Scala analysis: 461_D15
Diatonic tetrachord 9/8 * 15/14 * 448/405
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 135/112 323.352810 septimal wide minor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 448/405 174.6922 1: 9/8 203.9100 major whole tone 2: 15/14 119.4428 major diatonic semitone 3: 448/405 174.6922
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 15/14 119.443 cents major diatonic semitone 1: 1 448/405 174.692 cents 1: 1 9/8 203.910 cents major whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 135/112 323.353 cents septimal wide minor third 2: 1 56/45 378.602 cents septimal narrow 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 : 203.9 323.4 498.0 203.9: 119.4 294.1 498.0 323.4: 174.7 378.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 119.4428 .. 203.9100 cents 21/20, 84.4672 cents 15/14, 119.4428 cents 2: 294.1350 .. 378.6022 cents 21/20, 84.4672 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 15/14, 119.4428 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.389912 Largest / Average step : 1.228263 Largest / Smallest step : 1.707177 Median interval of one step : 448/405, 174.6922 cents, amount: 1 Least squares average step : 167.48219 cents, oct.: 502.44656 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 2335-tone equal temperament with octave 4/3 degrees: 956 1516 2335 Least number of segments generator : 1168 of 249.129 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1939 of 413.580 cents and inv. generated superset size: 52 = 49 more = 1733.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : LSM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 90.22500 cents Scale diversity : 1.295422 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.660805 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 : 3645/3584, 29.2178 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% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 7 Odd number limit : 405 (O: 135 U: 405) Highest odd numerator or denominator: 135 Scale harmonicity : 0.029983 Average absolute harmonicity : 0.123048 Specific harmonicity : 0.147614 Fundamental : 1/336, -8.3923 octaves, 0.7786 Hz. Guide tone : 540, 9.0768 octaves, 141277.805 Hz. Exponens Consonantiae : 1.814400E+05, 17.46913 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 135.5, average 45.16667 Mersenne's string divisions : 29393 Sum of van Prooijen's expressibility: 3.56170, average 1.18723 Sum of Tenney's harmonic distance : 7.11607, average 2.37202 Vogel's harmonic complexity : 15.66667 Wille's k value : 202 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 6 Triangular lattice diameter : 5 Lattice compactness : 26.21719, average 4.36953 Lattice compactness (without 2's) : 15.29132, average 2.54855 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -1.66667 9 3: -1 .. 3 1.33333 6 2 5: 0 .. 1 0.33333 1 7: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 4 / 3 = 1.33333 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is JI-epimorphic with val: <7 11 15 18| Scale is weakly epimorphic with val: <7 11 15 21| Scale is JI-epimorphic with val: <7 11 16 19| Scale is weakly epimorphic with val: <7 11 16 22| Scale is JI-epimorphic with val: <7 11 17 20| = patent Scale is weakly epimorphic with val: <7 11 18 18| Scale is JI-epimorphic with val: <7 11 18 21| Scale is weakly epimorphic with val: <7 11 19 19| Scale is JI-epimorphic with val: <7 11 19 22| Scale is weakly epimorphic with val: <7 12 15 19| Scale is weakly epimorphic with val: <7 12 15 22| Scale is weakly epimorphic with val: <7 12 16 20| Scale is weakly epimorphic with val: <7 12 17 18| Scale is weakly epimorphic with val: <7 12 17 21| Scale is weakly epimorphic with val: <7 12 18 19| Scale is weakly epimorphic with val: <7 12 18 22| Scale is weakly epimorphic with val: <7 12 19 20|
FIT/MODE
3: 1 1 1 SP B ME I SD: 22.4449 c. M: 37.8950 c. 5: 2 1 2 SP M ME I SD: 14.4168 c. M: 24.5258 c. 8: 3 2 3 SP M ME I SD: 12.1063 c. M: 17.1431 c. 9: 4 2 3 SP T3 SD: 11.2482 c. M:-17.4433 c. 12: 5 3 4 SP T3 SD: 5.4258 c. M:-8.6772 c. 17: 7 4 6 SP T3 SD: 0.9215 c. M:-1.1674 c. 54: 22 13 19 SP T3 SD: 0.6592 c. M: 1.0028 c. 71: 29 17 25 SP T3 SD: 0.4796 c. M: 0.6758 c. 83: 34 20 29 SP T3 SD: 0.3955 c. M:-0.6765 c. 100: 41 24 35 SP T3 SD: 0.2738 c. M:-0.3764 c. 117: 48 28 41 SP T3 SD: 0.2582 c. M:-0.4162 c. 137: 56 33 48 SP T3 SD: 0.2210 c. M: 0.3296 c. 154: 63 37 54 SP T3 SD: 0.0997 c. M: 0.1643 c. 171: 70 41 60 SP T3 SD: 0.0395 c. M: 0.0604 c. 442: 181 106 155 SP T3 SD: 0.0322 c. M:-0.0406 c. 596: 244 143 209 SP T3 SD: 0.0254 c. M:-0.0422 c. 613: 251 147 215 SP T3 SD: 0.0133 c. M:-0.0203 c. 767: 314 184 269 SP T3 SD: 0.0148 c. M:-0.0193 c. 784: 321 188 275 SP T3 SD: 0.0058 c. M:-0.0089 c. 1551: 635 372 544 SP T3 SD: 0.0047 c. M:-0.0072 c. 1722: 705 413 604 SP T3 SD: 0.0038 c. M: 0.0066 c. 2335: 956 560 819 SP T3 SD: 0.0019 c. M:-0.0032 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: 62.9609 cents 5 x 6:7 S SD: 42.4092 cents 6 x 7:8 S SD: 28.2410 cents 7:8 x 9 S SD: 34.3053 cents 8:9:10:11 H SD: 27.4916 cents 9:10:11:12 H SD: 10.7557 cents 12 x 14:16 S SD: 28.2410 cents 13:15:16:17 SD: 21.9997 cents 14:16:17:19 SD: 14.3198 cents 15:17:18:20 SD: 4.9745 cents 24:27:29:32 SD: 1.4231 cents 63:71:76:84 SD: 1.1222 cents 87:98:105:116 SD: 1.0416 cents 160:180:193:213 SD: 0.9984 cents 161:181:194:215 SD: 0.9975 cents 175:197:211:233 SD: 0.9187 cents 176:198:212:235 SD: 0.9067 cents 185:208:223:247 SD: 0.8533 cents 200:225:241:267 SD: 0.7409 cents 201:226:242:268 SD: 0.7328 cents 210:236:253:280 SD: 0.6742 cents 224:252:270:299 SD: 0.6437 cents 225:253:271:300 SD: 0.5219 cents 249:280:300:332 SD: 0.3643 cents 273:307:329:364 SD: 0.2592 cents 288:324:347:384 SD: 0.2375 cents 297:334:358:396 SD: 0.2164 cents 312:351:376:416 SD: 0.1096 cents 336:378:405:448 SD: 0.0000 cents