Scala analysis: valid6
well-temperament with six pure fifths
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 101.955 cents 101.955001 2: 198.883 cents 198.882856 3: 305.865 cents 305.865004 4: 396.090 cents 396.089998 5: 500.000 cents 500.000000 6: 600.000 cents 600.000000 7: 700.000 cents 700.000000 8: 803.910 cents 803.910002 9: 894.135 cents 894.134997 10: 1001.117 cents 1001.117144 11: 1098.045 cents 1098.044999 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 101.9550 cents 101.9550 1: 101.9550 cents 101.9550 2: 96.9279 cents 96.9279 3: 106.9821 cents 106.9821 4: 90.2250 cents 90.2250 5: 103.9100 cents 103.9100 6: 100.0000 cents 100.0000 7: 100.0000 cents 100.0000 8: 103.9100 cents 103.9100 9: 90.2250 cents 90.2250 10: 106.9821 cents 106.9821 11: 96.9279 cents 96.9279 12: 101.9550 cents 101.9550
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 90.22499 cents 1: 2 96.92786 cents 1: 2 100.00000 cents 1: 2 101.95500 cents 1: 2 103.91000 cents 1: 2 106.98215 cents 2: 2 194.13500 cents 2: 2 197.20714 cents 2: 2 198.88286 cents 2: 1 200.00000 cents 2: 5 203.91000 cents 3: 4 294.13500 cents 3: 2 300.83786 cents 3: 2 301.11714 cents 3: 2 303.91000 cents 3: 2 305.86500 cents 4: 2 394.13500 cents 4: 2 396.09000 cents 4: 1 397.76571 cents 4: 2 398.04500 cents 4: 2 401.11714 cents 4: 3 407.82000 cents 5: 6 498.04500 cents 5: 2 500.00000 cents 5: 2 501.11714 cents 5: 2 504.74786 cents 6: 1 588.26999 cents 6: 2 594.97285 cents 6: 2 598.04500 cents 6: 2 600.00000 cents 6: 2 601.95500 cents 6: 2 605.02715 cents 6: 1 611.73001 cents 7: 2 695.25214 cents 7: 2 698.88286 cents 7: 2 700.00000 cents 7: 6 701.95500 cents 8: 3 792.18000 cents 8: 2 798.88286 cents 8: 2 801.95500 cents 8: 1 802.23429 cents 8: 2 803.91000 cents 8: 2 805.86500 cents 9: 2 894.13500 cents 9: 2 896.09000 cents 9: 2 898.88286 cents 9: 2 899.16214 cents 9: 4 905.86500 cents 10: 5 996.09000 cents 10: 1 1000.00000 cents 10: 2 1001.11714 cents 10: 2 1002.79286 cents 10: 2 1005.86500 cents 11: 2 1093.01785 cents 11: 2 1096.09000 cents 11: 2 1098.04500 cents 11: 2 1100.00000 cents 11: 2 1103.07214 cents 11: 2 1109.77501 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 5.36364 = 59/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 102.0 198.9 305.9 396.1 500.0 600.0 700.0 803.9 894.1 1001.1 1098.0 1200.0 102.0 : 96.9 203.9 294.1 398.0 498.0 598.0 702.0 792.2 899.2 996.1 1098.0 1200.0 198.9 : 107.0 197.2 301.1 401.1 501.1 605.0 695.3 802.2 899.2 1001.1 1103.1 1200.0 305.9 : 90.2 194.1 294.1 394.1 498.0 588.3 695.3 792.2 894.1 996.1 1093.0 1200.0 396.1 : 103.9 203.9 303.9 407.8 498.0 605.0 702.0 803.9 905.9 1002.8 1109.8 1200.0 500.0 : 100.0 200.0 303.9 394.1 501.1 598.0 700.0 802.0 898.9 1005.9 1096.1 1200.0 600.0 : 100.0 203.9 294.1 401.1 498.0 600.0 702.0 798.9 905.9 996.1 1100.0 1200.0 700.0 : 103.9 194.1 301.1 398.0 500.0 602.0 698.9 805.9 896.1 1000.0 1100.0 1200.0 803.9 : 90.2 197.2 294.1 396.1 498.0 595.0 702.0 792.2 896.1 996.1 1096.1 1200.0 894.1 : 107.0 203.9 305.9 407.8 504.7 611.7 702.0 805.9 905.9 1005.9 1109.8 1200.0 1001.1: 96.9 198.9 300.8 397.8 504.7 595.0 698.9 798.9 898.9 1002.8 1093.0 1200.0 1098.0: 102.0 203.9 300.8 407.8 498.0 602.0 702.0 802.0 905.9 996.1 1103.