Scala analysis: Schlick1511_variation
Variation on Schlick (1511), all 5ths within 7c of pure
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 88.270 cents 88.270000 2: 196.090 cents 196.090000 3: 303.910 cents 303.910000 4: 392.180 cents 392.180000 5: 501.955 cents 501.955000 6: 589.248 cents 589.247500 7: 698.045 cents 698.045000 8: 797.000 cents 797.000000 9: 894.135 cents 894.135000 10: 1002.933 cents 1002.932500 11: 1090.225 cents 1090.225000 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 109.7750 cents 109.7750 1: 88.2700 cents 88.2700 2: 107.8200 cents 107.8200 3: 107.8200 cents 107.8200 4: 88.2700 cents 88.2700 5: 109.7750 cents 109.7750 6: 87.2925 cents 87.2925 7: 108.7975 cents 108.7975 8: 98.9550 cents 98.9550 9: 97.1350 cents 97.1350 10: 108.7975 cents 108.7975 11: 87.2925 cents 87.2925 12: 109.7750 cents 109.7750
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 87.29250 cents 1: 2 88.27000 cents 1: 1 97.13500 cents 1: 1 98.95500 cents 1: 2 107.82000 cents 1: 2 108.79750 cents 1: 2 109.77500 cents 2: 5 196.09000 cents 2: 2 197.06750 cents 2: 2 198.04500 cents 2: 1 205.93250 cents 2: 1 207.75250 cents 2: 1 215.64000 cents 3: 2 285.33750 cents 3: 1 293.22500 cents 3: 1 295.04500 cents 3: 2 303.91000 cents 3: 2 304.88750 cents 3: 4 305.86500 cents 4: 3 392.18000 cents 4: 2 393.15750 cents 4: 2 394.13500 cents 4: 1 403.00000 cents 4: 1 404.82000 cents 4: 3 413.68500 cents 5: 1 491.27000 cents 5: 1 493.09000 cents 5: 4 500.97750 cents 5: 6 501.95500 cents 6: 1 588.27000 cents 6: 2 589.24750 cents 6: 2 590.22500 cents 6: 1 599.09000 cents 6: 1 600.91000 cents 6: 2 609.77500 cents 6: 2 610.75250 cents 6: 1 611.73000 cents 7: 6 698.04500 cents 7: 4 699.02250 cents 7: 1 706.91000 cents 7: 1 708.73000 cents 8: 3 786.31500 cents 8: 1 795.18000 cents 8: 1 797.00000 cents 8: 2 805.86500 cents 8: 2 806.84250 cents 8: 3 807.82000 cents 9: 4 894.13500 cents 9: 2 895.11250 cents 9: 2 896.09000 cents 9: 1 904.95500 cents 9: 1 906.77500 cents 9: 2 914.66250 cents 10: 1 984.36000 cents 10: 1 992.24750 cents 10: 1 994.06750 cents 10: 2 1001.95500 cents 10: 2 1002.93250 cents 10: 5 1003.91000 cents 11: 2 1090.22500 cents 11: 2 1091.20250 cents 11: 2 1092.18000 cents 11: 1 1101.04500 cents 11: 1 1102.86500 cents 11: 2 1111.73000 cents 11: 2 1112.70750 cents Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 6.00000 = 6
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 88.3 196.1 303.9 392.2 502.0 589.2 698.0 797.0 894.1 1002.9 1090.2 1200.0 88.3 : 107.8 215.6 303.9 413.7 501.0 609.8 708.7 805.9 914.7 1002.0 1111.7 1200.0 196.1 : 107.8 196.1 305.9 393.2 502.0 600.9 698.0 806.8 894.1 1003.9 1092.2 1200.0 303.9 : 88.3 198.0 285.3 394.1 493.1 590.2 699.0 786.3 896.1 984.4 1092.2 1200.0 392.2 : 109.8 197.1 305.9 404.8 502.0 610.8 698.0 807.8 896.1 1003.9 1111.7 1200.0 502.0 : 87.3 196.1 295.0 392.2 501.0 