Scala analysis: xen18-ayers-table-56
7 Iterated Second Unnamed Means between 1/1 and 2/1
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 43/42 40.736798 2: 7/6 266.870906 septimal minor third 3: 67/54 373.442026 4: 3/2 701.955001 perfect fifth 5: 157/104 713.017237 6: 13/8 840.527662 tridecimal neutral sixth 7: 217/128 913.861479 8: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 256/217 286.1385 1: 43/42 40.7368 2: 49/43 226.1341 3: 67/63 106.5711 4: 81/67 328.5130 5: 157/156 11.0622 6: 169/157 127.5104 7: 217/208 73.3338 8: 256/217 286.1385
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 157/156 11.062 cents 1: 1 43/42 40.737 cents 1: 1 217/208 73.334 cents 1: 1 67/63 106.571 cents 1: 1 169/157 127.510 cents 1: 1 49/43 226.134 cents 1: 1 256/217 286.139 cents 1: 1 81/67 328.513 cents 2: 1 13/12 138.573 cents tridecimal 2/3-tone 2: 1 2821/2512 200.844 cents 2: 1 7/6 266.871 cents septimal minor third 2: 1 5504/4557 326.875 cents 2: 1 469/387 332.705 cents 2: 1 4239/3484 339.575 cents 2: 1 16/13 359.472 cents tridecimal neutral third 2: 1 9/7 435.084 cents septimal major third, BP third 3: 1 217/192 211.906 cents 3: 1 67/54 373.442 cents 3: 1 344/273 400.209 cents 3: 1 471/364 446.146 cents 3: 1 351/268 467.086 cents 3: 1 208/157 486.983 cents 3: 1 128/93 553.009 cents 3: 1 63/43 661.218 cents 4: 1 4/3 498.045 cents perfect fourth 4: 1 4472/3297 527.720 cents 4: 1 5859/4288 540.419 cents 4: 1 39/28 573.657 cents 4: 1 56/39 626.343 cents 4: 1 8576/5859 659.581 cents 4: 1 3297/2236 672.280 cents 4: 1 3/2 701.955 cents perfect fifth 5: 1 86/63 538.782 cents 5: 1 93/64 646.991 cents 5: 1 157/104 713.017 cents 5: 1 536/351 732.914 cents 5: 1 728/471 753.854 cents 5: 1 273/172 799.791 cents 5: 1 108/67 826.558 cents 5: 1 384/217 988.094 cents 6: 1 14/9 764.916 cents septimal minor sixth 6: 1 13/8 840.528 cents tridecimal neutral sixth 6: 1 6968/4239 860.425 cents 6: 1 774/469 867.295 cents 6: 1 4557/2752 873.125 cents 6: 1 12/7 933.129 cents septimal major sixth 6: 1 5024/2821 999.156 cents 6: 1 24/13 1061.427 cents tridecimal neutral seventh 7: 1 134/81 871.487 cents 7: 1 217/128 913.861 cents 7: 1 86/49 973.866 cents 7: 1 314/169 1072.490 cents 7: 1 126/67 1093.429 cents 7: 1 416/217 1126.666 cents 7: 1 84/43 1159.263 cents 7: 1 312/157 1188.938 cents Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 8.00000 = 8
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 40.7 266.9 373.4 702.0 713.0 840.5 913.9 1200.0 40.7 : 226.1 332.7 661.2 672.3 799.8 873.1 1159.3 1200.0 266.9 : 106.6 435.1 446.1 573.7 647.0 933.1 973.9 1200.0 373.4 : 328.5 339.6 467.1 540.4 826.6 867.3 1093.4 1200.0 702.0 : 11.1 138.6 211.9 498.0 538.8 764.9 871.5 1200.0 713.0 : 127.5 200.8 487.0 527.7 753.9 860.4 1188.9 1200.0 840.5 : 73.3 359.5 400.2 626.3 732.9 1061.4 1072.5 1200.0 913.9 : 286.1 326.9 553.0 659.6 988.1 999.2 1126.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 11.0622 .. 328.5130 cents 12636/10519, 317.4507 cents 157/156, 11.0622 cents 2: 138.5727 .. 