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.2250 .. 106.9821 cents 16.75715 cents 90.22499 cents 2: 194.1350 .. 203.9100 cents 9.77501 cents 87.15285 cents 3: 294.1350 .. 305.8650 cents 11.73001 cents 90.22499 cents 4: 394.1350 .. 407.8200 cents 13.68501 cents 88.26999 cents 5: 498.0450 .. 504.7479 cents 6.70286 cents 90.22499 cents 6: 588.2700 .. 611.7300 cents 23.46001 cents 83.52213 cents 7: 695.2521 .. 701.9550 cents 6.70286 cents 83.52213 cents 8: 792.1800 .. 805.8650 cents 13.68501 cents 90.22499 cents 9: 894.1350 .. 905.8650 cents 11.73001 cents 88.26999 cents 10: 996.0900 .. 1005.8650 cents 9.77501 cents 90.22499 cents 11: 1093.0179 .. 1109.7750 cents 16.75715 cents 87.15285 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 90.22499 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 106.98215 cents Average / Smallest step : 1.108340 Largest / Average step : 1.069821 Largest / Smallest step : 1.185726 Median interval of one step : 100.97750 cents, amount: 0 Least squares average step : 99.95360 cents, oct.: 1199.44315 cents Scale is strictly proper Step pattern alph. order: ABCDEFFEDCBA Step pattern size order : DBFAECCEAFBD Scale is a Constant Structure, by a margin of 83.52213 cents Scale diversity : 1.097595 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.882700 Rothenberg efficiency : 0.263122 redundancy: 0.736878 Efficiency x scale size : 3.157468 Number of different interval sizes : 59 = 5.36364 / class Number of one step interval sizes : 6 Highest interval variety : 7 Mean interval variety : 5.36364 = 59/11 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 0.27929 cents Most common intervals : 498.04500 cents & inv., amount: 6 Most common triad is 0.0 498.045 701.955 cents, amount: 5 Number of recognisable fifths : 12, average 700.0000 cents Scale is a well-temperament. It has 4 different sizes of fifth Best fifths form a closed circle Formal octave complements present : 12 = 100.0000% Limited transpositions with margin 11.7300 cents: 1 2 3 4 5 6 7 8 9 10 11 Limited inverse transpositions with margin 11.7300 cents: 1 2 3 4 5 6 7 8 9 10 11 Inversional symmetry on degrees : 0 6 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 3.0209 c. M: 5.8650 c. Twelve-tone Chromatic (1/11-comma) 82: 7 7 7 6 7 7 7 7 6 7 7 7 SP D3 I SD: 2.7438 c. M:-5.9952 c. 86: 7 7 8 6 8 7 7 8 6 8 7 7 SP D3 I SD: 3.3300 c. M: 5.3923 c. 91: 8 7 8 7 8 7 8 8 7 8 7 8 SP M ME SD: 2.6917 c. M: 6.5934 c. 94: 8 8 8 7 8 8 8 8 7 8 8 8 SP D3 I SD: 2.3737 c. M: 5.3725 c. 98: 8 8 9 7 9 8 8 9 7 9 8 8 SP D3 I SD: 2.8011 