Scala analysis: neogji12
Neo-Gothic 12-note JI tuning (primes 2/3/7/11) F-F with Eb key as D+1
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 392/363 133.060927 2: 9/8 203.910002 major whole tone 3: 147/121 336.970929 4: 14/11 417.507964 undecimal diminished fourth or major third 5: 4/3 498.044999 perfect fourth 6: 63/44 621.417966 7: 3/2 701.955001 perfect fifth 8: 196/121 835.015928 two (undecimal diminished fourth or major third) 9: 27/16 905.865003 Pythagorean major sixth 10: 56/33 915.552963 11: 21/11 1119.462965 undecimal major seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 22/21 80.5370 undecimal minor semitone 1: 392/363 133.0609 2: 3267/3136 70.8491 3: 392/363 133.0609 4: 22/21 80.5370 undecimal minor semitone 5: 22/21 80.5370 undecimal minor semitone 6: 189/176 123.3730 7: 22/21 80.5370 undecimal minor semitone 8: 392/363 133.0609 9: 3267/3136 70.8491 10: 896/891 9.6880 undecimal semicomma, pentacircle 11: 9/8 203.9100 major whole tone 12: 22/21 80.5370 undecimal minor semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 896/891 9.688 cents undecimal semicomma, pentacircle 1: 2 3267/3136 70.849 cents 1: 4 22/21 80.537 cents undecimal minor semitone 1: 1 189/176 123.373 cents 1: 3 392/363 133.061 cents 1: 1 9/8 203.910 cents major whole tone 2: 1 22/21 80.537 cents undecimal minor semitone 2: 1 484/441 161.074 cents two (undecimal minor semitone) 2: 5 9/8 203.910 cents major whole tone 2: 4 112/99 213.598 cents 2: 1 33/28 284.447 cents undecimal minor third 3: 1 112/99 213.598 cents 3: 6 33/28 284.447 cents undecimal minor third 3: 2 32/27 294.135 cents Pythagorean minor third 3: 2 147/121 336.971 cents 3: 1 14/11 417.508 cents undecimal diminished fourth or major third 4: 1 32/27 294.135 cents Pythagorean minor third 4: 3 121/98 364.984 cents 4: 1 81/64 407.820 cents Pythagorean major third 4: 5 14/11 417.508 cents undecimal diminished fourth or major third 4: 1 12544/9801 427.196 cents 4: 1 297/224 488.357 cents 5: 1 14/11 417.508 cents undecimal diminished fourth or major third 5: 2 297/224 488.357 cents 5: 8 4/3 498.045 cents perfect fourth 5: 1 63/44 621.418 cents 6: 1 4/3 498.045 cents perfect fourth 6: 3 1089/784 568.894 cents two (undecimal minor third) 6: 2 88/63 578.582 cents 6: 2 63/44 621.418 cents 6: 3 1568/1089 631.106 cents 6: 1 3/2 701.955 cents perfect fifth 7: 1 88/63 578.582 cents 7: 8 3/2 701.955 cents perfect fifth 7: 2 448/297 711.643 cents 7: 1 11/7 782.492 cents undecimal augmented fifth 8: 1 448/297 711.643 cents 8: 1 9801/6272 772.804 cents 8: 5 11/7 782.492 cents undecimal augmented fifth 8: 1 128/81 792.180 cents Pythagorean minor sixth 8: 3 196/121 835.016 cents two (undecimal diminished fourth or major third) 8: 1 27/16 905.865 cents Pythagorean major sixth 9: 1 11/7 782.492 cents undecimal augmented fifth 9: 2 242/147 863.029 cents 9: 2 27/16 905.865 cents Pythagorean major sixth 9: 6 56/33 915.553 cents 9: 1 99/56 986.402 cents 10: 1 56/33 915.553 