Scala analysis: 170_C7
Chromatic tetrachord 176/169 * 169/162 * 27/22
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 176/169 70.262619 2: 88/81 143.497939 2nd undecimal neutral second 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 27/22 354.5471 neutral third, Zalzal wosta of al-Farabi 1: 176/169 70.2626 2: 169/162 73.2353 3: 27/22 354.5471 neutral third, Zalzal wosta of al-Farabi
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 176/169 70.263 cents 1: 1 169/162 73.235 cents 1: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 2: 1 88/81 143.498 cents 2nd undecimal neutral second 2: 1 216/169 424.810 cents 2: 1 169/132 427.782 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 : 70.3 143.5 498.0 70.3 : 73.2 427.8 498.0 143.5: 354.5 424.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.2626 .. 354.5471 cents 4563/3872, 284.2844 cents 176/169, 70.2626 cents 2: 143.4979 .. 427.7824 cents 4563/3872, 284.2844 cents 1936/2187,-211.0491 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 176/169, 70.2626 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 27/22, 354.5471 cents Average / Smallest step : 2.362778 Largest / Average step : 2.135633 Largest / Smallest step : 5.046027 Median interval of one step : 169/162, 73.2353 cents, amount: 1 Least squares average step : 132.24239 cents, oct.: 396.72718 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1836-tone equal temperament with octave 4/3 degrees: 259 529 1836 Least number of segments generator : 919 of 249.294 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1049 of 284.558 cents and inv. generated superset size: 55 = 52 more = 1833.333% 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 70.26262 cents Scale diversity : 0.754804 Lumma stability : 0.282154 Lumma impropriety factor : 0.423755 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 : 28561/28512, 2.9727 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 281.3117 cents: 2 -- Rational properties -- Prime limit : 13 Odd number limit : 169 (O: 169 U: 169) Highest odd numerator or denominator: 169 Scale harmonicity : 0.012961 Average absolute harmonicity : 0.086908 Specific harmonicity : 0.063162 Fundamental : 1/13689, -13.7407 octaves, 0.0191 Hz. Guide tone : 176, 7.4594 octaves, 46046.099 Hz. Exponens Consonantiae : 2.409264E+06, 21.20016 octaves Euler's gradus suavitatis : 47 Sum of Mann's harmonic distance : 260.5, average 86.83333 Mersenne's string divisions : 408135 Sum of van Prooijen's expressibility: 4.61349, average 1.53783 Sum of Tenney's harmonic distance : 9.40555, average 3.13518 Vogel's harmonic complexity : 34.66667 Wille's k value : 2281 Wilson's harmonic complexity : 49 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 22.97914, average 3.82986 Lattice compactness (without 2's) : 17.44308, average 2.90718 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 4 3.00000 9 3: -4 .. 0 -1.66667 5 1 11: 0 .. 1 0.66667 2 1 13: -2 .. 0 -0.66667 2 1 Average exponent except 2's :-5 / 3 =-1.66667 Average absolute exponent except 2's: 9 / 3 = 3.00000 Scale is weakly epimorphic with val: <6 10 25 27| Scale is weakly epimorphic with val: <6 10 25 30| Scale is weakly epimorphic with val: <7 11 24 25| Scale is weakly epimorphic with val: <7 11 24 28| Scale is JI-epimorphic with val: <7 11 25 26| Scale is weakly epimorphic with val: <7 11 25 29| Scale is weakly epimorphic with val: <7 11 27 28| Scale is weakly epimorphic with val: <7 12 25 25| Scale is weakly epimorphic with val: <8 11 23 27| Scale is weakly epimorphic with val: <8 11 23 30| Scale is weakly epimorphic with val: <8 11 27 28| Scale is weakly epimorphic with val: <8 12 23 26| Scale is weakly epimorphic with val: <8 12 27 27| Scale is weakly epimorphic with val: <8 12 27 30|
