Scala analysis: 44_39-diat1
Diatonic involving 352:351 and 364:363
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 44/39 208.835280 2: 14/11 417.507964 undecimal diminished fourth or major third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 22/13 910.790281 tridecimal major sixth 6: 39/22 991.164720 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 44/39 208.8353 1: 44/39 208.8353 2: 273/242 208.6727 3: 22/21 80.5370 undecimal minor semitone 4: 9/8 203.9100 major whole tone 5: 44/39 208.8353 6: 507/484 80.3744 7: 44/39 208.8353
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 507/484 80.374 cents 1: 1 22/21 80.537 cents undecimal minor semitone 1: 1 9/8 203.910 cents major whole tone 1: 1 273/242 208.673 cents 1: 3 44/39 208.835 cents 2: 1 33/28 284.447 cents undecimal minor third 2: 3 13/11 289.210 cents tridecimal minor third 2: 1 33/26 412.745 cents tridecimal major third 2: 1 14/11 417.508 cents undecimal diminished fourth or major third 2: 1 1936/1521 417.671 cents 3: 2 117/88 493.120 cents tridecimal gentle fourth 3: 1 121/91 493.282 cents 3: 3 4/3 498.045 cents perfect fourth 3: 1 56/39 626.343 cents 4: 1 39/28 573.657 cents 4: 3 3/2 701.955 cents perfect fifth 4: 1 182/121 706.718 cents 4: 2 176/117 706.880 cents 5: 1 1521/968 782.329 cents 5: 1 11/7 782.492 cents undecimal augmented fifth 5: 1 52/33 787.255 cents tridecimal minor sixth 5: 3 22/13 910.790 cents tridecimal major sixth 5: 1 56/33 915.553 cents 6: 3 39/22 991.165 cents 6: 1 484/273 991.327 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 1 21/11 1119.463 cents undecimal major seventh 6: 1 968/507 1119.626 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 208.8 417.5 498.0 702.0 910.8 991.2 1200.0 208.8 : 208.7 289.2 493.1 702.0 782.3 991.2 1200.0 417.5 : 80.5 284.4 493.3 573.7 782.5 991.3 1200.0 498.0 : 203.9 412.7 493.1 702.0 910.8 1119.5 1200.0 702.0 : 208.8 289.2 498.0 706.9 915.6 996.1 1200.0 910.8 : 80.4 289.2 498.0 706.7 787.3 991.2 1200.0 991.2 : 208.8 417.7 626.3 706.9 910.8 1119.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.3744 .. 208.8353 cents 21296/19773, 128.4608 cents 507/484, 80.3744 cents 2: 284.4470 .. 417.6706 cents 4928/4563, 133.2235 cents 117/112, 75.6118 cents 3: 493.1197 .. 626.3432 cents 4928/4563, 133.2235 cents 177957/170368, 75.4492 cents 4: 573.6568 .. 706.8803 cents 4928/4563, 133.2235 cents 1521/1568,-52.6865 cents 5: 782.3294 .. 915.5530 cents 4928/4563, 133.2235 cents 177957/170368, 75.4492 cents 6: 991.1647 .. 1119.6256 cents 21296/19773, 128.4608 cents 117/112, 75.6118 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 507/484, 80.3744 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 44/39, 208.8353 cents Average / Smallest step : 2.132874 Largest / Average step : 1.218206 Largest / Smallest step : 2.598280 Median interval of one step : 273/242, 208.6727 cents, amount: 1 Most common interval of one step : 44/39, 208.8353 cents, amount: 3 Least squares average step : 173.19104 cents, oct.: 1212.33730 cents Scale is not proper Step