Scala analysis: synpor7
Seventh 81/80&250/243 scale = inverse synpor6
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 27/25 133.237575 large limma, BP small semitone, Zarlino semitone 2: 6/5 315.641287 minor third 3: 4/3 498.044999 perfect fourth 4: 40/27 680.448711 grave fifth 5: 8/5 813.686286 minor 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: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 2: 10/9 182.4037 minor whole tone 3: 10/9 182.4037 minor whole tone 4: 10/9 182.4037 minor whole tone 5: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 6: 10/9 182.4037 minor whole tone 7: 9/8 203.9100 major 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: 3 4/3 498.045 cents perfect fourth 3: 3 27/20 519.551 cents acute fourth 3: 1 1000/729 547.211 cents 4: 1 729/500 652.789 cents 4: 3 40/27 680.449 cents grave fifth 4: 3 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 : 133.2 315.6 498.0 680.4 813.7 996.1 1200.0 133.2 : 182.4 364.8 547.2 680.4 862.9 1066.8 1200.0 315.6 : 182.4 364.8 498.0 680.4 884.4 1017.6 1200.0 498.0 : 182.4 315.6 498.0 702.0 835.2 1017.6 1200.0 680.4 : 133.2 315.6 519.6 652.8 835.2 1017.6 1200.0 813.7 : 182.4 386.3 519.6 702.0 884.4 1066.8 1200.0 996.1 : 203.9 337.1 519.6 702.0 884.4 1017.6 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 .. 547.2111 cents 250/243, 49.1661 cents 16/15, 111.7313 cents 4: 652.7889 .. 701.9550 cents 250/243, 49.1661 cents 531441/500000, 105.5777 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 : 167.32444 cents, oct.: 1171.27107 cents Scale is strictly proper Step pattern alph. order: ABBBABC Step pattern size order : SMMMSML Scale is a Constant Structure, by a margin of 105.57773 cents Scale diversity : 1.330270 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.682482 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 : 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 intervals : 10/9, 182.4037 cents & inv., amount: 4 Most common triad is 0.0 182.404 1017.596 cents, amount: 2 Number of recognisable fifths : 3, average 701.9550 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Length of longest subharmonic part : 2 at degree 5 Formal octave complements present : 1 = 14.2857% Scale is differentially coherent in interval classes 1 and 2 combined Limited transpositions with margin 70.6724 cents: 4 Limited inverse transpositions with margin 70.6724 cents: 1 5 -- Rational properties -- Prime limit : 5 Odd number limit : 729 (O: 729 U: 729) Highest odd numerator or denominator: 27 Scale harmonicity : 0.025510 Average absolute harmonicity : 0.233242 Specific harmonicity : 0.161779 Fundamental : 1/675, -9.3987 octaves, 0.3876 Hz. Guide tone : 2160, 11.0768 octaves, 565111.221 Hz. Exponens Consonantiae : 1.458000E+06, 20.47556 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 89.0, average 12.71429 Mersenne's string divisions : 20120100 Sum of van Prooijen's expressibility: 5.69203, average 0.81315 Sum of Tenney's harmonic distance : 12.48048, average 1.78293 Vogel's harmonic complexity : 18.00000 Wille's k value : 364 Wilson's harmonic complexity : 33 Rectangular lattice diameter : 9 Triangular lattice diameter : 6 Lattice compactness : 90.63252, average 3.23688 Lattice compactness (without 2's) : 69.10453, average 2.46802 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 0 .. 