cents 10: 4 99/56 986.402 cents 10: 5 16/9 996.090 cents Pythagorean minor seventh 10: 1 441/242 1038.926 cents 10: 1 21/11 1119.463 cents undecimal major seventh 11: 1 16/9 996.090 cents Pythagorean minor seventh 11: 3 363/196 1066.939 cents 11: 1 352/189 1076.627 cents 11: 4 21/11 1119.463 cents undecimal major seventh 11: 2 6272/3267 1129.151 cents 11: 1 891/448 1190.312 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.27273 = 58/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 133.1 203.9 337.0 417.5 498.0 621.4 702.0 835.0 905.9 915.6 1119.5 1200.0 133.1 : 70.8 203.9 284.4 365.0 488.4 568.9 702.0 772.8 782.5 986.4 1066.9 1200.0 203.9 : 133.1 213.6 294.1 417.5 498.0 631.1 702.0 711.6 915.6 996.1 1129.2 1200.0 337.0 : 80.5 161.1 284.4 365.0 498.0 568.9 578.6 782.5 863.0 996.1 1066.9 1200.0 417.5 : 80.5 203.9 284.4 417.5 488.4 498.0 702.0 782.5 915.6 986.4 1119.5 1200.0 498.0 : 123.4 203.9 337.0 407.8 417.5 621.4 702.0 835.0 905.9 1038.9 1119.5 1200.0 621.4 : 80.5 213.6 284.4 294.1 498.0 578.6 711.6 782.5 915.6 996.1 1076.6 1200.0 702.0 : 133.1 203.9 213.6 417.5 498.0 631.1 702.0 835.0 915.6 996.1 1119.5 1200.0 835.0 : 70.8 80.5 284.4 365.0 498.0 568.9 702.0 782.5 863.0 986.4 1066.9 1200.0 905.9 : 9.7 213.6 294.1 427.2 498.0 631.1 711.6 792.2 915.6 996.1 1129.2 1200.0 915.6 : 203.9 284.4 417.5 488.4 621.4 702.0 782.5 905.9 986.4 1119.5 1190.3 1200.0 1119.5: 80.5 213.6 284.4 417.5 498.0 578.6 702.0 782.5 915.6 986.4 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 9.6880 .. 203.9100 cents 8019/7168, 194.2220 cents 896/891, 9.6880 cents 2: 80.5370 .. 284.4470 cents 9/8, 203.9100 cents 176/189,-123.3730 cents 3: 213.5980 .. 417.5080 cents 9/8, 203.9100 cents 3136/3267,-70.8491 cents 4: 294.1350 .. 488.3570 cents 8019/7168, 194.2220 cents 176/189,-123.3730 cents 5: 417.5080 .. 621.4180 cents 9/8, 203.9100 cents 3136/3267,-70.8491 cents 6: 498.0450 .. 701.9550 cents 9/8, 203.9100 cents 176/189,-123.3730 cents 7: 578.5820 .. 782.4920 cents 9/8, 203.9100 cents 176/189,-123.3730 cents 8: 711.6430 .. 905.8650 cents 8019/7168, 194.2220 cents 3136/3267,-70.8491 cents 9: 782.4920 .. 986.4020 cents 9/8, 203.9100 cents 176/189,-123.3730 cents 10: 915.5530 .. 1119.4630 cents 9/8, 203.9100 cents 3136/3267,-70.8491 cents 11: 996.0900 .. 1190.3120 cents 8019/7168, 194.2220 cents 176/189,-123.3730 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 896/891, 9.6880 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 10.322090 Largest / Average step : 2.039100 Largest / Smallest step : 21.047774 Median interval of one step : 22/21, 80.5370 cents, amount: 4 Most common interval of one step : 22/21, 80.5370 cents, amount: 4 Least squares average step : 100.08735 cents, oct.: 1201.04821 cents Scale is not proper Step pattern alph. order: ABACCDCABEFC Step pattern size order : EBECCDCEBAFC Scale is not a Constant Structure Scale diversity : 1.303960 Lumma stability : 0.016147 Lumma impropriety factor : 0.817332 