Scala analysis: portsmouth
Portsmouth, a 2.3.7.11 subgroup scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 22/21 80.537035 undecimal minor semitone 2: 8/7 231.174094 septimal whole tone 3: 7/6 266.870906 septimal minor third 4: 9/7 435.084095 septimal major third, BP third 5: 4/3 498.044999 perfect fourth 6: 11/8 551.317942 undecimal semi-augmented fourth 7: 3/2 701.955001 perfect fifth 8: 11/7 782.492036 undecimal augmented fifth 9: 12/7 933.129094 septimal major sixth 10: 7/4 968.825906 harmonic seventh 11: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-tone 1: 22/21 80.5370 undecimal minor semitone 2: 12/11 150.6371 undecimal neutral second, 3/4-tone 3: 49/48 35.6968 slendro diesis, septimal 1/6-tone 4: 54/49 168.2132 Zalzal's mujannab 5: 28/27 62.9609 Archytas' 1/3-tone 6: 33/32 53.2729 undecimal comma, al-Farabi's 1/4-tone 7: 12/11 150.6371 undecimal neutral second, 3/4-tone 8: 22/21 80.5370 undecimal minor semitone 9: 12/11 150.6371 undecimal neutral second, 3/4-tone 10: 49/48 35.6968 slendro diesis, septimal 1/6-tone 11: 22/21 80.5370 undecimal minor semitone 12: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 49/48 35.697 cents slendro diesis, septimal 1/6-tone 1: 1 33/32 53.273 cents undecimal comma, al-Farabi's 1/4-tone 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 3 22/21 80.537 cents undecimal minor semitone 1: 4 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 54/49 168.213 cents Zalzal's mujannab 2: 2 77/72 116.234 cents undecimal secor 2: 2 49/44 186.334 cents undecimal minor whole tone 2: 2 9/8 203.910 cents major whole tone 2: 6 8/7 231.174 cents septimal whole tone 3: 6 7/6 266.871 cents septimal minor third 3: 2 33/28 284.447 cents undecimal minor third 3: 1 176/147 311.711 cents 3: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 3: 2 96/77 381.811 cents 4: 1 77/64 320.144 cents Keemun minor third 4: 3 11/9 347.408 cents undecimal neutral third 4: 4 14/11 417.508 cents undecimal diminished fourth or major third 4: 3 9/7 435.084 cents septimal major third, BP third 4: 1 64/49 462.348 cents 2 septatones or septatonic major third 5: 3 21/16 470.781 cents narrow fourth 5: 7 4/3 498.045 cents perfect fourth 5: 1 66/49 515.621 cents 5: 1 108/77 585.721 cents 6: 2 49/36 533.742 cents Arabic lute acute fourth 6: 3 11/8 551.318 cents undecimal semi-augmented fourth 6: 1 88/63 578.582 cents 6: 1 63/44 621.418 cents 6: 3 16/11 648.682 cents undecimal semi-diminished fifth 6: 2 72/49 666.258 cents Arabic lute grave fifth 7: 1 77/54 614.279 cents 7: 1 49/33 684.379 cents 7: 7 3/2 701.955 cents perfect fifth 7: 3 32/21 729.219 cents wide fifth 8: 1 49/32 737.652 cents 8: 3 14/9 764.916 cents septimal minor sixth 8: 4 11/7 782.492 cents undecimal augmented fifth 8: 3 18/11 852.592 cents undecimal neutral sixth 8: 1 128/77 879.856 cents 9: 2 77/48 818.189 cents 9: 1 44/27 845.453 cents neutral sixth 9: 1 147/88 888.289 cents 9: 2 56/33 915.553 cents 9: 6 12/7 933.129 cents septimal major sixth 10: 6 7/4 968.826 cents harmonic seventh 10: 2 16/9 996.090 