588.3 698.0 786.3 894.1 1002.0 1090.2 1200.0 589.2 : 108.8 207.8 304.9 413.7 501.0 610.8 699.0 806.8 914.7 1002.9 1112.7 1200.0 698.0 : 99.0 196.1 304.9 392.2 502.0 590.2 698.0 805.9 894.1 1003.9 1091.2 1200.0 797.0 : 97.1 205.9 293.2 403.0 491.3 599.1 706.9 795.2 905.0 992.2 1101.0 1200.0 894.1 : 108.8 196.1 305.9 394.1 502.0 609.8 698.0 807.8 895.1 1003.9 1102.9 1200.0 1002.9: 87.3 197.1 285.3 393.2 501.0 589.2 699.0 786.3 895.1 994.1 1091.2 1200.0 1090.2: 109.8 198.0 305.9 413.7 502.0 611.7 699.0 807.8 906.8 1003.9 1112.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 87.2925 .. 109.7750 cents 22.48250 cents 87.29250 cents 2: 196.0900 .. 215.6400 cents 19.55000 cents 86.31500 cents 3: 285.3375 .. 305.8650 cents 20.52750 cents 69.69750 cents 4: 392.1800 .. 413.6850 cents 21.50500 cents 86.31500 cents 5: 491.2700 .. 501.9550 cents 10.68500 cents 77.58500 cents 6: 588.2700 .. 611.7300 cents 23.46000 cents 86.31500 cents 7: 698.0450 .. 708.7300 cents 10.68500 cents 86.31500 cents 8: 786.3150 .. 807.8200 cents 21.50500 cents 77.58500 cents 9: 894.1350 .. 914.6625 cents 20.52750 cents 86.31500 cents 10: 984.3600 .. 1003.9100 cents 19.55000 cents 69.69750 cents 11: 1090.2250 .. 1112.7075 cents 22.48250 cents 86.31500 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 87.29250 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 109.77500 cents Average / Smallest step : 1.145574 Largest / Average step : 1.097750 Largest / Smallest step : 1.257554 Median interval of one step : 103.38750 cents, amount: 0 Least squares average step : 99.59614 cents, oct.: 1195.15366 cents Scale is strictly proper Step pattern alph. order: ABBACDEFGEDC Step pattern size order : BEEBGAFDCFAG Scale is a Constant Structure, by a margin of 69.69750 cents Scale diversity : 1.147406 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.822533 Rothenberg efficiency : 0.254621 redundancy: 0.745379 Efficiency x scale size : 3.055447 Number of different interval sizes : 66 = 6.00000 / class Number of one step interval sizes : 7 Highest interval variety : 8 Mean interval variety : 6.00000 = 6 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 0.97750 cents Most common intervals : 501.95500 cents & inv., amount: 6 Most common triad is 0.0 501.955 698.045 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 22.4825 cents: 5 7 8 Limited inverse transpositions with margin 22.4825 cents: 4 8 9 11 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 6.4558 c. M:-11.7300 c. Twelve-tone Chromatic (1/11-comma) 43: 3 4 4 3 4 3 4 4 3 4 3 4 SP M ME SD: 4.1063 c. M:-12.3023 c. 50: 4 4 5 3 5 4 4 4 4 5 3 5 SP D3 S SD: 6.6187 c. M:-10.7525 c. 51: 4 4 5 4 4 4 5 4 4 5 3 5 SP D3 SD: 6.0124 c. M:-8.8322 c. 55: 4 5 5 4 5 4 5 5 4 5 4 5 SP M ME SD: 3.0342 c. M:-10.2727 c. 59: 4 6 5 4 6 4 5 5 5 5 5 5 SP D3 SD: 5.3301 c. M:-8.0801 c. 63: 5 5 6 5 5 5 6 5 