Scala analysis: xen09-wilson-marwa-08-06
Marwa permutation 6 from Figure 8, Archytas 28/27 8/7 9/8
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 256/243 90.224996 limma, Pythagorean minor second 2: 32/27 294.134997 Pythagorean minor third 3: 4/3 498.044999 perfect fourth 4: 112/81 561.005903 5: 128/81 792.179997 Pythagorean minor sixth 6: 16/9 996.089998 Pythagorean minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 1: 256/243 90.2250 limma, Pythagorean minor second 2: 9/8 203.9100 major whole tone 3: 9/8 203.9100 major whole tone 4: 28/27 62.9609 Archytas' 1/3-tone 5: 8/7 231.1741 septimal whole tone 6: 9/8 203.9100 major whole tone 7: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 1 256/243 90.225 cents limma, Pythagorean minor second 1: 4 9/8 203.910 cents major whole tone 1: 1 8/7 231.174 cents septimal whole tone 2: 1 7/6 266.871 cents septimal minor third 2: 3 32/27 294.135 cents Pythagorean minor third 2: 2 81/64 407.820 cents Pythagorean major third 2: 1 9/7 435.084 cents septimal major third, BP third 3: 1 21/16 470.781 cents narrow fourth 3: 5 4/3 498.045 cents perfect fourth 3: 1 81/56 638.994 cents 4: 1 112/81 561.006 cents 4: 5 3/2 701.955 cents perfect fifth 4: 1 32/21 729.219 cents wide fifth 5: 1 14/9 764.916 cents septimal minor sixth 5: 2 128/81 792.180 cents Pythagorean minor sixth 5: 3 27/16 905.865 cents Pythagorean major sixth 5: 1 12/7 933.129 cents septimal major sixth 6: 1 7/4 968.826 cents harmonic seventh 6: 4 16/9 996.090 cents Pythagorean minor seventh 6: 1 243/128 1109.775 cents Pythagorean major seventh 6: 1 27/14 1137.039 cents septimal major seventh Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.66667 = 11/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 90.2 294.1 498.0 561.0 792.2 996.1 1200.0 90.2 : 203.9 407.8 470.8 702.0 905.9 1109.8 1200.0 294.1 : 203.9 266.9 498.0 702.0 905.9 996.1 1200.0 498.0 : 63.0 294.1 498.0 702.0 792.2 996.1 1200.0 561.0 : 231.2 435.1 639.0 729.2 933.1 1137.0 1200.0 792.2 : 203.9 407.8 498.0 702.0 905.9 968.8 1200.0 996.1 : 203.9 294.1 498.0 702.0 764.9 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 231.1741 cents 54/49, 168.2132 cents 28/27, 62.9609 cents 2: 266.8709 .. 435.0841 cents 54/49, 168.2132 cents 49/48, 35.6968 cents 3: 470.7809 .. 638.9941 cents 54/49, 168.2132 cents 49/48, 35.6968 cents 4: 561.0059 .. 729.2191 cents 54/49, 168.2132 cents 6272/6561,-77.9882 cents 5: 764.9159 .. 933.1291 cents 54/49, 168.2132 cents 49/48, 35.6968 cents 6: 968.8259 .. 1137.0391 cents 54/49, 168.2132 cents 49/48, 35.6968 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 28/27, 62.9609 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 2.722778 Largest / Average step : 1.348516 Largest / Smallest step : 3.671709 Median interval of one step : 9/8, 203.9100 cents, amount: 4 Most common interval of one step : 9/8, 203.9100 cents, amount: 4 Least squares average step : 162.52924 cents, oct.: 1137.70468 cents Scale is not proper Step pattern alph. order: ABBCDBB Step pattern size order : BCCADCC Scale is a Constant Structure, by a margin of 35.69681 cents Scale diversity : 1.447201 Lumma stability : 0.223924 Lumma impropriety factor : 0.064990 Rothenberg efficiency : 0.496599 redundancy: 0.503401 Efficiency x scale size : 3.476190 Number of different interval sizes : 22 = 3.66667 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.66667 = 11/3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 64/63, 27.2641 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Most common triad is 0.0 498.045 701.955 cents, amount: 4 Number of recognisable fifths : 5, average 701.9550 cents Length of longest harmonic part : 2 at degree 4 Formal octave complements present : 1 = 14.2857% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined Limited inverse transpositions with margin 168.2132 cents: 4 -- Rational properties -- Prime limit : 7 Odd number limit : 243 (O: 243 U: 243) Highest odd numerator or denominator: 243 Scale harmonicity : 0.031627 Average absolute harmonicity : 0.220272 Specific harmonicity : 0.188050 Fundamental : 1/243, -7.9248 octaves, 1.0766 Hz. Guide tone : 1792, 10.8074 octaves, 468833.013 Hz. Exponens Consonantiae : 4.354560E+05, 18.73217 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 497.5, average 71.07143 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.06530, average 1.29504 Sum of Tenney's harmonic distance : 19.24233, average 2.74890 Vogel's harmonic complexity : 12.28571 Wille's k value : 121 Wilson's harmonic complexity : 22 Rectangular lattice diameter : 6 Triangular lattice diameter : 5 Lattice compactness : 118.98614, average 4.24950 Lattice compactness (without 2's) : 67.47298, average 2.40975 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 1 .. 8 4.42857 31 1 3: -5 .. 0 -2.71429 19 5 7: 0 .. 1 0.14286 1 1 Average exponent except 2's :-18 / 7 =-2.57143 Average absolute exponent except 2's: 20 / 7 = 2.85714 Scale is weakly epimorphic with val: <7 10 22| Scale is JI-epimorphic with val: <7 11 20| = patent Scale is weakly epimorphic with val: <7 12 18|
FIT/MODE
7: 1 1 1 0 2 1 1 N T3 SD: 48.8286 c. M:-81.2036 c. 8: 1 1 1 1 1 2 1 P M ME S SD: 41.6134 c. M:-59.7750 c. 9: 1 1 2 0 2 1 2 N D3 SD: 35.0987 c. M: 62.7567 c. 11: 1 2 2 0 2 2 2 N T3 SD: 26.6243 c. M:-47.4095 c. 12: 1 2 2 1 2 2 2 P M ME S SD: 15.7242 c. M:-38.9941 c. G.Mixolydian, G.Hyperdorian, M.Hypophrygian, M.Locrian, G.M.Hyperaeolian, Rut biscale descending, Pien chih: China, Makam Lami, Yishtabach: Jewish 13: 1 2 2 1 3 2 2 N T3 SD: 22.5071 c. M:-38.5892 c. 15: 1 3 2 1 3 2 3 N T3 SD: 18.7610 c. M: 36.0900 c. 17: 1 3 3 1 3 3 3 N M DE S SD: 11.0971 c. M: 19.6368 c. Safi al-Din's maqam Abu Salik 24: 2 4 4 1 5 4 4 N SD: 6.8800 c. M: 11.0059 c. 36: 3 6 6 2 7 6 6 N SD: 5.8829 c. M:-9.7750 c. 41: 3 7 7 2 8 7 7 N SD: 2.2984 c. M: 4.9083 c. 53: 4 9 9 3 10 9 9 N SD: 1.9114 c. M:-5.0318 c. 70: 5 12 12 4 13 12 12 N SD: 3.0922 c. M:-4.7084 c. 77: 6 13 13 4 15 13 13 N SD: 1.8397 c. M:-3.2815 c. 94: 7 16 16 5 18 16 16 N SD: 0.5509 c. M: 0.8633 c. 171: 13 29 29 9 33 29 29 N SD: 0.5821 c. M:-1.0031 c. 212: 16 36 36 11 41 36 36 N SD: 0.3049 c. M: 0.6285 c. 265: 20 45 45 14 51 45 45 N SD: 0.2698 c. M:-0.5035 c. 306: 23 52 52 16 59 52 52 N SD: 0.0853 c. M: 0.2216 c. 571: 43 97 97 30 110 97 97 N SD: 0.0911 c. M:-0.1428 c. 665: 50 113 113 35 128 113 113 N SD: 0.0745 c. M:-0.1971 c. 706: 53 120 120 37 136 120 120 N SD: 0.0870 c. M: 0.1400 c. 877: 66 149 149 46 169 149 149 N SD: 0.0465 c. M:-0.0829 c. 971: 73 165 165 51 187 165 165 N SD: 0.0251 c. M:-0.0652 c. 1183: 89 201 201 62 228 201 201 N SD: 0.0376 c. M: 0.0592 c. 1277: 96 217 217 67 246 217 217 N SD: 0.0077 c. M: 0.0136 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x 4 S SD: 45.1125 cents 3 x x 4 x 5 x 6 S SD: 30.7262 cents 4 x 5 x x 6:7:8 S SD: 32.9591 cents 5 x 6 x 7:8:9:10 S SD: 8.6025 cents 6 x 7:8 x 9:11:12 SD: 21.6535 cents 7 x 8:9:10:11:12:14 S SD: 20.5320 cents 8 x 9 x 11:13:14:16 SD: 21.2746 cents 9:10:11:12 x 14:16:18 S SD: 18.3169 cents 10:11:12:13:14:16:18:20 S SD: 13.8234 cents 11:12:13 x 15:17:20:22 SD: 14.1928 cents 12:13:14:16:17:19:21:24 SD: 10.6896 cents 14:15:17:19 x 22:25:28 SD: 10.1509 cents 15:16:18:20:21:24:27:30 S SD: 6.8699 cents 16:17:19:21:22:25:28:32 SD: 6.6872 cents 18:19:21:24:25:28:32:36 SD: 5.6380 cents 21:22:25:28:29:33:37:42 SD: 3.1724 cents 33:35:39:44:46:52:59:66 SD: 3.1172 cents 36:38:43:48:50:57:64:72 SD: 2.3203 cents 50:53:59:67:69:79:89:100 SD: 2.3123 cents 53:56:63:71:73:84:94:106 SD: 2.0513 cents 54:57:64:72:75:85:96:108 SD: 1.5439 cents 55:58:65:73:76:87:98:110 SD: 1.4921 cents 60:63:71:80:83:95:107:120 SD: 1.2910 cents 76:80:90:101:105:120:135:152 SD: 0.9333 cents 108:114:128:144:149:171:192:216 SD: 0.8782 cents 112:118:133:149:155:177:199:224 SD: 0.7778 cents 129:136:153:172:178:204:229:258 SD: 0.7004 cents 131:138:155:175:181:207:233:262 SD: 0.6648 cents 150:158:178:200:207:237:267:300 SD: 0.6560 cents 152:160:180:203:210:240:270:304 SD: 0.6101 cents 162:171:192:216:224:256:288:324 SD: 0.4826 cents 167:176:198:223:231:264:297:334 SD: 0.4239 cents 183:193:217:244:253:289:325:366 SD: 0.4233 cents 207:218:245:276:286:327:368:414 SD: 0.4051 cents 222:234:263:296:307:351:395:444 SD: 0.2991 cents 243:256:288:324:336:384:432:486 SD: 0.0000 cents