Scala analysis: 391_D6
Diatonic tetrachord 19/18 * 21/19 * 8/7, Safiyu-d-Din
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 19/18 93.603014 undevicesimal semitone 2: 7/6 266.870906 septimal minor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 19/18 93.6030 undevicesimal semitone 2: 21/19 173.2679 3: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 19/18 93.603 cents undevicesimal semitone 1: 1 21/19 173.268 cents 1: 1 8/7 231.174 cents septimal whole tone 2: 1 7/6 266.871 cents septimal minor third 2: 1 76/63 324.777 cents 2: 1 24/19 404.442 cents smaller undevicesimal major third Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 93.6 266.9 498.0 93.6 : 173.3 404.4 498.0 266.9: 231.2 324.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 93.6030 .. 231.1741 cents 144/133, 137.5711 cents 19/18, 93.6030 cents 2: 266.8709 .. 404.4420 cents 144/133, 137.5711 cents 49/48, 35.6968 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 19/18, 93.6030 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 1.773607 Largest / Average step : 1.392489 Largest / Smallest step : 2.469729 Median interval of one step : 21/19, 173.2679 cents, amount: 1 Least squares average step : 151.53427 cents, oct.: 454.60282 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1144-tone equal temperament with octave 4/3 degrees: 215 613 1144 Least number of segments generator : 573 of 249.458 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 651 of 283.415 cents and inv. generated superset size: 35 = 32 more = 1166.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SML Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 35.69681 cents Scale diversity : 1.170837 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.447556 Rothenberg efficiency : 0.666667 redundancy: 0.333333 Efficiency x scale size : 2.000000 Number of different interval sizes : 6 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 49/48, 35.6968 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best minor thirds form a closed circle Steps are strictly increasing Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 19 Odd number limit : 63 (O: 21 U: 63) Highest odd numerator or denominator: 19 Scale harmonicity : 0.018967 Average absolute harmonicity : 0.103562 Specific harmonicity : 0.100519 Fundamental : 1/18, -4.1699 octaves, 14.5348 Hz. Guide tone : 532, 9.0553 octaves, 139184.801 Hz. Exponens Consonantiae : 9.576000E+03, 13.22521 octaves Euler's gradus suavitatis : 32 Sum of Mann's harmonic distance : 28.5, average 9.50000 Mersenne's string divisions : 3367 Sum of van Prooijen's expressibility: 2.60097, average 0.86699 Sum of Tenney's harmonic distance : 5.23646, average 1.74549 Vogel's harmonic complexity : 11.66667 Wille's k value : 10 Wilson's harmonic complexity : 32 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 14.62856, average 2.43809 Lattice compactness (without 2's) : 8.79655, average 1.46609 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.00000 4 3: -2 ..-1 -1.33333 4 1 7: 0 .. 1 0.33333 1 1 19: 0 .. 1 0.33333 1 1 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <6 10 19 30| Scale is weakly epimorphic with val: <6 10 19 33| Scale is weakly epimorphic with val: <6 10 20 29| Scale is weakly epimorphic with val: <6 11 19 31| Scale is weakly epimorphic with val: <6 11 20 30| Scale is weakly epimorphic with val: <6 11 20 33| Scale is weakly epimorphic with val: <6 11 22 31| Scale is weakly epimorphic with val: <7 10 19 30| Scale is weakly epimorphic with val: <7 10 20 29| Scale is weakly epimorphic with val: <7 10 20 32| Scale is weakly epimorphic with val: <7 10 22 30| Scale is weakly epimorphic with val: <7 11 19 28| Scale is weakly epimorphic with val: <7 11 19 31| Scale is weakly epimorphic with val: <7 11 19 34| Scale is JI-epimorphic with val: <7 11 20 30| Scale is weakly epimorphic with val: <7 11 20 33| Scale is weakly epimorphic with val: <7 11 22 28| Scale is weakly epimorphic with val: <7 11 22 31| Scale is weakly epimorphic with val: <7 11 22 34| Scale is weakly epimorphic with val: <7 12 20 34| Scale is weakly epimorphic with val: <7 12 22 29| Scale is weakly epimorphic with val: <7 12 22 32| Scale is weakly epimorphic with val: <8 11 20 33| Scale is weakly epimorphic with val: <8 11 22 28| Scale is weakly epimorphic with val: <8 11 22 31| Scale is weakly epimorphic with val: <8 11 22 34|
FIT/MODE
3: 0 1 2 N G T3 SD: 79.4427 c. M: 100.8559 c. 4: 1 1 2 P M ME S SD: 20.6065 c. M:-30.9082 c. 5: 1 2 2 SP M ME S SD: 18.7729 c. M:-31.9561 c. 6: 1 2 3 P T3 SD: 11.9837 c. M: 17.8484 c. 9: 2 3 4 SP T3 SD: 11.3719 c. M:-17.0737 c. 10: 2 3 5 P T3 SD: 10.8726 c. M: 17.8484 c. 11: 2 4 5 SP T3 SD: 3.2784 c. M:-4.7900 c. 15: 3 5 7 SP T3 SD: 3.5415 c. M:-6.0060 c. 17: 3 6 8 SP T3 SD: 3.7804 c. M: 5.7127 c. 21: 4 7 10 SP T3 SD: 3.5344 c. M: 5.9902 c. 26: 5 9 12 SP T3 SD: 1.4650 c. M:-2.1749 c. 32: 6 11 15 SP T3 SD: 1.3250 c. M: 2.2845 c. 43: 8 15 20 SP T3 SD: 0.6098 c. M: 0.9435 c. 58: 11 20 27 SP T3 SD: 0.6282 c. M:-0.8538 c. 69: 13 24 32 SP T3 SD: 0.1754 c. M:-0.2316 c. 112: 21 39 52 SP T3 SD: 0.1316 c. M: 0.2196 c. 181: 34 63 84 SP T3 SD: 0.0349 c. M: 0.0476 c. 431: 81 150 200 SP T3 SD: 0.0363 c. M:-0.0627 c. 532: 100 185 247 SP T3 SD: 0.0362 c. M: 0.0611 c. 601: 113 209 279 SP T3 SD: 0.0291 c. M:-0.0394 c. 713: 134 248 331 SP T3 SD: 0.0209 c. M: 0.0361 c. 782: 147 272 363 SP T3 SD: 0.0143 c. M:-0.0193 c. 894: 168 311 415 SP T3 SD: 0.0137 c. M: 0.0213 c. 963: 181 335 447 SP T3 SD: 0.0051 c. M:-0.0067 c. 1144: 215 398 531 SP T3 SD: 0.0013 c. M: 0.0019 c.
FIT/HARMONIC
1 x x 2 S SD: 701.9550 cents 2 x x 3 S SD: 203.9100 cents 3 x x 4 S SD: 0.0000 cents 4 x x 5 S SD: 111.7313 cents 5 x 6:7 S SD: 48.7680 cents 6 x 7:8 S SD: 0.0000 cents 7 x 8:9 S SD: 36.1882 cents 8 x 9:11 SD: 41.2374 cents 9 x 11:12 SD: 40.2685 cents 10:11:12:13 H SD: 32.3142 cents 11:12:13:15 SD: 24.1881 cents 12:13:14:16 S SD: 14.9899 cents 16:17:19:21 SD: 14.1859 cents 17:18:20:23 SD: 9.8731 cents 18:19:21:24 SD: 0.0000 cents