Scala analysis: synpor4
Fourth 81/80&250/243 scale = transposed liu_major inverse synpor5
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 10/9 182.403712 minor whole tone 2: 6/5 315.641287 minor third 3: 27/20 519.551289 acute fourth 4: 3/2 701.955001 perfect fifth 5: 5/3 884.358713 major sixth, BP sixth 6: 9/5 1017.596288 just minor seventh, BP seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 10/9 182.4037 minor whole tone 2: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 3: 9/8 203.9100 major whole tone 4: 10/9 182.4037 minor whole tone 5: 10/9 182.4037 minor whole tone 6: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 7: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 4 10/9 182.404 cents minor whole tone 1: 1 9/8 203.910 cents major whole tone 2: 3 6/5 315.641 cents minor third 2: 1 243/200 337.148 cents acute minor third 2: 2 100/81 364.807 cents grave major third 2: 1 5/4 386.314 cents major third 3: 4 4/3 498.045 cents perfect fourth 3: 2 27/20 519.551 cents acute fourth 3: 1 25/18 568.717 cents classic augmented fourth 4: 1 36/25 631.283 cents classic diminished fifth 4: 2 40/27 680.449 cents grave fifth 4: 4 3/2 701.955 cents perfect fifth 5: 1 8/5 813.686 cents minor sixth 5: 2 81/50 835.193 cents acute minor sixth 5: 1 400/243 862.852 cents grave major sixth 5: 3 5/3 884.359 cents major sixth, BP sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 4 9/5 1017.596 cents just minor seventh, BP seventh 6: 2 50/27 1066.762 cents grave major seventh Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.33333 = 10/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 182.4 315.6 519.6 702.0 884.4 1017.6 1200.0 182.4 : 133.2 337.1 519.6 702.0 835.2 1017.6 1200.0 315.6 : 203.9 386.3 568.7 702.0 884.4 1066.8 1200.0 519.6 : 182.4 364.8 498.0 680.4 862.9 996.1 1200.0 702.0 : 182.4 315.6 498.0 680.4 813.7 1017.6 1200.0 884.4 : 133.2 315.6 498.0 631.3 835.2 1017.6 1200.0 1017.6: 182.4 364.8 498.0 702.0 884.4 1066.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 133.2376 .. 203.9100 cents 25/24, 70.6724 cents 27/25, 133.2376 cents 2: 315.6413 .. 386.3137 cents 25/24, 70.6724 cents 16/15, 111.7313 cents 3: 498.0450 .. 568.7174 cents 25/24, 70.6724 cents 16/15, 111.7313 cents 4: 631.2826 .. 701.9550 cents 25/24, 70.6724 cents 648/625, 62.5651 cents 5: 813.6863 .. 884.3587 cents 25/24, 70.6724 cents 16/15, 111.7313 cents 6: 996.0900 .. 1066.7624 cents 25/24, 70.6724 cents 16/15, 111.7313 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 27/25, 133.2376 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.286638 Largest / Average step : 1.189475 Largest / Smallest step : 1.530424 Median interval of one step : 10/9, 182.4037 cents, amount: 4 Most common interval of one step : 10/9, 182.4037 cents, amount: 4 Least squares average step : 172.19665 cents, oct.: 1205.37657 cents Scale is strictly proper Step pattern alph. order: ABCAABA Step pattern size order : MSLMMSM Scale is a Constant Structure, by a margin of 62.56515 cents Scale diversity : 1.349275 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.646638 Rothenberg efficiency : 0.478912 redundancy: 0.521088 Efficiency x scale size : 3.352381 Number of different interval sizes : 20 = 3.33333 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.33333 = 10/3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 81/80, 21.5063 cents Most common triad is 0.0 182.404 498.045 cents, amount: 3 Number of recognisable fifths : 4, average 701.9550 cents Scale is Hypolydian octave species of abstract