:27:28 SD: 6.3871 cents 15:16:17:18:19 x 21 x 23:25:27:29:30 SD: 5.4204 cents 16:17 x 19:20:21:22:24:25:27:29:31:32 SD: 4.8997 cents 17:18:20 x 21:22:24 x 26:28:31:33:34 SD: 6.4083 cents 18:19:21:22 x 23:25:27:28:30:32:35:36 SD: 5.2526 cents 19:20:22:23:24:25:26 x 29:32:34:37:38 SD: 6.5202 cents 20:22:23:24:25:26:28:30:31:33:36:39:40 SD: 3.9821 cents 22:24 x 26 x 28:31:33:34:37:40:43:44 SD: 5.4384 cents 23:25:27:28:29:30:32:35:36:38:41:45:46 SD: 4.9443 cents 24:26:28:29:30:31:33:36:37:40:43:47:48 SD: 2.9273 cents 31:33:36:37:39:40:43:47:48:52:56:60:62 SD: 2.7958 cents 35:38:41:42:44:45:49:53:54:58:63:68:70 SD: 2.7642 cents 36:39:42:43:45:47:50:54:56:60:65:70:72 SD: 2.2112 cents 44:47:51:53:55:57:61:66:68:73:79:85:88 SD: 1.9187 cents 48:52:56:58:60:62:67:72:74:80:86:93:96 SD: 1.7982 cents 49:53:57:59:61:63:68:74:76:82:88:95:98 SD: 1.7928 cents 51:55:59:61:64:66:71:77:79:85:92:99:102 SD: 1.3618 cents 64:69:74:77:80:83:89:96:99:107:115:124:128 SD: 1.0800 cents 75:81:87:90:94:97:104:113:116:125:135:145:150 SD: 1.0589 cents 76:82:88:91:95:98:106:114:118:127:137:147:152 SD: 0.8993 cents 99:107:115:119:124:128:138:149:153:165:178:192:198 SD: 0.8805 cents 100:108:116:120:125:129:139:150:155:167:180:194:200 SD: 0.5948 cents 130:140:151:156:163:168:181:195:201:217:234:252:260 SD: 0.4436 cents 168:181:195:201:210:217:234:252:260:280:302:326:336 SD: 0.4365 cents 192:207:223:230:240:248:267:288:297:320:345:372:384 SD: 0.3327 cents 206:222:239:247:258:266:287:309:319:344:370:399:412 SD: 0.3052 cents 242:261:281:290:303:313:337:363:375:404:435:469:484 SD: 0.2895 cents 268:289:311:321:335:346:373:402:415:447:482:519:536 SD: 0.2707 cents 286:308:332:343:358:369:398:429:443:477:514:554:572 SD: 0.2457 cents 298:321:346:357:373:385:415:447:461:497:536:577:596 SD: 0.2224 cents 322:347:374:386:403:416:448:483:499:537:579:624:644 SD: 0.1675 cents 398:429:462:477:498:514:554:597:616:664:716:771:796 SD: 0.1276 cents 528:569:613:633:661:682:735:792:818:881:949:1023:1056 SD: 0.1233 cents 589:635:684:706:737:761:820:884:912:983:1059:1141:1178 SD: 0.1224 cents 594:640:690:712:743:767:827:891:920:991:1068:1151:1188 SD: 0.1114 cents