Scala analysis: walker
Robert Walker's 2.3.11.13 scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 12/11 150.637059 undecimal neutral second, 3/4-tone 2: 11/9 347.407941 undecimal neutral third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 13/8 840.527662 tridecimal neutral sixth 6: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-tone 1: 12/11 150.6371 undecimal neutral second, 3/4-tone 2: 121/108 196.7709 3: 12/11 150.6371 undecimal neutral second, 3/4-tone 4: 9/8 203.9100 major whole tone 5: 13/12 138.5727 tridecimal 2/3-tone 6: 44/39 208.8353 7: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 13/12 138.573 cents tridecimal 2/3-tone 1: 3 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 121/108 196.771 cents 1: 1 9/8 203.910 cents major whole tone 1: 1 44/39 208.835 cents 2: 1 144/121 301.274 cents two (undecimal neutral second, 3/4-tone) 2: 1 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 2: 3 11/9 347.408 cents undecimal neutral third 2: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 2: 1 16/13 359.472 cents tridecimal neutral third 3: 1 117/88 493.120 cents tridecimal gentle fourth 3: 3 4/3 498.045 cents perfect fourth 3: 1 192/143 510.109 cents 3: 2 11/8 551.318 cents undecimal semi-augmented fourth 4: 2 16/11 648.682 cents undecimal semi-diminished fifth 4: 1 143/96 689.891 cents 4: 3 3/2 701.955 cents perfect fifth 4: 1 176/117 706.880 cents 5: 1 13/8 840.528 cents tridecimal neutral sixth 5: 1 44/27 845.453 cents neutral sixth 5: 3 18/11 852.592 cents undecimal neutral sixth 5: 1 64/39 857.517 cents 39th subharmonic 5: 1 121/72 898.726 cents 6: 1 39/22 991.165 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 1 216/121 1003.229 cents 6: 3 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 1 24/13 1061.427 cents tridecimal neutral seventh Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 150.6 347.4 498.0 702.0 840.5 1049.4 1200.0 150.6 : 196.8 347.4 551.3 689.9 898.7 1049.4 1200.0 347.4 : 150.6 354.5 493.1 702.0 852.6 1003.2 1200.0 498.0 : 203.9 342.5 551.3 702.0 852.6 1049.4 1200.0 702.0 : 138.6 347.4 498.0 648.7 845.5 996.1 1200.0 840.5 : 208.8 359.5 510.1 706.9 857.5 1061.4 1200.0 1049.4: 150.6 301.3 498.0 648.7 852.6 991.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 138.5727 .. 208.8353 cents 176/169, 70.2626 cents 13/12, 138.5727 cents 2: 301.2741 .. 359.4723 cents 121/117, 58.1982 cents 1404/1331, 92.4388 cents 3: 493.1197 .. 551.3179 cents 121/117, 58.1982 cents 1521/1408, 133.6474 cents 4: 648.6821 .. 706.8803 cents 121/117, 58.1982 cents 128/121, 97.3641 cents 5: 840.5277 .. 898.7259 cents 121/117, 58.1982 cents 1521/1408, 133.6474 cents 6: 991.1647 .. 1061.4273 cents 176/169, 70.2626 cents 1404/1331, 92.4388 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 13/12, 138.5727 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 44/39, 208.8353 cents Average / Smallest step : 1.237102 Largest / Average step : 1.218206 Largest / Smallest step : 1.507045 Median interval of one step : 12/11, 150.6371 cents, amount: 3 Most common interval of one step : 12/11, 150.6371 cents, amount: 3 Least squares average step : 171.75874 cents, oct.: 1202.31119 cents Scale is strictly proper Step pattern alph. order: ABACDEA Step pattern size order : BCBDAEB Scale is a Constant Structure, by a margin of 92.43884 cents Scale diversity : 1.309120 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.688902 Rothenberg efficiency : 0.385034 redundancy: 0.614966 Efficiency x scale size : 2.695238 Number of different interval sizes : 28 = 4.66667 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.66667 = 14/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 352/351, 4.9253 cents Number of recognisable fifths : 5, average 700.5272 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 1 3 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 5 = 71.4286% Scale is n-1 differentially coherent in interval classes 1 and 2 combined -- Rational properties -- Prime limit : 13 Odd number limit : 143 (O: 143 U: 143) Highest odd numerator or denominator: 13 Scale harmonicity : 0.013983 Average absolute harmonicity : 0.236975 Specific harmonicity : 0.098887 Fundamental : 1/792, -9.6294 octaves, 0.3303 Hz. Guide tone : 1716, 10.7448 octaves, 448949.470 Hz. Exponens Consonantiae : 1.359072E+06, 20.37419 octaves Euler's gradus suavitatis : 44 Sum of Mann's harmonic distance : 48.0, average 6.85714 Mersenne's string divisions : 164220 Sum of van Prooijen's expressibility: 5.19236, average 0.74177 Sum of Tenney's harmonic distance : 10.11115, average 1.44445 Vogel's harmonic complexity : 22.57143 Wille's k value : 643 Wilson's harmonic complexity : 44 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 77.91925, average 2.78283 Lattice compactness (without 2's) : 45.35361, average 1.61977 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 0.00000 10 1 3: -2 .. 1 -0.28571 6 2 11: -1 .. 1 0.14286 3 3 13: 0 .. 1 0.14286 1 1 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 10 / 7 = 1.42857 Scale is weakly epimorphic with val: <7 10 26 29| Scale is weakly epimorphic with val: <7 11 23 27| Scale is JI-epimorphic with val: <7 11 24 26| = patent Scale is weakly epimorphic with val: <7 12 23 29|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 15.5328 c. M:-20.7915 c. Lebeng 17: 2 3 2 3 2 3 2 SP M ME I SD: 6.3598 c. M:-9.4606 c. Neutral Dorian, Maqamic-7 24: 3 4 3 4 3 4 3 SP M ME I SD: 3.8711 c. M:-9.4723 c. Neutral Dorian, Misaelides 2nd Byzantine mode, Iced Fridgian, Maqam Sikah Baladi, Maqamic-7 41: 5 7 5 7 5 7 5 SP M DE I SD: 4.1406 c. M:-8.2528 c. Maqamic-7 49: 6 8 6 9 5 9 6 SP SD: 5.9302 c. M: 8.2491 c. 53: 7 8 7 9 6 9 7 SP SD: 5.2341 c. M:-7.8535 c. 55: 7 9 7 9 7 9 7 SP M DE I SD: 4.5953 c. M:-10.3814 c. 56: 7 9 7 10 6 10 7 SP SD: 3.7515 c. M:-5.1879 c. 63: 8 10 8 11 7 11 8 SP SD: 2.6313 c. M: 4.5508 c. 80: 10 13 10 14 9 14 10 SP SD: 1.9061 c. M:-3.0450 c. 87: 11 14 11 15 10 15 11 SP SD: 1.4246 c. M: 2.5804 c. 104: 13 17 13 18 12 18 13 SP SD: 1.3473 c. M:-1.8912 c. 111: 14 18 14 19 13 19 14 SP SD: 1.2901 c. M:-2.7156 c. 159: 20 26 20 27 18 28 20 SP SD: 1.0722 c. M: 2.7918 c. 166: 21 27 21 28 19 29 21 SP SD: 1.0647 c. M: 1.9734 c. 176: 22 29 22 30 20 31 22 SP SD: 0.8188 c. M: 1.8913 c. 183: 23 30 23 31 21 32 23 SP SD: 0.4905 c. M: 1.1834 c. 190: 24 31 24 32 22 33 24 SP SD: 0.7253 c. M:-0.9419 c. 200: 25 33 25 34 23 35 25 SP SD: 0.4543 c. M:-0.6371 c. 207: 26 34 26 35 24 36 26 SP SD: 0.3172 c. M: 0.5057 c. 287: 36 47 36 49 33 50 36 SP SD: 0.3032 c. M: 0.4840 c. 294: 37 48 37 50 34 51 37 SP SD: 0.2957 c. M: 0.4692 c. 311: 39 51 39 53 36 54 39 SP SD: 0.3023 c. M:-0.6299 c. 407: 51 67 51 69 47 71 51 SP SD: 0.2835 c. M:-0.5036 c. 470: 59 77 59 80 54 82 59 SP SD: 0.2294 c. M: 0.5277 c. 477: 60 78 60 81 55 83 60 SP SD: 0.2171 c. M:-0.3063 c. 494: 62 81 62 84 57 86 62 SP SD: 0.0458 c. M:-0.0693 c. 1195: 150 196 150 203 138 208 150 SP SD: 0.0246 c. M:-0.0398 c. 1689: 212 277 212 287 195 294 212 SP SD: 0.0154 c. M: 0.0303 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 0.0000 cents 3 x x 4 x 5 x 6 S SD: 14.6104 cents 4 x 5 x 6 x 7:8 S SD: 22.3605 cents 5 x 6:7 x 8:9:10 S SD: 19.8730 cents 6 x 7:8:9:10:11:12 S SD: 15.2820 cents 7:8 x 9 x 11:13:14 SD: 23.9311 cents 8:9:10:11:12:13:15:16 SD: 13.3274 cents 10:11:12:13:15:16:18:20 SD: 9.9655 cents 12:13:15:16:18:20:22:24 SD: 8.5480 cents 14:15:17:19:21:23:26:28 SD: 7.6881 cents 18:20:22:24:27:29:33:36 SD: 5.0101 cents 22:24:27:29:33:36:40:44 SD: 4.0265 cents 24:26:29:32:36:39:44:48 SD: 3.3105 cents 30:33:37:40:45:49:55:60 SD: 3.2898 cents 32:35:39:43:48:52:59:64 SD: 2.5645 cents 42:46:51:56:63:68:77:84 SD: 2.0926 cents 54:59:66:72:81:88:99:108 SD: 0.8003 cents 90:98:110:120:135:146:165:180 SD: 0.6239 cents 120:131:147:160:180:195:220:240 SD: 0.5871 cents 144:157:176:192:216:234:264:288 SD: 0.1432 cents 342:373:418:456:513:556:627:684 SD: 0.1265 cents 450:491:550:600:675:731:825:900 SD: 0.0962 cents 504:550:616:672:756:819:924:1008 SD: 0.0818 cents 594:648:726:792:891:965:1089:1188 SD: 0.0641 cents