Rothenberg efficiency : 0.404960 redundancy: 0.595040 Efficiency x scale size : 4.859524 Number of different interval sizes : 38 = 3.45455 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 5.27273 = 58/11 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 896/891, 9.6880 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 9 Most common triad is 0.0 498.045 701.955 cents, amount: 6 Number of recognisable fifths : 12, average 704.3770 cents Scale contains a complete diamond : 1 3 Formal octave complements present : 3 = 25.0000% -- Rational properties -- Prime limit : 11 Odd number limit : 9801 (O: 9801 U: 9801) Highest odd numerator or denominator: 363 Scale harmonicity : 0.013405 Average absolute harmonicity : 0.155279 Specific harmonicity : 0.066179 Fundamental : 1/5808, -12.5038 octaves, 0.0450 Hz. Guide tone : 10584, 13.3696 octaves, 2769044.983 Hz. Exponens Consonantiae : 6.147187E+07, 25.87342 octaves Euler's gradus suavitatis : 48 Sum of Mann's harmonic distance : 834.0, average 69.50000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 15.83132, average 1.31928 Sum of Tenney's harmonic distance : 31.69014, average 2.64085 Vogel's harmonic complexity : 27.58333 Wille's k value : 4900 Wilson's harmonic complexity : 48 Rectangular lattice diameter : 8 Triangular lattice diameter : 6 Lattice compactness : 275.40671, average 3.53086 Lattice compactness (without 2's) : 175.43227, average 2.24913 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 3 0.16667 22 1 3: -1 .. 3 0.58333 13 4 7: 0 .. 2 0.83333 10 11: -2 .. 0 -0.83333 10 7 Average exponent except 2's : 7 / 12 = 0.58333 Average absolute exponent except 2's: 33 / 12 = 2.75000
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 0 2 1 N T3 SD: 20.6746 c. M: 36.9709 c. 17: 2 1 2 1 1 2 1 2 1 0 3 1 N SD: 9.2623 c. M:-15.9702 c. 29: 3 2 3 2 2 3 2 3 2 0 5 2 N SD: 4.5634 c. M: 8.9230 c. 46: 5 3 5 3 3 5 3 5 3 0 8 3 N SD: 3.3014 c. M:-7.1785 c. 60: 7 3 7 4 4 6 4 7 3 1 10 4 N SD: 3.7392 c. M:-6.9391 c. 69: 8 4 7 5 5 7 4 8 4 1 11 5 N SD: 4.8782 c. M: 6.5361 c. 70: 8 4 8 4 5 7 5 8 4 0 12 5 N SD: 4.2734 c. M: 6.9815 c. 72: 8 4 8 5 5 7 5 8 4 1 12 5 N SD: 2.9694 c. M: 5.8650 c. 89: 10 5 10 6 6 9 6 10 5 1 15 6 N SD: 1.2201 c. M: 2.4942 c. 118: 13 7 13 8 8 12 8 13 7 1 20 8 N SD: 0.7710 c. M: 1.3777 c. 135: 15 8 15 9 9 14 9 15 8 1 23 9 N SD: 0.5079 c. M:-0.8068 c. 224: 25 13 25 15 15 23 15 25 13 2 38 15 N SD: 0.4447 c. M:-0.8676 c. 253: 28 15 28 17 17 26 17 28 15 2 43 17 N SD: 0.1349 c. M: 0.2546 c. 641: 71 38 71 43 43 66 43 71 38 5 109 43 N SD: 0.1051 c. M:-0.2192 c. 730: 81 43 81 49 49 75 49 81 43 6 124 49 N SD: 0.0570 c. M: 0.1116 c. 983: 109 58 109 66 66 101 66 109 58 8 167 66 N SD: 0.0341 c. M: 0.0664 c. 1118: 124 66 124 75 75 115 75 124 66 9 190 75 N SD: 0.0338 c. M:-0.0595 c. 1371: 152 81 152 92 92 141 92 152 81 11 233 92 N SD: 0.0198 c. M:-0.0431 c. 2101: 233 124 233 141 141 216 141 233 124 17 357 141 N SD: 0.0095 c. M:-0.0186 c. 2354: 261 139 261 158 158 