Scala analysis: hahnmaxr
Paul Hahn's 12_hahn7 marvel projected to the 5-limit
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 135/128 92.178716 major chroma, major limma 2: 75/64 274.582429 classic augmented second 3: 6/5 315.641287 minor third 4: 5/4 386.313714 major third 5: 4/3 498.044999 perfect fourth 6: 45/32 590.223716 diatonic tritone 7: 3/2 701.955001 perfect fifth 8: 8/5 813.686286 minor sixth 9: 5/3 884.358713 major sixth, BP sixth 10: 225/128 976.537429 augmented sixth 11: 15/8 1088.268715 classic major seventh 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 135/128 92.1787 major chroma, major limma 2: 10/9 182.4037 minor whole tone 3: 128/125 41.0589 minor diesis, diesis 4: 25/24 70.6724 classic chromatic semitone, minor chroma 5: 16/15 111.7313 minor diatonic semitone 6: 135/128 92.1787 major chroma, major limma 7: 16/15 111.7313 minor diatonic semitone 8: 16/15 111.7313 minor diatonic semitone 9: 25/24 70.6724 classic chromatic semitone, minor chroma 10: 135/128 92.1787 major chroma, major limma 11: 16/15 111.7313 minor diatonic semitone 12: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 128/125 41.059 cents minor diesis, diesis 1: 2 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 3 135/128 92.179 cents major chroma, major limma 1: 5 16/15 111.731 cents minor diatonic semitone 1: 1 10/9 182.404 cents minor whole tone 2: 1 16/15 111.731 cents minor diatonic semitone 2: 1 1125/1024 162.851 cents double augmented prime 2: 2 10/9 182.404 cents minor whole tone 2: 4 9/8 203.910 cents major whole tone 2: 3 256/225 223.463 cents Neapolitan diminished third 2: 1 75/64 274.582 cents classic augmented second 3: 1 256/225 223.463 cents Neapolitan diminished third 3: 3 75/64 274.582 cents classic augmented second 3: 2 32/27 294.135 cents Pythagorean minor third 3: 5 6/5 315.641 cents minor third 3: 1 5/4 386.314 cents major third 4: 1 6/5 315.641 cents minor third 4: 6 5/4 386.314 cents major third 4: 1 512/405 405.866 cents narrow diminished fourth 4: 1 81/64 407.820 cents Pythagorean major third 4: 2 32/25 427.373 cents classic diminished fourth 4: 1 4/3 498.045 cents perfect fourth 5: 1 32/25 427.373 cents classic diminished fourth 5: 2 675/512 478.492 cents wide augmented third 5: 7 4/3 498.045 cents perfect fourth 5: 1 512/375 539.104 cents double diminished fifth 5: 1 45/32 590.224 cents diatonic tritone 6: 1 512/375 539.104 cents double diminished fifth 6: 1 25/18 568.717 cents classic augmented fourth 6: 4 45/32 590.224 cents diatonic tritone 6: 4 64/45 609.776 cents 2nd tritone 6: 1 36/25 631.283 cents classic diminished fifth 6: 1 375/256 660.896 cents double augmented fourth 7: 1 64/45 609.776 cents 2nd tritone 7: 1 375/256 660.896 cents double augmented fourth 7: 7 3/2 701.955 cents perfect fifth 7: 2 1024/675 721.508 cents narrow diminished sixth 7: 1 25/16 772.627 cents classic augmented fifth 8: 1 3/2 701.955 cents perfect fifth 8: 2 25/16 772.627 cents classic augmented fifth 8: 1 128/81 792.180 cents Pythagorean minor sixth 8: 1 405/256 794.134 cents wide augmented fifth 8: 6 8/5 813.686 cents minor sixth 8: 1 5/3 884.359 cents major sixth, BP sixth 9: 1 8/5 813.686 cents minor sixth 9: 5 5/3 884.359 cents major sixth, BP sixth 9: 2 27/16 905.865 cents Pythagorean major sixth 9: 