Scala analysis: msdiat7
Diatonic scale, symmetrical tetrachords based on 14:11 and 13:11 thirds
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: 21/11 1119.462965 undecimal major seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 22/21 80.5370 undecimal minor semitone 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: 273/242 208.6727 7: 22/21 80.5370 undecimal minor semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 22/21 80.537 cents undecimal minor semitone 1: 1 9/8 203.910 cents major whole tone 1: 2 273/242 208.673 cents 1: 2 44/39 208.835 cents 2: 1 33/28 284.447 cents undecimal minor third 2: 2 13/11 289.210 cents tridecimal minor third 2: 1 968/819 289.372 cents 2: 1 33/26 412.745 cents tridecimal major third 2: 2 14/11 417.508 cents undecimal diminished fourth or major third 3: 1 117/88 493.120 cents tridecimal gentle fourth 3: 1 121/91 493.282 cents 3: 4 4/3 498.045 cents perfect fourth 3: 1 63/44 621.418 cents 4: 1 88/63 578.582 cents 4: 4 3/2 701.955 cents perfect fifth 4: 1 182/121 706.718 cents 4: 1 176/117 706.880 cents 5: 2 11/7 782.492 cents undecimal augmented fifth 5: 1 52/33 787.255 cents tridecimal minor sixth 5: 1 819/484 910.628 cents 5: 2 22/13 910.790 cents tridecimal major sixth 5: 1 56/33 915.553 cents 6: 2 39/22 991.165 cents 6: 2 484/273 991.327 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 21/11 1119.463 cents undecimal major seventh Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 208.8 417.5 498.0 702.0 910.8 1119.5 1200.0 208.8 : 208.7 289.2 493.1 702.0 910.6 991.2 1200.0 417.5 : 80.5 284.4 493.3 702.0 782.5 991.3 1200.0 498.0 : 203.9 412.7 621.4 702.0 910.8 1119.5 1200.0 702.0 : 208.8 417.5 498.0 706.9 915.6 996.1 1200.0 910.8 : 208.7 289.2 498.0 706.7 787.3 991.2 1200.0 1119.5: 80.5 289.4 498.0 578.6 782.5 991.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.5370 .. 208.8353 cents 14/13, 128.2982 cents 22/21, 80.5370 cents 2: 284.4470 .. 417.5080 cents 392/363, 133.0609 cents 117/112, 75.6118 cents 3: 493.1197 .. 621.4180 cents 14/13, 128.2982 cents 117/112, 75.6118 cents 4: 578.5820 .. 706.8803 cents 14/13, 128.2982 cents 3872/3969,-42.8359 cents 5: 782.4920 .. 915.5530 cents 392/363, 133.0609 cents 117/112, 75.6118 cents 6: 991.1647 .. 1119.4630 cents 14/13, 128.2982 cents 117/112, 75.6118 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 22/21, 80.5370 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 44/39, 208.8353 cents Average / Smallest step : 2.128568 Largest / Average step : 1.218206 Largest / Smallest step : 2.593034 Median interval of one step : 273/242, 208.6727 cents, amount: 2 Least squares average step : 178.68954 cents, oct.: 1250.82677 cents Scale is not proper Step pattern alph. order: ABCDABC Step pattern size order : DCABDCA Scale is a Constant Structure, by a margin of 42.83593 cents Scale diversity : 1.313761 Lumma stability : 0.386268 Lumma impropriety factor : 0.035697 Rothenberg efficiency : 0.421769 redundancy: 0.578231 Efficiency x scale size : 2.952381 Number of different interval sizes : 26 = 4.33333 / class Number of one step interval sizes : 4 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 10648/10647, 0.1626 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Number of recognisable fifths : 6, average 703.5697 cents Scale is Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords 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 : 3 = 42.8571% Scale is differentially coherent in interval classes 3 and 4 combined Limited inverse transpositions with margin 133.0609 cents: 2 -- Rational properties -- Prime limit : 13 Odd number limit : 819 (O: 819 U: 819) Highest odd numerator or denominator: 39 Scale harmonicity : 0.012964 Average absolute harmonicity : 0.228497 Specific harmonicity : 0.069291 Fundamental : 1/858, -9.7448 octaves, 0.3049 Hz. Guide tone : 924, 9.8517 octaves, 241742.022 Hz. Exponens Consonantiae : 7.927920E+05, 19.59658 octaves Euler's gradus suavitatis : 46 Sum of Mann's harmonic distance : 95.0, average 13.57143 Mersenne's string divisions : 1394400 Sum of van Prooijen's expressibility: 6.02286, average 0.86041 Sum of Tenney's harmonic distance : 12.40038, average 1.77148 Vogel's harmonic complexity : 27.14286 Wille's k value : 643 Wilson's harmonic complexity : 48 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 60.72590, average 2.16878 Lattice compactness (without 2's) : 46.14394, average 1.64800 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.85714 8 1 3: -1 .. 