Scala analysis: prop31strange
Strange diatonic-like strictly proper scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 116.129 cents 116.129032 2: 387.097 cents 387.096774 3: 425.806 cents 425.806452 4: 696.774 cents 696.774194 5: 812.903 cents 812.903226 6: 1006.452 cents 1006.451613 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 193.5484 cents 193.5484 1: 116.1290 cents 116.1290 2: 270.9677 cents 270.9677 3: 38.7097 cents 38.7097 4: 270.9677 cents 270.9677 5: 116.1290 cents 116.1290 6: 193.5484 cents 193.5484 7: 193.5484 cents 193.5484
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 38.70968 cents 1: 2 116.12903 cents 1: 2 193.54839 cents 1: 2 270.96774 cents 2: 4 309.67742 cents 2: 3 387.09677 cents 3: 2 425.80645 cents 3: 2 503.22581 cents 3: 3 580.64516 cents 4: 3 619.35484 cents 4: 2 696.77419 cents 4: 2 774.19355 cents 5: 3 812.90323 cents 5: 4 890.32258 cents 6: 2 929.03226 cents 6: 2 1006.45161 cents 6: 2 1083.87097 cents 6: 1 1161.29032 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 116.1 387.1 425.8 696.8 812.9 1006.5 1200.0 116.1 : 271.0 309.7 580.6 696.8 890.3 1083.9 1200.0 387.1 : 38.7 309.7 425.8 619.4 812.9 929.0 1200.0 425.8 : 271.0 387.1 580.6 774.2 890.3 1161.3 1200.0 696.8 : 116.1 309.7 503.2 619.4 890.3 929.0 1200.0 812.9 : 193.5 387.1 503.2 774.2 812.9 1083.9 1200.0 1006.5: 193.5 309.7 580.6 619.4 890.3 1006.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.7097 .. 270.9677 cents 232.25806 cents 38.70968 cents 2: 309.6774 .. 387.0968 cents 77.41935 cents 38.70968 cents 3: 425.8065 .. 580.6452 cents 154.83871 cents 38.70968 cents 4: 619.3548 .. 774.1935 cents 154.83871 cents 38.70968 cents 5: 812.9032 .. 890.3226 cents 77.41935 cents 38.70968 cents 6: 929.0323 .. 1161.2903 cents 232.25806 cents 38.70968 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 38.70968 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 270.96774 cents Average / Smallest step : 4.428571 Largest / Average step : 1.580645 Largest / Smallest step : 7.000000 Median interval of one step : 193.54839 cents, amount: 2 Least squares average step : 167.55760 cents, oct.: 1172.90323 cents Scale is strictly proper Scale is a mode of a 31-tone equal temperament with octave 1200.000 cents degrees: 3 10 11 18 21 26 31 Least number of segments generator : 21 of 812.903 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 18 of 696.774 cents and inv. generated superset size: 13 = 6 more = 185.714% Number of contiguous 1-step segments: 1 Step pattern alph. order: ABCBADD Step pattern size order : BDADBCC Interval vector is [ 1 0 2 0 2 0 2 4 0 3 2 0 2 0 3 ] Scale is a Constant Structure, by a margin of 38.70968 cents Scale diversity : 1.470079 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.225806 Rothenberg efficiency : 0.466667 redundancy: 0.533333 Efficiency x scale size : 3.266667 Number of different interval sizes : 18 = 3.00000 