Scala analysis: 177_C8
Chromatic tetrachord 18/17 * 34/33 * 11/9
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 18/17 98.954592 Arabic lute index finger 2: 12/11 150.637059 undecimal neutral second, 3/4-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 11/9 347.4079 undecimal neutral third 1: 18/17 98.9546 Arabic lute index finger 2: 34/33 51.6825 3: 11/9 347.4079 undecimal neutral third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 34/33 51.682 cents 1: 1 18/17 98.955 cents Arabic lute index finger 1: 1 11/9 347.408 cents undecimal neutral third 2: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 2: 1 34/27 399.090 cents septendecimal major third 2: 1 22/17 446.363 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 : 99.0 150.6 498.0 99.0 : 51.7 399.1 498.0 150.6: 347.4 446.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 51.6825 .. 347.4079 cents 121/102, 295.7255 cents 34/33, 51.6825 cents 2: 150.6371 .. 446.3625 cents 121/102, 295.7255 cents 108/121,-196.7709 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 34/33, 51.6825 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 11/9, 347.4079 cents Average / Smallest step : 3.212211 Largest / Average step : 2.092630 Largest / Smallest step : 6.721969 Median interval of one step : 18/17, 98.9546 cents, amount: 1 Least squares average step : 135.31169 cents, oct.: 405.93508 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2149-tone equal temperament with octave 4/3 degrees: 427 650 2149 Least number of segments generator : 1075 of 249.138 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1760 of 407.892 cents and inv. generated superset size: 38 = 35 more = 1266.667% 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 51.68247 cents Scale diversity : 0.751515 Lumma stability : 0.207541 Lumma impropriety factor : 0.395087 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 : 297/289, 47.2721 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 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 : 17 Odd number limit : 33 (O: 17 U: 33) Highest odd numerator or denominator: 17 Scale harmonicity : 0.017153 Average absolute harmonicity : 0.095162 Specific harmonicity : 0.089603 Fundamental : 1/561, -9.1319 octaves, 0.4664 Hz. Guide tone : 36, 5.1699 octaves, 9418.520 Hz. Exponens Consonantiae : 2.019600E+04, 14.30178 octaves Euler's gradus suavitatis : 35 Sum of Mann's harmonic distance : 32.5, average 10.83333 Mersenne's string divisions : 805 Sum of van Prooijen's expressibility: 2.74896, average 0.91632 Sum of Tenney's harmonic distance : 5.68548, average 1.89516 Vogel's harmonic complexity : 25.33333 Wille's k value : 148 Wilson's harmonic complexity : 37 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 14.68774, average 2.44796 Lattice compactness (without 2's) : 11.78068, average 1.96345 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.66667 5 3: -1 .. 2 0.66667 4 1 11: -1 .. 