Scala analysis: ra1
random 1 scale, "Inverse quahog"
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 154.839 cents 154.838710 2: 309.677 cents 309.677419 3: 464.516 cents 464.516129 4: 696.774 cents 696.774194 5: 851.613 cents 851.612903 6: 967.742 cents 967.741935 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 232.2581 cents 232.2581 1: 154.8387 cents 154.8387 2: 154.8387 cents 154.8387 3: 154.8387 cents 154.8387 4: 232.2581 cents 232.2581 5: 154.8387 cents 154.8387 6: 116.1290 cents 116.1290 7: 232.2581 cents 232.2581
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 116.12903 cents 1: 4 154.83871 cents 1: 2 232.25806 cents 2: 1 270.96774 cents 2: 2 309.67742 cents 2: 1 348.38710 cents 2: 3 387.09677 cents 3: 1 464.51613 cents 3: 3 503.22581 cents 3: 3 541.93548 cents 4: 3 658.06452 cents 4: 3 696.77419 cents 4: 1 735.48387 cents 5: 3 812.90323 cents 5: 1 851.61290 cents 5: 2 890.32258 cents 5: 1 929.03226 cents 6: 2 967.74194 cents 6: 4 1045.16129 cents 6: 1 1083.87097 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.33333 = 10/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 154.8 309.7 464.5 696.8 851.6 967.7 1200.0 154.8 : 154.8 309.7 541.9 696.8 812.9 1045.2 1200.0 309.7 : 154.8 387.1 541.9 658.1 890.3 1045.2 1200.0 464.5 : 232.3 387.1 503.2 735.5 890.3 1045.2 1200.0 696.8 : 154.8 271.0 503.2 658.1 812.9 967.7 1200.0 851.6 : 116.1 348.4 503.2 658.1 812.9 1045.2 1200.0 967.7 : 232.3 387.1 541.9 696.8 929.0 1083.9 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 116.1290 .. 232.2581 cents 116.12903 cents 116.12903 cents 2: 270.9677 .. 387.0968 cents 116.12903 cents 38.70968 cents 3: 464.5161 .. 541.9355 cents 77.41935 cents 77.41935 cents 4: 658.0645 .. 735.4839 cents 77.41935 cents 116.12903 cents 5: 812.9032 .. 929.0323 cents 116.12903 cents 77.41935 cents 6: 967.7419 .. 1083.8710 cents 116.12903 cents 38.70968 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 116.12903 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 232.25806 cents Average / Smallest step : 1.476190 Largest / Average step : 1.354839 Largest / Smallest step : 2.000000 Median interval of one step : 154.83871 cents, amount: 4 Most common interval of one step : 154.83871 cents, amount: 4 Least squares average step : 167.28111 cents, oct.: 1170.96774 cents Scale is strictly proper Scale is a mode of a 31-tone equal temperament with octave 1200.000 cents degrees: 4 8 12 18 22 25 31 Least number of segments generator : 17 of 658.065 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 22 of 851.613 cents and inv. generated superset size: 14 = 7 more = 200.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: AAABACB Step pattern size order : MMMLMSL Interval vector is [ 0 0 1 4 0 2 1 2 1 3 0 1 3 3 0 ] Scale is a Constant Structure, by a margin of 38.70968 cents Scale diversity : 1.451723 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.483871 Rothenberg efficiency : 0.466667 redundancy: 0.533333 Efficiency x scale size : 3.266667 Number of different interval sizes : 20 = 3.33333 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.33333 = 10/3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 38.70968 cents Most common intervals : 154.83871 cents & inv., amount: 4 Most common triad is 0.0 154.839 1045.161 cents, amount: 2 Number of recognisable fifths : 3, average 696.7742 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 1 = 14.2857% -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 33.1797 c. M:-60.8295 c. Lebeng 10: 1 2 1 2 1 1 2 P M ME S SD: 25.9672 c. M:-50.3226 c. 11: 1 2 1 2 2 1 2 P M ME S SD: 28.3404 c. M: 45.7478 c. 14: 2 2 1 3 2 1 3 P T3 SD: 22.1691 c. M: 35.9447 c. 15: 2 2 2 3 2 1 3 P D3 SD: 15.9380 c. M:-28.3871 c. 16: 2 2 2 3 2 2 3 SP M ME S SD: 14.9419 c. M: 26.6129 c. Antilydian 20: 3 2 3 4 2 2 4 P S SD: 15.5872 c. M:-25.1613 c. 21: 3 2 3 4 3 2 4 SP T3 SD: 12.3654 c. M: 23.9631 c. 24: 3 3 3 5 3 2 5 P SD: 9.6774 c. M: 17.7419 c. 30: 4 4 4 5 4 3 6 SP SD: 11.0137 c. M: 16.7742 c. 31: 4 4 4 6 4 3 6 SP SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 2.5904 cents 3 x x 4 x 5 x 6 S SD: 15.6222 cents 4 x 5 x 6 x 7:8 S SD: 19.2047 cents 5 x 6 x 7:8:9:10 S SD: 26.0885 cents 6 x 7:8:9:10:11:12 S SD: 17.2544 cents 7:8 x 9:10:11:12:14 S SD: 22.9464 cents 8:9:10 x 12:13:14:16 S SD: 15.3043 cents 9:10:11:12:13:15:16:18 SD: 13.4030 cents 10:11:12:13:15:16:17:20 SD: 9.1709 cents 14:15:17:18:21:23:24:28 SD: 9.1530 cents 16:18:19:21:24:26:28:32 SD: 7.4862 cents 19:21:23:25:28:31:33:38 SD: 5.8989 cents 20:22:24:26:30:33:35:40 SD: 3.2216 cents 32:35:38:42:48:52:56:64 SD: 2.6272 cents 36:39:43:47:54:59:63:72 SD: 2.5504 cents 42:46:50:55:63:69:73:84 SD: 2.3787 cents 51:56:61:67:76:83:89:102 SD: 2.1966 cents 52:57:62:68:78:85:91:104 SD: 1.2150 cents 77:84:92:101:115:126:135:154 SD: 1.2108 cents 85:93:102:111:127:139:149:170 SD: 1.1168 cents 87:95:104:114:130:142:152:174 SD: 0.8544 cents 97:106:116:127:145:159:170:194 SD: 0.8447 cents 107:117:128:140:160:175:187:214 SD: 0.2327 cents 266:291:318:348:398:435:465:532 SD: 0.2275 cents 331:362:396:433:495:541:579:662 SD: 0.2050 cents 351:384:420:459:525:574:614:702 SD: 0.1915 cents 438:479:524:573:655:716:766:876 SD: 0.1729 cents 458:501:548:599:685:749:801:916 SD: 0.1531 cents 546:597:653:714:817:893:955:1092 SD: 0.1447 cents 565:618:676:739:845:924:988:1130 SD: 0.1432 cents 598:654:715:782:894:978:1046:1196 SD: 0.1086 cents