cents Pythagorean minor seventh 10: 2 88/49 1013.666 cents undecimal minor seventh 10: 2 144/77 1083.766 cents 11: 1 49/27 1031.787 cents 11: 4 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 11: 3 21/11 1119.463 cents undecimal major seventh 11: 1 27/14 1137.039 cents septimal major seventh 11: 1 64/33 1146.727 cents 33rd subharmonic 11: 2 96/49 1164.303 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.90909 = 54/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 80.5 231.2 266.9 435.1 498.0 551.3 702.0 782.5 933.1 968.8 1049.4 1200.0 80.5 : 150.6 186.3 354.5 417.5 470.8 621.4 702.0 852.6 888.3 968.8 1119.5 1200.0 231.2 : 35.7 203.9 266.9 320.1 470.8 551.3 702.0 737.7 818.2 968.8 1049.4 1200.0 266.9 : 168.2 231.2 284.4 435.1 515.6 666.3 702.0 782.5 933.1 1013.7 1164.3 1200.0 435.1 : 63.0 116.2 266.9 347.4 498.0 533.7 614.3 764.9 845.5 996.1 1031.8 1200.0 498.0 : 53.3 203.9 284.4 435.1 470.8 551.3 702.0 782.5 933.1 968.8 1137.0 1200.0 551.3 : 150.6 231.2 381.8 417.5 498.0 648.7 729.2 879.9 915.6 1083.8 1146.7 1200.0 702.0 : 80.5 231.2 266.9 347.4 498.0 578.6 729.2 764.9 933.1 996.1 1049.4 1200.0 782.5 : 150.6 186.3 266.9 417.5 498.0 648.7 684.4 852.6 915.6 968.8 1119.5 1200.0 933.1 : 35.7 116.2 266.9 347.4 498.0 533.7 702.0 764.9 818.2 968.8 1049.4 1200.0 968.8 : 80.5 231.2 311.7 462.3 498.0 666.3 729.2 782.5 933.1 1013.7 1164.3 1200.0 1049.4: 150.6 231.2 381.8 417.5 585.7 648.7 702.0 852.6 933.1 1083.8 1119.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 35.6968 .. 168.2132 cents 2592/2401, 132.5164 cents 49/48, 35.6968 cents 2: 116.2338 .. 231.1741 cents 576/539, 114.9402 cents 3773/3888,-51.9793 cents 3: 266.8709 .. 381.8112 cents 576/539, 114.9402 cents 49/48, 35.6968 cents 4: 320.1438 .. 462.3482 cents 4096/3773, 142.2043 cents 5929/6144,-61.6673 cents 5: 470.7809 .. 585.7212 cents 576/539, 114.9402 cents 1029/1024, 8.4327 cents 6: 533.7418 .. 666.2582 cents 2592/2401, 132.5164 cents 3773/3888,-51.9793 cents 7: 614.2788 .. 729.2191 cents 576/539, 114.9402 cents 3773/3888,-51.9793 cents 8: 737.6518 .. 879.8562 cents 4096/3773, 142.2043 cents 1029/1024, 8.4327 cents 9: 818.1888 .. 933.1291 cents 576/539, 114.9402 cents 5929/6144,-61.6673 cents 10: 968.8259 .. 1083.7662 cents 576/539, 114.9402 cents 49/48, 35.6968 cents 11: 1031.7868 .. 1164.3032 cents 2592/2401, 132.5164 cents 3773/3888,-51.9793 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 49/48, 35.6968 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 54/49, 168.2132 cents Average / Smallest step : 2.801371 Largest / Average step : 1.682132 Largest / Smallest step : 4.712275 Median interval of one step : 22/21, 80.5370 cents, amount: 3 Most common interval of one step : 12/11, 150.6371 cents, amount: 4 Least squares average step : 98.59231 cents, oct.: 1183.10772 cents Scale is not proper Step pattern alph. order: ABCDEFBABCAB Step pattern size order : DEAFCBEDEADE Scale is a Constant Structure, by a margin of 7.13912 cents Scale diversity : 1.548399 Lumma stability : 0.133044 Lumma impropriety factor : 0.276043 