Scala analysis: 433_D11
Diatonic tetrachord 12/11 * 55/51 * 17/15
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 12/11 150.637059 undecimal neutral second, 3/4-tone 2: 20/17 281.358304 septendecimal augmented second 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 17/15 216.6867 septendecimal whole tone 1: 12/11 150.6371 undecimal neutral second, 3/4-tone 2: 55/51 130.7212 3: 17/15 216.6867 septendecimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 55/51 130.721 cents 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 17/15 216.687 cents septendecimal whole tone 2: 1 20/17 281.358 cents septendecimal augmented second 2: 1 11/9 347.408 cents undecimal neutral third 2: 1 68/55 367.324 cents 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 : 150.6 281.4 498.0 150.6: 130.7 347.4 498.0 281.4: 216.7 367.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 130.7212 .. 216.6867 cents 289/275, 85.9654 cents 55/51, 130.7212 cents 2: 281.3583 .. 367.3238 cents 289/275, 85.9654 cents 300/289, 64.6716 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 55/51, 130.7212 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 17/15, 216.6867 cents Average / Smallest step : 1.269992 Largest / Average step : 1.305224 Largest / Smallest step : 1.657624 Median interval of one step : 12/11, 150.6371 cents, amount: 1 Least squares average step : 157.67776 cents, oct.: 473.03329 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1825-tone equal temperament with octave 4/3 degrees: 552 1031 1825 Least number of segments generator : 913 of 249.159 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1399 of 381.789 cents and inv. generated superset size: 47 = 44 more = 1566.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 64.67161 cents Scale diversity : 1.345202 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.654788 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 : 612/605, 19.9158 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle 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% Limited inverse transpositions with margin 85.9654 cents: 2 -- Rational properties -- Prime limit : 17 Odd number limit : 55 (O: 55 U: 55) Highest odd numerator or denominator: 17 Scale harmonicity : 0.016121 Average absolute harmonicity : 0.094671 Specific harmonicity : 0.085976 Fundamental : 1/561, -9.1319 octaves, 0.4664 Hz. Guide tone : 60, 5.9069 octaves, 15697.534 Hz. Exponens Consonantiae : 3.366000E+04, 15.03875 octaves Euler's gradus suavitatis : 37 Sum of Mann's harmonic distance : 33.5, average 11.16667 Mersenne's string divisions : 5957 Sum of van Prooijen's expressibility: 2.74896, average 0.91632 Sum of Tenney's harmonic distance : 5.73123, average 1.91041 Vogel's harmonic complexity : 25.33333 Wille's k value : 93 Wilson's harmonic complexity : 39 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 13.10317, average 2.18386 Lattice compactness (without 2's) : 9.79655, average 1.63276 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 2 2.00000 6 3: -1 .. 1 0.00000 2 1 5: 0 .. 1 0.33333 1 11: -1 .. 0 -0.33333 1 1 17: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is weakly epimorphic with val: <6 10 18 24 27| Scale is weakly epimorphic with val: <6 10 18 27 27| Scale is weakly epimorphic with val: <6 10 19 24 28| Scale is weakly epimorphic with val: <6 10 19 27 28| Scale is weakly epimorphic with val: <6 11 18 24 27| Scale is weakly epimorphic with val: <6 11 18 27 27| Scale is weakly epimorphic with val: <6 11 19 24 28| Scale is weakly epimorphic with val: <6 11 19 27 28| Scale is weakly epimorphic with val: <7 10 16 25 27| Scale is weakly epimorphic with val: <7 10 17 25 28| Scale is weakly epimorphic with