1 0.00000 4 2 7: 0 .. 1 0.28571 2 11: -1 .. 1 0.00000 4 2 13: -1 .. 0 -0.28571 2 2 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: 51.6013 c. M: 90.8915 c. Lebeng 8: 1 2 0 2 1 1 1 P D3 S SD: 44.8418 c. M: 69.4630 c. 9: 2 1 1 1 2 1 1 P M ME S SD: 36.7174 c. M:-57.8314 c. 10: 2 1 1 2 2 1 1 P D3 S SD: 35.6743 c. M: 57.5080 c. Pseudo Rast 11: 2 2 0 2 2 2 1 N T3 SD: 35.3741 c. M: 61.6814 c. 12: 2 2 1 2 2 2 1 P M ME S SD: 11.2597 c. M: 19.4630 c. G.Lydian, M.Ionian, M.Hypolydian, Major, Bilaval That, Mela Shankarabharanam, Raga Atana, Ghana Heptatonic, Peruvian Major, Matzore, Rast ascending: Greece, 4th plagal Byzantine, Ararai: Ethiopia, Makam Cargah, Ajam Ashiran, Dastgah-e Mahur, Dastgah-e Rast Panjgah, Xin: China, DS2, Heptatonia prima 17: 3 3 1 3 3 3 1 N M DE S SD: 5.6275 c. M:-9.9488 c. Seventeen-tone Major 29: 5 5 2 5 5 5 2 N M DE S SD: 1.9695 c. M: 3.7149 c. Twenty-nine tone Major 46: 8 8 3 8 8 8 3 N M DE S SD: 1.7624 c. M: 2.3928 c. 75: 13 13 5 13 13 13 5 N M DE S SD: 1.3673 c. M:-2.0450 c. 104: 18 18 7 18 18 18 7 N M DE S SD: 1.3929 c. M: 2.1233 c. 132: 23 23 9 22 23 23 9 N SD: 1.3466 c. M:-1.9550 c. 137: 24 24 9 23 24 24 9 N SD: 1.5322 c. M:-2.9300 c. 149: 26 26 10 25 26 26 10 N SD: 0.9089 c. M:-1.2840 c. 166: 29 29 11 28 29 29 11 N SD: 0.9213 c. M:-1.7691 c. 178: 31 31 12 30 31 31 12 N SD: 0.5628 c. M:-0.8314 c. 195: 34 34 13 33 34 34 13 N SD: 0.4930 c. M:-0.9536 c. 207: 36 36 14 35 36 36 14 N SD: 0.4389 c. M: 0.6454 c. 224: 39 39 15 38 39 39 15 N SD: 0.1797 c. M:-0.3492 c. 253: 44 44 17 43 44 44 17 N SD: 0.0903 c. M: 0.1396 c. 477: 83 83 32 81 83 83 32 N SD: 0.0671 c. M:-0.1021 c. 730: 127 127 49 124 127 127 49 N SD: 0.0525 c. M: 0.1053 c. 983: 171 171 66 167 171 171 66 N SD: 0.0554 c. M: 0.1087 c. 1029: 179 179 69 175 179 179 69 N SD: 0.0631 c. M: 0.0889 c. 1207: 210 210 81 205 210 210 81 N SD: 0.0554 c. M: 0.1026 c. 1253: 218 218 84 213 218 218 84 N SD: 0.0497 c. M:-0.0901 c. 1506: 262 262 101 256 262 262 101 N SD: 0.0427 c. M: 0.0703 c. 1759: 306 306 118 299 306 306 118 N SD: 0.0419 c. M: 0.0803 c. 1983: 345 345 133 337 345 345 133 N SD: 0.0394 c. M: 0.0607 c. 2236: 389 389 150 380 389 389 150 N SD: 0.0383 c. M: 0.0696 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 6:7 x 8 S SD: 16.4720 cents 5 x 6:7 x 8 x 10 S SD: 41.0341 cents 6:7 x 8:9:10:11:12 S SD: 15.7945 cents 7:8:9 x 11:12:13:14 SD: 16.7285 cents 8:9:10:11:12:14:15:16 S SD: 12.9178 cents 10:11:13 x 15:17:19:20 SD: 9.7160 cents 13:15 x 17:20:22:25:26 SD: 11.4560 cents 14:16:18:19:21:24:27:28 SD: 7.2208 cents 16:18:20:21:24:27:31:32 SD: 7.0260 cents 18:20:23:24:27:30:34:36 SD: 6.0330 cents 22:25:28:29:33:37:42:44 SD: 3.6783 cents 30:34:38:40:45:51:57:60 SD: 2.3029 cents 48:54:61:64:72:81:92:96 SD: 1.4440 cents 62:70:79:83:93:105:118:124 SD: 1.3101 cents 78:88:99:104:117:132:149:156 SD: 0.6969 cents 110:124:140:147:165:186:210:220 SD: 0.6315 cents 132:149:168:176:198:223:252:264 SD: 0.4449 cents 180:203:229:240:270:305:344:360 SD: 0.4292 cents 186:210:237:248:279:315:355:372 SD: 0.3883 cents 210:237:267:280:315:355:401:420 SD: 0.3809 cents 228:257:290:304:342:386:435:456 SD: 0.3272 cents 234:264:298:312:351:396:447:468 SD: 0.2135 cents 264:298:336:352:396:447:504:528 SD: 0.1806 cents 312:352:397:416:468:528:596:624 SD: 0.1612 cents 396:447:504:528:594:670:756:792 SD: 0.1398 cents 462:521:588:616:693:782:882:924 SD: 0.1198 cents 546:616:695:728:819:924:1042:1092 SD: 0.0922 cents 594:670:756:792:891:1005:1134:1188 SD: 0.0803 cents