5 6 4 6 SP D3 SD: 5.0638 c. M:-7.8200 c. 66: 5 6 6 5 6 4 6 6 5 6 5 6 SP D3 SD: 4.9645 c. M:-7.8200 c. 67: 5 6 6 5 6 5 6 6 5 6 5 6 SP M ME SD: 2.8525 c. M:-8.9701 c. 74: 5 7 7 5 7 5 7 6 6 7 5 7 SP D3 S SD: 3.4444 c. M: 7.1889 c. 79: 6 7 7 6 7 6 7 7 6 7 6 7 SP M ME SD: 3.0275 c. M:-8.0633 c. 80: 6 7 7 6 7 6 8 6 7 7 6 7 SP D3 SD: 4.1280 c. M: 6.9550 c. 83: 6 7 8 6 8 6 7 7 7 7 6 8 SP SD: 3.9692 c. M: 8.1382 c. 84: 6 8 7 6 8 6 8 7 7 7 6 8 SP T3 SD: 3.7792 c. M: 6.4657 c. 86: 6 8 8 6 8 6 8 7 7 8 6 8 SP D3 S SD: 2.1157 c. M: 4.5491 c. 98: 7 9 9 7 9 7 9 8 8 9 7 9 SP D3 S SD: 1.1746 c. M: 2.5557 c. 110: 8 10 10 8 10 8 10 9 9 10 8 10 SP D3 S SD: 0.6679 c. M:-1.5445 c. 122: 9 11 11 9 11 9 11 10 10 11 9 11 SP D3 S SD: 0.8009 c. M:-1.5783 c. 232: 17 21 21 17 21 17 21 19 19 21 17 21 SP D3 S SD: 0.6662 c. M:-1.2624 c. 342: 25 31 31 25 31 25 31 28 28 31 25 31 SP D3 S SD: 0.6474 c. M:-1.3532 c. 354: 26 32 32 26 32 26 32 29 29 32 26 32 SP D3 S SD: 0.7004 c. M:-1.3004 c. 385: 28 35 35 28 35 28 35 32 31 35 28 35 SP SD: 0.6951 c. M:-1.5445 c. 397: 29 36 36 29 36 29 36 33 32 36 29 36 SP SD: 0.6887 c. M:-1.3797 c. 404: 30 36 36 30 37 29 37 33 33 37 29 37 SP S SD: 0.6374 c. M: 1.1287 c. 408: 30 37 36 30 38 29 37 34 33 37 30 37 SP SD: 0.7508 c. M: 1.0122 c. 409: 30 37 37 30 37 30 37 34 33 37 30 37 SP SD: 0.7330 c. M:-1.2245 c. 411: 30 37 37 30 38 30 37 34 33 37 30 38 SP SD: 0.7115 c. M: 1.4726 c. 416: 31 37 37 31 38 30 38 34 34 38 30 38 SP S SD: 0.6196 c. M:-1.1531 c. 435: 32 39 39 32 40 32 39 36 35 40 31 40 SP SD: 0.5520 c. M:-1.2054 c. 450: 33 41 40 33 41 33 41 37 36 41 33 41 SP SD: 0.5369 c. M:-1.2433 c. 459: 34 41 41 34 42 33 42 38 37 42 33 42 SP SD: 0.4957 c. M: 1.0122 c. 471: 35 42 42 35 43 34 43 39 38 43 34 43 SP SD: 0.4959 c. M:-0.9020 c. 514: 38 46 46 38 47 37 47 42 42 47 37 47 SP S SD: 0.4942 c. M:-0.9586 c. 518: 38 47 46 38 48 37 47 43 42 47 38 47 SP SD: 0.5789 c. M:-0.8947 c. 521: 38 47 47 38 48 38 47 43 42 47 38 48 SP SD: 0.5100 c. M: 1.0131 c. 526: 39 47 47 39 48 38 48 43 43 48 38 48 SP S SD: 0.4764 c. M:-0.8698 c. 533: 39 48 48 39 49 39 48 44 43 48 39 49 SP SD: 0.4455 c. M: 1.0563 c. 545: 40 49 49 40 50 40 49 45 44 49 40 50 SP SD: 0.4270 c. M: 1.0976 c. 568: 42 51 51 42 52 41 51 47 46 52 41 52 SP SD: 0.5354 c. M: 0.8619 c. 569: 42 51 51 42 52 41 52 47 46 52 41 52 SP SD: 0.3866 c. M:-0.9339 c. 581: 43 52 52 43 53 42 53 48 47 53 42 53 SP SD: 0.3823 c. M:-0.8541 c. 593: 44 53 53 44 54 43 54 49 48 54 43 54 SP SD: 0.4208 c. M:-0.7774 c. 631: 46 57 57 46 58 46 57 52 51 57 46 58 SP SD: 0.4087 c. M: 0.7898 c. 643: 47 58 58 47 59 47 58 53 52 58 47 59 SP SD: 0.3492 c. M: 0.7552 c. 655: 48 59 59 48 60 48 59 54 53 59 48 60 SP SD: 0.3287 c. M: 0.7951 c. 666: 49 60 60 49 61 48 60 55 54 61 48 61 SP SD: 0.4977 c. M: 0.7477 c. 667: 49 60 60 49 61 49 60 55 54 60 49 61 SP SD: 0.3493 c. M:-0.8574 c. 678: 50 61 61 50 62 49 61 56 55 62 49 