0 -0.33333 1 1 17: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is JI-epimorphic with val: <7 11 23 28| Scale is weakly epimorphic with val: <7 11 23 31| Scale is weakly epimorphic with val: <7 11 24 27| Scale is weakly epimorphic with val: <7 11 24 30| Scale is weakly epimorphic with val: <7 11 24 33| Scale is weakly epimorphic with val: <7 11 26 28| Scale is weakly epimorphic with val: <7 11 26 31| Scale is weakly epimorphic with val: <7 11 27 27| Scale is weakly epimorphic with val: <7 11 27 30| Scale is weakly epimorphic with val: <7 11 27 33| Scale is weakly epimorphic with val: <7 12 23 27| Scale is weakly epimorphic with val: <7 12 23 30| Scale is weakly epimorphic with val: <7 12 23 33| Scale is weakly epimorphic with val: <7 12 25 28| Scale is weakly epimorphic with val: <8 11 23 27| Scale is weakly epimorphic with val: <8 11 24 29| Scale is weakly epimorphic with val: <8 11 24 32| Scale is weakly epimorphic with val: <8 11 26 27| Scale is weakly epimorphic with val: <8 12 23 29| Scale is weakly epimorphic with val: <8 12 25 27| Scale is weakly epimorphic with val: <8 12 25 30| Scale is weakly epimorphic with val: <8 12 25 33| Scale is weakly epimorphic with val: <8 12 26 29|
FIT/MODE
3: 1 0 2 N G T3 SD: 39.7223 c. M:-67.0604 c. 4: 1 0 3 N G T3 SD: 21.1006 c. M: 26.1258 c. 6: 1 1 4 N M DE S SD: 12.7905 c. M: 15.9471 c. 9: 2 1 6 N T3 SD: 11.1638 c. M:-15.3779 c. 10: 2 1 7 N T3 SD: 0.8011 c. M: 1.2236 c. 56: 11 6 39 N T3 SD: 0.7240 c. M: 1.1243 c. 66: 13 7 46 N T3 SD: 0.5204 c. M: 0.8548 c. 76: 15 8 53 N T3 SD: 0.3822 c. M: 0.6562 c. 86: 17 9 60 N T3 SD: 0.2933 c. M: 0.5038 c. 96: 19 10 67 N T3 SD: 0.2459 c. M: 0.3832 c. 106: 21 11 74 N T3 SD: 0.2324 c. M: 0.2853 c. 231: 46 24 161 N T3 SD: 0.2093 c. M:-0.2857 c. 241: 48 25 168 N T3 SD: 0.1896 c. M:-0.2411 c. 251: 50 26 175 N T3 SD: 0.1767 c. M:-0.2576 c. 261: 52 27 182 N T3 SD: 0.1703 c. M:-0.2728 c. 271: 54 28 189 N T3 SD: 0.1695 c. M:-0.2868 c. 297: 59 31 207 N T3 SD: 0.1652 c. M:-0.2857 c. 307: 61 32 214 N T3 SD: 0.1366 c. M:-0.2365 c. 317: 63 33 221 N T3 SD: 0.1110 c. M:-0.1904 c. 327: 65 34 228 N T3 SD: 0.0889 c. M:-0.1472 c. 337: 67 35 235 N T3 SD: 0.0715 c. M:-0.1065 c. 347: 69 36 242 N T3 SD: 0.0608 c. M:-0.0803 c. 357: 71 37 249 N T3 SD: 0.0586 c. M:-0.0964 c. 423: 84 44 295 N T3 SD: 0.0511 c. M:-0.0716 c. 433: 86 45 302 N T3 SD: 0.0317 c. M:-0.0417 c. 443: 88 46 309 N T3 SD: 0.0139 c. M: 0.0201 c. 453: 90 47 316 N T3 SD: 0.0087 c. M: 0.0142 c. 896: 178 93 625 N T3 SD: 0.0073 c. M: 0.0126 c. 1349: 268 140 941 N T3 SD: 0.0066 c. M: 0.0101 c. 1696: 337 176 1183 N T3 SD: 0.0074 c. M:-0.0098 c. 1706: 339 177 1190 N T3 SD: 0.0072 c. M:-0.0121 c. 1802: 358 187 1257 N T3 SD: 0.0067 c. M: 0.0089 c. 2139: 425 222 1492 N T3 SD: 0.0062 c. M:-0.0105 c. 2149: 427 223 1499 N T3 SD: 0.0042 c. M:-0.0055 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: 92.6837 cents 6 x 7:8 S SD: 58.1169 cents 7 x 8:9 S SD: 51.1133 cents 8 x 9:11 SD: 37.6697 cents 9 x 10:12 S SD: 15.8833 cents 10 x 11:13 SD: 23.0628 cents 11 x 12:15 S SD: 19.4529 cents 12 x 13:16 SD: 6.0322 cents 13 x 14:17 SD: 20.1813 cents 14:15 x 19 SD: 18.4303 cents 15:16 x 20 S SD: 6.3883 cents 16:17 x 21 SD: 13.9583 cents 18:19:20:24 S SD: 10.7381 cents 20:21:22:27 SD: 9.8816 cents 21:22:23:28 SD: 6.5508 cents 26 x 28:35 S SD: 13.9058 cents 27:29 x 36 SD: 12.3788 cents 28:30:31:37 SD: 12.0868 cents 29:31:32:39 SD: 9.9145 cents 30:32:33:40 SD: 6.4088 cents 31:33:34:41 SD: 6.4018 cents 32:34:35:43 SD: 5.1402 cents 33:35:36:44 SD: 0.9707 cents 87:92:95:116 SD: 0.9215 cents 120:127:131:160 SD: 0.4816 cents 153:162:167:204 SD: 0.3142 cents 186:197:203:248 SD: 0.3107 cents 339:359:370:452 SD: 0.2990 cents 342:362:373:456 SD: 0.2344 cents 375:397:409:500 SD: 0.1541 cents 408:432:445:544 SD: 0.1179 cents 528:559:576:704 SD: 0.0607 cents 561:594:612:748 SD: 0.0000 cents