Scala analysis: ragaldoj
Raga-like medieval European Dorian mode with 7/6 and 7/4, just version
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 44/39 208.835280 2: 7/6 266.870906 septimal minor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 22/13 910.790281 tridecimal major sixth 6: 7/4 968.825906 harmonic seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 44/39 208.8353 2: 91/88 58.0356 3: 8/7 231.1741 septimal whole tone 4: 9/8 203.9100 major whole tone 5: 44/39 208.8353 6: 91/88 58.0356 7: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 91/88 58.036 cents 1: 1 9/8 203.910 cents major whole tone 1: 2 44/39 208.835 cents 1: 2 8/7 231.174 cents septimal whole tone 2: 2 7/6 266.871 cents septimal minor third 2: 2 13/11 289.210 cents tridecimal minor third 2: 1 33/26 412.745 cents tridecimal major third 2: 1 9/7 435.084 cents septimal major third, BP third 2: 1 352/273 440.009 cents 3: 1 21/16 470.781 cents narrow fourth 3: 1 117/88 493.120 cents tridecimal gentle fourth 3: 4 4/3 498.045 cents perfect fourth 3: 1 132/91 643.919 cents 4: 1 91/66 556.081 cents 4: 4 3/2 701.955 cents perfect fifth 4: 1 176/117 706.880 cents 4: 1 32/21 729.219 cents wide fifth 5: 1 273/176 759.991 cents 5: 1 14/9 764.916 cents septimal minor sixth 5: 1 52/33 787.255 cents tridecimal minor sixth 5: 2 22/13 910.790 cents tridecimal major sixth 5: 2 12/7 933.129 cents septimal major sixth 6: 2 7/4 968.826 cents harmonic seventh 6: 2 39/22 991.165 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 176/91 1141.964 cents 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 : 208.8 266.9 498.0 702.0 910.8 968.8 1200.0 208.8 : 58.0 289.2 493.1 702.0 760.0 991.2 1200.0 266.9 : 231.2 435.1 643.9 702.0 933.1 1142.0 1200.0 498.0 : 203.9 412.7 470.8 702.0 910.8 968.8 1200.0 702.0 : 208.8 266.9 498.0 706.9 764.9 996.1 1200.0 910.8 : 58.0 289.2 498.0 556.1 787.3 991.2 1200.0 968.8 : 231.2 440.0 498.0 729.2 933.1 1142.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 58.0356 .. 231.1741 cents 704/637, 173.1385 cents 91/88, 58.0356 cents 2: 266.8709 .. 440.0094 cents 704/637, 173.1385 cents 49/48, 35.6968 cents 3: 470.7809 .. 643.9194 cents 704/637, 173.1385 cents 5733/5632, 30.7715 cents 4: 556.0806 .. 729.2191 cents 704/637, 173.1385 cents 8281/8712,-87.8387 cents 5: 759.9906 .. 933.1291 cents 704/637, 173.1385 cents 5733/5632, 30.7715 cents 6: 968.8259 .. 1141.9644 cents 704/637, 173.1385 cents 49/48, 35.6968 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 91/88, 58.0356 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 2.953851 Largest / Average step : 1.348516 Largest / Smallest step : 3.983314 Median interval of one step : 44/39, 208.8353 cents, amount: 2 Least squares average step : 170.08171 cents, oct.: 1190.57195 cents Scale is not proper Step pattern alph. order: ABCDABC Step pattern