Scala analysis: 44_39-12
12-note chromatic tuning with 352:351, 364:363 (G=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: 44/39 208.835280 3: 13/11 289.209719 tridecimal minor third 4: 14/11 417.507964 undecimal diminished fourth or major third 5: 4/3 498.044999 perfect fourth 6: 56/39 626.343244 7: 3/2 701.955001 perfect fifth 8: 11/7 782.492036 undecimal augmented fifth 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: 22/21 80.5370 undecimal minor semitone 3: 507/484 80.3744 4: 14/13 128.2982 2/3-tone 5: 22/21 80.5370 undecimal minor semitone 6: 14/13 128.2982 2/3-tone 7: 117/112 75.6118 8: 22/21 80.5370 undecimal minor semitone 9: 14/13 128.2982 2/3-tone 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 : 128.3 208.8 289.2 417.5 498.0 626.3 702.0 782.5 910.8 991.2 1119.5 1200.0 128.3 : 80.5 160.9 289.2 369.7 498.0 573.7 654.2 782.5 862.9 991.2 1071.7 1200.0 208.8 : 80.4 208.7 289.2 417.5 493.1 573.7 702.0 782.3 910.6 991.2 1119.5 1200.0 289.2 : 128.3 208.8 337.1 412.7 493.3 621.6 702.0 830.3 910.8 1039.1 1119.6 1200.0 417.5 : 80.5 208.8 284.4 365.0 493.3 573.7 702.0 782.5 910.8 991.3 1071.7 1200.0 498.0 : 128.3 203.9 284.4 412.7 493.1 621.4 702.0 830.3 910.8 991.2 1119.5 1200.0 626.3 : 75.6 156.1 284.4 364.8 493.1 573.7 702.0 782.5 862.9 991.2 1071.7 1200.0 702.0 : 80.5 208.8 289.2 417.5 498.0 626.3 706.9 787.3 915.6 996.1 1124.4 1200.0 782.5 : 128.3 208.7 337.0 417.5 545.8 626.3 706.7 835.0 915.6 1043.9 1119.5 1200.0 910.8 : 80.4 208.7 289.2 417.5 498.0 578.4 706.7 787.3 915.6 991.2 1071.7 1200.0 991.2 : 128.3 208.8 337.1 417.7 498.0 626.3 706.9 835.2 910.8 991.3 1119.6 1200.0 1119.5: 80.5 208.8 289.4 369.7 498.0 578.6 706.9 782.5 863.0 991.3 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 : 100.50521 cents, oct.: 1206.06255 cents Scale is strictly proper Step pattern alph. order: ABCABADBACAB Step pattern size order : DCBDCDACDBDC 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 Scale contains a complete diamond : 11 13 39 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 9 = 75.0000% Limited inverse transpositions with margin 52.6865 cents: 9 -- Rational properties -- Prime limit : 13 Odd number limit : 1521 (O: 1521 U: 1521) Highest odd numerator or denominator: 39 Scale harmonicity : 0.009044 Average absolute harmonicity : 0.144856 Specific harmonicity : 0.052085 Fundamental : 1/6006, -12.5522 octaves, 0.0436 Hz. Guide tone : 24024, 14.5522 octaves, 6285292.581 Hz. Exponens Consonantiae : 1.442881E+08, 27.10438 octaves Euler's gradus suavitatis : 65 Sum of Mann's harmonic distance : 207.5, average 17.29167 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 12.47427, average 1.03952 Sum of Tenney's harmonic distance : 24.97502, average 2.08125 Vogel's harmonic complexity : 34.41667 Wille's k value : 5323 Wilson's harmonic complexity : 68 Rectangular lattice diameter : 8 Triangular lattice diameter : 4 Lattice compactness : 187.94091, average 2.40950 Lattice compactness (without 2's) : 143.95097, average 1.84553 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 0.75000 13 1 3: -1 .. 