c. M: 4.2533 c. 103: 9 8 9 8 9 8 9 9 8 9 8 9 SP M ME SD: 2.4397 c. M: 5.8252 c. 106: 9 9 9 8 9 9 9 9 8 9 9 9 SP D3 I SD: 2.1426 c. M: 4.8907 c. 110: 9 9 10 8 10 9 9 10 8 10 9 9 SP D3 I SD: 2.4278 c. M:-3.7732 c. 115: 10 9 10 9 10 9 10 10 9 10 9 10 SP M ME SD: 2.2829 c. M: 5.2174 c. 118: 10 10 10 9 10 10 10 10 9 10 10 10 SP D3 I SD: 2.0055 c. M: 4.5070 c. 122: 10 10 11 9 11 10 10 11 9 11 10 10 SP D3 I SD: 2.1673 c. M:-3.5943 c. 128: 11 10 12 9 11 11 11 11 9 12 10 11 SP I SD: 2.3438 c. M: 3.5100 c. 130: 11 11 11 10 11 11 11 11 10 11 11 11 SP D3 I SD: 1.9316 c. M:-4.1941 c. 134: 11 11 12 10 12 11 11 12 10 12 11 11 SP D3 I SD: 1.9905 c. M:-3.4475 c. 140: 12 11 13 10 12 12 12 12 10 13 11 12 SP I SD: 1.9401 c. M: 2.8571 c. 142: 12 12 12 11 12 12 12 12 11 12 12 12 SP D3 I SD: 1.8992 c. M: 3.9340 c. 146: 12 12 13 11 13 12 12 13 11 13 12 12 SP D3 I SD: 1.8757 c. M: 3.3249 c. 152: 13 12 14 11 13 13 13 13 11 14 12 13 SP I SD: 1.6139 c. M: 2.6316 c. 164: 14 13 15 12 14 14 14 14 12 15 13 14 SP I SD: 1.3525 c. M:-2.4390 c. 176: 15 14 16 13 15 15 15 15 13 16 14 15 SP I SD: 1.1485 c. M: 2.2727 c. 188: 16 15 17 14 16 16 16 16 14 17 15 16 SP I SD: 0.9971 c. M: 2.1277 c. 200: 17 16 18 15 17 17 17 17 15 18 16 17 SP I SD: 0.8952 c. M: 2.0000 c. 204: 17 17 18 15 18 17 17 18 15 18 17 17 SP I SD: 1.2221 c. M: 1.9724 c. 212: 18 17 19 16 18 18 18 18 16 19 17 18 SP I SD: 0.8384 c. M: 1.8868 c. 224: 19 18 20 17 19 19 19 19 17 20 18 19 SP I SD: 0.8203 c. M: 1.7857 c. 236: 20 19 21 18 20 20 20 20 18 21 19 20 SP I SD: 0.8320 c. M: 1.6949 c. 248: 21 20 22 19 21 21 21 21 19 22 20 21 SP I SD: 0.8646 c. M: 1.6129 c. 260: 22 21 23 20 22 22 22 22 20 23 21 22 SP I SD: 0.9104 c. M: 1.5385 c. 272: 23 22 24 21 23 23 23 23 21 24 22 23 SP I SD: 0.9637 c. M: 1.4706 c. 278: 24 22 25 21 24 23 23 24 21 25 22 24 SP I SD: 0.8902 c. M:-1.6421 c. 290: 25 23 26 22 25 24 24 25 22 26 23 25 SP I SD: 0.8383 c. M:-1.4933 c. 302: 26 24 27 23 26 25 25 26 23 27 24 26 SP I SD: 0.8083 c. M:-1.3563 c. 314: 27 25 28 24 27 26 26 27 24 28 25 27 SP I SD: 0.7975 c. M:-1.3622 c. 334: 28 27 30 25 29 28 28 29 25 30 27 28 SP I SD: 0.8975 c. M:-1.3562 c. 338: 29 27 30 26 29 28 28 29 26 30 27 29 SP I SD: 0.8200 c. M: 1.5431 c. 340: 29 27 31 25 30 28 28 30 25 31 27 29 SP I SD: 0.9245 c. M: 1.2358 c. 342: 29 28 30 26 30 28 29 29 26 30 28 29 SP SD: 0.9027 c. M:-1.7544 c. 345: 29 28 31 26 30 28 29 30 26 31 28 29 SP SD: 0.8235 c. M: 1.7391 c. 352: 30 28 32 26 31 29 29 31 26 32 28 30 SP I SD: 0.8206 c. M: 1.1556 c. 357: 30 29 32 27 31 29 30 31 27 32 29 30 SP SD: 0.8144 c. M: 1.6807 c. 364: 31 29 33 27 32 30 30 32 27 33 29 31 SP I SD: 0.7304 c. M:-1.0989 c. 376: 32 30 34 28 33 31 31 33 28 34 30 32 SP I SD: 0.6545 c. M: 1.0638 c. 388: 33 31 35 29 34 32 32 34 29 35 31 33 SP I SD: 0.5937 c. M:-1.0309 c. 400: 34 32 36 30 35 33 33 35 30 36 32 34 SP I SD: 0.5489 c. M: 1.0000 c. 412: 35 33 37 31 36 34 34 36 31 37 33 35 SP