size order : CADBCAD Scale is a Constant Structure, by a margin of 30.77153 cents Scale diversity : 1.356248 Lumma stability : 0.207507 Lumma impropriety factor : 0.073199 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 : 352/351, 4.9253 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Number of recognisable fifths : 5, average 702.9401 cents Scale is Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords Scale contains a complete diamond : 1 3 Length of longest harmonic part : 2 at degree 2 Formal octave complements present : 3 = 42.8571% Scale is differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 13 Odd number limit : 273 (O: 273 U: 273) Highest odd numerator or denominator: 39 Scale harmonicity : 0.016679 Average absolute harmonicity : 0.240927 Specific harmonicity : 0.089370 Fundamental : 1/156, -7.2854 octaves, 1.6771 Hz. Guide tone : 924, 9.8517 octaves, 241742.022 Hz. Exponens Consonantiae : 1.441440E+05, 17.13715 octaves Euler's gradus suavitatis : 37 Sum of Mann's harmonic distance : 78.5, average 11.21429 Mersenne's string divisions : 1246245 Sum of van Prooijen's expressibility: 5.34945, average 0.76421 Sum of Tenney's harmonic distance : 10.91965, average 1.55995 Vogel's harmonic complexity : 18.85714 Wille's k value : 136 Wilson's harmonic complexity : 37 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 67.64120, average 2.41576 Lattice compactness (without 2's) : 39.97736, average 1.42776 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.28571 10 1 3: -1 .. 1 -0.28571 4 2 7: 0 .. 1 0.28571 2 2 11: 0 .. 1 0.28571 2 13: -1 .. 0 -0.28571 2 2 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 10 / 7 = 1.42857 Scale is weakly epimorphic with val: <7 10 22 22 27| Scale is weakly epimorphic with val: <7 10 22 23 28| Scale is weakly epimorphic with val: <7 10 22 24 29| Scale is weakly epimorphic with val: <7 11 19 23 24| Scale is weakly epimorphic with val: <7 11 19 24 25| Scale is weakly epimorphic with val: <7 11 19 25 26| Scale is weakly epimorphic with val: <7 11 19 26 27| Scale is JI-epimorphic with val: <7 11 20 22 24| Scale is JI-epimorphic with val: <7 11 20 23 25| Scale is JI-epimorphic with val: <7 11 20 24 26| = patent Scale is JI-epimorphic with val: <7 11 20 25 27| Scale is JI-epimorphic with val: <7 11 20 26 28| Scale is weakly epimorphic with val: <7 12 18 22 28| Scale is weakly epimorphic with val: <7 12 18 23 29| Scale is weakly epimorphic with val: <7 12 22 22 25| Scale is weakly epimorphic with val: <7 12 22 23 26| Scale is weakly epimorphic with val: <7 12 22 24 27| Scale is weakly epimorphic with val: <7 12 22 25 28| 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: 44.9575 c. M:-75.9862 c. Lebeng 8: 1 1 1 2 1 0 2 N D3 SD: 44.7680 c. M: 68.8259 c. 9: 2 0 2 1 2 0 2 N T3 I SD: 32.9566 c. M:-57.8314 c. 10: 2 0 2 2 2 0 2 N M DE I SD: 