242 158 261 139 19 400 158 N SD: 0.0070 c. M: 0.0126 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: 0.0000 cents 3 x x x x 4 x x x 5 x x 6 S SD: 7.1688 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 15.4335 cents 5 x x 6 x x 7 x 8 x x x 10 S SD: 12.3074 cents 6 x 7 x x 8 x 9 x 10 x 11:12 S SD: 16.1078 cents 7 x 8 x 9 x 10 x 11 x 12:13:14 S SD: 11.4433 cents 8 x 9 x 10:11 x 12:13 x 14:15:16 S SD: 10.9349 cents 9 x 10:11 x 12:13:14 x 15 x 17:18 SD: 9.3276 cents 10:11 x 12:13 x 14:15:16 x 17:19:20 SD: 7.7532 cents 11:12 x 13:14:15:16:17:18 x 19:21:22 SD: 9.3627 cents 12:13:14 x 15:16:17:18:19:20 x 23:24 SD: 8.5867 cents 13:14:15:16 x 17:19:20:21 x 22:25:26 SD: 8.3496 cents 14:15:16:17:18:19:20:21:23 x 24:27:28 SD: 5.3068 cents 15:16:17:18:19:20:21:23:24:25 x 29:30 SD: 6.7406 cents 16:17:18:19:20:21:23:24:26:27 x 31:32 SD: 6.2948 cents 17:18:19:21:22:23:24:26:28 x 29:32:34 SD: 7.5150 cents 18:19:20:22:23:24:26:27:29:30:31:34:36 SD: 5.2371 cents 19 x 21:23:24:25:27:29:31:32 x 36:38 SD: 5.5586 cents 20:22:23:24:25:27:29:30:32 x 34:38:40 SD: 6.6611 cents 21:23:24:26:27:28:30:32:34:35:36:40:42 SD: 5.4453 cents 22:24:25:27:28:29:32:33:36:37 x 42:44 SD: 4.4521 cents 23:25:26:28:29:31:33:35:37 x 39:44:46 SD: 3.6517 cents 24:26:27:29:31:32:34:36:39 x 41:46:48 SD: 3.3052 cents 25:27:28:30:32:33:36:38:40:42 x 48:50 SD: 4.2147 cents 26:28:29:32:33:35:37:39:42 x 44:50:52 SD: 3.3580 cents 27:29:30:33:34:36:39:41:44 x 46:52:54 SD: 4.1334 cents 28:30:32:34:36:37:40:42:45:47:48:53:56 SD: 3.9898 cents 29:31:33:35:37:39:42:44:47:49 x 55:58 SD: 4.0547 cents 30:32:34:36:38:40:43:45:49 x 51:57:60 SD: 3.4366 cents 32:35:36:39:41:43:46:48:52:54 x 61:64 SD: 2.7528 cents 33:36:37:40:42:44:47:50:53 x 56:63:66 SD: 2.8228 cents 34:37:38:41:43:45:49:51:55:57:58:65:68 SD: 2.7698 cents 35:38:39:43:45:47:50:53:57:59 x 67:70 SD: 3.6313 cents 36:39:41:44:46:48:52:54:58 x 61:69:72 SD: 2.8886 cents 37:40:42:45:47:49:53:56:60:62:63:71:74 SD: 2.5054 cents 38:41:43:46:48:51:54:57:62:64 x 73:76 SD: 2.7240 cents 39:42:44:47:50:52:56:59:63 x 66:74:78 SD: 2.5717 cents 40:43:45:49:51:53:57:60:65 x 68:76:80 SD: 2.1742 cents 42:45:47:51:53:56:60:63:68:71 x 80:84 SD: 2.0929 cents 43:46:48:52:55:57:62:65:70 x 73:82:86 SD: 3.0015 cents 44:48:50:53:56:59:63:66:71:74:75:84:88 SD: 2.7183 cents 45:49:51:55:57:60:64:68:73:76 x 86:90 SD: 2.6622 cents 46:50:52:56:59:61:66:69:75 x 78:88:92 SD: 2.2876 cents 47:51:53:57:60:63:67:71:76:79:80:90:94 SD: 1.9113 cents 48:52:54:58:61:64:69:72:78:81 x 92:96 SD: 1.4340 cents 49:53:55:60:62:65:70:74:79 x 83:94:98 SD: 2.3881 cents 50:54:56:61:64:67:72:75:81:84:85:95:100 SD: 1.8986 cents 51:55:57:62:65:68:73:77:83:86:87:97:102 SD: 1.7888 cents 52:56:59:63:66:69:74:78:84 x 88:99:104 SD: 2.1031 cents 54:58:61:66:69:72:77:81:87:91:92:103:108 SD: 1.8395 cents 55:59:62:67:70:73:79:83:89:93 x 105:110 SD: 1.7818 cents 56:60:63:68:71:75:80:84:91 x 95:107:112 SD: 1.6713 cents 58:63:65:70:74:77:83:87:94:98 x 111:116 SD: 1.7607 