I SD: 0.5204 c. M: 0.9709 c. 424: 36 34 38 32 37 35 35 37 32 38 34 36 SP I SD: 0.5079 c. M: 0.9434 c. 436: 37 35 39 33 38 36 36 38 33 39 35 37 SP I SD: 0.5097 c. M:-0.9174 c. 446: 38 36 40 33 39 37 37 39 33 40 36 38 SP I SD: 0.4837 c. M: 0.8615 c. 458: 39 37 41 34 40 38 38 40 34 41 37 39 SP I SD: 0.4042 c. M: 0.6852 c. 470: 40 38 42 35 41 39 39 41 35 42 38 40 SP I SD: 0.3340 c. M: 0.5180 c. 482: 41 39 43 36 42 40 40 42 36 43 39 41 SP I SD: 0.2755 c. M:-0.4149 c. 494: 42 40 44 37 43 41 41 43 37 44 40 42 SP I SD: 0.2330 c. M: 0.4049 c. 506: 43 41 45 38 44 42 42 44 38 45 41 43 SP I SD: 0.2118 c. M: 0.3953 c. 518: 44 42 46 39 45 43 43 45 39 46 42 44 SP I SD: 0.2147 c. M:-0.3861 c. 530: 45 43 47 40 46 44 44 46 40 47 43 45 SP I SD: 0.2377 c. M: 0.3774 c. 682: 58 55 61 51 59 57 57 59 51 61 55 58 SP I SD: 0.1928 c. M: 0.2934 c. 694: 59 56 62 52 60 58 58 60 52 62 56 59 SP I SD: 0.1520 c. M: 0.2882 c. 706: 60 57 63 53 61 59 59 61 53 63 57 60 SP I SD: 0.1235 c. M: 0.2833 c. 718: 61 58 64 54 62 60 60 62 54 64 58 61 SP I SD: 0.1140 c. M: 0.2786 c. 730: 62 59 65 55 63 61 61 63 55 65 59 62 SP I SD: 0.1258 c. M: 0.2740 c. 742: 63 60 66 56 64 62 62 64 56 66 60 63 SP I SD: 0.1524 c. M: 0.2695 c. 1118: 95 90 100 84 97 93 93 97 84 100 90 95 SP I SD: 0.1488 c. M: 0.3140 c. 1130: 96 91 101 85 98 94 94 98 85 101 91 96 SP I SD: 0.1423 c. M: 0.2988 c. 1154: 98 93 103 87 100 96 96 100 87 103 93 98 SP I SD: 0.1504 c. M: 0.2693 c. 1166: 99 94 104 88 101 97 97 101 88 104 94 99 SP I SD: 0.1631 c. M: 0.2551 c. 1176: 100 95 105 88 102 98 98 102 88 105 95 100 SP I SD: 0.1369 c. M: 0.2574 c. 1188: 101 96 106 89 103 99 99 103 89 106 96 101 SP I SD: 0.1088 c. M: 0.1956 c. 1200: 102 97 107 90 104 100 100 104 90 107 97 102 SP I SD: 0.0837 c. M: 0.1350 c. 1212: 103 98 108 91 105 101 101 105 91 108 98 103 SP I SD: 0.0646 c. M: 0.1270 c. 1224: 104 99 109 92 106 102 102 106 92 109 99 104 SP I SD: 0.0565 c. M: 0.1368 c. 1906: 162 154 170 143 165 159 159 165 143 170 154 162 SP I SD: 0.0781 c. M: 0.1161 c. 1918: 163 155 171 144 166 160 160 166 144 171 155 163 SP I SD: 0.0659 c. M: 0.1043 c. 1930: 164 156 172 145 167 161 161 167 145 172 156 164 SP I SD: 0.0577 c. M: 0.1036 c. 1942: 165 157 173 146 168 162 162 168 146 173 157 165 SP I SD: 0.0552 c. M: 0.1030 c. 1954: 166 158 174 147 169 163 163 169 147 174 158 166 SP I SD: 0.0588 c. M: 0.1024 c. 1966: 167 159 175 148 170 164 164 170 148 175 159 167 SP I SD: 0.0673 c. M: 0.1017 c. 2318: 197 187 207 174 201 193 193 201 174 207 187 197 SP I SD: 0.0681 c. M: 0.0908 c. 2330: 198 188 208 175 202 194 194 202 175 208 188 198 SP I SD: 0.0573 c. M: 0.0858 c. 2342: 199 189 209 176 203 195 195 203 176 209 189 199 SP I SD: 0.0493 c. M: 0.0854 c. 2354: 200 190 210 177 204 196 196 204 177 210 190 200 SP I SD: 0.0456 c. M: 0.0850 c. 2366: 201 191 211 178 205 197 197 205 178 211 191 201 SP I SD: 0.0469 c. M: 0.0845 c. 2378: 202 192 212 179 206 198 