Scala analysis: synmav5
Fifth 81/80&135/128 scale = inverse synmav4
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 6/5 315.641287 minor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 27/16 905.865003 Pythagorean major sixth 6: 16/9 996.089998 Pythagorean minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 1: 9/8 203.9100 major whole tone 2: 16/15 111.7313 minor diatonic semitone 3: 10/9 182.4037 minor whole tone 4: 9/8 203.9100 major whole tone 5: 9/8 203.9100 major whole tone 6: 256/243 90.2250 limma, Pythagorean minor second 7: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 256/243 90.225 cents limma, Pythagorean minor second 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 10/9 182.404 cents minor whole tone 1: 4 9/8 203.910 cents major whole tone 2: 3 32/27 294.135 cents Pythagorean minor third 2: 1 6/5 315.641 cents minor third 2: 1 5/4 386.314 cents major third 2: 2 81/64 407.820 cents Pythagorean major third 3: 5 4/3 498.045 cents perfect fourth 3: 1 27/20 519.551 cents acute fourth 3: 1 45/32 590.224 cents diatonic tritone 4: 1 64/45 609.776 cents 2nd tritone 4: 1 40/27 680.449 cents grave fifth 4: 5 3/2 701.955 cents perfect fifth 5: 2 128/81 792.180 cents Pythagorean minor sixth 5: 1 8/5 813.686 cents minor sixth 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 3 27/16 905.865 cents Pythagorean major sixth 6: 4 16/9 996.090 cents Pythagorean minor seventh 6: 1 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 15/8 1088.269 cents classic major seventh 6: 1 243/128 1109.775 cents Pythagorean major seventh Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.66667 = 11/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.9 315.6 498.0 702.0 905.9 996.1 1200.0 203.9 : 111.7 294.1 498.0 702.0 792.2 996.1 1200.0 315.6 : 182.4 386.3 590.2 680.4 884.4 1088.3 1200.0 498.0 : 203.9 407.8 498.0 702.0 905.9 1017.6 1200.0 702.0 : 203.9 294.1 498.0 702.0 813.7 996.1 1200.0 905.9 : 90.2 294.1 498.0 609.8 792.2 996.1 1200.0 996.1 : 203.9 407.8 519.6 702.0 905.9 1109.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.2250 .. 203.9100 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 2: 294.1350 .. 407.8200 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 3: 498.0450 .. 590.2237 cents 135/128, 92.1787 cents 256/243, 90.2250 cents 4: 609.7763 .. 701.9550 cents 135/128, 92.1787 cents 2048/2025, 19.5526 cents 5: 792.1800 .. 905.8650 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 6: 996.0900 .. 1109.7750 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 256/243, 90.2250 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.900012 Largest / Average step : 1.189475 Largest / Smallest step : 2.260017 Median interval of one step : 9/8, 203.9100 cents, amount: 4 Most common interval of one step : 9/8, 203.9100 cents, amount: 4 Least squares average step : 171.73580 cents, oct.: 1202.15063 cents Scale is strictly proper Step pattern alph. order: ABCAADA Step pattern size order : DBCDDAD Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.461397 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.467419 Rothenberg efficiency : 0.496599 redundancy: 0.503401 Efficiency x scale size : 3.476190 Number of different interval sizes : 22 = 3.66667 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.66667 = 11/3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 2048/2025, 19.5526 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Most common triad is 0.0 498.045 701.955 cents, amount: 4 Number of recognisable fifths : 5, average 701.9550 cents Best major thirds form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 1 3 9 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 