Scala analysis: synpor5
Fifth 81/80&250/243 scale = transposed al-farabi_dor inverse synpor4
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: 5/4 386.313714 major 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: 9/8 203.9100 major whole tone 3: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 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 : 182.4 386.3 519.6 702.0 884.4 1017.6 1200.0 182.4 : 203.9 337.1 519.6 702.0 835.2 1017.6 1200.0 386.3 : 133.2 315.6 498.0 631.3 813.7 996.1 1200.0 519.6 : 182.4 364.8 498.0 680.4 862.9 1066.8 1200.0 702.0 : 182.4 315.6 498.0 680.4 884.4 1017.6 1200.0 884.4 : 133.2 315.6 498.0 702.0 835.2 1017.6 1200.0 1017.6: 182.4 364.8 568.7 702.0 884.4 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 : 173.20626 cents, oct.: 1212.44382 cents Scale is strictly proper Step pattern alph. order: ABCAACA Step pattern size order : MLSMMSM Scale is sum-free (all different intervals) 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 0.0 701.955 1017.596 cents, amount: 3 Number of recognisable fifths : 4, average 701.9550 cents Scale is Hypophrygian 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 : 5 9 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 at degree 0 Formal octave complements present : 3 = 42.8571% Scale is differentially coherent in interval classes 1 and 2 combined Scale is differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined Limited inverse transpositions with margin 70.6724 cents: 1 -- 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 : 0.246686 Specific harmonicity : 0.181234 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 : 52.5, average 7.50000 Mersenne's string divisions : 2250360 Sum of van Prooijen's expressibility: 5.21491, average 0.74499 Sum of Tenney's harmonic distance : 9.89615, average 1.41374 Vogel's harmonic complexity : 14.57143 Wille's k value : 121 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 78.58438, average 2.80658 Lattice compactness (without 2's) : 61.92906, average 2.21175 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 1 -0.42857 7 1 3: -2 .. 3 0.42857 9 1 5: -1 .. 1 0.14286 5 5 Average exponent except 2's : 4 / 7 = 0.57143 Average absolute exponent except 2's: 14 / 7 = 2.00000 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: 21.2521 c. M: 43.4566 c. Lebeng 12: 2 2 1 2 2 1 2 P M ME S SD: 14.3293 c. M: 19.5513 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: 7.6579 c. M: 14.2881 c. Nineteen-tone Mixolydian 26: 4 4 3 4 4 3 4 SP M ME S SD: 9.1854 c. M: 17.0829 c. 27: 4 5 3 4 4 3 4 SP T3 SD: 8.6554 c. M:-13.7820 c. 34: 5 6 4 5 5 4 5 SP T3 SD: 5.2205 c. M:-9.8605 c. 41: 6 7 5 6 6 5 6 SP T3 SD: 5.5969 c. M:-7.2780 c. 46: 7 8 5 7 7 5 7 SP SD: 2.4568 c. M:-4.9906 c. 53: 8 9 6 8 8 6 8 SP SD: 1.0997 c. M: 1.4081 c. 99: 15 17 11 15 15 11 15 SP SD: 1.0205 c. M:-1.6608 c. 118: 18 20 13 18 18 13 18 SP SD: 0.5202 c. M: 0.9072 c. 171: 26 29 19 26 26 19 26 SP SD: 0.1903 c. M: 0.3488 c. 388: 59 66 43 59 59 43 59 SP SD: 0.1388 c. M:-0.2842 c. 441: 67 75 49 67 67 49 67 SP SD: 0.0938 c. M:-0.1766 c. 559: 85 95 62 85 85 62 85 SP SD: 0.0605 c. M:-0.0906 c. 612: 93 104 68 93 93 68 93 SP SD: 0.0413 c. M:-0.0566 c. 1000: 152 170 111 152 152 111 152 SP SD: 0.0440 c. M:-0.0863 c. 1171: 178 199 130 178 178 130 178 SP SD: 0.0110 c. M:-0.0228 c. 1783: 271 303 198 271 271 198 271 SP SD: 0.0121 c. M:-0.0225 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: 12.1926 cents 5 x 6:7 x 8:9:10 S SD: 23.6248 cents 6:7 x 8:9:10:11:12 S SD: 15.4617 cents 7:8:9 x 11:12:13:14 SD: 21.4407 cents 8:9:10:11:12:13:14:16 S SD: 10.8528 cents 10:11 x 14:15:17:18:20 SD: 12.2951 cents 11:12:14:15:17:18:20:22 SD: 11.3100 cents 12:13:15:16:18:20:22:24 SD: 8.3211 cents 16:18:20:22:24:27:29:32 SD: 6.5117 cents 20:22:25:27:30:33:36:40 SD: 3.5152 cents 28:31:35:38:42:47:50:56 SD: 3.0771 cents 36:40:45:49:54:60:65:72 SD: 2.1658 cents 48:53:60:65:72:80:86:96 SD: 2.0742 cents 52:58:65:70:78:87:94:104 SD: 1.8474 cents 60:67:75:81:90:100:108:120 SD: 1.2335 cents 72:80:90:97:108:120:130:144 SD: 0.9167 cents 80:89:100:108:120:133:144:160 SD: 0.6919 cents 100:111:125:135:150:167:180:200 SD: 0.5526 cents 144:160:180:194:216:240:259:288 SD: 0.5440 cents 160:178:200:216:240:267:288:320 SD: 0.4369 cents 180:200:225:243:270:300:324:360 SD: 0.0000 cents