198 206 179 212 192 202 SP I SD: 0.0527 c. M: 0.0841 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: 0.9775 cents 3 x x x x 4 x x x 5 x x 6 S SD: 3.3233 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 8.4488 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 5.5445 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 10.4767 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 10.6353 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.8156 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 7.8508 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 6.9211 cents 11 x 12:13:14:15:16 x x 18:20:21:22 S SD: 11.1839 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 6.4161 cents 13:14:15 x 16:17:18:19:21:22:23:25:26 SD: 9.6159 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 7.1106 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 4.6583 cents 22:23:25:26:28:29:31:33:35:37:39:41:44 SD: 4.5076 cents 24:25:27:29:30:32:34:36:38:40:43:45:48 SD: 3.6531 cents 27:29:30:32:34:36:38:40:43:45:48:51:54 SD: 3.2062 cents 31:33:35:37:39:41:44:46:49:52:55:58:62 SD: 2.7980 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.1676 cents 36:38:40:43:45:48:51:54:57:60:64:68:72 SD: 2.1347 cents 46:49:52:55:58:61:65:69:73:77:82:87:92 SD: 1.7884 cents 50:53:56:60:63:67:71:75:80:84:89:94:100 SD: 1.5923 cents 51:54:57:61:64:68:72:76:81:85:91:96:102 SD: 1.4225 cents 63:67:71:75:79:84:89:94:100:106:112:119:126 SD: 1.3821 cents 66:70:74:79:83:88:93:99:105:111:118:124:132 SD: 1.1006 cents 82:87:92:98:103:109:116:123:130:137:146:155:164 SD: 1.0486 cents 83:88:93:99:104:111:117:124:132:139:148:157:166 SD: 0.9706 cents 96:102:108:115:121:128:136:144:153:161:171:181:192 SD: 0.9523 cents 97:103:109:116:122:129:137:145:154:163:173:183:194 SD: 0.9320 cents 98:104:110:117:123:131:139:147:156:164:175:185:196 SD: 0.6733 cents 114:121:128:136:143:152:161:171:181:191:203:215:228 SD: 0.5857 cents 147:156:165:175:185:196:208:220:234:246:262:277:294 SD: 0.5311 cents 149:158:167:178:187:199:211:223:237:250:266:281:298 SD: 0.4761 cents 164:174:184:196:206:219:232:246:261:275:292:309:328 SD: 0.3956 cents 198:210:222:236:249:264:280:297:315:332:353:373:396 SD: 0.3296 cents 213:226:239:254:268:284:301:319:339:357:380:402:426 SD: 0.3154 cents 229:243:257:273:288:306:324:343:364:384:408:432:458 SD: 0.3119 cents 263:279:295:314:331:351:372:394:418:441:469:496:526 SD: 0.2540 cents 281:298:315:335:353:375:397:421:447:471:501:530:562 SD: 0.2443 cents 295:313:331:352:371:394:417:442:469:494:526:556:590 SD: 0.2275 cents 311:330:349:371:391:415:440:466:495:521:554:586:622 SD: 0.2260 cents 331:351:371:395:416:442:468:496:527:555:590:624:662 SD: 0.1903 cents 377:400:423:450:474:503:533:565:600:632:672:711:754 SD: 0.1371 cents 526:558:590:628:661:702:744:788:837:882:938:992:1052 SD: 0.1295 cents 594:630:666:709:747:793:840:890:945:996:1059:1120:1188 SD: 0.1168 cents