62 SP SD: 0.4804 c. M:-0.7404 c. 679: 50 61 61 50 62 49 62 56 55 61 50 62 SP SD: 0.3423 c. M: 0.8706 c. 691: 51 62 62 51 63 50 63 57 56 63 50 63 SP SD: 0.3390 c. M:-0.8302 c. 698: 51 63 63 51 64 51 63 58 56 63 51 64 SP SD: 0.3814 c. M:-0.7077 c. 703: 52 63 63 52 64 51 64 58 57 64 51 64 SP SD: 0.3654 c. M:-0.7659 c. 706: 52 63 64 52 64 52 64 58 57 64 51 65 SP SD: 0.4237 c. M: 0.7066 c. 707: 52 64 63 52 65 51 64 59 57 64 51 65 SP SD: 0.4221 c. M:-0.7983 c. 710: 52 64 64 52 65 52 64 59 57 64 52 65 SP SD: 0.3713 c. M:-0.7465 c. 715: 53 64 64 53 65 52 65 59 58 65 52 65 SP SD: 0.4174 c. M:-0.7039 c. 719: 53 64 65 53 66 52 65 60 58 65 52 66 SP SD: 0.4111 c. M: 0.8188 c. 722: 53 65 65 53 66 53 65 60 58 65 53 66 SP SD: 0.3920 c. M:-0.7839 c. 729: 54 65 66 53 67 53 66 60 59 66 53 67 SP SD: 0.3715 c. M:-0.6189 c. 741: 54 67 67 54 68 54 67 61 60 67 54 68 SP SD: 0.3651 c. M: 0.8206 c. 753: 55 68 68 55 69 55 68 62 61 68 55 69 SP SD: 0.3121 c. M: 0.6206 c. 765: 56 69 69 56 70 56 69 63 62 69 56 70 SP SD: 0.2903 c. M: 0.5796 c. 816: 60 73 74 60 74 60 74 67 66 74 59 75 SP SD: 0.3737 c. M: 0.5191 c. 817: 60 74 73 60 75 59 74 68 66 74 59 75 SP SD: 0.3597 c. M:-0.7276 c. 820: 60 74 74 60 75 60 74 68 66 74 60 75 SP SD: 0.3246 c. M:-0.5610 c. 827: 61 74 74 61 76 60 75 68 67 75 60 76 SP SD: 0.3269 c. M: 0.6452 c. 839: 62 75 75 62 77 61 76 69 68 76 61 77 SP SD: 0.3081 c. M: 0.6919 c. 851: 63 76 77 62 78 62 77 70 69 77 62 78 SP SD: 0.3044 c. M:-0.6728 c. 870: 64 78 78 64 80 63 79 72 70 79 63 80 SP SD: 0.3039 c. M: 0.5698 c. 875: 64 79 79 64 80 64 79 72 71 79 64 80 SP SD: 0.2871 c. M:-0.5471 c. 882: 65 79 79 65 81 64 80 73 71 80 64 81 SP SD: 0.2643 c. M: 0.5086 c. 894: 66 80 80 66 82 65 81 74 72 81 65 82 SP SD: 0.2520 c. M: 0.5543 c. 925: 68 83 83 68 85 67 84 76 75 84 67 85 SP SD: 0.2844 c. M: 0.4953 c. 937: 69 84 84 69 86 68 85 77 76 85 68 86 SP SD: 0.2365 c. M: 0.4152 c. 949: 70 85 85 70 87 69 86 78 77 86 69 87 SP SD: 0.2134 c. M: 0.4327 c. 980: 72 88 88 72 90 71 89 81 79 89 71 90 SP SD: 0.2194 c. M: 0.4291 c. 992: 73 89 89 73 91 72 90 82 80 90 72 91 SP SD: 0.1711 c. M: 0.3056 c. 1004: 74 90 90 74 92 73 91 83 81 91 73 92 SP SD: 0.1523 c. M: 0.3243 c. 1047: 77 94 94 77 96 76 95 86 85 95 76 96 SP SD: 0.1812 c. M: 0.4384 c. 1059: 78 95 95 78 97 77 96 87 86 96 77 97 SP SD: 0.1523 c. M: 0.3994 c. 1090: 80 98 98 80 100 79 99 90 88 99 79 100 SP SD: 0.1675 c. M: 0.3167 c. 1102: 81 99 99 81 101 80 100 91 89 100 80 101 SP SD: 0.1076 c. M: 0.2069 c. 1114: 82 100 100 82 102 81 101 92 90 101 81 102 SP SD: 0.0739 c. M: 0.1398 c. 1224: 90 110 110 90 112 89 111 101 99 111 89 112 SP SD: 0.0254 c. M:-0.0588 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: 1.9550 cents 3 x x x x 4 x x x 5 x x 6 S SD: 3.5097 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 8.7069 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 5.2017 