Scala analysis: 44_39-12_C
44_39-12.scl with C as 1/1 (Eb-G#)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 14/13 128.298245 2/3-tone 2: 9/8 203.910002 major whole tone 3: 33/28 284.447037 undecimal minor third 4: 33/26 412.745281 tridecimal major third 5: 117/88 493.119721 tridecimal gentle fourth 6: 63/44 621.417966 7: 3/2 701.955001 perfect fifth 8: 21/13 830.253246 9: 22/13 910.790281 tridecimal major sixth 10: 39/22 991.164720 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: 14/13 128.2982 2/3-tone 2: 117/112 75.6118 3: 22/21 80.5370 undecimal minor semitone 4: 14/13 128.2982 2/3-tone 5: 507/484 80.3744 6: 14/13 128.2982 2/3-tone 7: 22/21 80.5370 undecimal minor semitone 8: 14/13 128.2982 2/3-tone 9: 22/21 80.5370 undecimal minor semitone 10: 507/484 80.3744 11: 14/13 128.2982 2/3-tone 12: 22/21 80.5370 undecimal minor semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 117/112 75.612 cents 1: 2 507/484 80.374 cents 1: 4 22/21 80.537 cents undecimal minor semitone 1: 5 14/13 128.298 cents 2/3-tone 2: 1 429/392 156.149 cents 2: 1 169/154 160.911 cents 2: 1 9/8 203.910 cents major whole tone 2: 3 273/242 208.673 cents 2: 6 44/39 208.835 cents 3: 3 33/28 284.447 cents undecimal minor third 3: 5 13/11 289.210 cents tridecimal minor third 3: 1 968/819 289.372 cents 3: 1 147/121 336.971 cents 3: 2 616/507 337.134 cents 4: 1 1521/1232 364.821 cents 4: 1 121/98 364.984 cents 4: 2 26/21 369.747 cents 4: 2 33/26 412.745 cents tridecimal major third 4: 5 14/11 417.508 cents undecimal diminished fourth or major third 4: 1 1936/1521 417.671 cents 5: 3 117/88 493.120 cents tridecimal gentle fourth 5: 2 121/91 493.282 cents 5: 6 4/3 498.045 cents perfect fourth 5: 1 196/143 545.806 cents 6: 4 39/28 573.657 cents 6: 1 169/121 578.419 cents two (tridecimal minor third) 6: 1 88/63 578.582 cents 6: 1 63/44 621.418 cents 6: 1 242/169 621.581 cents 6: 4 56/39 626.343 cents 7: 1 143/98 654.194 cents 7: 6 3/2 701.955 cents perfect fifth 7: 2 182/121 706.718 cents 7: 3 176/117 706.880 cents 8: 1 1521/968 782.329 cents 8: 5 11/7 782.492 cents undecimal augmented fifth 8: 2 52/33 787.255 cents tridecimal minor sixth 8: 2 21/13 830.253 cents 8: 1 196/121 835.016 cents two (undecimal diminished fourth or major third) 8: 1 2464/1521 835.179 cents 9: 2 507/308 862.866 cents 9: 1 242/147 863.029 cents 9: 1 819/484 910.628 cents 9: 5 22/13 910.790 cents tridecimal major sixth 9: 3 56/33 915.553 cents 10: 6 39/22 991.165 cents 10: 3 484/273 991.327 cents 10: 1 16/9 996.090 cents Pythagorean minor seventh 10: 1 308/169 1039.089 cents 10: 1 784/429 1043.851 cents 11: 5 13/7 1071.702 cents 16/3-tone 11: 4 21/11 1119.463 cents undecimal major seventh 11: 2 968/507 1119.626 cents 11: 1 224/117 1124.388 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.90909 = 54/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 128.3 203.9 284.4 412.7 493.1 621.4 702.0 830.3 910.8 991.2 1119.5 1200.0 128.3 : 75.6 156.1 284.4 364.8 493.1 573.7 702.0 782.5 862.9 991.2 1071.7 1200.0 203.9 : 80.5 208.8 289.2 417.5 498.0 626.3 706.9 787.3 915.6 996.1 1124.4 1200.0 284.4 : 128.3 208.7 337.0 417.5 545.8 626.3 706.7 835.0 915.6 1043.9 1119.5 1200.0 412.7 : 80.4 208.7 289.2 417.5 498.0 578.4 706.7 787.3 915.6 991.2 1071.7 1200.0 