Scala analysis: 115_E13
Enharmonic tetrachord 256/255 * 17/16 * 5/4, Hofmann
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 256/255 6.775876 septendecimal kleisma 2: 16/15 111.731285 minor diatonic semitone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 5/4 386.3137 major third 1: 256/255 6.7759 septendecimal kleisma 2: 17/16 104.9554 17th harmonic 3: 5/4 386.3137 major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 256/255 6.776 cents septendecimal kleisma 1: 1 17/16 104.955 cents 17th harmonic 1: 1 5/4 386.314 cents major third 2: 1 16/15 111.731 cents minor diatonic semitone 2: 1 64/51 393.090 cents 2: 1 85/64 491.269 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 : 6.8 111.7 498.0 6.8 : 105.0 491.3 498.0 111.7: 386.3 393.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 6.7759 .. 386.3137 cents 1275/1024, 379.5378 cents 256/255, 6.7759 cents 2: 111.7313 .. 491.2691 cents 1275/1024, 379.5378 cents 64/75,-274.5824 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 256/255, 6.7759 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 5/4, 386.3137 cents Average / Smallest step : 24.500892 Largest / Average step : 2.326981 Largest / Smallest step : 57.013105 Median interval of one step : 17/16, 104.9554 cents, amount: 1 Least squares average step : 123.16953 cents, oct.: 369.50860 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1471-tone equal temperament with octave 4/3 degrees: 20 330 1471 Least number of segments generator : 736 of 249.192 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1461 of 494.659 cents and inv. generated superset size: 34 = 31 more = 1133.333% 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 6.77588 cents Scale diversity : 0.313443 Lumma stability : 0.027210 Lumma impropriety factor : 0.551321 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 : 256/255, 6.7759 cents Number of recognisable fifths : 0 Number of recognisable fourths : 1, average 491.2691 cents All steps are superparticular (epimoric) Steps are strictly increasing 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 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 17 Odd number limit : 255 (O: 85 U: 255) Highest odd numerator or denominator: 255 Scale harmonicity : 0.021193 Average absolute harmonicity : 0.104003 Specific harmonicity : 0.106700 Fundamental : 1/255, -7.9944 octaves, 1.0260 Hz. Guide tone : 256, 8.0000 octaves, 66976.145 Hz. Exponens Consonantiae : 6.528000E+04, 15.99435 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 274.5, average 91.50000 Mersenne's string divisions : 15841 Sum of van Prooijen's expressibility: 4.05975, average 1.35325 Sum of Tenney's harmonic distance : 8.27417, average 2.75806 Vogel's harmonic complexity : 17.66667 Wille's k value : 42 Wilson's harmonic complexity : 25 Rectangular lattice diameter : 3 Triangular lattice diameter : 2 Lattice compactness : 27.18765, average 4.53127 Lattice compactness (without 2's) : 7.56048, average 1.26008 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 8 4.66667 14 3: -1 ..-1 -1.00000 3 1 5: -1 .. 0 -0.66667 2 1 17: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-6 / 3 =-2.00000 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <7 10 15 29| Scale is weakly epimorphic with val: <7 10 15 32| Scale is weakly epimorphic with val: <7 10 16 27| Scale is JI-epimorphic with val: <7 11 15 29| Scale is weakly epimorphic with val: <7 11 15 32| Scale is weakly epimorphic with val: <7 11 16 27| Scale is weakly epimorphic with val: <7 11 16 30| Scale is weakly epimorphic with val: <7 11 16 33| Scale is weakly epimorphic with val: <7 11 18 29| Scale is weakly epimorphic with val: <7 11 18 32| Scale is weakly epimorphic with val: <7 11 19 27| Scale is weakly epimorphic with val: <7 11 19 30| Scale is weakly epimorphic with val: <7 11 19 33| Scale is weakly epimorphic with val: <8 11 17 33| Scale is weakly epimorphic with val: <8 11 18 28| Scale is weakly epimorphic with val: <8 11 18 31| Scale is weakly epimorphic with val: <8 12 17 27| Scale is weakly epimorphic with val: <8 12 17 30| Scale is weakly epimorphic with val: <8 12 17 33| Scale is weakly epimorphic with val: <8 12 18 31|
