Scala analysis: 459_D15
Diatonic tetrachord 14/13 * 9/8 * 208/189, Avicenna
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 14/13 128.298245 2/3-tone 2: 63/52 332.208246 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 208/189 165.8368 1: 14/13 128.2982 2/3-tone 2: 9/8 203.9100 major whole tone 3: 208/189 165.8368
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 14/13 128.298 cents 2/3-tone 1: 1 208/189 165.837 cents 1: 1 9/8 203.910 cents major whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 63/52 332.208 cents 2: 1 26/21 369.747 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 : 128.3 332.2 498.0 128.3: 203.9 369.7 498.0 332.2: 165.8 294.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 128.2982 .. 203.9100 cents 117/112, 75.6118 cents 14/13, 128.2982 cents 2: 294.1350 .. 369.7468 cents 117/112, 75.6118 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 14/13, 128.2982 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.293977 Largest / Average step : 1.228263 Largest / Smallest step : 1.589344 Median interval of one step : 208/189, 165.8368 cents, amount: 1 Least squares average step : 163.34641 cents, oct.: 490.03923 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1844-tone equal temperament with octave 4/3 degrees: 475 1230 1844 Least number of segments generator : 923 of 249.293 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1369 of 369.752 cents and inv. generated superset size: 23 = 20 more = 766.667% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SLM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 90.22500 cents Scale diversity : 1.340169 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.696366 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 : 1352/1323, 37.5385 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 : 13 Odd number limit : 189 (O: 63 U: 189) Highest odd numerator or denominator: 63 Scale harmonicity : 0.022502 Average absolute harmonicity : 0.089777 Specific harmonicity : 0.095947 Fundamental : 1/156, -7.2854 octaves, 1.6771 Hz. Guide tone : 252, 7.9773 octaves, 65929.642 Hz. Exponens Consonantiae : 3.931200E+04, 15.26268 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 74.5, average 24.83333 Mersenne's string divisions : 21735 Sum of van Prooijen's expressibility: 3.39041, average 1.13014 Sum of Tenney's harmonic distance : 6.85460, average 2.28487 Vogel's harmonic complexity : 15.33333 Wille's k value : 94 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 17.93210, average 2.98868 Lattice compactness (without 2's) : 11.91238, average 1.98540 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.33333 5 3: -1 .. 2 0.33333 3 1 7: 0 .. 1 0.66667 2 13: -1 .. 0 -0.66667 2 2 Average exponent except 2's : 1 / 3 = 0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 20 25| Scale is weakly epimorphic with val: <6 10 21 26| Scale is weakly epimorphic with val: <6 10 22 27| Scale is weakly epimorphic with val: <6 11 18 25| Scale is weakly epimorphic with val: <6 11 19 26| Scale is weakly epimorphic with val: <6 11 20 27| Scale is weakly epimorphic with val: <6 11 21 28| Scale is weakly epimorphic with val: <6 11 22 29| Scale is weakly epimorphic with val: <7 10 21 25| Scale is weakly epimorphic with val: <7 10 22 26| Scale is weakly epimorphic with val: <7 11 18 27| Scale is weakly epimorphic with val: <7 11 18 30| Scale is JI-epimorphic with val: <7 11 19 25| Scale is weakly epimorphic with val: <7 11 19 28| Scale is JI-epimorphic with val: <7 11 20 26| Scale is weakly epimorphic with val: <7 11 20 29| Scale is JI-epimorphic with val: <7 11 21 27| Scale is weakly epimorphic with val: <7 11 21 30| Scale is weakly epimorphic with val: <7 11 22 25| Scale is JI-epimorphic with val: <7 11 22 28| Scale is weakly epimorphic with val: <8 11 20 25| Scale is weakly epimorphic with val: <8 11 21 26| Scale is weakly epimorphic with val: <8 11 22 27|