493.1 : 128.3 208.8 337.1 417.7 498.0 626.3 706.9 835.2 910.8 991.3 1119.6 1200.0 621.4 : 80.5 208.8 289.4 369.7 498.0 578.6 706.9 782.5 863.0 991.3 1071.7 1200.0 702.0 : 128.3 208.8 289.2 417.5 498.0 626.3 702.0 782.5 910.8 991.2 1119.5 1200.0 830.3 : 80.5 160.9 289.2 369.7 498.0 573.7 654.2 782.5 862.9 991.2 1071.7 1200.0 910.8 : 80.4 208.7 289.2 417.5 493.1 573.7 702.0 782.3 910.6 991.2 1119.5 1200.0 991.2 : 128.3 208.8 337.1 412.7 493.3 621.6 702.0 830.3 910.8 1039.1 1119.6 1200.0 1119.5: 80.5 208.8 284.4 365.0 493.3 573.7 702.0 782.5 910.8 991.3 1071.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 75.6118 .. 128.2982 cents 1568/1521, 52.6865 cents 117/112, 75.6118 cents 2: 156.1488 .. 208.8353 cents 1568/1521, 52.6865 cents 5577/5488, 27.8505 cents 3: 284.4470 .. 337.1335 cents 1568/1521, 52.6865 cents 117/112, 75.6118 cents 4: 364.8215 .. 417.6706 cents 2385152/2313441, 52.8491 cents 771147/758912, 27.6880 cents 5: 493.1197 .. 545.8062 cents 1568/1521, 52.6865 cents 177957/170368, 75.4492 cents 6: 573.6568 .. 626.3432 cents 1568/1521, 52.6865 cents 5577/5488, 27.8505 cents 7: 654.1938 .. 706.8803 cents 1568/1521, 52.6865 cents 5577/5488, 27.8505 cents 8: 782.3294 .. 835.1785 cents 2385152/2313441, 52.8491 cents 177957/170368, 75.4492 cents 9: 862.8665 .. 915.5530 cents 1568/1521, 52.6865 cents 771147/758912, 27.6880 cents 10: 991.1647 .. 1043.8512 cents 1568/1521, 52.6865 cents 117/112, 75.6118 cents 11: 1071.7018 .. 1124.3882 cents 1568/1521, 52.6865 cents 5577/5488, 27.8505 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 117/112, 75.6118 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 14/13, 128.2982 cents Average / Smallest step : 1.322546 Largest / Average step : 1.282982 Largest / Smallest step : 1.696803 Median interval of one step : 22/21, 80.5370 cents, amount: 4 Most common interval of one step : 14/13, 128.2982 cents, amount: 5 Least squares average step : 100.94325 cents, oct.: 1211.31896 cents Scale is strictly proper Step pattern alph. order: ABCADACACDAC Step pattern size order : DACDBDCDCBDC Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 27.68795 cents Scale diversity : 1.264845 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.516770 Rothenberg efficiency : 0.291312 redundancy: 0.708688 Efficiency x scale size : 3.495743 Number of different interval sizes : 54 = 4.90909 / class Number of one step interval sizes : 4 Highest interval variety : 6 Mean interval variety : 4.90909 = 54/11 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 10648/10647, 0.1626 cents Number of recognisable fifths : 11, average 704.1642 cents Best fifths form a closed circle Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 8.3333% Limited inverse transpositions with margin 52.6865 cents: 11 -- Rational properties -- Prime limit : 13 Odd number limit : 1521 (O: 1521 U: 1521) Highest odd numerator or denominator: 117 Scale harmonicity : 0.009044 Average absolute harmonicity : 0.135961 Specific harmonicity : 0.051451 Fundamental : 1/8008, -12.9672 octaves, 0.0327 Hz. Guide tone : 18018, 14.1372 octaves, 4713969.436 Hz. Exponens Consonantiae : 1.442881E+08, 27.10438 octaves Euler's gradus suavitatis : 65 Sum of Mann's harmonic distance : 323.0, average 26.91667 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 14.79931, average 1.23328 Sum of Tenney's harmonic distance : 28.74083, average 2.39507 Vogel's harmonic complexity : 34.83333 Wille's k value : 5323 Wilson's harmonic complexity : 68 Rectangular lattice diameter : 8 Triangular lattice diameter : 4 Lattice compactness : 206.55555, average 2.64815 Lattice compactness (without 2's) : 147.33936, average 1.88897 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -0.83333 16 1 3: 0 .. 