val: <7 10 18 25 29| Scale is weakly epimorphic with val: <7 10 19 25 30| Scale is weakly epimorphic with val: <7 11 15 23 28| Scale is weakly epimorphic with val: <7 11 15 23 31| Scale is JI-epimorphic with val: <7 11 15 24 27| Scale is weakly epimorphic with val: <7 11 15 24 30| Scale is weakly epimorphic with val: <7 11 15 24 33| Scale is weakly epimorphic with val: <7 11 15 26 28| Scale is weakly epimorphic with val: <7 11 15 26 31| Scale is weakly epimorphic with val: <7 11 15 27 27| Scale is weakly epimorphic with val: <7 11 15 27 30| Scale is weakly epimorphic with val: <7 11 15 27 33| Scale is weakly epimorphic with val: <7 11 16 23 29| Scale is weakly epimorphic with val: <7 11 16 23 32| Scale is JI-epimorphic with val: <7 11 16 24 28| Scale is weakly epimorphic with val: <7 11 16 24 31| Scale is weakly epimorphic with val: <7 11 16 26 29| Scale is weakly epimorphic with val: <7 11 16 26 32| Scale is weakly epimorphic with val: <7 11 16 27 28| Scale is weakly epimorphic with val: <7 11 16 27 31| Scale is weakly epimorphic with val: <7 11 17 23 27| Scale is weakly epimorphic with val: <7 11 17 23 30| Scale is weakly epimorphic with val: <7 11 17 23 33| Scale is JI-epimorphic with val: <7 11 17 24 29| Scale is weakly epimorphic with val: <7 11 17 24 32| Scale is weakly epimorphic with val: <7 11 17 26 27| Scale is weakly epimorphic with val: <7 11 17 26 30| Scale is weakly epimorphic with val: <7 11 17 26 33| Scale is weakly epimorphic with val: <7 11 17 27 29| Scale is weakly epimorphic with val: <7 11 17 27 32| Scale is weakly epimorphic with val: <7 11 18 23 28| Scale is weakly epimorphic with val: <7 11 18 23 31| Scale is weakly epimorphic with val: <7 11 18 24 27| Scale is JI-epimorphic with val: <7 11 18 24 30| Scale is weakly epimorphic with val: <7 11 18 24 33| Scale is weakly epimorphic with val: <7 11 18 26 28| Scale is weakly epimorphic with val: <7 11 18 26 31| Scale is weakly epimorphic with val: <7 11 18 27 27| Scale is weakly epimorphic with val: <7 11 18 27 30| Scale is weakly epimorphic with val: <7 11 18 27 33| Scale is weakly epimorphic with val: <7 11 19 23 29| Scale is weakly epimorphic with val: <7 11 19 23 32| Scale is weakly epimorphic with val: <7 11 19 24 28| Scale is JI-epimorphic with val: <7 11 19 24 31| Scale is weakly epimorphic with val: <7 11 19 26 29| Scale is weakly epimorphic with val: <7 11 19 26 32| Scale is weakly epimorphic with val: <7 11 19 27 28| Scale is weakly epimorphic with val: <7 11 19 27 31| Scale is weakly epimorphic with val: <7 12 15 23 28| Scale is weakly epimorphic with val: <7 12 15 23 31| Scale is weakly epimorphic with val: <7 12 16 23 29| Scale is weakly epimorphic with val: <7 12 16 23 32| Scale is weakly epimorphic with val: <7 12 16 25 27| Scale is weakly epimorphic with val: <7 12 17 23 27| Scale is weakly epimorphic with val: <7 12 17 23 30| Scale is weakly epimorphic with val: <7 12 17 23 33| Scale is weakly epimorphic with val: <7 12 17 25 28| Scale is weakly epimorphic with val: <7 12 18 23 28| Scale is weakly epimorphic with val: <7 12 18 23 31| Scale is weakly epimorphic with val: <7 12 18 25 29| Scale is weakly epimorphic with val: <7 12 19 23 29| Scale is weakly epimorphic with val: <7 12 19 23 32| Scale is weakly epimorphic with val: <7 12 19 25 30| Scale is weakly epimorphic with val: <8 11 15 23 28| Scale is weakly epimorphic with val: <8 11 15 24 27| Scale is weakly epimorphic with val: <8 11 15 24 30| Scale is weakly epimorphic with val: <8 11 15 24 33| Scale is weakly epimorphic with val: <8 11 15 26 28| Scale is weakly epimorphic with val: <8 11 16 23 29| Scale is weakly epimorphic with val: <8 11 16 24 28| Scale is weakly epimorphic with val: <8 11 16 24 