at degree 2 Formal octave complements present : 5 = 71.4286% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 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 : 0.036058 Average absolute harmonicity : 0.270975 Specific harmonicity : 0.231213 Fundamental : 1/720, -9.4919 octaves, 0.3634 Hz. Guide tone : 432, 8.7549 octaves, 113022.244 Hz. Exponens Consonantiae : 3.110400E+05, 18.24674 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 55.5, average 7.92857 Mersenne's string divisions : 4221525 Sum of van Prooijen's expressibility: 4.99306, average 0.71329 Sum of Tenney's harmonic distance : 10.28666, average 1.46952 Vogel's harmonic complexity : 16.00000 Wille's k value : 607 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 6 Triangular lattice diameter : 5 Lattice compactness : 106.66417, average 3.80943 Lattice compactness (without 2's) : 56.87705, average 2.03132 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 4 0.00000 16 1 3: -2 .. 3 0.57143 10 5 5: -1 .. 0 -0.14286 1 1 Average exponent except 2's : 3 / 7 = 0.42857 Average absolute exponent except 2's: 11 / 7 = 1.57143 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: 28.6660 c. M: 48.7221 c. Lebeng 11: 2 1 1 2 2 1 2 P D3 S SD: 33.1512 c. M: 61.6814 c. 12: 2 1 2 2 2 1 2 P M ME I SD: 6.7323 c. M: 15.6413 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 29: 5 3 4 5 5 2 5 SP SD: 6.3168 c. M:-15.3932 c. 34: 6 3 5 6 6 2 6 P SD: 6.5146 c. M:-11.7821 c. 37: 6 4 5 7 6 3 6 SP SD: 8.6287 c. M:-11.5585 c. 41: 7 4 6 7 7 3 7 SP SD: 2.5147 c. M:-6.3099 c. 53: 9 5 8 9 9 4 9 SP SD: 0.5187 c. M:-1.3398 c. 118: 20 11 18 20 20 9 20 SP SD: 0.4528 c. M: 0.7803 c. 171: 29 16 26 29 29 13 29 SP SD: 0.3352 c. M: 0.6018 c. 224: 38 21 34 38 38 17 38 SP SD: 0.3228 c. M: 0.5079 c. 335: 57 31 51 57 57 25 57 SP SD: 0.2721 c. M: 0.4174 c. 388: 66 36 59 66 66 29 66 SP SD: 0.1884 c. M:-0.3206 c. 441: 75 41 67 75 75 33 75 SP SD: 0.1414 c. M:-0.2574 c. 494: 84 46 75 84 84 37 84 SP SD: 0.1272 c. M:-0.2079 c. 506: 86 47 77 86 86 38 86 SP SD: 0.0924 c. M: 0.2263 c. 559: 95 52 85 95 95 42 95 SP SD: 0.0362 c. M: 0.0778 c. 612: 104 57 93 104 104 46 104 SP SD: 0.0195 c. M:-0.0450 c. 1171: 199 109 178 199 199 88 199 SP SD: 0.0159 c. M:-0.0274 c. 1783: 303 166 271 303 303 134 303 SP SD: 0.0134 c. M:-0.0239 c. 2395: 407 223 364 407 407 180 407 SP SD: 0.0137 c. M:-0.0223 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: 18.9373 cents 5 x 6:7 x 8:9:10 S SD: 25.3725 cents 6 x 7:8:9:10:11:12 S SD: 12.5599 cents 7:8 x 9:11:12 x 14 SD: 21.8513 cents 8:9:10:11:12 x 14:16 S SD: 15.4344 cents 9:10:11:12:14:15:16:18 S SD: 10.9714 cents 10:11:12:13:15:17:18:20 SD: 9.1032 cents 12 x 14:16:18:20:21:24 S SD: 9.9783 cents 14:16:17:19:21:24:25:28 SD: 7.6995 cents 15:17:18:20:23:25:27:30 SD: 7.1943 cents 16:18:19:21:24:27:28:32 SD: 6.0866 cents 22:25:26:29:33:37:39:44 SD: 5.4421 cents 24:27:29:32:36:41:43:48 SD: 3.9803 cents 26:29:31:35:39:44:46:52 SD: 3.8149 cents 30:34:36:40:45:51:53:60 SD: 3.0112 cents 39:44:47:52:59:66:69:78 SD: 2.8202 cents 40:45:48:53:60:68:71:80 SD: 2.4260 cents 48:54:58:64:72:81:85:96 SD: 1.9663 cents 54:61:65:72:81:91:96:108 SD: 1.3144 cents 64:72:77:85:96:108:114:128 SD: 1.2584 cents 80:90:96:107:120:135:142:160 SD: 0.8632 cents 90:101:108:120:135:152:160:180 SD: 0.6444 cents 144:162:173:192:216:243:256:288 SD: 0.2861 cents 240:270:288:320:360:405:427:480 SD: 0.1931 cents 336:378:403:448:504:567:597:672 SD: 0.1847 cents 384:432:461:512:576:648:683:768 SD: 0.1615 cents 400:450:480:533:600:675:711:800 SD: 0.1594 cents 480:540:576:640:720:810:853:960 SD: 0.0966 cents 576:648:691:768:864:972:1024:1152 SD: 0.0716 cents