Scala analysis: 409_D7
Diatonic tetrachord 225/203 * 203/192 * 256/225
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 225/203 178.134329 2: 75/64 274.582429 classic augmented second 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 256/225 223.4626 Neapolitan diminished third 1: 225/203 178.1343 2: 203/192 96.4481 3: 256/225 223.4626 Neapolitan diminished third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 203/192 96.448 cents 1: 1 225/203 178.134 cents 1: 1 256/225 223.463 cents Neapolitan diminished third 2: 1 75/64 274.582 cents classic augmented second 2: 1 812/675 319.911 cents 2: 1 256/203 401.597 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 : 178.1 274.6 498.0 178.1: 96.4 319.9 498.0 274.6: 223.5 401.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 96.4481 .. 223.4626 cents 16384/15225, 127.0145 cents 203/192, 96.4481 cents 2: 274.5824 .. 401.5969 cents 16384/15225, 127.0145 cents 16875/16384, 51.1199 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 203/192, 96.4481 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 256/225, 223.4626 cents Average / Smallest step : 1.721288 Largest / Average step : 1.346038 Largest / Smallest step : 2.316920 Median interval of one step : 225/203, 178.1343 cents, amount: 1 Least squares average step : 158.67387 cents, oct.: 476.02161 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 945-tone equal temperament with octave 4/3 degrees: 338 521 945 Least number of segments generator : 473 of 249.286 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 536 of 282.489 cents and inv. generated superset size: 30 = 27 more = 1000.000% 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 51.11986 cents Scale diversity : 1.186673 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.489948 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 : 51968/50625, 45.3282 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best fifths form a closed circle Best minor thirds form a closed circle Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 29 Odd number limit : 675 (O: 225 U: 675) Highest odd numerator or denominator: 225 Scale harmonicity : 0.010735 Average absolute harmonicity : 0.090997 Specific harmonicity : 0.054250 Fundamental : 1/38976, -15.2503 octaves, 0.0067 Hz. Guide tone : 900, 9.8138 octaves, 235463.009 Hz. Exponens Consonantiae : 3.507840E+07, 25.06408 octaves Euler's gradus suavitatis : 57 Sum of Mann's harmonic distance : 287.0, average 95.66667 Mersenne's string divisions : 416444 Sum of van Prooijen's expressibility: 4.70437, average 1.56812 Sum of Tenney's harmonic distance : 9.42010, average 3.14003 Vogel's harmonic complexity : 40.33333 Wille's k value : 22837 Wilson's harmonic complexity : 55 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 30.89065, average 5.14844 Lattice compactness (without 2's) : 14.83181, average 2.47197 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -6 .. 2 -1.33333 8 3: -1 .. 2 0.66667 4 1 5: 0 .. 2 1.33333 4 1 7: -1 .. 0 -0.33333 1 29: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 4 / 3 = 1.33333 Average absolute exponent except 2's: 10 / 3 = 3.33333 Scale is weakly epimorphic with val: <6 10 18 18 35| Scale is weakly epimorphic with val: <6 10 18 19 34| Scale is weakly epimorphic with val: <6 10 18 20 33| Scale is weakly epimorphic with val: <6 10 18 21 32| Scale is weakly epimorphic with val: <6 11 18 18 37| Scale is weakly epimorphic with val: <6 11 18 19 36| Scale is weakly epimorphic with val: <6 11 18 20 35| Scale is weakly epimorphic with val: <6 11 18 21 34| Scale is weakly epimorphic with val: <6 11 18 22 33| Scale is weakly epimorphic with val: <7 10 17 18 33| Scale is weakly epimorphic with val: <7 10 17 19 32| Scale is weakly epimorphic with val: <7 11 15 18 33| Scale is weakly epimorphic with val: <7 11 15 18 36| Scale is weakly epimorphic with val: <7 11 15 19 32| Scale is weakly epimorphic with val: <7 11 15 19 35| Scale is weakly epimorphic with val: <7 11 15 19 38| Scale is weakly epimorphic with val: <7 11 15 20 34| Scale is weakly epimorphic with val: <7 11 15 20 37| Scale is weakly epimorphic with val: <7 11 15 21 33| Scale is weakly epimorphic with val: <7 11 15 21 36| Scale is weakly epimorphic with val: <7 11 15 22 32| Scale is weakly epimorphic with val: <7 11 15 22 35| Scale is weakly epimorphic with val: <7 11 15 22 