2 1.00000 12 2 7: -1 .. 1 0.25000 5 11: -1 .. 1 -0.08333 7 3 13: -1 .. 1 -0.16667 6 6 Average exponent except 2's : 12 / 12 = 1.00000 Average absolute exponent except 2's: 30 / 12 = 2.50000 Scale is JI-epimorphic with val: <12 19 31 39 42| Scale is JI-epimorphic with val: <12 19 32 40 43| Scale is JI-epimorphic with val: <12 19 33 41 44| Scale is JI-epimorphic with val: <12 19 34 42 45| Scale is JI-epimorphic with val: <12 19 35 43 46| Scale is JI-epimorphic with val: <12 19 36 44 47|
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 16.3780 c. M: 30.2532 c. Twelve-tone Chromatic (1/11-comma) 17: 2 1 1 2 1 2 1 2 1 1 2 1 P M ME SD: 9.1022 c. M:-16.8056 c. Twelve-tone Chromatic (2/11-comma positive) 29: 3 2 2 3 2 3 2 3 2 2 3 2 SP M ME SD: 2.6614 c. M:-5.2081 c. Twelve-tone Chromatic (1/14-comma positive) 46: 5 3 3 5 3 5 3 5 3 3 5 3 SP M DE SD: 3.1633 c. M:-4.7857 c. Twelve-tone Chromatic (1/9-comma positive) 75: 8 5 5 8 5 8 5 8 5 5 8 5 SP M DE SD: 2.3216 c. M:-4.0900 c. Twelve-tone Chromatic (2/21-comma positive) 104: 11 7 7 11 7 11 7 11 7 7 11 7 SP M DE SD: 2.1795 c. M:-4.0145 c. Twelve-tone Chromatic (2/23-comma positive) 119: 13 7 8 13 8 13 8 12 8 8 13 8 SP SD: 2.5621 c. M:-3.9274 c. 120: 13 7 8 13 8 13 8 13 8 8 13 8 SP SD: 2.2985 c. M: 4.4470 c. 121: 13 8 8 13 8 13 8 13 8 8 13 8 SP M DE SD: 2.5743 c. M:-4.3545 c. Twelve-tone Chromatic (1/10-comma positive), Leapday-12 122: 13 8 8 13 8 13 8 13 9 8 13 8 SP SD: 2.3483 c. M: 4.0237 c. 130: 14 8 9 14 8 14 9 14 9 8 14 9 SP SD: 2.3021 c. M: 3.8890 c. 131: 14 8 9 14 9 14 9 14 8 9 14 9 SP SD: 2.1560 c. M: 3.9201 c. 132: 14 8 9 14 9 14 9 14 9 9 14 9 SP SD: 2.4025 c. M: 3.9100 c. 133: 14 9 9 14 9 14 9 14 9 9 14 9 SP M DE SD: 2.1837 c. M:-4.2748 c. Twelve-tone Chromatic (1/12-comma positive) 134: 14 9 9 14 9 14 9 15 9 9 14 9 SP SD: 2.3155 c. M: 3.5075 c. 137: 15 8 9 15 9 15 9 15 9 9 15 9 SP SD: 2.0575 c. M: 4.1551 c. 146: 16 9 10 15 10 16 9 16 10 10 15 10 SP SD: 2.3144 c. M:-3.3558 c. 147: 16 9 10 16 9 16 10 16 10 9 16 10 SP SD: 2.2857 c. M:-3.5812 c. 148: 16 9 10 16 10 16 10 15 10 10 16 10 SP SD: 2.0180 c. M:-3.4504 c. 149: 16 9 10 16 10 16 10 16 10 10 16 10 SP SD: 1.4603 c. M: 2.5678 c. 159: 17 10 11 17 10 17 11 17 11 10 17 11 SP SD: 1.8764 c. M: 2.5537 c. 160: 17 10 11 17 11 17 11 17 10 11 17 11 SP SD: 1.7808 c. M: 3.2903 c. 166: 18 10 11 18 11 18 11 18 11 11 18 11 SP SD: 1.2345 c. M: 2.5193 c. 178: 19 11 12 19 12 19 12 19 12 12 19 12 SP SD: 0.9815 c. M: 1.6628 c. 195: 21 12 13 21 13 21 13 21 13 13 21 13 SP SD: 0.6577 c. M: 1.3701 c. 207: 22 13 14 22 14 22 14 22 14 14 22 14 SP SD: 0.7731 c. M: 1.2677 c. 224: 24 14 15 24 15 24 15 24 15 15 24 15 SP SD: 0.2369 c. M: 0.5185 c. 253: 27 16 17 27 17 27 17 27 17 17 27 17 SP SD: 0.1309 c. M: 0.2350 c. 477: 51 30 32 51 32 51 32 51 32 