Scala analysis: xen09-wilson-marwa-08-01
Marwa permutation 1 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: 28/27 62.960904 Archytas' 1/3-tone 2: 7/6 266.870906 septimal minor third 3: 21/16 470.780907 narrow fourth 4: 112/81 561.005903 5: 14/9 764.915905 septimal minor sixth 6: 7/4 968.825906 harmonic seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 28/27 62.9609 Archytas' 1/3-tone 2: 9/8 203.9100 major whole tone 3: 9/8 203.9100 major whole tone 4: 256/243 90.2250 limma, Pythagorean minor second 5: 9/8 203.9100 major whole tone 6: 9/8 203.9100 major whole tone 7: 8/7 231.1741 septimal 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 : 63.0 266.9 470.8 561.0 764.9 968.8 1200.0 63.0 : 203.9 407.8 498.0 702.0 905.9 1137.0 1200.0 266.9 : 203.9 294.1 498.0 702.0 933.1 996.1 1200.0 470.8 : 90.2 294.1 498.0 729.2 792.2 996.1 1200.0 561.0 : 203.9 407.8 639.0 702.0 905.9 1109.8 1200.0 764.9 : 203.9 435.1 498.0 702.0 905.9 996.1 1200.0 968.8 : 231.2 294.1 498.0 702.0 792.2 996.1 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 : 159.21860 cents, oct.: 1114.53020 cents Scale is not proper Step pattern alph. order: ABBCBBD Step pattern size order : ACCBCCD Scale is sum-free (all different intervals) 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 : 1 at degree 0 Length of longest subharmonic part : 2 at degree 5 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 140.9491 cents: 4 -- Rational properties -- Prime limit : 7 Odd number limit : 243 (O: 243 U: 243) Highest odd numerator or denominator: 81 Scale harmonicity : 0.031627 Average absolute harmonicity : 0.194514 Specific harmonicity : 0.178557 Fundamental : 1/1296, -10.3399 octaves, 0.2019 Hz. Guide tone : 336, 8.3923 octaves, 87906.190 Hz. Exponens Consonantiae : 4.354560E+05, 18.73217 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 167.5, average 23.92857 Mersenne's string divisions : 352301235 Sum of van Prooijen's expressibility: 7.30651, average 1.04379 Sum of Tenney's harmonic distance : 14.83437, average 2.11920 Vogel's harmonic complexity : 18.28571 Wille's k value : 850 Wilson's harmonic complexity : 22 Rectangular lattice diameter : 6 Triangular lattice diameter : 5 Lattice compactness : 107.08303, average 3.82439 Lattice compactness (without 2's) : 61.69976, average 2.20356 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 4 0.14286 15 1 3: -4 .. 1 -1.28571 11 7: 0 .. 1 0.85714 6 6 Average exponent except 2's :-3 / 7 =-0.42857 Average absolute exponent except 2's: 17 / 7 = 2.42857 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: 0 1 1 1 1 1 2 N T3 SD: 84.8247 c. M: 127.9238 c. 8: 0 2 1 1 1 1 2 P D3 S SD: 41.3582 c. M: 68.8259 c. 10: 1 1 2 1 1 2 2 P D3 S SD: 33.1153 c. M:-57.0391 c. 11: 0 2 2 1 2 2 2 N T3 SD: 33.6612 c. M: 62.9609 c. 13: 1 2 2 1 2 2 3 N T3 SD: 23.5789 c. M: 45.7490 c. 15: 1 2 3 1 3 2 3 N T3 SD: 18.5440 c. M:-35.0841 c. 17: 1 3 3 1 3 3 3 N M DE S SD: 13.9714 