38| Scale is weakly epimorphic with val: <7 11 16 18 34| Scale is weakly epimorphic with val: <7 11 16 18 37| Scale is weakly epimorphic with val: <7 11 16 19 33| Scale is weakly epimorphic with val: <7 11 16 19 36| Scale is weakly epimorphic with val: <7 11 16 20 32| Scale is weakly epimorphic with val: <7 11 16 20 35| Scale is weakly epimorphic with val: <7 11 16 20 38| Scale is weakly epimorphic with val: <7 11 16 21 34| Scale is weakly epimorphic with val: <7 11 16 21 37| Scale is weakly epimorphic with val: <7 11 16 22 33| Scale is weakly epimorphic with val: <7 11 16 22 36| Scale is weakly epimorphic with val: <7 11 18 18 33| Scale is weakly epimorphic with val: <7 11 18 18 36| Scale is weakly epimorphic with val: <7 11 18 19 32| Scale is weakly epimorphic with val: <7 11 18 19 35| Scale is weakly epimorphic with val: <7 11 18 19 38| Scale is weakly epimorphic with val: <7 11 18 20 34| Scale is weakly epimorphic with val: <7 11 18 20 37| Scale is weakly epimorphic with val: <7 11 18 21 33| Scale is weakly epimorphic with val: <7 11 18 21 36| Scale is weakly epimorphic with val: <7 11 18 22 32| Scale is weakly epimorphic with val: <7 11 18 22 35| Scale is weakly epimorphic with val: <7 11 18 22 38| Scale is weakly epimorphic with val: <7 11 19 19 33| Scale is weakly epimorphic with val: <7 11 19 19 36| Scale is weakly epimorphic with val: <7 11 19 20 32| Scale is weakly epimorphic with val: <7 11 19 20 35| Scale is weakly epimorphic with val: <7 11 19 20 38| Scale is weakly epimorphic with val: <7 11 19 21 34| Scale is weakly epimorphic with val: <7 11 19 21 37| Scale is weakly epimorphic with val: <7 11 19 22 33| Scale is weakly epimorphic with val: <7 11 19 22 36| Scale is weakly epimorphic with val: <7 12 17 18 37| Scale is weakly epimorphic with val: <7 12 17 19 36| Scale is weakly epimorphic with val: <7 12 17 20 35| Scale is weakly epimorphic with val: <7 12 17 21 34| Scale is weakly epimorphic with val: <7 12 17 22 33| Scale is weakly epimorphic with val: <8 11 16 18 33| Scale is weakly epimorphic with val: <8 11 16 19 32| Scale is weakly epimorphic with val: <8 11 19 19 38| Scale is weakly epimorphic with val: <8 11 19 20 37| Scale is weakly epimorphic with val: <8 11 19 21 36| Scale is weakly epimorphic with val: <8 11 19 22 35| Scale is weakly epimorphic with val: <8 12 16 18 35| Scale is weakly epimorphic with val: <8 12 16 19 34| Scale is weakly epimorphic with val: <8 12 16 20 33| Scale is weakly epimorphic with val: <8 12 16 21 32| Scale is weakly epimorphic with val: <8 12 19 21 38| Scale is weakly epimorphic with val: <8 12 19 22 37|
FIT/MODE
3: 1 1 1 SP B ME I SD: 33.8974 c. M:-57.4476 c. 4: 1 1 2 P M ME S SD: 34.2965 c. M: 53.6231 c. 5: 2 1 2 SP M ME I SD: 18.5501 c. M:-24.2446 c. 6: 2 1 3 P T3 SD: 16.3319 c. M: 25.5599 c. 8: 3 1 4 P T3 SD: 15.5760 c. M: 25.5599 c. 9: 3 2 4 SP T3 SD: 7.1023 c. M: 12.1193 c. 11: 4 2 5 SP T3 SD: 2.4065 c. M:-2.9729 c. 20: 7 4 9 SP T3 SD: 2.2371 c. M: 3.8186 c. 31: 11 6 14 SP T3 SD: 1.1717 c. M: 1.4610 c. 42: 15 8 19 SP T3 SD: 1.0750 c. M: 1.8435 c. 56: 20 11 25 SP T3 SD: 0.6646 c. M:-1.1211 c. 67: 24 13 30 SP T3 SD: 0.3066 c. M:-0.4573 c. 98: 35 19 44 SP T3 SD: 0.1737 c. M: 0.2611 c. 165: 59 32 74 SP T3 SD: 0.0618 c. M:-0.0969 c. 274: 98 53 123 SP T3 SD: 0.0649 c. M: 0.1124 c. 341: 122 66 153 SP T3 SD: 0.0299 c. M:-0.0519 c. 439: 157 85 197 SP T3 SD: 0.0221 c. M: 0.0337 c. 506: 181 98 227 SP T3 SD: 0.0215 c. M:-0.0313 c. 604: 216 117 271 SP T3 SD: 0.0148 c. M: 0.0255 c. 780: 279 151 350 SP T3 SD: 0.0132 c. M: 0.0192 c. 945: 338 183 424 SP T3 SD: 0.0015 c. M:-0.0024 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: 46.9589 cents 6 x 7:8 S SD: 3.8558 cents 7 x 8:9 S SD: 38.2373 cents 8:9 x 11 SD: 29.5905 cents 9:10:11:12 H SD: 24.3169 cents 10:11:12:13 H SD: 20.4922 cents 11:12:13:15 SD: 16.6123 cents 12:13:14:16 S SD: 13.4354 cents 14 x 16:19 SD: 26.5670 cents 15:17:18:20 SD: 18.7738 cents 16:18:19:21 SD: 14.6573 cents 17:19:20:23 SD: 9.9594 cents 18:20:21:24 S SD: 2.9382 cents 57:63:67:76 SD: 2.3878 cents 63:70:74:84 SD: 1.9560 cents 75:83:88:100 SD: 1.1432 cents 93:103:109:124 SD: 0.4491 cents 111:123:130:148 SD: 0.3734 cents 204:226:239:272 SD: 0.3151 cents 267:296:313:356 SD: 0.2372 cents 285:316:334:380 SD: 0.2087 cents 360:399:422:480 SD: 0.1723 cents 378:419:443:504 SD: 0.0626 cents 489:542:573:652 SD: 0.0475 cents