Scala analysis: xen09-wilson-marwa-05-01
Marwa permutation 1 from Figure 5, Pythagoras 256/243 9/8 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: 1024/729 588.269995 Pythagorean diminished fifth 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: 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: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 256/243 90.225 cents limma, Pythagorean minor second 1: 5 9/8 203.910 cents major whole tone 2: 4 32/27 294.135 cents Pythagorean minor third 2: 3 81/64 407.820 cents Pythagorean major third 3: 6 4/3 498.045 cents perfect fourth 3: 1 729/512 611.730 cents Pythagorean tritone 4: 1 1024/729 588.270 cents Pythagorean diminished fifth 4: 6 3/2 701.955 cents perfect fifth 5: 3 128/81 792.180 cents Pythagorean minor sixth 5: 4 27/16 905.865 cents Pythagorean major sixth 6: 5 16/9 996.090 cents Pythagorean minor seventh 6: 2 243/128 1109.775 cents Pythagorean major seventh Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 90.2 294.1 498.0 588.3 792.2 996.1 1200.0 90.2 : 203.9 407.8 498.0 702.0 905.9 1109.8 1200.0 294.1 : 203.9 294.1 498.0 702.0 905.9 996.1 1200.0 498.0 : 90.2 294.1 498.0 702.0 792.2 996.1 1200.0 588.3 : 203.9 407.8 611.7 702.0 905.9 1109.8 1200.0 792.2 : 203.9 407.8 498.0 702.0 905.9 996.1 1200.0 996.1 : 203.9 294.1 498.0 702.0 792.2 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.2250 .. 203.9100 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 2: 294.1350 .. 407.8200 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 3: 498.0450 .. 611.7300 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 4: 588.2700 .. 701.9550 cents 2187/2048, 113.6850 cents 524288/531441,-23.4600 cents 5: 792.1800 .. 905.8650 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 6: 996.0900 .. 1109.7750 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 256/243, 90.2250 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.900012 Largest / Average step : 1.189475 Largest / Smallest step : 2.260017 Median interval of one step : 9/8, 203.9100 cents, amount: 5 Most common interval of one step : 9/8, 203.9100 cents, amount: 5 Least squares average step : 163.30821 cents, oct.: 1143.15750 cents Scale is not proper Scale has Myhill's property chromas: 2187/2048, 113.6850 cents and 531441/524288, 23.4600 cents, ratio: 4.845906 generators: 3 of 498.04500 cents and 701.95500 cents ET pair of linear temperament : 12&41 Scale is distributional even Scale is a mode of a 665-tone equal temperament with octave 2/1 degrees: 50 163 276 326 439 552 665 generators: 276 and 389 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBABBB Step pattern size order : SLLSLLL Scale is a Constant Structure, by a margin of 23.46001 cents Ratio Whole / Half tone : 2.260017 Scale diversity : 1.288369 Lumma stability : 0.451125 Lumma impropriety factor : 0.019550 Rothenberg efficiency : 0.761905 redundancy: 0.238095 Efficiency x scale size : 5.333333 Number of different interval sizes : 12 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 531441/524288, 23.4600 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 6 Scale is a chain of 3 triads 0.0 498.045 996.090 cents Most common triad is 0.0 498.045 701.955 cents, amount: 5 Number of recognisable fifths : 6, average 701.9550 cents Scale is Mixolydian octave species of abstract tetrachord Scale is Lydian octave species of abstract tetrachord Scale is Phrygian octave species of abstract tetrachord Scale contains two identical conjunct tetrachords Best major thirds form a closed circle Best minor thirds form a closed circle Scale is a complete genus musicum : 2^m 3^6 Formal octave complements present : 1 = 14.2857% Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval class 3 Scale is n-1 differentially coherent in interval class 4 Limited inverse transpositions : 4 Inversional symmetry on degrees : 2 Inversional symmetry on intervals : 5-6 -- Rational properties -- Prime limit : 3 Odd number limit : 729 (O: 729 