Rothenberg efficiency : 0.307284 redundancy: 0.692716 Efficiency x scale size : 3.687410 Number of different interval sizes : 54 = 4.90909 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 4.90909 = 54/11 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 243/242, 7.1391 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 7 Number of recognisable fifths : 7, average 701.9550 cents Scale contains a complete diamond : 1 3 7 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 7 = 58.3333% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined -- Rational properties -- Prime limit : 11 Odd number limit : 147 (O: 147 U: 147) Highest odd numerator or denominator: 21 Scale harmonicity : 0.018956 Average absolute harmonicity : 0.167123 Specific harmonicity : 0.102037 Fundamental : 1/168, -7.3923 octaves, 1.5573 Hz. Guide tone : 5544, 12.4367 octaves, 1450452.134 Hz. Exponens Consonantiae : 9.313920E+05, 19.82903 octaves Euler's gradus suavitatis : 35 Sum of Mann's harmonic distance : 93.0, average 7.75000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.73527, average 0.81127 Sum of Tenney's harmonic distance : 19.01574, average 1.58464 Vogel's harmonic complexity : 15.00000 Wille's k value : 115 Wilson's harmonic complexity : 34 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 217.87215, average 2.79323 Lattice compactness (without 2's) : 129.13110, average 1.65553 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 3 0.08333 17 1 3: -1 .. 2 0.00000 8 2 7: -1 .. 1 -0.25000 7 5 11: 0 .. 1 0.33333 4 4 Average exponent except 2's : 1 / 12 = 0.08333 Average absolute exponent except 2's: 19 / 12 = 1.58333 Scale is JI-epimorphic with val: <12 19 34 42| = patent
FIT/MODE
12: 0 2 0 2 0 1 1 1 2 0 1 2 N T3 SD: 65.1140 c. M: 101.9550 c. 13: 1 1 1 1 1 1 1 1 2 0 1 2 N D3 SD: 37.0631 c. M: 65.8533 c. 14: 1 2 0 2 1 0 2 1 2 0 1 2 N SD: 18.3957 c. M: 37.0322 c. 15: 1 2 0 2 1 1 2 1 2 0 1 2 N SD: 18.1473 c. M: 35.0841 c. 17: 1 2 1 2 1 1 2 1 2 1 1 2 P M ME SD: 12.2514 c. M:-19.4094 c. 22: 1 3 1 3 1 1 3 1 3 1 1 3 N M DE SD: 12.0559 c. M: 25.9916 c. 26: 2 3 1 3 2 1 3 2 3 1 2 3 N SD: 9.4619 c. M: 19.6995 c. 27: 2 3 1 4 1 1 4 2 3 1 2 3 N SD: 10.8581 c. M: 17.9846 c. 31: 2 4 1 4 2 1 4 2 4 1 2 4 N SD: 5.4768 c. M: 9.3825 c. 41: 3 5 1 6 2 2 5 3 5 1 3 5 N SD: 4.2008 c. M:-7.7519 c. 57: 4 7 2 8 3 2 7 4 7 2 4 7 N SD: 4.9918 c. M:-7.2182 c. 58: 4 7 2 8 3 3 7 4 7 2 4 7 N SD: 3.4780 c. M:-7.3027 c. 63: 4 8 2 9 3 3 8 4 8 2 4 8 N SD: 2.3074 c. M: 4.3466 c. 72: 5 9 2 10 4 3 9 5 9 2 5 9 N SD: 1.6017 c. M:-2.7963 c. 104: 7 13 3 15 5 5 13 7 13 3 7 13 N SD: 1.6997 c. M:-3.3774 c. 118: 8 15 3 17 6 5 15 8 15 3 8 15 N SD: 1.8548 c. M:-2.7242 c. 130: 9 16 4 18 7 6 16 9 16 4 9 16 N SD: 1.5700 c. M:-2.9448 c. 135: 9 17 4 19 7 6 17 9 17 4 9 17 N SD: 0.3007 c. M: 0.5370 c. 342: 23 43 10 48 18 15 43 23 43 10 23 43 N SD: 0.2537 c. M: 0.4407 c. 477: 32 60 14 67 25 21 60 32 60 14 32 60 N SD: 0.2052 c. M: 0.3745 c. 535: 36 67 16 75 28 24 67 36 67 16 36 67 N SD: 0.2138 c. M:-0.4578 c. 566: 38 71 17 79 30 25 71 38 71 17 38 71 