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.00000 = 3 Median interval variety : 2.5 Lowest interval variety : 2 Smallest interval difference : 38.70968 cents Most common intervals : 309.67742 cents & inv., amount: 4 Most common triad is 0.0 309.677 890.323 cents, amount: 3 Number of recognisable fifths : 2, average 696.7742 cents Best fifths form a closed circle Formal octave complements present : 3 = 42.8571% Limited inverse transpositions : 5 Inversional symmetry on degrees : 6 Inversional symmetry on intervals : 2-3 -- Rational properties --
FIT/MODE
7: 1 1 0 2 1 1 1 N T3 SD: 45.4572 c. M: 82.9493 c. 9: 1 2 0 2 1 2 1 N D3 SD: 28.8525 c. M:-60.2151 c. 10: 1 2 1 2 1 1 2 P M ME S SD: 31.8873 c. M:-54.1935 c. 11: 1 2 1 2 1 2 2 P M ME S SD: 34.9637 c. M: 59.8240 c. 12: 1 3 0 3 1 2 2 P S SD: 13.6859 c. M: 25.8065 c. 19: 2 4 1 4 2 3 3 SP S SD: 8.6438 c. M:-16.2988 c. 29: 3 6 1 7 3 4 5 P SD: 11.0993 c. M: 14.6830 c. 31: 3 7 1 7 3 5 5 SP S SD: 0.0000 c. M: 0.0000 c. Strange Diatonic
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: 33.8695 cents 4 x 5 x 6 x 7:8 S SD: 9.4972 cents 5 x 6 x 7:8:9:10 S SD: 27.0455 cents 6 x x 8:9:10:11:12 S SD: 22.0839 cents 7:8 x 9:10:11:13:14 SD: 26.2415 cents 8:9:10 x 12:13:14:16 S SD: 16.5930 cents 10:11 x 13:15:16:18:20 SD: 9.6428 cents 11:12 x 14:16:18:20:22 S SD: 12.8695 cents 12:13:15 x 18:19:21:24 SD: 7.9017 cents 14:15 x 18:21:22:25:28 SD: 5.4154 cents 15:16 x 19:22:24:27:30 SD: 6.5740 cents 16:17:20 x 24:26:29:32 SD: 6.3469 cents 18:19 x 23:27:29:32:36 SD: 4.7335 cents 19:20:24 x 28:30:34:38 SD: 7.7951 cents 20:21:25:26:30:32:36:40 SD: 6.3273 cents 22:24 x 28:33:35:39:44 SD: 6.6722 cents 23:25:29 x 34:37:41:46 SD: 6.5353 cents 24:26:30:31:36:38:43:48 SD: 4.8236 cents 25:27:31:32:37:40:45:50 SD: 4.4304 cents 26:28 x 33:39:42:47:52 SD: 5.2435 cents 27:29:34:35:40:43:48:54 SD: 4.9043 cents 28:30:35:36:42:45:50:56 SD: 2.0389 cents 30:32 x 38:45:48:54:60 SD: 3.5170 cents 32:34:40:41:48:51:57:64 SD: 2.2479 cents 34:36 x 43:51:54:61:68 SD: 4.9046 cents 35:37:44:45:52:56:63:70 SD: 4.0908 cents 36:39:45:46:54:58:64:72 SD: 4.0495 cents 37:40:46:47:55:59:66:74 SD: 3.9125 cents 39:42:49:50:58:62:70:78 SD: 3.1017 cents 40:43:50:51:60:64:72:80 SD: 2.3113 cents 43:46:54:55:64:69:77:86 SD: 1.8086 cents 57:61:71:73:85:91:102:114 SD: 1.3551 cents 72:77:90:92:108:115:129:144 SD: 0.9495 cents 100:107:125:128:150:160:179:200 SD: 0.8303 cents 115:123:144:147:172:184:206:230 SD: 0.5330 cents 147:157:184:188:220:235:263:294 SD: 0.4456 cents 172:184:215:220:257:275:308:344 SD: 0.4149 cents 200:214:250:256:299:320:358:400 SD: 0.3859 cents 204:218:255:261:305:326:365:408 SD: 0.3280 cents 232:248:290:297:347:371:415:464 SD: 0.3021 cents 244:261:305:312:365:390:436:488 SD: 0.2982 cents 287:307:359:367:429:459:513:574 SD: 0.2076 cents 359:384:449:459:537:574:642:718 SD: 0.1183 cents 563:602:704:720:842:900:1007:1126 SD: 0.1164 cents 591:632:739:756:884:945:1057:1182 SD: 0.0952 cents