Scala analysis: xen09-wilson-marwa-04-02
Marwa permutation 2 from Figure 4, Didymus 16/15 10/9 9/8
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 81/64 407.820003 Pythagorean major third 3: 27/20 519.551289 acute fourth 4: 3/2 701.955001 perfect fifth 5: 27/16 905.865003 Pythagorean major sixth 6: 9/5 1017.596288 just minor seventh, BP seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 9/8 203.9100 major whole tone 2: 9/8 203.9100 major whole tone 3: 16/15 111.7313 minor diatonic semitone 4: 10/9 182.4037 minor whole tone 5: 9/8 203.9100 major whole tone 6: 16/15 111.7313 minor diatonic semitone 7: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 16/15 111.731 cents minor diatonic semitone 1: 2 10/9 182.404 cents minor whole tone 1: 3 9/8 203.910 cents major whole tone 2: 2 32/27 294.135 cents Pythagorean minor third 2: 2 6/5 315.641 cents minor third 2: 2 5/4 386.314 cents major third 2: 1 81/64 407.820 cents Pythagorean major third 3: 5 4/3 498.045 cents perfect fourth 3: 1 27/20 519.551 cents acute fourth 3: 1 45/32 590.224 cents diatonic tritone 4: 1 64/45 609.776 cents 2nd tritone 4: 1 40/27 680.449 cents grave fifth 4: 5 3/2 701.955 cents perfect fifth 5: 1 128/81 792.180 cents Pythagorean minor sixth 5: 2 8/5 813.686 cents minor sixth 5: 2 5/3 884.359 cents major sixth, BP sixth 5: 2 27/16 905.865 cents Pythagorean major sixth 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 2 9/5 1017.596 cents just minor seventh, BP seventh 6: 2 15/8 1088.269 cents classic major seventh Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.33333 = 10/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 203.9 407.8 519.6 702.0 905.9 1017.6 1200.0 203.9 : 203.9 315.6 498.0 702.0 813.7 996.1 1200.0 407.8 : 111.7 294.1 498.0 609.8 792.2 996.1 1200.0 519.6 : 182.4 386.3 498.0 680.4 884.4 1088.3 1200.0 702.0 : 203.9 315.6 498.0 702.0 905.9 1017.6 1200.0 905.9 : 111.7 294.1 498.0 702.0 813.7 996.1 1200.0 1017.6: 182.4 386.3 590.2 702.0 884.4 1088.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 203.9100 cents 135/128, 92.1787 cents 16/15, 111.7313 cents 2: 294.1350 .. 407.8200 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 3: 498.0450 .. 590.2237 cents 135/128, 92.1787 cents 256/243, 90.2250 cents 4: 609.7763 .. 701.9550 cents 135/128, 92.1787 cents 2048/2025, 19.5526 cents 5: 792.1800 .. 905.8650 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 6: 996.0900 .. 1088.2687 cents 135/128, 92.1787 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.534293 Largest / Average step : 1.189475 Largest / Smallest step : 1.825004 Median interval of one step : 10/9, 182.4037 cents, amount: 2 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 174.43519 cents, oct.: 1221.04633 cents Scale is strictly proper Step pattern alph. order: AABCABC Step pattern size order : LLSMLSM Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.415885 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.503263 Rothenberg efficiency : 0.540136 redundancy: 0.459864 Efficiency x scale size : 3.780952 Number of different interval sizes : 20 = 3.33333 / class Number of one step interval sizes : 3 Highest interval variety : 4 Mean interval variety : 3.33333 = 10/3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 2048/2025, 19.5526 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 5, average 701.9550 cents Scale is Hypophrygian octave species of abstract tetrachord Scale is Hypodorian octave species of abstract tetrachord Best major thirds form a closed circle Best minor thirds form a closed circle All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 at degree 3 Formal octave complements present : 1 = 14.2857% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined Limited inverse transpositions with margin 113.6850 cents: 1 -- Rational properties -- Prime limit : 5 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 81 Scale harmonicity : 0.041551 