c. M:-23.3367 c. Safi al-Din's maqam Abu Salik 21: 1 4 3 2 3 4 4 N SD: 12.9665 c. M: 22.0588 c. 22: 1 4 4 1 4 4 4 N M DE S SD: 11.4801 c. M:-20.1282 c. 26: 1 5 4 2 5 4 5 N SD: 11.3920 c. M:-19.6995 c. 27: 1 5 5 2 4 5 5 N SD: 12.6483 c. M: 18.5165 c. 28: 1 5 5 2 5 5 5 N T3 SD: 10.9660 c. M: 20.1038 c. 30: 2 5 5 2 5 5 6 N SD: 9.6419 c. M:-17.0391 c. 32: 2 5 6 2 5 6 6 N SD: 10.0457 c. M:-16.7191 c. 33: 2 5 6 2 6 6 6 N SD: 9.7348 c. M: 15.5514 c. 35: 2 6 6 2 6 6 7 N SD: 8.5937 c. M: 12.4345 c. 36: 2 6 6 3 6 6 7 N SD: 3.1729 c. M:-5.6608 c. 41: 2 7 7 3 7 7 8 N SD: 3.5084 c. M: 4.9083 c. 58: 3 10 10 4 10 10 11 N SD: 2.6706 c. M:-5.0812 c. 77: 4 13 13 6 13 13 15 N SD: 1.8145 c. M: 3.2484 c. 94: 5 16 16 7 16 16 18 N SD: 1.0793 c. M:-1.5595 c. 135: 7 23 23 10 23 23 26 N SD: 0.5257 c. M: 1.0059 c. 171: 9 29 29 13 29 29 33 N SD: 0.3315 c. M: 0.6055 c. 265: 14 45 45 20 45 45 51 N SD: 0.3266 c. M:-0.5035 c. 306: 16 52 52 23 52 52 59 N SD: 0.1920 c. M: 0.2216 c. 400: 21 68 68 30 68 68 77 N SD: 0.1217 c. M:-0.2191 c. 571: 30 97 97 43 97 97 110 N SD: 0.0605 c. M:-0.1149 c. 706: 37 120 120 53 120 120 136 N SD: 0.0520 c. M: 0.0994 c. 877: 46 149 149 66 149 149 169 N SD: 0.0484 c. M: 0.0854 c. 971: 51 165 165 73 165 165 187 N SD: 0.0644 c. M:-0.0739 c. 1106: 58 188 188 83 188 188 213 N SD: 0.0570 c. M:-0.1052 c. 1277: 67 217 217 96 217 217 246 N SD: 0.0052 c. M:-0.0100 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: 31.4805 cents 3 x x 4 x x 5:6 S SD: 29.5861 cents 4 x x 5 x 6:7:8 S SD: 26.3377 cents 5 x 6 x 7:8:9:10 S SD: 17.4335 cents 6 x 7:8 x 9:11:12 SD: 21.1600 cents 7 x 8:9:10:11:12:14 S SD: 14.2614 cents 8 x 9 x 11:12:14:16 SD: 17.9131 cents 9 x 11:12 x 14:16:18 SD: 17.8582 cents 10 x 12:13:14:16:18:20 S SD: 14.7880 cents 12:13:14:16:17:19:21:24 SD: 13.6748 cents 13:14:15:17:18:20:23:26 SD: 10.5026 cents 16:17:19:21:22:25:28:32 SD: 7.6342 cents 18:19:21:24:25:28:32:36 SD: 7.1215 cents 19:20:22:25:26:30:33:38 SD: 6.4195 cents 20:21:23:26:28:31:35:40 SD: 6.1584 cents 23:24:27:30:32:36:40:46 SD: 3.7589 cents 29:30:34:38:40:45:51:58 SD: 2.0580 cents 52:54:61:68:72:81:91:104 SD: 1.7338 cents 55:57:64:72:76:86:96:110 SD: 1.7132 cents 60:62:70:79:83:93:105:120 SD: 1.4808 cents 76:79:89:100:105:118:133:152 SD: 1.3562 cents 79:82:92:104:109:123:138:158 SD: 1.1564 cents 83:86:97:109:115:129:145:166 SD: 0.8534 cents 108:112:126:142:149:168:189:216 SD: 0.7038 cents 131:136:153:172:181:204:229:262 SD: 0.5773 cents 144:149:168:189:199:224:252:288 SD: 0.5696 cents 157:163:183:206:217:244:275:314 SD: 0.4963 cents 185:192:216:243:256:288:324:370 SD: 0.4676 cents 191:198:223:251:264:297:334:382 SD: 0.4348 cents 211:219:246:277:292:328:369:422 SD: 0.4181 cents 240:249:280:315:332:373:420:480 SD: 0.2705 cents 295:306:344:387:408:459:516:590 SD: 0.2320 cents 324:336:378:425:448:504:567:648 SD: 0.1454 cents 432:448:504:567:597:672:756:864 SD: 0.1381 cents 515:534:601:676:712:801:901:1030 SD: 0.1160 cents