pattern alph. order: ABCDAEA Step pattern size order : EDBCEAE Scale is a Constant Structure, by a margin of 52.68649 cents Scale diversity : 1.316613 Lumma stability : 0.385726 Lumma impropriety factor : 0.043905 Rothenberg efficiency : 0.385034 redundancy: 0.614966 Efficiency x scale size : 2.695238 Number of different interval sizes : 28 = 4.66667 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.66667 = 14/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 10648/10647, 0.1626 cents Number of recognisable fifths : 6, average 704.3905 cents Best major thirds form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 1 3 Formal octave complements present : 5 = 71.4286% Scale is n-1 differentially coherent in interval classes 3 and 4 combined Limited inverse transpositions with margin 133.0609 cents: 1 -- Rational properties -- Prime limit : 13 Odd number limit : 1521 (O: 1521 U: 1521) Highest odd numerator or denominator: 39 Scale harmonicity : 0.010071 Average absolute harmonicity : 0.227155 Specific harmonicity : 0.061998 Fundamental : 1/858, -9.7448 octaves, 0.3049 Hz. Guide tone : 12012, 13.5522 octaves, 3142646.290 Hz. Exponens Consonantiae : 1.030630E+07, 23.29702 octaves Euler's gradus suavitatis : 58 Sum of Mann's harmonic distance : 109.5, average 15.64286 Mersenne's string divisions : 2658075 Sum of van Prooijen's expressibility: 6.29171, average 0.89882 Sum of Tenney's harmonic distance : 12.97025, average 1.85289 Vogel's harmonic complexity : 27.85714 Wille's k value : 760 Wilson's harmonic complexity : 61 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 64.88205, average 2.31722 Lattice compactness (without 2's) : 47.53206, average 1.69757 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.71429 9 1 3: -1 .. 1 0.00000 4 2 7: 0 .. 1 0.14286 1 11: -1 .. 1 0.00000 4 1 13: -1 .. 1 -0.14286 3 3 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 12 / 7 = 1.71429 Scale is weakly epimorphic with val: <7 10 20 22 27| Scale is weakly epimorphic with val: <7 10 21 22 28| Scale is weakly epimorphic with val: <7 10 21 23 28| Scale is weakly epimorphic with val: <7 10 22 23 29| Scale is weakly epimorphic with val: <7 10 22 24 29| Scale is JI-epimorphic with val: <7 11 18 23 25| Scale is weakly epimorphic with val: <7 11 18 24 25| Scale is JI-epimorphic with val: <7 11 19 24 26| Scale is weakly epimorphic with val: <7 11 19 25 26| Scale is JI-epimorphic with val: <7 11 20 25 27| Scale is weakly epimorphic with val: <7 11 20 26 27| Scale is JI-epimorphic with val: <7 11 21 26 28| Scale is weakly epimorphic with val: <7 12 18 22 25| Scale is weakly epimorphic with val: <7 12 19 23 26| Scale is weakly epimorphic with val: <7 12 20 24 27| Scale is weakly epimorphic with val: <7 12 21 22 28| Scale is weakly epimorphic with val: <7 12 21 25 28| Scale is weakly epimorphic with val: <7 12 22 23 29| Scale is weakly epimorphic with val: <7 12 22 26 29|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 41.0171 c. M: 74.6508 c. Lebeng 9: 2 1 1 1 2 0 2 N T3 SD: 37.7855 c. M: 57.8314 