4 2.00000 14 1 3: -3 .. 3 -0.28571 10 2 5: -2 .. 1 -0.42857 5 4 Average exponent except 2's :-5 / 7 =-0.71429 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: 27.8626 c. M:-43.4566 c. Lebeng 12: 1 2 2 2 1 2 2 P M ME S SD: 16.6393 c. M: 33.2376 c. G.Dorian, M.Phrygian, G.M.Hypoaeolian, Bhairavi That, Mela Hanumatodi, Raga Asavari (Asaveri), Bilashkhani Todi, Ghanta, Makam Kurd, Gregorian nr.3, In, Zokuso: Japan, Ousak: Greece, Major inverse 16: 2 2 3 2 2 2 3 SP M ME S SD: 16.2774 c. M:-26.9550 c. Pseudo Pelog, Pelogic-7, Antiionian 18: 2 3 2 3 2 3 3 SP M ME S SD: 15.5387 c. M: 31.3783 c. 19: 2 3 3 3 2 3 3 SP M ME S SD: 8.9989 c. M:-14.4363 c. Nineteen-tone Phrygian 34: 4 5 5 5 4 5 6 SP D3 SD: 5.9172 c. M: 9.8605 c. 46: 5 7 7 7 5 7 8 SP SD: 3.2277 c. M: 4.9906 c. 53: 6 8 8 8 6 8 9 SP SD: 1.3131 c. M:-2.6115 c. 99: 11 15 15 15 11 15 17 SP SD: 1.2671 c. M: 2.1506 c. 118: 13 18 18 18 13 18 20 SP SD: 0.5851 c. M: 1.0342 c. 171: 19 26 26 26 19 26 29 SP SD: 0.2444 c. M:-0.4012 c. 388: 43 59 59 59 43 59 66 SP SD: 0.1821 c. M: 0.2842 c. 441: 49 67 67 67 49 67 75 SP SD: 0.1094 c. M: 0.1766 c. 559: 62 85 85 85 62 85 95 SP SD: 0.0739 c. M: 0.1428 c. 612: 68 93 93 93 68 93 104 SP SD: 0.0480 c. M:-0.0958 c. 1000: 111 152 152 152 111 152 170 SP SD: 0.0574 c. M: 0.0900 c. 1171: 130 178 178 178 130 178 199 SP SD: 0.0145 c. M: 0.0228 c. 1783: 198 271 271 271 198 271 303 SP SD: 0.0137 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: 10.7531 cents 3 x x 4 x 5 x 6 S SD: 23.5575 cents 4 x 5 x 6 x 7:8 S SD: 19.6857 cents 5 x 6:7 x 8:9:10 S SD: 17.4324 cents 6 x 7:8:9:10:11:12 S SD: 17.2189 cents 7 x 8:9:10:11:12:14 S SD: 23.5702 cents 8:9:10:11:12:13:14:16 S SD: 17.3520 cents 9:10:11:12:13:14:16:18 S SD: 12.5569 cents 10:11:12:13:15:16:18:20 SD: 8.8702 cents 14:15:17:19:21:22:25:28 SD: 7.8819 cents 15:16:18:20:22:24:27:30 S SD: 5.0057 cents 23:25:28:31:34:37:41:46 SD: 4.9871 cents 24:26:29:32:36:38:43:48 SD: 4.8333 cents 25:27:30:33:37:40:44:50 SD: 3.5239 cents 35:38:42:47:52:56:62:70 SD: 2.4663 cents 40:43:48:53:59:64:71:80 SD: 2.2465 cents 48:52:58:64:71:77:85:96 SD: 2.2384 cents 50:54:60:67:74:80:89:100 SD: 1.2955 cents 60:65:72:80:89:96:107:120 SD: 1.1277 cents 75:81:90:100:111:120:133:150 SD: 0.6667 cents 125:135:150:167:185:200:222:250 SD: 0.6055 cents 135:146:162:180:200:216:240:270 SD: 0.3390 cents 210:227:252:280:311:336:373:420 SD: 0.3227 cents 225:243:270:300:333:360:400:450 SD: 0.2474 cents 315:340:378:420:467:504:560:630 SD: 0.2288 cents 351:379:421:468:520:562:624:702 SD: 0.2180 cents 360:389:432:480:533:576:640:720 SD: 0.2002 cents 390:421:468:520:578:624:693:780 SD: 0.1923 cents 450:486:540:600:667:720:800:900 SD: 0.1236 cents 525:567:630:700:778:840:933:1050 SD: 0.1131 cents 540:583:648:720:800:864:960:1080 SD: 0.0848 cents 600:648:720:800:889:960:1067:1200 SD: 0.0832 cents