Scala analysis: synchrome3
Third 25/24&81/80 = ionic and inverse synchrome2
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: 5/4 386.313714 major third 3: 4/3 498.044999 perfect 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: 9/8 203.9100 major whole tone 2: 10/9 182.4037 minor whole tone 3: 16/15 111.7313 minor diatonic semitone 4: 9/8 203.9100 major 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: 1 16/15 111.731 cents minor diatonic semitone 1: 1 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 3 10/9 182.404 cents minor whole tone 1: 2 9/8 203.910 cents major whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 3 6/5 315.641 cents minor third 2: 3 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: 3 8/5 813.686 cents minor sixth 5: 3 5/3 884.359 cents major sixth, BP sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 3 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 50/27 1066.762 cents grave major seventh 6: 1 15/8 1088.269 cents classic 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 : 203.9 386.3 498.0 702.0 884.4 1017.6 1200.0 203.9 : 182.4 294.1 498.0 680.4 813.7 996.1 1200.0 386.3 : 111.7 315.6 498.0 631.3 813.7 1017.6 1200.0 498.0 : 203.9 386.3 519.6 702.0 905.9 1088.3 1200.0 702.0 : 182.4 315.6 498.0 702.0 884.4 996.1 1200.0 884.4 : 133.2 315.6 519.6 702.0 813.7 1017.6 1200.0 1017.6: 182.4 386.3 568.7 680.4 884.4 1066.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 203.9100 cents 135/128, 92.1787 cents 16/15, 111.7313 cents 2: 294.1350 .. 386.3137 cents 135/128, 92.1787 cents 256/243, 90.2250 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 .. 905.8650 cents 135/128, 92.1787 cents 16/15, 111.7313 cents 6: 996.0900 .. 1088.2687 cents 135/128, 92.1787 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.534293 Largest / Average step : 1.189475 Largest / Smallest step : 1.825004 Median interval of one step : 10/9, 182.4037 cents, amount: 3 Most common interval of one step : 10/9, 182.4037 cents, amount: 3 Least squares average step : 172.89903 cents, oct.: 1210.29319 cents Scale is strictly proper Step pattern alph. order: ABCABDB Step pattern size order : DCADCBC Scale is a Constant Structure, by a margin of 62.56515 cents Scale diversity : 1.405280 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.574950 Rothenberg efficiency : 0.466667 redundancy: 0.533333 Efficiency x scale size : 3.266667 Number of different interval sizes : 20 = 3.33333 / class Number of one step interval sizes : 4 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 intervals : 4/3, 498.0450 cents & inv., amount: 4 Most common triad is 0.0 498.045 701.955 cents, amount: 2 Number of recognisable fifths : 4, average 701.9550 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Scale is fully connected 5-limit major-minor triadic Scale contains a complete diamond : 1 3 Length of longest harmonic part : 2 at degree 0 Length of longest subharmonic part : 2 at degree 6 Formal octave complements present : 3 = 42.8571% Scale is n-1 differentially coherent in interval class 1 Scale is differentially coherent in interval class 2 Scale is n-1 differentially coherent in interval classes 3 and 4 combined Limited inverse transpositions with margin 92.1787 cents: 1 -- Rational properties -- Prime limit : 5 Odd number limit : 27 (O: 27 U: 27) Highest odd numerator or denominator: 9 Scale harmonicity : 0.038760 Average absolute harmonicity : 0.274511 Specific harmonicity : 0.229720 Fundamental : 1/120, -6.9069 octaves, 2.1802 Hz. Guide tone : 180, 7.4919 octaves, 47092.602 Hz. Exponens Consonantiae : 2.160000E+04, 14.39874 octaves Euler's gradus suavitatis : 20 Sum of Mann's harmonic distance : 31.5, average 4.50000 Mersenne's string divisions : 42840 Sum of van Prooijen's expressibility: 4.26067, average 0.60867 Sum of Tenney's harmonic distance : 8.14603, average 1.16372 Vogel's harmonic complexity : 12.57143 Wille's k value : 67 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 76.69133, average 2.73898 Lattice compactness (without 2's) : 47.77387, average 1.70621 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.42857 9 1 3: -1 .. 2 0.42857 7 3 5: -1 .. 1 0.14286 3 3 Average exponent except 2's : 4 / 7 = 0.57143 Average absolute exponent except 2's: 10 / 7 = 1.42857 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: 24.8774 c. M: 43.4566 c. Lebeng 12: 2 2 1 2 2 1 2 P M ME S SD: 10.4507 c. M: 17.5963 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 19: 3 3 2 3 3 2 3 SP M ME S SD: 7.7171 c. M: 14.4363 c. Nineteen-tone Mixolydian 31: 5 5 3 5 5 3 5 SP M DE S SD: 6.7763 c. M: 11.1447 c. Intense Diatonic Hypophrygian, M.Mixolydian 34: 6 5 3 6 5 4 5 SP SD: 4.3991 c. M:-7.8547 c. 41: 7 6 4 7 6 5 6 SP SD: 4.1631 c. M:-6.7940 c. 46: 8 7 4 8 7 5 7 SP SD: 3.0718 c. M:-4.9906 c. 53: 9 8 5 9 8 6 8 SP SD: 0.8802 c. M: 1.4081 c. 118: 20 18 11 20 18 13 18 SP SD: 0.3762 c. M: 0.6471 c. 171: 29 26 16 29 26 19 26 SP SD: 0.2354 c. M: 0.4012 c. 388: 66 59 36 66 59 43 59 SP SD: 0.1629 c. M:-0.2842 c. 441: 75 67 41 75 67 49 67 SP SD: 0.0918 c. M:-0.1716 c. 559: 95 85 52 95 85 62 85 SP SD: 0.0527 c. M:-0.0906 c. 612: 104 93 57 104 93 68 93 SP SD: 0.0301 c. M:-0.0508 c. 1171: 199 178 109 199 178 130 178 SP SD: 0.0132 c. M:-0.0228 c. 1783: 303 271 166 303 271 198 271 SP SD: 0.0095 c. M:-0.0160 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: 0.0000 cents 4 x 5 x 6 x 7:8 S SD: 12.1926 cents 5 x 6:7 x 8:9:10 S SD: 26.1717 cents 6:7 x 8:9:10:11:12 S SD: 11.7535 cents 7:8:9 x 11:12:13:14 SD: 20.3538 cents 8:9:10:11:12:13:14:16 S SD: 12.0693 cents 9:10:11:12:14:15:16:18 S SD: 11.4310 cents 10:11 x 13:15:17:18:20 SD: 11.3163 cents 12:14:15:16:18:20:22:24 S SD: 10.0744 cents 14:16:18:19:21:23:25:28 SD: 9.9710 cents 15:17:19:20:23:25:27:30 SD: 6.6038 cents 16:18:20:21:24:27:29:32 SD: 5.2477 cents 24:27:30:32:36:40:43:48 SD: 1.1477 cents 72:81:90:96:108:120:130:144 SD: 0.7622 cents 96:108:120:128:144:160:173:192 SD: 0.2861 cents 120:135:150:160:180:200:216:240 SD: 0.0000 cents