FIT/MODE
3: 0 1 2 N G T3 SD: 42.5983 c. M: 70.2626 c. 4: 0 1 3 N G T3 SD: 42.0211 c. M: 70.2626 c. 5: 1 0 4 N G T3 SD: 30.4820 c. M: 43.8889 c. 6: 1 1 4 N M DE S SD: 14.9382 c. M:-22.5171 c. 7: 1 1 5 N M DE S SD: 0.8611 c. M: 1.1994 c. 87: 12 13 62 N T3 SD: 0.9310 c. M: 1.5668 c. 93: 13 14 66 N T3 SD: 0.7336 c. M:-1.0958 c. 94: 13 14 67 N T3 SD: 0.8389 c. M: 1.3841 c. 100: 14 15 71 N T3 SD: 0.6224 c. M:-0.9351 c. 107: 15 16 76 N T3 SD: 0.5257 c. M:-0.7955 c. 114: 16 17 81 N T3 SD: 0.4411 c. M:-0.6730 c. 121: 17 18 86 N T3 SD: 0.3663 c. M:-0.5647 c. 128: 18 19 91 N T3 SD: 0.2999 c. M:-0.4682 c. 135: 19 20 96 N T3 SD: 0.2407 c. M:-0.3817 c. 142: 20 21 101 N T3 SD: 0.1876 c. M:-0.3038 c. 149: 21 22 106 N T3 SD: 0.1403 c. M:-0.2332 c. 156: 22 23 111 N T3 SD: 0.0986 c. M:-0.1689 c. 163: 23 24 116 N T3 SD: 0.0641 c. M:-0.1101 c. 170: 24 25 121 N T3 SD: 0.0433 c. M:-0.0562 c. 347: 49 51 247 N T3 SD: 0.0423 c. M:-0.0665 c. 517: 73 76 368 N T3 SD: 0.0418 c. M:-0.0609 c. 687: 97 101 489 N T3 SD: 0.0419 c. M:-0.0581 c. 857: 121 126 610 N T3 SD: 0.0420 c. M:-0.0565 c. 864: 122 127 615 N T3 SD: 0.0419 c. M:-0.0632 c. 972: 137 143 692 N T3 SD: 0.0409 c. M: 0.0649 c. 979: 138 144 697 N T3 SD: 0.0396 c. M: 0.0581 c. 986: 139 145 702 N T3 SD: 0.0394 c. M: 0.0514 c. 1121: 158 165 798 N T3 SD: 0.0379 c. M: 0.0654 c. 1128: 159 166 803 N T3 SD: 0.0343 c. M: 0.0595 c. 1135: 160 167 808 N T3 SD: 0.0313 c. M: 0.0536 c. 1142: 161 168 813 N T3 SD: 0.0291 c. M: 0.0479 c. 1149: 162 169 818 N T3 SD: 0.0277 c. M: 0.0422 c. 1156: 163 170 823 N T3 SD: 0.0273 c. M: 0.0366 c. 1298: 183 191 924 N T3 SD: 0.0264 c. M: 0.0452 c. 1305: 184 192 929 N T3 SD: 0.0232 c. M: 0.0402 c. 1312: 185 193 934 N T3 SD: 0.0207 c. M: 0.0352 c. 1319: 186 194 939 N T3 SD: 0.0190 c. M: 0.0303 c. 1326: 187 195 944 N T3 SD: 0.0183 c. M: 0.0255 c. 1333: 188 196 949 N T3 SD: 0.0188 c. M: 0.0251 c. 1475: 208 217 1050 N T3 SD: 0.0176 c. M: 0.0298 c. 1482: 209 218 1055 N T3 SD: 0.0147 c. M: 0.0255 c. 1489: 210 219 1060 N T3 SD: 0.0126 c. M: 0.0212 c. 1496: 211 220 1065 N T3 SD: 0.0115 c. M: 0.0170 c. 1503: 212 221 1070 N T3 SD: 0.0118 c. M: 0.0159 c. 1652: 233 243 1176 N T3 SD: 0.0109 c. M: 0.0178 c. 1659: 234 244 1181 N T3 SD: 0.0081 c. M: 0.0140 c. 1666: 235 245 1186 N T3 SD: 0.0062 c. M: 0.0102 c. 1673: 236 246 1191 N T3 SD: 0.0062 c. M: 0.0086 c. 1829: 258 269 1302 N T3 SD: 0.0060 c. M: 0.0080 c. 1836: 259 270 1307 N T3 SD: 0.0029 c. M: 0.0046 c. 1843: 260 271 1312 N T3 SD: 0.0017 c. M: 0.0026 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: 95.8750 cents 6 x 7:8 S SD: 61.6865 cents 7 x 8:9 S SD: 53.9703 cents 8 x 9:11 SD: 40.2729 cents 9 x 10:12 S SD: 19.4529 cents 10 x 11:13 SD: 24.4115 cents 11 x 12:15 S SD: 19.7777 cents 12 x 13:16 SD: 2.4626 cents 13 x 14:17 SD: 18.4469 cents 14 x 15:19 SD: 19.4781 cents 15 x 16:20 S SD: 15.8833 cents 16:17 x 21 SD: 22.0620 cents 17:18 x 23 SD: 19.1181 cents 18:19:20:24 S SD: 15.1233 cents 19:20:21:25 SD: 13.9671 cents 20:21:22:27 SD: 11.1893 cents 21:22:23:28 SD: 5.7873 cents 24:25:26:32 SD: 1.6474 cents 69:72:75:92 SD: 1.1745 cents 93:97:101:124 SD: 0.9058 cents 117:122:127:156 SD: 0.8860 cents 150:156:163:200 SD: 0.7983 cents 171:178:186:228 SD: 0.7403 cents 174:181:189:232 SD: 0.6695 cents 195:203:212:260 SD: 0.4588 cents 219:228:238:292 SD: 0.2541 cents 243:253:264:324 SD: 0.1484 cents 531:553:577:708 SD: 0.1113 cents 555:578:603:740 SD: 0.0374 cents