435.0841 cents 108/91, 296.5114 cents 871/972,-189.9403 cents 3: 211.9065 .. 661.2182 cents 1728/1333, 449.3117 cents 1519/1728,-223.1776 cents 4: 498.0450 .. 701.9550 cents 9/8, 203.9100 cents 172/189,-163.1732 cents 5: 538.7818 .. 988.0935 cents 1728/1333, 449.3117 cents 172/189,-163.1732 cents 6: 764.9159 .. 1061.4273 cents 108/91, 296.5114 cents 1519/1728,-223.1776 cents 7: 871.4870 .. 1188.9378 cents 12636/10519, 317.4507 cents 871/972,-189.9403 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 157/156, 11.0622 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 81/67, 328.5130 cents Average / Smallest step : 13.559646 Largest / Average step : 2.190086 Largest / Smallest step : 29.696797 Median interval of one step : 117.04077 cents, amount: 0 Least squares average step : 142.68582 cents, oct.: 1141.48656 cents Scale is not proper Step pattern alph. order: ABCDEFGH Step pattern size order : BFDHAECG Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 1.63766 cents Scale diversity : 1.766749 Lumma stability : 0.018437 Lumma impropriety factor : 0.664111 Rothenberg efficiency : 0.250000 redundancy: 0.750000 Efficiency x scale size : 2.000000 Number of different interval sizes : 56 = 8.00000 / class Number of one step interval sizes : 8 Highest interval variety : 8 Mean interval variety : 8.00000 = 8 Median interval variety : 8 Lowest interval variety : 8 Smallest interval difference : 369117/368768, 1.6377 cents Number of recognisable fifths : 2, average 707.4861 cents Length of longest harmonic part : 1 at degree 0 Formal octave complements present : 1 = 12.5000% -- Rational properties -- Prime limit : 157 Odd number limit : 5859 (O: 5859 U: 5859) Highest odd numerator or denominator: 217 Scale harmonicity : 0.011969 Fundamental : 1/314496, -18.2627 octaves, 0.0008 Hz. Guide tone : too high to compute Exponens Consonantiae : 2.407755E+15, 51.09661 octaves Euler's gradus suavitatis : 347 Sum of Mann's harmonic distance : 427.0, average 53.37500 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.42807, average 1.30351 Sum of Tenney's harmonic distance : 20.19125, average 2.52391 Vogel's harmonic complexity : 70.62500 Wille's k value : 266584 Wilson's harmonic complexity : 350 Rectangular lattice diameter : 12 Triangular lattice diameter : 5 Lattice compactness : 123.31277, average 3.42535 Lattice compactness (without 2's) : 63.32330, average 1.75898 Number of different primes : 8 Prime exponents' range, average, count, tones@limit: 2: -7 .. 1 -2.00000 18 1 3: -3 .. 1 -0.50000 6 1 7: -1 .. 1 0.12500 3 1 13: -1 .. 1 0.00000 2 1 31: 0 .. 1 0.12500 1 1 43: 0 .. 1 0.12500 1 1 67: 0 .. 1 0.12500 1 1 157: 0 .. 