U: 729) Highest odd numerator or denominator: 729 Scale harmonicity : 0.038462 Average absolute harmonicity : 0.220041 Specific harmonicity : 0.196118 Fundamental : 1/729, -9.5098 octaves, 0.3589 Hz. Guide tone : 1024, 10.0000 octaves, 267904.579 Hz. Exponens Consonantiae : 7.464960E+05, 19.50978 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 1277.5, average 182.50000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.01955, average 1.43136 Sum of Tenney's harmonic distance : 21.15766, average 3.02252 Vogel's harmonic complexity : 14.28571 Wille's k value : 364 Wilson's harmonic complexity : 18 Rectangular lattice diameter : 6 Triangular lattice diameter : 6 Lattice compactness : 143.82407, average 5.13657 Lattice compactness (without 2's) : 77.00000, average 2.75000 Number of different primes : 2 Prime exponents' range, average, count, tones@limit: 2: 1 .. 10 5.28571 37 1 3: -6 .. 0 -3.00000 21 6 Average exponent except 2's :-21 / 7 =-3.00000 Average absolute exponent except 2's: 21 / 7 = 3.00000 Scale is weakly epimorphic with val: <7 10| Scale is JI-epimorphic with val: <7 11| = patent Scale is weakly epimorphic with val: <7 12|
FIT/MODE
7: 0 1 1 1 1 1 2 N T3 SD: 109.1497 c. M: 155.1879 c. 8: 1 1 1 1 1 2 1 P M ME S SD: 39.1678 c. M:-59.7750 c. 9: 1 1 2 0 2 1 2 N D3 SD: 39.4166 c. M: 62.7567 c. 10: 1 1 2 1 2 1 2 P M ME S SD: 33.5295 c. M: 54.1350 c. 12: 1 2 2 1 2 2 2 P M ME S SD: 7.0489 c. M:-11.7300 c. G.Mixolydian, G.Hyperdorian, M.Hypophrygian, M.Locrian, G.M.Hyperaeolian, Rut biscale descending, Pien chih: China, Makam Lami, Yishtabach: Jewish 29: 2 5 5 2 5 5 5 N M DE S SD: 5.3841 c. M: 8.9596 c. 41: 3 7 7 3 7 7 7 N M DE S SD: 1.7452 c. M: 2.9041 c. 53: 4 9 9 4 9 9 9 N M DE S SD: 0.2459 c. M:-0.4093 c. 200: 15 34 34 15 34 34 34 N M DE S SD: 0.1622 c. M: 0.2700 c. 253: 19 43 43 19 43 43 43 N M DE S SD: 0.0767 c. M: 0.1277 c. 306: 23 52 52 23 52 52 52 N M DE S SD: 0.0209 c. M: 0.0347 c. 359: 27 61 61 27 61 61 61 N M DE S SD: 0.0185 c. M:-0.0308 c. 665: 50 113 113 50 113 113 113 N M DE S SD: 0.0004 c. M:-0.0007 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: 7.5385 cents 6 x 7:8 x 9:11:12 SD: 21.6535 cents 7 x 8:9:10:11:12:14 S SD: 18.8854 cents 8 x 9 x 11:13:14:16 SD: 22.4382 cents 9:10:11:12:13:14:16:18 S SD: 17.1522 cents 10:11:12:13:14:16:18:20 S SD: 13.5027 cents 11:12:13:15 x 17:20:22 SD: 15.0801 cents 12:13:14:16:17:19:21:24 SD: 9.0942 cents 15:16:18:20:21:24:27:30 S SD: 6.1995 cents 17:18:20:23:24:27:30:34 SD: 4.9361 cents 22:23:26:29:31:35:39:44 SD: 3.9930 cents 32:34:38:43:45:51:57:64 SD: 3.6200 cents 33:35:39:44:46:52:59:66 SD: 3.0516 cents 36:38:43:48:51:57:64:72 SD: 2.9323 cents 37:39:44:49:52:58:66:74 SD: 2.8647 cents 39:41:46:52:55:62:69:78 SD: 2.5048 cents 42:44:50:56:59:66:75:84 SD: 2.5017 cents 50:53:59:67:70:79:89:100 SD: 2.4055 cents 53:56:63:71:74:84:94:106 SD: 2.3465 cents 54:57:64:72:76:85:96:108 SD: 1.1844 cents 76:80:90:101:107:120:135:152 SD: 1.0735 cents 91:96:108:121:128:144:162:182 SD: 1.0194 cents 93:98:110:124:131:147:165:186 SD: 0.9927 cents 96:101:114:128:135:152:171:192 SD: 0.9418 cents 108:114:128:144:152:171:192:216 SD: 0.8358 cents 114:120:135:152:160:180:203:228 SD: 0.5751 cents 129:136:153:172:181:204:229:258 SD: 0.5496 cents 168:177:199:224:236:265:299:336 SD: 0.5453 cents 171:180:203:228:240:270:304:342 SD: 0.5380 cents 183:193:217:244:257:289:325:366 SD: 0.4248 cents 207:218:245:276:291:327:368:414 SD: 0.4086 cents 210:221:249:280:295:332:373:420 SD: 0.3772 cents 222:234:263:296:312:351:395:444 SD: 0.3250 cents 243:256:288:324:341:384:432:486 SD: 0.2416 cents 297:313:352:396:417:469:528:594 SD: 0.2250 cents 319:336:378:425:448:504:567:638 SD: 0.2221 cents 336:354:398:448:472:531:597:672 SD: 0.1975 cents 378:398:448:504:531:597:672:756 SD: 0.1960 cents 393:414:466:524:552:621:699:786 SD: 0.1688 cents 432:455:512:576:607:683:768:864 SD: 0.1547 cents 486:512:576:648:683:768:864:972 SD: 0.1207 cents 600:632:711:800:843:948:1067:1200 SD: 0.1181 cents