tetrachord Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 3 5 Length of longest harmonic part : 2 at degree 2 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 5 = 71.4286% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 5 Odd number limit : 243 (O: 243 U: 243) Highest odd numerator or denominator: 27 Scale harmonicity : 0.034325 Average absolute harmonicity : 0.243870 Specific harmonicity : 0.182440 Fundamental : 1/180, -7.4919 octaves, 1.4535 Hz. Guide tone : 270, 8.0768 octaves, 70638.903 Hz. Exponens Consonantiae : 4.860000E+04, 15.56867 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 53.5, average 7.64286 Mersenne's string divisions : 8251320 Sum of van Prooijen's expressibility: 5.21491, average 0.74499 Sum of Tenney's harmonic distance : 10.07224, average 1.43889 Vogel's harmonic complexity : 14.00000 Wille's k value : 121 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 75.55036, average 2.69823 Lattice compactness (without 2's) : 62.34328, average 2.22655 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 1 0.00000 6 1 3: -2 .. 3 0.57143 10 1 5: -1 .. 1 -0.14286 5 5 Average exponent except 2's : 3 / 7 = 0.42857 Average absolute exponent except 2's: 15 / 7 = 2.14286 Scale is JI-epimorphic with val: <7 11 16| = patent
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 16.9613 c. M: 27.2159 c. Lebeng 12: 2 1 2 2 2 1 2 P M ME I SD: 14.6123 c. M: 19.5513 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 19: 3 2 3 3 3 2 3 SP M ME I SD: 7.1341 c. M: 14.2881 c. Nineteen-tone Dorian 26: 4 3 4 4 4 3 4 SP M ME I SD: 7.1120 c. M: 11.8590 c. 27: 4 3 5 4 4 3 4 SP T3 SD: 7.1477 c. M:-13.7820 c. 33: 5 4 5 5 5 4 5 SP M ME I SD: 8.4743 c. M:-11.6314 c. 34: 5 4 6 5 5 4 5 SP T3 SD: 5.2250 c. M:-9.8605 c. 39: 6 4 7 6 6 4 6 SP SD: 5.0920 c. M: 7.9490 c. 41: 6 5 7 6 6 5 6 SP T3 SD: 5.6713 c. M:-7.2780 c. 46: 7 5 8 7 7 5 7 SP SD: 1.8552 c. M: 2.5978 c. 53: 8 6 9 8 8 6 8 SP SD: 1.0874 c. M: 1.3398 c. 99: 15 11 17 15 15 11 15 SP SD: 0.8519 c. M:-1.6608 c. 118: 18 13 20 18 18 13 18 SP SD: 0.5382 c. M: 0.9072 c. 171: 26 19 29 26 26 19 26 SP SD: 0.1482 c. M: 0.2530 c. 388: 59 43 66 59 59 43 59 SP SD: 0.1106 c. M: 0.1774 c. 441: 67 49 75 67 67 49 67 SP SD: 0.0887 c. M:-0.1766 c. 559: 85 62 95 85 85 62 85 SP SD: 0.0579 c. M:-0.0778 c. 612: 93 68 104 93 93 68 93 SP SD: 0.0421 c. M:-0.0566 c. 783: 119 87 133 119 119 87 119 SP SD: 0.0421 c. M:-0.0675 c. 1000: 152 111 170 152 152 111 152 SP SD: 0.0335 c. M:-0.0487 c. 1171: 178 130 199 178 178 130 178 SP SD: 0.0086 c. M: 0.0136 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: 7.1688 cents 4 x 5 x 6 x 7:8 S SD: 21.4668 cents 5 x 6:7 x 8:9:10 S SD: 18.9300 cents 6 x 7:8:9:10:11:12 S SD: 10.3417 cents 7:8 x 9:11:12:13:14 SD: 24.3273 cents 8:9:10:11:12:13:14:16 S SD: 14.8227 cents 9:10:11:12:14:15:16:18 S SD: 10.9714 cents 10:11:12:14:15:17:18:20 SD: 10.5387 cents 14:16:17:19:21:23:25:28 SD: 8.6810 cents 15:17:18:20:23:25:27:30 SD: 7.9356 cents 16:18:19:22:24:27:29:32 SD: 7.0078 cents 18:20:22:24:27:30:32:36 S SD: 6.2827 cents 20:22:24:27:30:33:36:40 S SD: 3.5152 cents 26:29:31:35:39:43:47:52 SD: 2.9476 cents 34:38:41:46:51:57:61:68 SD: 2.5721 cents 36:40:43:49:54:60:65:72 SD: 2.4510 cents 44:49:53:59:66:73:79:88 SD: 2.3754 cents 45:50:54:61:68:75:81:90 SD: 2.0888 cents 46:51:55:62:69:77:83:92 SD: 1.6618 cents 54:60:65:73:81:90:97:108 SD: 0.9774 cents 80:89:96:108:120:133:144:160 SD: 0.6919 cents 100:111:120:135:150:167:180:200 SD: 0.5526 cents 126:140:151:170:189:210:227:252 SD: 0.4193 cents 180:200:216:243:270:300:324:360 SD: 0.0000 cents