c. 10: 2 1 1 2 2 0 2 P D3 S SD: 34.4808 c. M: 57.5080 c. 11: 2 2 0 2 2 1 2 N T3 SD: 33.8722 c. M: 61.6814 c. 12: 2 2 1 2 2 1 2 P M ME S SD: 9.1552 c. M: 17.5080 c. G.Hypophrygian, G.Ionian (Iastian), M.Mixolydian, G.M.Hypoionian, Hypermixolydian, Mischung 3, Khamaj That, Mela Harikambhoji, Raga Balahamsa, Bhim, Devamanohari, Harini, Janjhuti, Kaamaai, Khambhavati, Surati, Gregorian nr.7, Enharmonic Byzantine Liturgical, Rast descending: Greece, Ching, Shang: China 17: 3 3 1 3 3 1 3 N M DE S SD: 4.3307 c. M:-6.8568 c. Safi al-Din's maqam `Ussaq 29: 5 5 2 5 5 2 5 N M DE S SD: 1.9263 c. M: 3.7149 c. 46: 8 8 3 8 8 3 8 N M DE S SD: 1.5391 c. M: 2.3928 c. 75: 13 13 5 13 13 5 13 N M DE S SD: 1.3886 c. M:-2.0450 c. 132: 23 23 9 22 23 9 23 N SD: 1.2602 c. M:-1.9550 c. 149: 26 26 10 25 26 10 26 N SD: 0.9333 c. M:-1.2840 c. 161: 28 28 11 27 28 11 28 N SD: 0.9089 c. M: 1.4735 c. 166: 29 29 11 28 29 11 29 N SD: 0.8903 c. M:-1.7691 c. 178: 31 31 12 30 31 12 31 N SD: 0.5490 c. M:-0.8314 c. 195: 34 34 13 33 34 13 34 N SD: 0.4735 c. M:-0.9536 c. 207: 36 36 14 35 36 14 36 N SD: 0.3743 c. M: 0.6454 c. 224: 39 39 15 38 39 15 39 N SD: 0.1701 c. M:-0.3492 c. 253: 44 44 17 43 44 17 44 N SD: 0.0982 c. M: 0.1396 c. 477: 83 83 32 81 83 32 83 N SD: 0.0668 c. M:-0.1021 c. 730: 127 127 49 124 127 49 127 N SD: 0.0584 c. M: 0.1053 c. 1000: 174 174 67 170 174 67 174 N SD: 0.0465 c. M:-0.0920 c. 1029: 179 179 69 175 179 69 179 N SD: 0.0663 c. M: 0.0889 c. 1207: 210 210 81 205 210 81 210 N SD: 0.0588 c. M: 0.1026 c. 1224: 213 213 82 208 213 82 213 N SD: 0.0531 c. M:-0.1391 c. 1253: 218 218 84 213 218 84 218 N SD: 0.0420 c. M:-0.0563 c. 1477: 257 257 99 251 257 99 257 N SD: 0.0416 c. M:-0.0953 c. 1730: 301 301 116 294 301 116 301 N SD: 0.0391 c. M:-0.0643 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 0.0000 cents 3 x x 4 x 5 x 6 S SD: 8.8105 cents 4 x 5 x 6 x 7:8 S SD: 9.5920 cents 5 x 6:7 x 8:9:10 S SD: 33.2502 cents 6:7 x 8:9:10:11:12 S SD: 14.3892 cents 7:8:9 x 11:12 x 14 SD: 17.6558 cents 8:9:10:11:12 x 14:16 S SD: 10.9727 cents 10:11:13 x 15:17:18:20 SD: 10.5788 cents 13:15 x 17:20:22:23:26 SD: 11.2751 cents 14:16:18:19:21:24:25:28 SD: 7.0067 cents 16:18:20:21:24:27:28:32 S SD: 6.7973 cents 18:20:23:24:27:30:32:36 SD: 5.4745 cents 22:25:28:29:33:37:39:44 SD: 3.6783 cents 30:34:38:40:45:51:53:60 SD: 2.1511 cents 40:45:51:53:60:68:71:80 SD: 2.1101 cents 48:54:61:64:72:81:85:96 SD: 1.0935 cents 62:70:79:83:93:105:110:124 SD: 1.0859 cents 78:88:99:104:117:132:138:156 SD: 0.8375 cents 84:95:107:112:126:142:149:168 SD: 0.7075 cents 110:124:140:147:165:186:195:220 SD: 0.6315 cents 132:149:168:176:198:223:234:264 SD: 0.4449 cents 150:169:191:200:225:254:266:300 SD: 0.3967 cents 172:194:219:229:258:291:305:344 SD: 0.3923 cents 180:203:229:240:270:305:319:360 SD: 0.3475 cents 228:257:290:304:342:386:404:456 SD: 0.3089 cents 234:264:298:312:351:396:415:468 SD: 0.1858 cents 264:298:336:352:396:447:468:528 SD: 0.1806 cents 312:352:397:416:468:528:553:624 SD: 0.0697 cents 546:616:695:728:819:924:968:1092 SD: 0.0398 cents