3 128/75 925.418 cents diminished seventh 9: 1 225/128 976.537 cents augmented sixth 10: 1 128/75 925.418 cents diminished seventh 10: 3 225/128 976.537 cents augmented sixth 10: 4 16/9 996.090 cents Pythagorean minor seventh 10: 2 9/5 1017.596 cents just minor seventh, BP seventh 10: 1 2048/1125 1037.149 cents double diminished octave 10: 1 15/8 1088.269 cents classic major seventh 11: 1 9/5 1017.596 cents just minor seventh, BP seventh 11: 5 15/8 1088.269 cents classic major seventh 11: 3 256/135 1107.821 cents octave - major chroma 11: 2 48/25 1129.328 cents classic diminished octave 11: 1 125/64 1158.941 cents classic augmented seventh, octave - minor diesis Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.45455 = 60/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 92.2 274.6 315.6 386.3 498.0 590.2 702.0 813.7 884.4 976.5 1088.3 1200.0 92.2 : 182.4 223.5 294.1 405.9 498.0 609.8 721.5 792.2 884.4 996.1 1107.8 1200.0 274.6 : 41.1 111.7 223.5 315.6 427.4 539.1 609.8 702.0 813.7 925.4 1017.6 1200.0 315.6 : 70.7 182.4 274.6 386.3 498.0 568.7 660.9 772.6 884.4 976.5 1158.9 1200.0 386.3 : 111.7 203.9 315.6 427.4 498.0 590.2 702.0 813.7 905.9 1088.3 1129.3 1200.0 498.0 : 92.2 203.9 315.6 386.3 478.5 590.2 702.0 794.1 976.5 1017.6 1088.3 1200.0 590.2 : 111.7 223.5 294.1 386.3 498.0 609.8 702.0 884.4 925.4 996.1 1107.8 1200.0 702.0 : 111.7 182.4 274.6 386.3 498.0 590.2 772.6 813.7 884.4 996.1 1088.3 1200.0 813.7 : 70.7 162.9 274.6 386.3 478.5 660.9 702.0 772.6 884.4 976.5 1088.3 1200.0 884.4 : 92.2 203.9 315.6 407.8 590.2 631.3 702.0 813.7 905.9 1017.6 1129.3 1200.0 976.5 : 111.7 223.5 315.6 498.0 539.1 609.8 721.5 813.7 925.4 1037.1 1107.8 1200.0 1088.3: 111.7 203.9 386.3 427.4 498.0 609.8 702.0 813.7 925.4 996.1 1088.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 41.0589 .. 182.4037 cents 625/576, 141.3449 cents 128/125, 41.0589 cents 2: 111.7313 .. 274.5824 cents 1125/1024, 162.8511 cents 24/25,-70.6724 cents 3: 223.4626 .. 386.3137 cents 1125/1024, 162.8511 cents 16384/16875,-51.1199 cents 4: 315.6413 .. 498.0450 cents 10/9, 182.4037 cents 24/25,-70.6724 cents 5: 427.3726 .. 590.2237 cents 1125/1024, 162.8511 cents 24/25,-70.6724 cents 6: 539.1039 .. 660.8961 cents 140625/131072, 121.7923 cents 16384/16875,-51.1199 cents 7: 609.7763 .. 772.6274 cents 1125/1024, 162.8511 cents 16384/16875,-51.1199 cents 8: 701.9550 .. 884.3587 cents 10/9, 182.4037 cents 24/25,-70.6724 cents 9: 813.6863 .. 976.5374 cents 1125/1024, 162.8511 cents 24/25,-70.6724 cents 10: 925.4176 .. 1088.2687 cents 1125/1024, 162.8511 cents 16384/16875,-51.1199 cents 11: 1017.5963 .. 1158.9411 cents 625/576, 141.3449 cents 24/25,-70.6724 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 128/125, 41.0589 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 10/9, 182.4037 cents Average / Smallest step : 2.435528 Largest / Average step : 1.824037 Largest / Smallest step : 4.442494 Median interval of one step : 101.95500 cents, amount: 0 Most common interval of one step : 16/15, 111.7313 cents, amount: 5 Least squares average step : 99.51357 cents, oct.: 1194.16289 cents Scale is not proper Step pattern alph. order: ABCDEAEEDAEE Step pattern size order : CEABDCDDBCDD Scale is not a Constant Structure Scale diversity : 1.391489 Lumma stability : 0.068431 Lumma impropriety factor : 0.523762 Rothenberg efficiency : 0.365723 redundancy: 0.634277 Efficiency x scale size : 4.388672 Number of different interval sizes : 40 = 3.63636 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 5.45455 = 60/11 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 32805/32768, 1.9537 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 8 Number of recognisable fifths : 8, average 701.9550 cents Scale is fully connected 5-limit major-minor triadic Scale contains a complete diamond : 1 3 5 Formal octave complements present : 7 = 58.3333% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined -- Rational properties -- Prime limit : 5 Odd number limit : 1125 (O: 1125 U: 1125) Highest odd numerator or denominator: 225 Scale harmonicity : 0.025084 Average absolute harmonicity : 0.183150 Specific harmonicity : 0.146820 Fundamental : 1/1920, -10.9069 octaves, 0.1363 Hz. Guide tone : 5400, 12.3987 octaves, 1412778.053 Hz. Exponens Consonantiae : 1.036800E+07, 23.30563 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 455.5, average 37.95833 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 12.93700, average 1.07808 Sum of Tenney's harmonic distance : 25.33039, average 2.11087 Vogel's harmonic complexity : 18.16667 Wille's k value : 1687 Wilson's harmonic complexity : 27 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 361.09044, average 4.62936 Lattice compactness (without 2's) : 153.87428, average 1.97275 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -7 .. 3 -2.00000 38 1 3: -1 .. 3 0.75000 13 2 5: -1 .. 2 0.58333 11 9 Average exponent except 2's : 16 / 12 = 1.33333 Average absolute exponent except 2's: 24 / 12 = 2.00000 Scale is weakly epimorphic with val: <12 17 27|
FIT/MODE
12: 1 2 0 1 1 1 1 1 1 1 1 1 N T3 SD: 14.0312 c. M:-25.4176 c. 22: 2 3 1 1 2 2 2 2 1 2 2 2 N SD: 8.3304 c. M:-16.9122 c. 29: 2 5 1 1 3 2 3 3 1 3 2 3 N SD: 12.0006 c. M:-16.5660 c. 31: 2 5 1 2 3 2 3 3 2 2 3 3 N SD: 6.7416 c. M: 14.7594 c. 34: 3 5 1 2 3 3 3 3 2 3 3 3 N SD: 6.8379 c. M:-13.7036 c. 39: 3 6 1 3 3 3 4 3 3 3 3 4 N SD: 8.1535 c. M: 13.6863 c. 41: 3 6 2 2 4 3 4 4 2 3 4 4 N SD: 6.1787 c. M: 11.1678 c. 43: 3 7 1 3 4 3 4 4 3 3 4 4 N SD: 5.2789 c. M: 8.6645 c. 53: 4 8 2 3 5 4 5 5 3 4 5 5 N SD: 1.6270 c. M: 2.9525 c. 65: 5 10 2 4 6 5 6 6 4 5 6 6 N SD: 1.3233 c. M:-2.3406 c. 118: 9 18 4 7 11 9 11 11 7 9 11 11 N SD: 0.3078 c. M: 0.6533 c. 323: 25 49 11 19 30 25 30 30 19 25 30 30 N SD: 0.3377 c. M:-0.7005 c. 376: 29 57 13 22 35 29 35 35 22 29 35 35 N SD: 0.2039 c. M:-0.3745 c. 441: 34 67 15 26 41 34 41 41 26 34 41 41 N SD: 0.1840 c. M:-0.3383 c. 494: 38 75 17 29 46 38 46 46 29 38 46 46 N SD: 0.0887 c. M: 0.1482 c. 612: 47 93 21 36 57 47 57 57 36 47 57 57 N SD: 0.0401 c. M: 0.0726 c. 1171: 90 178 40 69 109 90 109 109 69 90 109 109 N SD: 0.0340 c. M:-0.0638 c. 1289: 99 196 44 76 120 99 120 120 76 99 120 120 N SD: 0.0305 c. M:-0.0491 c. 1783: 137 271 61 105 166 137 166 166 105 137 166 166 N SD: 0.0120 c. M:-0.0254 c. 1901: 146 289 65 112 177 146 177 177 112 146 177 177 N SD: 0.0108 c. M: 0.0179 c. 2395: 184 364 82 141 223 184 223 223 141 184 223 223 N SD: 0.0097 c. M:-0.0163 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: 0.0000 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 1.9279 