1 0.12500 1 1 Average exponent except 2's : 1 / 8 = 0.12500 Average absolute exponent except 2's: 15 / 8 = 1.87500 Scale is weakly epimorphic with val: <8 12 21 30 42 43 49 57| Scale is weakly epimorphic with val: <8 12 21 31 40 43 50 58| Scale is weakly epimorphic with val: <8 12 21 31 40 44 50 57| Scale is weakly epimorphic with val: <8 12 21 31 41 43 49 58| Scale is weakly epimorphic with val: <8 12 21 31 41 44 49 57| Scale is weakly epimorphic with val: <8 12 22 30 41 43 49 57| Scale is weakly epimorphic with val: <8 12 22 31 39 43 50 58| Scale is weakly epimorphic with val: <8 12 22 31 40 43 49 58| Scale is weakly epimorphic with val: <8 12 23 31 38 44 50 57| Scale is weakly epimorphic with val: <8 12 23 31 39 44 49 57| Scale is weakly epimorphic with val: <8 13 22 30 38 42 49 57| Scale is weakly epimorphic with val: <8 13 22 30 41 45 50 58| Scale is weakly epimorphic with val: <8 13 22 31 38 41 49 58| Scale is weakly epimorphic with val: <8 13 22 31 38 41 50 57| Scale is weakly epimorphic with val: <8 13 22 31 40 45 50 59| Scale is weakly epimorphic with val: <8 13 23 30 40 45 50 58| Scale is weakly epimorphic with val: <8 13 23 30 42 43 50 58| Scale is weakly epimorphic with val: <8 13 23 31 39 45 50 59| Scale is weakly epimorphic with val: <8 13 23 31 42 42 50 59|
FIT/MODE
8: 0 1 1 2 0 1 1 2 N B D3 SD: 80.8294 c. M: 116.8709 c. 9: 0 2 1 2 0 1 1 2 N SD: 31.1852 c. M: 46.3506 c. 10: 0 2 1 3 0 1 1 2 N SD: 25.1636 c. M:-46.1385 c. 12: 0 3 1 3 0 1 1 3 N SD: 26.1492 c. M: 40.7368 c. 13: 0 3 1 4 0 1 1 3 N G SD: 22.1883 c. M: 40.7368 c. 17: 1 3 1 5 0 2 1 4 N SD: 14.4672 c. M:-29.8514 c. 20: 1 3 2 6 0 2 1 5 N SD: 15.1682 c. M: 26.8709 c. 22: 1 4 2 6 0 2 2 5 N SD: 11.4054 c. M: 22.3458 c. 26: 1 5 2 7 0 3 2 6 N SD: 10.3092 c. M: 20.7095 c. 27: 1 5 2 8 0 3 2 6 N SD: 10.0975 c. M:-19.4719 c. 29: 1 5 3 8 0 3 2 7 N SD: 8.8097 c. M: 18.5950 c. 30: 1 6 2 9 0 3 2 7 N SD: 9.7848 c. M:-18.0450 c. 31: 1 6 3 8 0 4 2 7 N SD: 10.3142 c. M: 16.2430 c. 32: 1 6 3 9 0 3 2 8 N SD: 8.4906 c. M: 15.5277 c. 34: 1 7 3 9 0 4 2 8 N SD: 8.7427 c. M:-15.4820 c. 36: 1 7 3 10 0 4 2 9 N SD: 8.0462 c. M: 13.8615 c. 39: 1 8 3 11 0 4 3 9 N SD: 7.5792 c. M:-10.0522 c. 41: 1 8 4 11 0 5 2 10 N SD: 7.2127 c. M: 11.4685 c. 49: 2 9 4 14 0 5 3 12 N SD: 6.2178 c. M:-8.2491 c. 50: 2 9 5 13 1 5 3 12 N SD: 5.7056 c. M:-10.5580 c. 51: 2 9 5 14 0 6 3 12 N SD: 5.4454 c. M: 8.0474 c. 54: 2 10 5 15 0 6 3 13 N SD: 4.2273 c. M:-9.1561 c. 60: 2 11 6 16 1 6 4 14 N SD: 4.7605 c. M:-6.9828 c. 62: 2 12 5 17 1 6 4 15 N SD: 4.6878 c. M: 8.2696 c. 63: 2 12 6 17 0 7 4 15 N SD: 4.2654 c. M: 8.2553 c. 64: 2 12 6 17 1 7 4 15 N SD: 4.0908 c. M: 8.2050 c. 67: 2 13 6 18 1 7 4 16 N SD: 2.7330 c. M: 4.9159 c. 84: 3 16 7 23 1 9 5 20 N SD: 2.2461 c. M:-4.5577 c. 91: 3 17 8 25 1 10 5 22 N SD: 2.8866 c. M: 4.2113 c. 94: 3 18 8 26 1 10 6 22 N SD: 2.5851 c. M:-5.2875 c. 96: 3 18 9 26 1 10 6 23 N SD: 2.4269 c. M: 4.3709 c. 109: 4 20 10 30 1 11 7 26 N SD: 2.4221 c. M: 3.8304 c. 113: 4 21 10 31 1 12 7 27 N SD: 1.3394 c. M: 1.7606 c. 180: 6 34 16 49 2 19 11 43 N SD: 0.7965 c. M: 1.9550 c. 234: 8 44 21 64 2 25 14 56 N SD: 0.5817 c. M: 1.0410 c. 328: 11 62 29 90 3 35 20 78 N SD: 0.5271 c. M:-0.9358 c. 347: 12 65 31 95 3 37 21 83 N SD: 0.5189 c. M: 0.8932 c. 414: 14 78 37 113 4 44 25 99 N SD: 0.3900 c. M: 0.8180 c. 441: 15 83 39 121 4 47 27 105 N SD: 0.3069 c. M: 0.6529 c. 508: 17 96 45 139 5 54 31 121 N SD: 0.3421 c. M: 0.5793 c. 562: 