1 0.00000 6 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 : 0 / 12 = 0.00000 Average absolute exponent except 2's: 24 / 12 = 2.00000 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: 15.5007 c. M: 28.2982 c. Twelve-tone Chromatic (1/11-comma) 17: 2 1 1 2 1 2 1 1 2 1 2 1 P M ME SD: 6.8283 c. M:-12.8782 c. 29: 3 2 2 3 2 3 2 2 3 2 3 2 SP M ME SD: 2.8015 c. M: 5.6536 c. 46: 5 3 3 5 3 5 3 3 5 3 5 3 SP M DE SD: 1.6197 c. M: 2.3928 c. 75: 8 5 5 8 5 8 5 5 8 5 8 5 SP M DE SD: 1.3875 c. M: 2.3432 c. 121: 13 8 8 13 8 13 8 8 13 8 13 8 SP M DE SD: 1.3367 c. M:-2.1772 c. 132: 14 9 9 14 9 14 8 9 14 9 14 9 SP SD: 1.2253 c. M:-1.9550 c. 149: 16 10 10 16 10 16 9 10 16 10 16 10 SP SD: 0.9994 c. M:-1.8447 c. 161: 17 11 11 17 11 17 10 11 17 11 17 11 SP SD: 1.0274 c. M: 1.5902 c. 178: 19 12 12 19 12 19 11 12 19 12 19 12 SP SD: 0.5285 c. M:-0.8314 c. 207: 22 14 14 22 14 22 13 14 22 14 22 14 SP SD: 0.4513 c. M: 0.7620 c. 224: 24 15 15 24 15 24 14 15 24 15 24 15 SP SD: 0.2297 c. M:-0.4425 c. 253: 27 17 17 27 17 27 16 17 27 17 27 17 SP SD: 0.1370 c. M: 0.2563 c. 477: 51 32 32 51 32 51 30 32 51 32 51 32 SP SD: 0.0693 c. M:-0.1021 c. 730: 78 49 49 78 49 78 46 49 78 49 78 49 SP SD: 0.0604 c. M: 0.1053 c. 1207: 129 81 81 129 81 129 76 81 129 81 129 81 SP SD: 0.0578 c. M: 0.1026 c. 1253: 134 84 84 134 84 134 79 84 134 84 134 84 SP SD: 0.0451 c. M:-0.0901 c. 1506: 161 101 101 161 101 161 95 101 161 101 161 101 SP SD: 0.0426 c. M: 0.0703 c. 1730: 185 116 116 185 116 185 109 116 185 116 185 116 SP SD: 0.0436 c. M:-0.0746 c. 1983: 212 133 133 212 133 212 125 133 212 133 212 133 SP SD: 0.0399 c. M:-0.0607 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: 8.8105 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 9.5920 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 13.1019 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 11.2850 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 8.6503 cents 8 x 9 x 10:11 x 12:13 x 14:15:16 S SD: 11.6429 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 8.2867 cents 10:11 x 12:13 x 14:15:16:17:18:19:20 S SD: 8.4357 cents 11:12 x 13:14:15:16 x 17:19:20:21:22 SD: 8.0740 cents 12:13 x 14:15:16:17:18:19:20:21:23:24 SD: 5.4073 cents 13:14:15 x x 17:19 x 20:22:23:25:26 SD: 7.9360 cents 14:15:16:17:18:19:20:21:22:24:25:27:28 SD: 5.9353 cents 16:17:18:19:20:21:23:24:25:27:28:31:32 SD: 5.0227 cents 21:23:24:25:27:28:30:32:33:36:37:40:42 SD: 4.7643 cents 22:24:25:26:28:29:32:33:35:37:39:42:44 SD: 3.8333 cents 23:25:26:27:29:31:33:35:36:39:41:44:46 SD: 3.5393 cents 26:28:29:31:33:35:37:39:41:44:46:50:52 SD: 3.0863 cents 30:32:34:35:38:40:43:45:47:51:53:57:60 SD: 2.7710 cents 37:40:42:44:47:49:53:56:58:63:66:71:74 SD: 2.6428 cents 38:41:43:45:48:51:55:57:60:64:67:73:76 SD: 2.4733 cents 39:42:44:46:50:52:56:59:61:66:69:74:78 SD: 2.0034 cents 48:52:54:57:61:64:69:72:75:81:85:92:96 SD: 1.6269 cents 54:58:61:64:69:72:78:81:85:91:96:103:108 SD: 1.4216 cents 62:67:70:73:79:83:89:93:97:105:110:118:124 SD: 1.2417 cents 66:71:74:78:84:88:95:99:104:112:117:126:132 SD: 1.1257 cents 78:84:88:92:99:104:112:117:123:132:138:149:156 SD: 0.7623 cents 110:118:124:130:140:147:158:165:173:186:195:210:220 SD: 0.6851 cents 117:126:132:138:149:156:168:176:184:198:207:223:234 SD: 0.6374 cents 126:136:142:149:160:168:181:189:198:213:223:241:252 SD: 0.6355 cents 132:142:149:156:168:176:190:198:207:223:234:252:264 SD: 0.5513 cents 142:153:160:168:181:189:204:213:223:240:252:271:284 SD: 0.5005 cents 154:166:174:182:196:205:221:231:242:261:273:294:308 SD: 0.4128 cents 186:200:210:220:237:248:267:279:292:315:330:355:372 SD: 0.3881 cents 198:213:223:234:252:264:284:297:311:335:351:378:396 SD: 0.3407 cents 220:237:248:260:280:293:316:330:346:372:390:420:440 SD: 0.2719 cents 264:284:298:312:336:352:379:396:415:447:468:504:528 SD: 0.1971 cents 312:336:352:369:397:416:448:468:490:528:553:596:624 SD: 0.1669 cents 374:403:422:442:476:499:537:561:588:633:663:714:748 SD: 0.1473 cents 484:521:546:572:616:645:695:726:761:819:858:924:968 SD: 0.1290 cents 546:588:616:645:695:728:784:819:858:924:968:1042:1092 SD: 0.0824 cents