32 51 32 SP SD: 0.0906 c. M: 0.1703 c. 730: 78 46 49 78 49 78 49 78 49 49 78 49 SP SD: 0.0765 c. M: 0.1425 c. 983: 105 62 66 105 66 105 66 105 66 66 105 66 SP SD: 0.0824 c. M: 0.1413 c. 1207: 129 76 81 129 81 129 81 129 81 81 129 81 SP SD: 0.0780 c. M: 0.1521 c. 1253: 134 79 84 134 84 134 84 134 84 84 134 84 SP SD: 0.0666 c. M:-0.1303 c. 1477: 158 93 99 158 99 158 99 158 99 99 158 99 SP SD: 0.0620 c. M:-0.1122 c. 1506: 161 95 101 161 101 161 101 161 101 101 161 101 SP SD: 0.0564 c. M:-0.1074 c. 1730: 185 109 116 185 116 185 116 185 116 116 185 116 SP SD: 0.0469 c. M:-0.0849 c. 1983: 212 125 133 212 133 212 133 212 133 133 212 133 SP SD: 0.0422 c. M:-0.0724 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: 8.9622 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 8.6518 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 11.7641 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 11.0791 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 11.3561 cents 8 x 9 x 10:11 x 12:13 x 14:15:16 S SD: 9.4069 cents 9 x 10:11 x 12:13:14 x 15:16:17:18 S SD: 10.9477 cents 10:11 x 12 x 13:14:15:16:17:18:19:20 S SD: 8.0317 cents 11:12 x 13:14:15:16:17:18:19:20:21:22 S SD: 8.8857 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 5.6954 cents 13:14 x 15 x 17:19:20:21:22:23:25:26 SD: 7.4351 cents 14:15:16:17:18:19:20:21:23:24:25:27:28 SD: 7.0180 cents 15:16:17:18:19:20:21:23:24:25:27:29:30 SD: 6.7483 cents 16:17:18:19:20:21:23:24:26:27:28:31:32 SD: 4.7457 cents 22:24:25:26:28:29:32:33:36:37:39:42:44 SD: 4.1047 cents 23:25:26:27:29:31:33:35:37:39:41:44:46 SD: 3.6000 cents 26:28:29:31:33:35:37:39:42:44:46:50:52 SD: 3.0833 cents 30:32:34:35:38:40:43:45:48:51:53:57:60 SD: 2.9179 cents 34:37:38:40:43:45:49:51:55:58:60:65:68 SD: 2.5786 cents 39:42:44:46:50:52:56:59:63:66:69:74:78 SD: 2.2337 cents 40:43:45:47:51:53:57:60:65:68:71:76:80 SD: 1.7533 cents 49:53:55:58:62:65:70:74:79:83:87:94:98 SD: 1.7029 cents 55:59:62:65:70:73:79:83:89:93:98:105:110 SD: 1.5388 cents 56:60:63:66:71:74:80:84:90:95:99:107:112 SD: 1.5156 cents 62:67:70:73:79:82:89:93:100:105:110:118:124 SD: 1.3539 cents 66:71:74:78:84:88:95:99:107:112:117:126:132 SD: 1.3235 cents 67:72:75:79:85:89:96:101:108:113:119:128:134 SD: 1.2580 cents 74:80:83:87:94:98:106:111:120:125:131:141:148 SD: 1.2087 cents 78:84:88:92:99:104:112:117:126:132:138:149:156 SD: 0.7790 cents 88:95:99:104:112:117:126:132:142:149:156:168:176 SD: 0.6842 cents 118:127:133:139:150:157:169:177:191:200:209:225:236 SD: 0.5734 cents 130:140:146:153:165:173:186:195:210:220:230:248:260 SD: 0.4720 cents 146:157:164:172:185:194:209:219:236:247:259:279:292 SD: 0.4510 cents 167:180:188:197:212:222:239:251:270:283:296:319:334 SD: 0.4372 cents 185:199:208:218:235:246:265:278:299:313:328:353:370 SD: 0.3665 cents 208:224:234:245:264:277:298:312:336:352:369:397:416 SD: 0.2888 cents 234:252:263:276:297:311:335:351:378:396:415:447:468 SD: 0.2151 cents 312:336:351:368:396:415:447:468:504:528:553:596:624 SD: 0.1806 cents 352:379:396:415:447:468:504:528:569:596:624:672:704 SD: 0.1547 cents 442:476:497:521:561:588:633:663:714:748:784:844:884 SD: 0.1469 cents 494:532:556:582:627:657:707:741:798:836:876:943:988 SD: 0.1244 cents 598:644:673:705:759:795:856:897:966:1012:1060:1142:1196 SD: 0.0932 cents