19 106 50 154 5 60 34 134 N SD: 0.3459 c. M:-0.7535 c. 617: 21 116 55 169 6 65 38 147 N SD: 0.3457 c. M:-0.7591 c. 621: 21 117 55 170 6 66 38 148 N SD: 0.2722 c. M: 0.5057 c. 624: 21 118 55 171 6 66 38 149 N SD: 0.3215 c. M:-0.4443 c. 675: 23 127 60 185 6 72 41 161 N SD: 0.1943 c. M:-0.3612 c. 764: 26 144 68 209 7 81 47 182 N SD: 0.2003 c. M:-0.3800 c. 855: 29 161 76 234 8 91 52 204 N SD: 0.1405 c. M: 0.2042 c. 1205: 41 227 107 330 11 128 74 287 N SD: 0.1288 c. M:-0.3294 c. 1385: 47 261 123 379 13 147 85 330 N SD: 0.1013 c. M:-0.2179 c. 1439: 49 271 128 394 13 153 88 343 N SD: 0.1080 c. M:-0.1993 c. 1619: 55 305 144 443 15 172 99 386 N SD: 0.0506 c. M:-0.1219 c. 2060: 70 388 183 564 19 219 126 491 N SD: 0.0576 c. M:-0.1191 c. 2176: 74 410 193 596 20 231 133 519 N SD: 0.0660 c. M: 0.0964 c. 2294: 78 432 204 628 21 244 140 547 N SD: 0.0594 c. M:-0.1001 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x x 4 S SD: 0.0000 cents 3 x x 4 x x x 5:6 S SD: 42.6827 cents 4 x x 5:6 x x 7:8 S SD: 14.1129 cents 5 x 6 x x x 8 x 10 S SD: 18.5562 cents 6 x 7 x 9 x x 10:12 SD: 7.3757 cents 7 x 8:9 x x 11:12:14 SD: 18.7759 cents 8 x 9:10:12 x 13:14:16 S SD: 14.0938 cents 9 x x 11 x 14 x 15:18 SD: 16.2820 cents 10 x 12 x 15 x 16:17:20 SD: 11.1747 cents 11:12:13:14 x 17:18:19:22 SD: 18.8224 cents 12:13:14:15:18 x x 20:24 S SD: 17.1658 cents 13:14:15:16 x 20:21:22:26 SD: 13.8630 cents 14:15:16:17:21 x 23:24:28 SD: 13.9901 cents 15:16:18:19 x 23:24:25:30 SD: 14.9965 cents 16:17:19:20:24 x 26:27:32 SD: 10.3929 cents 17:18:20:21 x 26:28:29:34 SD: 9.9248 cents 18:19:21:22:27 x 29:31:36 SD: 9.5156 cents 19:20:22:24 x 29:31:32:38 SD: 9.0158 cents 20:21:23:25:30 x 33:34:40 SD: 8.3544 cents 21:22:25:26 x 32:34:36:42 SD: 8.4456 cents 22:23:26:27:33 x 36:37:44 SD: 7.1498 cents 23:24:27:29 x 35:37:39:46 SD: 7.1043 cents 24:25:28:30:36 x 39:41:48 SD: 5.0250 cents 25:26:29:31 x 38:41:42:50 SD: 5.4921 cents 26:27:30:32:39 x 42:44:52 SD: 5.1136 cents 27:28:32:34 x 41:44:46:54 SD: 6.5404 cents 28:29:33:35:42 x 46:47:56 SD: 5.5849 cents 29:30:34:36 x 44:47:49:58 SD: 3.2772 cents 30:31:35:37:45 x 49:51:60 SD: 3.0829 cents 31:32:36:38 x 47:50:53:62 SD: 4.8280 cents 32:33:37:40:48 x 52:54:64 SD: 3.5796 cents 33:34:39:41 x 50:54:56:66 SD: 4.0731 cents 34:35:40:42:51 x 55:58:68 SD: 3.3030 cents 35:36:41:43 x 53:57:59:70 SD: 3.3354 cents 36:37:42:45:54 x 59:61:72 SD: 2.9569 cents 37:38:43:46 x 56:60:63:74 SD: 1.8960 cents 38:39:44:47:57 x 62:64:76 SD: 2.8451 cents 39:40:46:48 x 59:63:66:78 SD: 3.7558 cents 40:41:47:50:60 x 65:68:80 SD: 2.6512 cents 41:42:48:51 x 62:67:70:82 SD: 2.5113 cents 42:43:49:52:63 x 68:71:84 SD: 1.2655 cents 43:44:50:53 x 65:70:73:86 SD: 1.9483 cents 44:45:51:55:66 x 72:75:88 SD: 3.2894 cents 45:46:53:56 x 68:73:76:90 SD: 2.7031 cents 46:47:54:57:69 x 75:78:92 SD: 1.8394 cents 47:48:55:58 x 71:76:80:94 SD: 2.2859 cents 48:49:56:60:72 x 78:81:96 SD: 2.2814 cents 49:50:57:61 x 74:80:83:98 SD: 1.8129 cents 50:51:58:62:75 x 81:85:100 SD: 1.9819 cents 51:52:60:63 x 77:83:86:102 SD: 2.8964 cents 