FIT/MODE
3: 0 1 2 N G T3 SD: 31.5839 c. M:-54.2837 c. 4: 0 1 3 N G T3 SD: 8.3514 c. M:-12.7800 c. 5: 0 1 4 N G T3 SD: 8.0179 c. M: 12.1223 c. 9: 0 2 7 N G T3 SD: 3.9592 c. M: 6.7759 c. 23: 0 5 18 N G T3 SD: 4.3927 c. M: 6.7759 c. 26: 0 6 20 N G T3 SD: 4.3269 c. M: 6.7759 c. 27: 0 6 21 N G T3 SD: 3.9592 c. M: 6.7759 c. 31: 0 7 24 N G T3 SD: 3.9347 c. M: 6.7759 c. 39: 1 8 30 N T3 SD: 3.9238 c. M:-5.9945 c. 40: 1 8 31 N T3 SD: 3.2821 c. M:-5.6752 c. 44: 1 9 34 N T3 SD: 2.7553 c. M:-4.5433 c. 45: 1 9 35 N T3 SD: 2.5516 c. M:-4.2918 c. 48: 1 10 37 N T3 SD: 2.4993 c. M:-3.6001 c. 49: 1 10 38 N T3 SD: 1.9567 c. M:-3.3883 c. 50: 1 10 39 N T3 SD: 2.2223 c. M:-3.1850 c. 52: 1 11 40 N T3 SD: 2.4566 c. M:-3.2022 c. 53: 1 11 41 N T3 SD: 1.6268 c. M:-2.6212 c. 54: 1 11 42 N T3 SD: 1.5385 c. M:-2.4472 c. 57: 1 12 44 N T3 SD: 1.5600 c. M:-1.9618 c. 58: 1 12 45 N T3 SD: 1.0473 c. M:-1.8111 c. 62: 1 13 48 N T3 SD: 0.8394 c. M:-1.2571 c. 63: 1 13 49 N T3 SD: 0.8922 c. M:-1.1296 c. 67: 1 14 52 N T3 SD: 0.4020 c. M:-0.6576 c. 71: 1 15 55 N T3 SD: 0.3221 c. M:-0.5042 c. 76: 1 16 59 N T3 SD: 0.2282 c. M: 0.3265 c. 143: 2 30 111 N T3 SD: 0.1956 c. M: 0.2807 c. 147: 2 31 114 N T3 SD: 0.0431 c. M:-0.0747 c. 370: 5 78 287 N T3 SD: 0.0267 c. M: 0.0455 c. 517: 7 109 401 N T3 SD: 0.0209 c. M: 0.0325 c. 664: 9 140 515 N T3 SD: 0.0221 c. M:-0.0288 c. 731: 10 154 567 N T3 SD: 0.0218 c. M:-0.0373 c. 807: 11 170 626 N T3 SD: 0.0168 c. M: 0.0260 c. 954: 13 201 740 N T3 SD: 0.0087 c. M:-0.0109 c. 1101: 15 232 854 N T3 SD: 0.0055 c. M:-0.0095 c. 1324: 18 279 1027 N T3 SD: 0.0063 c. M: 0.0097 c. 1471: 20 310 1141 N T3 SD: 0.0026 c. M: 0.0044 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 x 7 SD: 84.4672 cents 6 x 7:8 S SD: 77.5698 cents 7 x 8:9 S SD: 67.5105 cents 8 x 9:11 SD: 53.2328 cents 9 x 10:12 S SD: 35.3362 cents 10 x 11:13 SD: 34.4934 cents 11 x 12:15 S SD: 27.5105 cents 12 x 13:16 SD: 13.4207 cents 13 x 14:17 SD: 18.7389 cents 14 x 15:19 SD: 15.7988 cents 15 x 16:20 S SD: 0.0000 cents 16 x 17:21 SD: 14.0467 cents 17 x 18:23 SD: 14.1599 cents 18 x 19:24 SD: 9.0641 cents 19 x 20:25 S SD: 16.2144 cents 20 x 21:27 SD: 17.3627 cents 21 x 22:28 SD: 15.5971 cents 22 x 23:29 SD: 20.0048 cents 23 x 25:31 SD: 18.8048 cents 24 x 26:32 SD: 13.4207 cents 25 x 27:33 SD: 13.8317 cents 26 x 28:35 S SD: 11.7146 cents 27 x 29:36 SD: 5.9905 cents 28 x 30:37 SD: 8.6682 cents 57:58:61:76 SD: 8.0053 cents 59:60:63:79 SD: 7.8541 cents 60:61:64:80 SD: 7.2801 cents 63:64:67:84 SD: 7.0427 cents 69:70:74:92 SD: 6.8061 cents 70:71:75:93 SD: 6.7823 cents 71:72:76:95 S SD: 6.4818 cents 72:73:77:96 SD: 5.8954 cents 74:75:79:99 SD: 5.8428 cents 75:76:80:100 S SD: 5.3849 cents 78:79:83:104 SD: 5.2788 cents 84:85:90:112 SD: 5.2440 cents 86:87:92:115 SD: 5.0085 cents 87:88:93:116 SD: 4.5111 cents 89:90:95:119 SD: 4.5093 cents 90:91:96:120 SD: 4.1180 cents 93:94:99:124 SD: 4.0830 cents 101:102:108:135 S SD: 3.9767 cents 102:103:109:136 SD: 3.5341 cents 105:106:112:140 SD: 3.2113 cents 117:118:125:156 SD: 2.8090 cents 120:121:128:160 SD: 2.5304 cents 132:133:141:176 SD: 2.2510 cents 135:136:144:180 S SD: 2.0003 cents 147:148:157:196 SD: 1.8100 cents 150:151:160:200 SD: 1.5758 cents 162:163:173:216 SD: 1.4548 cents 165:166:176:220 SD: 1.2283 cents 177:178:189:236 SD: 1.1655 cents 180:181:192:240 SD: 0.9385 cents 192:193:205:256 SD: 0.9293 cents 195:196:208:260 SD: 0.6932 cents 210:211:224:280 SD: 0.4828 cents 225:226:240:300 SD: 0.3005 cents 240:241:256:320 SD: 0.1409 cents 255:256:272:340 S SD: 0.0000 cents