26.3060 c. M:-49.2097 c. 12: 2 1 2 2 2 1 2 P M ME I SD: 18.0139 c. M:-33.1291 c. G.Phrygian, M.Dorian, M.Hypomixolydian, Kafi That, Mela Kharaharapriya, Raga Bageshri, Bhimpalasi, Huseni, Kanara, Kapi, Nayaki Kanada, Ritigaula, Sriraga, Mischung 5, Gregorian nr.8, Eskimo Heptatonic, Yu: China, Hyojo, Oshikicho, Banshikicho: Japan, Nam: Vietnam 17: 3 1 3 3 3 1 3 N M DE I SD: 10.0204 c. M:-19.4094 c. Supra-7 22: 4 1 4 4 4 1 4 N M DE I SD: 9.7392 c. M:-16.4824 c. Supra-7 29: 5 1 6 5 5 1 6 N SD: 9.6115 c. M: 18.5950 c. 31: 5 2 6 5 6 1 6 N SD: 9.5476 c. M:-18.2420 c. 32: 6 1 6 6 5 2 6 N SD: 9.6905 c. M:-16.1647 c. 33: 6 1 7 5 6 2 6 N SD: 9.6731 c. M:-12.9923 c. 34: 6 2 6 6 6 1 7 N SD: 9.0905 c. M: 15.8847 c. 36: 6 2 7 6 6 2 7 N SD: 5.4359 c. M: 10.7903 c. Diatonic + Soft Chromatic Diesis Phrygian 41: 7 2 8 7 7 2 8 N SD: 2.6450 c. M: 3.9572 c. 58: 10 3 11 10 10 3 11 N SD: 1.9152 c. M:-3.5879 c. 63: 11 3 12 11 11 3 12 N SD: 2.2445 c. M:-3.4954 c. 99: 17 5 19 17 17 5 19 N SD: 1.3990 c. M: 2.7747 c. 104: 18 5 20 18 18 5 20 N SD: 1.2757 c. M:-1.8912 c. 125: 22 6 24 21 22 6 24 N SD: 1.4164 c. M:-2.3647 c. 145: 25 7 28 25 25 7 28 N SD: 1.3572 c. M: 2.0433 c. 149: 26 7 29 25 26 7 29 N SD: 1.2547 c. M: 2.3830 c. 161: 28 8 31 27 28 8 31 N SD: 1.0604 c. M: 1.4735 c. 166: 29 8 32 28 29 8 32 N SD: 0.5549 c. M:-0.8033 c. 207: 36 10 40 35 36 10 40 N SD: 0.4619 c. M: 0.7100 c. 265: 46 13 51 45 46 13 51 N SD: 0.3377 c. M: 0.6016 c. 270: 47 13 52 46 47 13 52 N SD: 0.2050 c. M:-0.3208 c. 436: 76 21 84 74 76 21 84 N SD: 0.1700 c. M:-0.3390 c. 477: 83 23 92 81 83 23 92 N SD: 0.1393 c. M: 0.2724 c. 535: 93 26 103 91 93 26 103 N SD: 0.1301 c. M: 0.2371 c. 701: 122 34 135 119 122 34 135 N SD: 0.0966 c. M:-0.1762 c. 747: 130 36 144 127 130 36 144 N SD: 0.1021 c. M: 0.2042 c. 805: 140 39 155 137 140 39 155 N SD: 0.1098 c. M:-0.1568 c. 913: 159 44 176 155 159 44 176 N SD: 0.0984 c. M: 0.1512 c. 971: 169 47 187 165 169 47 187 N SD: 0.0400 c. M:-0.0721 c. 1448: 252 70 279 246 252 70 279 N SD: 0.0218 c. M: 0.0414 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 x 5:6 x 7:8 S SD: 27.9328 cents 5 x 6:7 x 8:9:10 S SD: 29.2034 cents 6 x 7:8:9:10:11:12 S SD: 14.1272 cents 7:8 x 9:11:12 x 14 SD: 21.3994 cents 8:9 x 11:12 x 14:16 SD: 10.7000 cents 11:12:13:15:17 x 19:22 SD: 15.4407 cents 12 x 14:16:18:20:21:24 S SD: 4.4053 cents 13 x 15:17:20:22:23:26 SD: 10.2405 cents 14:16 x 19:21:24:25:28 SD: 9.3694 cents 16:18:19:21:24:27:28:32 SD: 5.9432 cents 20 x 23:27:30:34:35:40 SD: 5.6389 cents 23:26:27:31:35:39:40:46 SD: 5.0009 cents 24:27:28:32:36:41:42:48 SD: 2.4349 cents 36:41:42:48:54:61:63:72 SD: 2.3518 cents 48:54:56:64:72:81:84:96 S SD: 0.9951 cents 72:81:84:96:108:122:126:144 SD: 0.7697 cents 84:95:98:112:126:142:147:168 SD: 0.6584 cents 108:122:126:144:162:183:189:216 SD: 0.4413 cents 156:176:182:208:234:264:273:312 SD: 0.0000 cents