FIT/MODE
3: 1 1 1 SP B ME I SD: 21.7760 c. M:-37.7168 c. 5: 1 2 2 SP M ME S SD: 25.4125 c. M: 33.3812 c. 7: 2 3 2 SP M ME I SD: 15.8120 c. M:-23.5382 c. 8: 2 3 3 SP M ME S SD: 12.2802 c. M: 20.9301 c. 9: 2 4 3 SP T3 SD: 10.1743 c. M: 17.6216 c. 11: 3 4 4 SP M ME S SD: 9.8306 c. M: 15.2705 c. 12: 3 5 4 SP T3 SD: 2.1888 c. M: 3.7870 c. 27: 7 11 9 SP T3 SD: 0.4870 c. M:-0.8245 c. 39: 10 16 13 SP T3 SD: 0.3583 c. M: 0.5944 c. 66: 17 27 22 SP T3 SD: 0.1032 c. M: 0.1782 c. 159: 41 65 53 SP T3 SD: 0.1268 c. M: 0.1782 c. 171: 44 70 57 SP T3 SD: 0.1331 c. M: 0.1782 c. 225: 58 92 75 SP T3 SD: 0.1144 c. M: 0.1782 c. 237: 61 97 79 SP T3 SD: 0.1208 c. M: 0.1782 c. 291: 75 119 97 SP T3 SD: 0.1093 c. M: 0.1782 c. 303: 78 124 101 SP T3 SD: 0.1149 c. M: 0.1782 c. 357: 92 146 119 SP T3 SD: 0.1068 c. M: 0.1782 c. 423: 109 173 141 SP T3 SD: 0.1054 c. M: 0.1782 c. 466: 120 191 155 SP T3 SD: 0.1062 c. M:-0.1780 c. 478: 123 196 159 SP T3 SD: 0.1268 c. M:-0.1691 c. 481: 124 197 160 SP T3 SD: 0.1111 c. M:-0.1669 c. 489: 126 200 163 SP T3 SD: 0.1046 c. M: 0.1782 c. 493: 127 202 164 SP T3 SD: 0.0915 c. M:-0.1585 c. 505: 130 207 168 SP T3 SD: 0.1008 c. M:-0.1505 c. 508: 131 208 169 SP T3 SD: 0.1157 c. M:-0.1486 c. 516: 133 211 172 SP T3 SD: 0.1114 c. M: 0.1782 c. 520: 134 213 173 SP T3 SD: 0.0853 c. M:-0.1410 c. 532: 137 218 177 SP T3 SD: 0.0810 c. M:-0.1338 c. 544: 140 223 181 SP T3 SD: 0.1028 c. M:-0.1269 c. 547: 141 224 182 SP T3 SD: 0.0866 c. M:-0.1253 c. 559: 144 229 186 SP T3 SD: 0.0686 c. M:-0.1187 c. 571: 147 234 190 SP T3 SD: 0.0797 c. M:-0.1125 c. 586: 151 240 195 SP T3 SD: 0.0644 c. M:-0.1051 c. 598: 154 245 199 SP T3 SD: 0.0617 c. M:-0.0994 c. 613: 158 251 204 SP T3 SD: 0.0678 c. M:-0.0926 c. 625: 161 256 208 SP T3 SD: 0.0505 c. M:-0.0874 c. 637: 164 261 212 SP T3 SD: 0.0636 c. M:-0.0824 c. 652: 168 267 217 SP T3 SD: 0.0479 c. M:-0.0764 c. 664: 171 272 221 SP T3 SD: 0.0465 c. M:-0.0718 c. 679: 175 278 226 SP T3 SD: 0.0531 c. M:-0.0663 c. 691: 178 283 230 SP T3 SD: 0.0358 c. M:-0.0620 c. 718: 185 294 239 SP T3 SD: 0.0346 c. M:-0.0530 c. 730: 188 299 243 SP T3 SD: 0.0347 c. M:-0.0492 c. 757: 195 310 252 SP T3 SD: 0.0238 c. M:-0.0411 c. 784: 202 321 261 SP T3 SD: 0.0240 c. M:-0.0335 c. 796: 205 326 265 SP T3 SD: 0.0258 c. M: 0.0329 c. 823: 212 337 274 SP T3 SD: 0.0138 c. M:-0.0235 c. 850: 219 348 283 SP T3 SD: 0.0159 c. M:-0.0216 c. 889: 229 364 296 SP T3 SD: 0.0058 c. M:-0.0085 c. 955: 246 391 318 SP T3 SD: 0.0043 c. M: 0.0060 c. 1844: 475 755 614 SP T3 SD: 0.0035 c. M: 0.0057 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: 54.1055 cents 5 x 6:7 S SD: 43.0383 cents 6 x 7:8 S SD: 32.6687 cents 7 x 8:9 S SD: 59.5231 cents 8:9:10:11 H SD: 35.7189 cents 9:10:11:12 H SD: 18.7333 cents 12:13:15:16 SD: 18.3575 cents 13:14:16:17 S SD: 14.4278 cents 14:15:17:19 SD: 10.7121 cents 15:16:18:20 S SD: 7.8097 cents 24:26:29:32 SD: 3.7505 cents 39:42:47:52 SD: 3.0614 cents 51:55:62:68 SD: 2.1313 cents 66:71:80:88 SD: 0.6837 cents 90:97:109:120 SD: 0.5010 cents 156:168:189:208 SD: 0.0000 cents