Average absolute harmonicity : 0.240323 Specific harmonicity : 0.223411 Fundamental : 1/320, -8.3219 octaves, 0.8176 Hz. Guide tone : 162, 7.3399 octaves, 42383.342 Hz. Exponens Consonantiae : 5.184000E+04, 15.66178 octaves Euler's gradus suavitatis : 20 Sum of Mann's harmonic distance : 137.0, average 19.57143 Mersenne's string divisions : 209234130 Sum of van Prooijen's expressibility: 7.15682, average 1.02240 Sum of Tenney's harmonic distance : 13.67227, average 1.95318 Vogel's harmonic complexity : 13.85714 Wille's k value : 202 Wilson's harmonic complexity : 17 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 98.98321, average 3.53511 Lattice compactness (without 2's) : 53.92568, average 1.92592 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -6 .. 1 -2.14286 17 1 3: 0 .. 4 2.14286 15 4 5: -1 .. 0 -0.28571 2 2 Average exponent except 2's : 13 / 7 = 1.85714 Average absolute exponent except 2's: 17 / 7 = 2.42857 Scale is JI-epimorphic with val: <7 11 16| = patent
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 33.9348 c. M: 64.9629 c. Lebeng 9: 2 1 1 1 2 1 1 P M ME S SD: 35.0452 c. M:-62.7567 c. 11: 2 2 1 1 2 1 2 N D3 SD: 30.0363 c. M: 47.4095 c. 12: 2 2 1 2 2 1 2 P M ME S SD: 10.7341 c. M: 19.5513 c. G.Hypophrygian, G.Ionian (Iastian), M.Mixolydian, G.M.Hypoionian, Hypermixolydian, Mischung 3, Khamaj That, Mela Harikambhoji, Raga Balahamsa, Bhim, Devamanohari, Harini, Janjhuti, Kaamaai, Khambhavati, Surati, Gregorian nr.7, Enharmonic Byzantine Liturgical, Rast descending: Greece, Ching, Shang: China 27: 5 4 3 4 4 3 4 SP T3 S SD: 11.8313 c. M:-18.3122 c. 29: 5 5 3 4 5 3 4 SP SD: 9.9273 c. M:-18.3797 c. 32: 5 6 3 5 5 3 5 P SD: 8.3875 c. M: 16.4100 c. 33: 6 5 3 5 6 3 5 SP T3 SD: 8.5107 c. M:-14.2718 c. 34: 6 6 3 5 6 3 5 P SD: 9.2207 c. M:-15.7094 c. 37: 6 7 3 6 6 3 6 N SD: 8.9834 c. M:-13.8016 c. 39: 7 6 4 6 6 4 6 SP T3 S SD: 7.8090 c. M: 13.5573 c. 41: 7 7 4 6 7 4 6 SP SD: 3.8942 c. M:-7.2780 c. 53: 9 9 5 8 9 5 8 SP SD: 0.6766 c. M:-1.2716 c. 118: 20 20 11 18 20 11 18 SP SD: 0.6836 c. M: 1.0403 c. 171: 29 29 16 26 29 16 26 SP SD: 0.4266 c. M: 0.8025 c. 224: 38 38 21 34 38 21 34 SP SD: 0.3657 c. M: 0.6771 c. 277: 47 47 26 42 47 26 42 SP SD: 0.3729 c. M: 0.5998 c. 330: 56 56 31 50 56 31 50 SP SD: 0.3975 c. M:-0.5855 c. 335: 57 57 31 51 57 31 51 SP SD: 0.3036 c. M:-0.5382 c. 388: 66 66 36 59 66 36 59 SP SD: 0.2232 c. M:-0.4274 c. 441: 75 75 41 67 75 41 67 SP SD: 0.1929 c. M:-0.3433 c. 494: 84 84 46 75 84 46 75 SP SD: 0.1977 c. M:-0.2868 c. 506: 86 86 47 77 86 47 77 SP SD: 0.1130 c. M: 0.2050 c. 559: 95 95 52 85 95 52 85 SP SD: 0.0412 c. M: 0.0650 c. 612: 104 104 57 93 104 57 93 SP SD: 0.0311 c. M:-0.0566 c. 1171: 199 199 109 178 199 109 178 SP SD: 0.0191 c. M:-0.0365 c. 1783: 303 303 166 271 303 166 271 SP SD: 0.0194 c. M:-0.0319 c. 2395: 407 407 223 364 407 223 364 SP SD: 0.0213 c. M:-0.0312 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: 10.1382 cents 4 x 5 x 6 x 7:8 S SD: 13.3254 cents 5 x 6:7 x 8:9:10 S SD: 28.9537 cents 6:7 x 8:9:10:11:12 S SD: 12.8000 cents 7:8:9 x 11:12:13:14 SD: 17.9843 cents 8:9:10:11:12 x 14:16 S SD: 10.3417 cents 14:16:18:19:21:24:25:28 SD: 7.1482 cents 16:18:20:22:24:27:29:32 SD: 5.7413 cents 22:25:28:30:33:37:40:44 SD: 4.5985 cents 26:29:33:35:39:44:47:52 SD: 2.6659 cents 34:38:43:46:51:57:61:68 SD: 2.4975 cents 42:47:53:57:63:71:76:84 SD: 2.4183 cents 46:52:58:62:69:78:83:92 SD: 2.0550 cents 48:54:61:65:72:81:86:96 SD: 1.7116 cents 64:72:81:86:96:108:115:128 SD: 1.2255 cents 80:90:101:108:120:135:144:160 SD: 0.6114 cents 128:144:162:173:192:216:230:256 SD: 0.5163 cents 154:173:195:208:231:260:277:308 SD: 0.4493 cents 166:187:210:224:249:280:299:332 SD: 0.4164 cents 192:216:243:259:288:324:346:384 SD: 0.3439 cents 214:241:271:289:321:361:385:428 SD: 0.3426 cents 234:263:296:316:351:395:421:468 SD: 0.3135 cents 240:270:304:324:360:405:432:480 SD: 0.2035 cents 320:360:405:432:480:540:576:640 S SD: 0.0000 cents