53:54:62:66 x 80:86:90:106 SD: 1.7287 cents 55:56:64:68 x 83:89:93:110 SD: 2.1304 cents 57:58:67:71 x 86:93:97:114 SD: 2.9282 cents 58:59:68:72:87:88:94:98:116 SD: 2.2640 cents 59:60:69:73 x 89:96:100:118 SD: 1.9339 cents 61:62:71:76 x 92:99:103:122 SD: 2.3998 cents 62:63:72:77:93:94:101:105:124 SD: 2.2146 cents 63:65:74:78 x 95:102:107:126 SD: 2.8002 cents 64:66:75:79:96:97:104:109:128 SD: 2.5205 cents 65:67:76:81 x 98:106:110:130 SD: 2.3069 cents 66:68:77:82:99:100:107:112:132 SD: 1.6986 cents 67:69:78:83 x 101:109:114:134 SD: 1.8868 cents 69:71:81:86 x 104:112:117:138 SD: 2.3209 cents 70:72:82:87:105:106:114:119:140 SD: 1.7179 cents 71:73:83:88 x 107:115:120:142 SD: 1.6782 cents 72:74:84:89:108:109:117:122:144 SD: 1.3198 cents 73:75:85:91 x 110:119:124:146 SD: 1.8380 cents 74:76:86:92:111:112:120:125:148 SD: 1.5746 cents 75:77:88:93 x 113:122:127:150 SD: 1.6924 cents 76:78:89:94:114:115:124:129:152 SD: 1.5792 cents 77:79:90:96 x 116:125:131:154 SD: 1.7308 cents 78:80:91:97:117:118:127:132:156 SD: 0.9674 cents 79:81:92:98 x 119:128:134:158 SD: 1.0797 cents 81:83:95:101 x 122:132:137:162 SD: 2.0982 cents 82:84:96:102:123:124:133:139:164 SD: 1.0896 cents 83:85:97:103 x 125:135:141:166 SD: 0.9191 cents 85:87:99:105 x 128:138:144:170 SD: 1.3480 cents 86:88:100:107:129:130:140:146:172 SD: 1.1027 cents 87:89:102:108 x 131:141:147:174 SD: 1.7465 cents 88:90:103:109:132:133:143:149:176 SD: 0.9034 cents 89:91:104:110 x 134:145:151:178 SD: 1.4326 cents 90:92:105:112:135:136:146:153:180 SD: 1.0338 cents 91:93:106:113 x 137:148:154:182 SD: 1.0399 cents 93:95:109:115 x 140:151:158:186 SD: 1.7616 cents 94:96:110:117:141:142:153:159:188 SD: 1.2549 cents 95:97:111:118 x 143:154:161:190 SD: 1.2391 cents 96:98:112:119:144:145:156:163:192 SD: 0.7491 cents 97:99:113:120 x 146:158:164:194 SD: 1.6075 cents 98:100:114:122:147:148:159:166:196 SD: 1.2642 cents 99:101:116:123 x 149:161:168:198 SD: 1.6347 cents 100:102:117:124:150:151:163:170:200 SD: 1.3604 cents 101:103:118:125 x 152:164:171:202 SD: 1.4760 cents 102:104:119:127:153:154:166:173:204 SD: 1.2183 cents 103:105:120:128 x 155:167:175:206 SD: 1.6171 cents 104:106:121:129:156:157:169:176:208 SD: 1.2027 cents 108:111:126:134:162:163:176:183:216 SD: 1.0463 cents 112:115:131:139:168:169:182:190:224 SD: 0.8555 cents 120:123:140:149:180:181:195:203:240 SD: 0.5832 cents 162:166:189:201:243:245:263:275:324 SD: 0.5568 cents 170:174:198:211:255:257:276:288:340 SD: 0.5461 cents 174:178:203:216:261:263:283:295:348 SD: 0.3895 cents 204:209:238:253:306:308:332:346:408 SD: 0.3842 cents 208:213:243:258:312:314:338:353:416 SD: 0.3839 cents 216:221:252:268:324:326:351:366:432 SD: 0.1856 cents 336:344:392:417:504:507:546:570:672 SD: 0.1825 cents 378:387:441:469:567:571:614:641:756 SD: 0.1741 cents 420:430:490:521:630:634:683:712:840 SD: 0.1659 cents 456:467:532:566:684:688:741:773:912 SD: 0.1629 cents 498:510:581:618:747:752:809:844:996 SD: 0.1342 cents 552:565:644:685:828:833:897:936:1104 SD: 0.1118 cents 594:608:693:737:891:897:965:1007:1188 SD: 0.1029 cents