cents 59:64:66:72:75:79:84:89:96 x 100:113:118 SD: 2.1553 cents 60:65:68:73:76:80:86:90:97:101:102:115:120 SD: 1.5770 cents 62:67:70:75:79:83:89:93:100 x 105:118:124 SD: 1.4736 cents 63:68:71:77:80:84:90:95:102:106:107:120:126 SD: 1.3884 cents 65:70:73:79:83:87:93:98:105 x 110:124:130 SD: 1.3954 cents 66:71:74:80:84:88:95:99:107:111:112:126:132 SD: 1.2171 cents 68:73:77:83:87:91:97:102:110:115 x 130:136 SD: 2.0079 cents 69:75:78:84:88:92:99:104:112:116:117:132:138 SD: 1.6140 cents 70:76:79:85:89:93:100:105:113:118:119:134:140 SD: 1.3038 cents 71:77:80:86:90:95:102:107:115:120 x 136:142 SD: 1.6121 cents 72:78:81:87:92:96:103:108:117 x 122:137:144 SD: 1.3996 cents 73:79:82:89:93:97:105:110:118:123:124:139:146 SD: 1.3541 cents 74:80:83:90:94:99:106:111:120:125:126:141:148 SD: 0.9580 cents 75:81:84:91:95:100:107:113:121 x 127:143:150 SD: 1.5683 cents 76:82:86:92:97:101:109:114:123:128:129:145:152 SD: 1.2429 cents 78:84:88:95:99:104:112:117:126 x 132:149:156 SD: 1.1481 cents 81:87:91:98:103:108:116:122:131:137 x 155:162 SD: 1.3984 cents 84:91:95:102:107:112:120:126:136:142:143:160:168 SD: 1.1426 cents 87:94:98:106:111:116:125:131:141:147:148:166:174 SD: 1.0319 cents 88:95:99:107:112:117:126:132:143 x 149:168:176 SD: 0.7718 cents 91:98:102:111:116:121:130:137:147 x 154:174:182 SD: 1.4374 cents 92:99:104:112:117:123:132:138:149:155:156:176:184 SD: 1.1147 cents 96:104:108:117:122:128:137:144:156:162:163:183:192 SD: 0.9798 cents 98:106:110:119:125:131:140:147:159:165:166:187:196 SD: 0.8623 cents 102:110:115:124:130:136:146:153:165:172:173:195:204 SD: 0.5331 cents 104:112:117:126:132:139:149:156:168 x 176:199:208 SD: 1.1040 cents 105:113:118:128:134:140:150:158:170:177:178:200:210 SD: 1.0678 cents 106:114:119:129:135:141:152:159:172:179:180:202:212 SD: 0.9085 cents 110:119:124:134:140:147:158:165:178:186:187:210:220 SD: 0.8910 cents 111:120:125:135:141:148:159:167:180:187:188:212:222 SD: 0.7106 cents 122:132:137:148:155:163:175:183:198:206:207:233:244 SD: 0.7061 cents 126:136:142:153:160:168:180:189:204:213:214:241:252 SD: 0.6691 cents 135:146:152:164:172:180:193:203:219:228:229:258:270 SD: 0.5862 cents 150:162:169:182:191:200:215:225:243:253:255:286:300 SD: 0.4611 cents 162:175:182:197:206:216:232:243:262:273:275:309:324 SD: 0.4328 cents 176:190:198:214:224:235:252:264:285:297:299:336:352 SD: 0.2951 cents 224:242:252:272:285:299:321:336:363:378:380:428:448 SD: 0.2700 cents 264:285:297:321:336:352:378:396:428:446:448:504:528 SD: 0.2416 cents 326:352:367:396:415:435:467:489:528:550:553:622:652 SD: 0.2001 cents 352:380:396:428:448:469:504:528:570:594:597:672:704 SD: 0.1904 cents 400:432:450:486:509:533:573:600:648:675:679:764:800 SD: 0.1446 cents 498:538:560:605:634:664:713:747:807:840:845:951:996 SD: 0.1367 cents 502:542:565:610:639:669:719:753:813:847:852:958:1004 SD: 0.1347 cents 528:570:594:641:672:704:756:792:855:891:896:1008:1056 SD: 0.1212 cents 576:622:648:700:733:768:825:864:933:972:977:1100:1152 SD: 0.1081 cents