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.3805 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 11.0133 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.4883 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.3352 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.0553 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 10.9882 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 7.4524 cents 13:14:15 x 16:17:18:19:21:22:23:24:26 SD: 9.7685 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 7.6223 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 4.8386 cents 20:21:22:24:25:27:28:30:32:34:36:38:40 SD: 4.6076 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 4.2442 cents 24:25:27:29:30:32:34:36:38:40:43:45:48 SD: 3.0421 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.3187 cents 36:38:40:43:45:48:51:54:57:60:64:68:72 SD: 2.2747 cents 40:42:45:48:50:53:56:60:63:67:71:75:80 SD: 2.2585 cents 41:43:46:49:51:55:58:61:65:69:73:77:82 SD: 2.0658 cents 42:44:47:50:53:56:59:63:67:70:75:79:84 SD: 1.7679 cents 51:54:57:61:64:68:72:76:81:85:91:96:102 SD: 1.7267 cents 56:59:63:67:70:75:79:84:89:94:100:105:112 SD: 1.3207 cents 59:62:66:70:74:79:83:88:93:99:105:111:118 SD: 1.3182 cents 72:76:81:86:90:96:101:108:114:121:129:135:144 SD: 1.3179 cents 74:78:83:88:93:99:104:111:117:124:132:139:148 SD: 0.7425 cents 98:103:110:117:123:131:138:147:155:164:175:184:196 SD: 0.7225 cents 99:104:111:118:124:132:139:148:157:166:177:186:198 SD: 0.6112 cents 135:142:151:161:169:180:190:202:214:226:241:253:270 SD: 0.5965 cents 149:157:167:178:187:199:209:223:236:250:266:280:298 SD: 0.5553 cents 151:159:169:180:189:202:212:226:239:253:270:283:302 SD: 0.5522 cents 157:165:176:187:197:210:221:235:249:263:280:295:314 SD: 0.4361 cents 173:182:194:206:217:231:243:259:274:290:309:325:346 SD: 0.3315 cents 209:220:234:249:262:279:294:313:331:350:373:392:418 SD: 0.3140 cents 244:257:273:291:306:326:343:365:387:409:435:458:488 SD: 0.3084 cents 250:263:280:298:314:334:351:374:396:419:446:469:500 SD: 0.2925 cents 286:301:320:341:359:382:402:428:453:479:510:537:572 SD: 0.2740 cents 291:306:326:347:365:389:409:436:461:488:519:546:582 SD: 0.2605 cents 303:319:339:361:380:405:426:453:480:508:541:569:606 SD: 0.2551 cents 306:322:343:365:384:409:430:458:485:513:546:574:612 SD: 0.2214 cents 318:335:356:379:399:425:447:476:504:533:568:597:636 SD: 0.2118 cents 342:360:383:408:429:457:481:512:542:573:610:642:684 SD: 0.2107 cents 366:385:410:436:459:489:514:548:580:613:653:687:732 SD: 0.2056 cents 385:405:431:459:483:514:541:576:610:645:687:723:770 SD: 0.2016 cents 401:422:449:478:503:536:564:600:635:672:716:753:802 SD: 0.1783 cents 417:439:467:497:523:557:586:624:661:699:744:783:834 SD: 0.1258 cents 515:542:577:614:646:688:724:771:816:863:919:967:1030 SD: 0.1231 cents 594:625:665:708:745:794:835:889:941:996:1060:1115:1188 SD: 0.1045 cents