31| Scale is weakly epimorphic with val: <8 11 16 26 29| Scale is weakly epimorphic with val: <8 11 17 23 30| Scale is weakly epimorphic with val: <8 11 17 24 29| Scale is weakly epimorphic with val: <8 11 17 24 32| Scale is weakly epimorphic with val: <8 11 17 26 30| Scale is weakly epimorphic with val: <8 11 18 23 31| Scale is weakly epimorphic with val: <8 11 18 24 27| Scale is weakly epimorphic with val: <8 11 18 24 30| Scale is weakly epimorphic with val: <8 11 18 24 33| Scale is weakly epimorphic with val: <8 11 18 26 31| Scale is weakly epimorphic with val: <8 11 19 23 32| Scale is weakly epimorphic with val: <8 11 19 24 28| Scale is weakly epimorphic with val: <8 11 19 24 31| Scale is weakly epimorphic with val: <8 11 19 26 32| Scale is weakly epimorphic with val: <8 12 15 23 28| Scale is weakly epimorphic with val: <8 12 15 25 29| Scale is weakly epimorphic with val: <8 12 15 25 32| Scale is weakly epimorphic with val: <8 12 15 26 28| Scale is weakly epimorphic with val: <8 12 16 23 29| Scale is weakly epimorphic with val: <8 12 16 25 27| Scale is weakly epimorphic with val: <8 12 16 25 30| Scale is weakly epimorphic with val: <8 12 16 25 33| Scale is weakly epimorphic with val: <8 12 16 26 29| Scale is weakly epimorphic with val: <8 12 17 23 30| Scale is weakly epimorphic with val: <8 12 17 25 28| Scale is weakly epimorphic with val: <8 12 17 25 31| Scale is weakly epimorphic with val: <8 12 17 26 30| Scale is weakly epimorphic with val: <8 12 18 23 31| Scale is weakly epimorphic with val: <8 12 18 25 29| Scale is weakly epimorphic with val: <8 12 18 25 32| Scale is weakly epimorphic with val: <8 12 18 26 31| Scale is weakly epimorphic with val: <8 12 19 23 32| Scale is weakly epimorphic with val: <8 12 19 25 27| Scale is weakly epimorphic with val: <8 12 19 25 30| Scale is weakly epimorphic with val: <8 12 19 25 33| Scale is weakly epimorphic with val: <8 12 19 26 32|
FIT/MODE
3: 1 1 1 SP B ME I SD: 30.5729 c. M:-50.6717 c. 4: 1 1 2 P M ME S SD: 24.0011 c. M: 32.3358 c. 6: 2 1 3 P T3 SD: 20.6727 c. M: 32.3358 c. 7: 2 2 3 SP M ME S SD: 5.1646 c. M: 8.3385 c. 16: 5 4 7 SP T3 SD: 2.9709 c. M:-5.0020 c. 23: 7 6 10 SP T3 SD: 0.5502 c. M:-0.9419 c. 53: 16 14 23 SP T3 SD: 0.3594 c. M:-0.5540 c. 76: 23 20 33 SP T3 SD: 0.2535 c. M:-0.4303 c. 99: 30 26 43 SP T3 SD: 0.2672 c. M:-0.3641 c. 175: 53 46 76 SP T3 SD: 0.2544 c. M:-0.3929 c. 195: 59 51 85 SP T3 SD: 0.2386 c. M: 0.4098 c. 202: 61 53 88 SP T3 SD: 0.2134 c. M: 0.2834 c. 225: 68 59 98 SP T3 SD: 0.1539 c. M: 0.2396 c. 248: 75 65 108 SP T3 SD: 0.1182 c. M: 0.2039 c. 271: 82 71 118 SP T3 SD: 0.1069 c. M: 0.1742 c. 278: 84 73 121 SP T3 SD: 0.0998 c. M: 0.1486 c. 301: 91 79 131 SP T3 SD: 0.0555 c. M: 0.0704 c. 324: 98 85 141 SP T3 SD: 0.0320 c. M: 0.0551 c. 377: 114 99 164 SP T3 SD: 0.0266 c. M: 0.0346 c. 400: 121 105 174 SP T3 SD: 0.0248 c. M:-0.0371 c. 701: 212 184 305 SP T3 SD: 0.0105 c. M: 0.0157 c. 724: 219 190 315 SP T3 SD: 0.0088 c. M:-0.0147 c. 1101: 333 289 479 SP T3 SD: 0.0046 c. M:-0.0077 c. 1425: 431 374 620 SP T3 SD: 0.0038 c. M: 0.0066 c. 1825: 552 479 794 SP T3 SD: 0.0031 c. M:-0.0045 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 5 x S SD: 104.9554 cents 5 x 6:7 S SD: 45.5797 cents 6 x 7:8 S SD: 7.2437 cents 7 x 8:9 S SD: 40.2571 cents 8:9 x 11 SD: 37.6697 cents 9:10:11:12 H SD: 24.4306 cents 10:11:12:13 H SD: 19.1570 cents 11:12:13:15 SD: 13.2300 cents 12:13:14:16 S SD: 6.2843 cents 33:36:39:44 SD: 2.6171 cents 45:49:53:60 SD: 1.2469 cents 108:118:127:144 SD: 0.9291 cents 120:131:141:160 SD: 0.8255 cents 141:154:166:188 SD: 0.7951 cents 153:167:180:204 SD: 0.3142 cents 198:216:233:264 SD: 0.1457 cents 363:396:427:484 SD: 0.0795 cents 561:612:660:748 SD: 0.0000 cents