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 8.3554 cents 6 x 7 x x 8 x 9 x 10 x 11:12 S SD: 6.6104 cents 7 x 8 x 9 x 10 x 11 x 12:13:14 S SD: 12.8873 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 10.6714 cents 9:10 x 11 x 12:13 x 14:15:16:17:18 S SD: 13.2526 cents 10:11 x 12 x 13:14:15:16:17:18:19:20 S SD: 10.3301 cents 11:12:13 x 14:15 x 17 x 18:19:21:22 SD: 12.0144 cents 12:13:14 x 15:16:17:18:19:20:21:23:24 SD: 5.8993 cents 13:14:15 x 16:17:18:20:21:22:23:24:26 S SD: 8.3004 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 8.2157 cents 15:16 x 18:19:20:21:23:24:25:26:28:30 SD: 5.0324 cents 16:17 x 19:20:21:23:24:26:27:28:30:32 SD: 5.6958 cents 17:18:20 x 21:23:24:26:27:28:30:32:34 SD: 4.9803 cents 20:21:23:24:25:27:28:30:32:33:35:38:40 SD: 4.1946 cents 21:22 x 25:26:28:30:32:34:35:37:39:42 SD: 4.8082 cents 22:23:26 x 28:29:31:33:35:37:39:41:44 SD: 4.5363 cents 24:25:28:29:30:32:34:36:38:40:42:45:48 SD: 2.9070 cents 27:28:32 x 34:36:38:41:43:45:47:51:54 SD: 4.4217 cents 28:30:33:34:35:37:39:42:45:47:49:53:56 SD: 4.0104 cents 29:31:34:35:36:39:41:44:46:48:51:54:58 SD: 3.7221 cents 30:32:35:36:38:40:42:45:48:50:53:56:60 SD: 2.8409 cents 32:34 x 38:40:43:45:48:51:53:56:60:64 SD: 2.7221 cents 35:37:41:42:44:47:49:53:56:58:62:66:70 SD: 2.5937 cents 36:38:42:43:45:48:51:54:58:60:63:68:72 SD: 2.1336 cents 40:42:47:48:50:53:56:60:64:67:70:75:80 SD: 1.6500 cents 54:57:63:65:68:72:76:81:86:90:95:101:108 SD: 1.5369 cents 57:60:67:68:71:76:80:86:91:95:100:107:114 SD: 1.4964 cents 60:63:70:72:75:80:84:90:96:100:105:113:120 SD: 1.4357 cents 69:73:81:83:86:92:97:104:110:115:121:129:138 SD: 1.2705 cents 72:76:84:86:90:96:101:108:115:120:127:135:144 SD: 1.1459 cents 75:79:88:90:94:100:105:113:120:125:132:141:150 SD: 1.1028 cents 87:92:102:104:109:116:122:131:139:145:153:163:174 SD: 1.0461 cents 88:93:103:106:110:117:124:132:141:147:155:165:176 SD: 0.9487 cents 96:101:113:115:120:128:135:144:154:160:169:180:192 SD: 0.8864 cents 104:110:122:125:130:139:146:156:166:173:183:195:208 SD: 0.8026 cents 105:111:123:126:131:140:148:158:168:175:185:197:210 SD: 0.7961 cents 111:117:130:133:139:148:156:167:178:185:195:208:222 SD: 0.6667 cents 120:127:141:144:150:160:169:180:192:200:211:225:240 SD: 0.6655 cents 128:135:150:154:160:171:180:192:205:213:225:240:256 SD: 0.5392 cents 144:152:169:173:180:192:203:216:230:240:253:270:288 SD: 0.5311 cents 145:153:170:174:181:193:204:218:232:242:255:272:290 SD: 0.5224 cents 150:158:176:180:188:200:211:225:240:250:264:281:300 SD: 0.5144 cents 165:174:193:198:206:220:232:248:264:275:290:309:330 SD: 0.4682 cents 168:177:197:202:210:224:236:252:269:280:295:315:336 SD: 0.4143 cents 180:190:211:216:225:240:253:270:288:300:316:338:360 SD: 0.3177 cents 216:228:253:259:270:288:304:324:346:360:380:405:432 SD: 0.2960 cents 240:253:281:288:300:320:338:360:384:400:422:450:480 SD: 0.2626 cents 256:270:300:307:320:341:360:384:410:427:450:480:512 SD: 0.2474 cents 315:332:369:378:394:420:443:473:504:525:554:591:630 SD: 0.2419 cents 330:348:387:396:413:440:464:495:528:550:580:619:660 SD: 0.2146 cents 360:380:422:432:450:480:506:540:576:600:633:675:720 SD: 0.1511 cents 384:405:450:461:480:512:540:576:614:640:675:720:768 SD: 0.1129 cents 600:633:703:720:750:800:844:900:960:1000:1055:1125:1200 SD: 0.0783 cents