N SD: 0.1994 c. M: 0.4551 c. 612: 41 77 18 86 32 27 77 41 77 18 41 77 N SD: 0.1997 c. M: 0.3433 c. 670: 45 84 20 94 35 30 84 45 84 20 45 84 N SD: 0.1504 c. M:-0.3238 c. 701: 47 88 21 98 37 31 88 47 88 21 47 88 N SD: 0.1356 c. M: 0.2767 c. 805: 54 101 24 113 42 36 101 54 101 24 54 101 N SD: 0.1274 c. M:-0.2349 c. 836: 56 105 25 117 44 37 105 56 105 25 56 105 N SD: 0.1111 c. M: 0.1954 c. 877: 59 110 26 123 46 39 110 59 110 26 59 110 N SD: 0.0965 c. M:-0.1927 c. 1012: 68 127 30 142 53 45 127 68 127 30 68 127 N SD: 0.0673 c. M:-0.1167 c. 1147: 77 144 34 161 60 51 144 77 144 34 77 144 N SD: 0.0642 c. M:-0.1382 c. 1371: 92 172 41 192 72 61 172 92 172 41 92 172 N SD: 0.0713 c. M:-0.1044 c. 1506: 101 189 45 211 79 67 189 101 189 45 101 189 N SD: 0.0589 c. M:-0.0984 c. 1578: 106 198 47 221 83 70 198 106 198 47 106 198 N SD: 0.0511 c. M: 0.1031 c. 1641: 110 206 49 230 86 73 206 110 206 49 110 206 N SD: 0.0593 c. M: 0.0983 c. 1713: 115 215 51 240 90 76 215 115 215 51 115 215 N SD: 0.0256 c. M: 0.0578 c. 1848: 124 232 55 259 97 82 232 124 232 55 124 232 N SD: 0.0137 c. M: 0.0245 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x x x x 4 S SD: 0.0000 cents 3 x x x x 4 x x x 5 x x 6 S SD: 16.2568 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 12.1926 cents 5 x x 6 x x 7 x 8 x x 9:10 S SD: 14.6066 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 8.1284 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 9.9770 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 11.1829 cents 9 x 10:11 x 12 x x 14:15:16:17:18 S SD: 15.2923 cents 10 x 11:12:13 x 14:15:16:17 x 18:20 S SD: 11.2700 cents 11:12 x 13:14 x 15 x 17:19 x 20:22 SD: 10.5609 cents 12:13 x 14:15:16:17:18:19 x 21:22:24 SD: 9.2674 cents 13:14:15 x 17 x 18 x 20:22:23:24:26 SD: 8.5433 cents 14:15:16 x 18 x 19:21:22:24:25:26:28 SD: 6.1222 cents 15:16:17:18:19:20:21:23:24 x 26:28:30 SD: 8.5623 cents 16:17:18:19 x 21:22:24:25:27:28:29:32 SD: 5.9293 cents 17:18:19:20:22:23 x 26:27:29:30:31:34 SD: 6.1952 cents 18:19 x 21:23:24:25:27:28:31:32:33:36 SD: 3.7533 cents 19:20 x 22:24:25:26:29:30 x 33:35:38 SD: 5.4649 cents 20:21:23 x 26:27:28:30:31:34:35:37:40 SD: 4.9407 cents 21:22:24:25:27:28:29:32:33:36:37:39:42 SD: 4.2974 cents 24:25:27:28:31:32:33:36:38:41:42:44:48 SD: 2.7783 cents 25:26 x 29:32:33:34:38:39:43:44:46:50 SD: 3.8958 cents 26:27:30 x 33:35:36:39:41:45:46:48:52 SD: 4.3017 cents 27:28:31:32:35:36:37:41:42:46:47:50:54 SD: 4.2605 cents 28:29:32:33:36:37:39:42:44:48:49:51:56 SD: 3.2995 cents 32:34 x 37:41:43:44:48:50:55:56:59:64 SD: 3.2383 cents 35:37:40:41:45:47:48:53:55:60:61:64:70 SD: 2.3673 cents 40:42:46:47:51:53:55:60:63:69:70:73:80 SD: 2.3649 cents 42:44:48:49:54:56:58:63:66:72:74:77:84 SD: 1.1598 cents 77:81:88:90:99:103:106:116:121:132:135:141:154 SD: 1.0780 cents 84:88:96:98:108:112:116:126:132:144:147:154:168 SD: 0.6232 cents 120:126:137:140:154:160:165:180:189:206:210:220:240 SD: 0.5905 cents 126:132:144:147:162:168:173:189:198:216:221:231:252 SD: 0.3875 cents 168:176:192:196:216:224:231:252:264:288:294:308:336 SD: 0.0000 cents