Scala analysis: xen09-wilson-marwa-07-06
Marwa permutation 6 from Figure 7, 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: 9/8 203.910002 major whole tone 2: 81/64 407.820003 Pythagorean major third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 27/16 905.865003 Pythagorean major 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: 9/8 203.9100 major whole tone 2: 9/8 203.9100 major whole tone 3: 256/243 90.2250 limma, Pythagorean minor second 4: 9/8 203.9100 major whole tone 5: 9/8 203.9100 major whole tone 6: 28/27 62.9609 Archytas' 1/3-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 : 203.9 407.8 498.0 702.0 905.9 968.8 1200.0 203.9 : 203.9 294.1 498.0 702.0 764.9 996.1 1200.0 407.8 : 90.2 294.1 498.0 561.0 792.2 996.1 1200.0 498.0 : 203.9 407.8 470.8 702.0 905.9 1109.8 1200.0 702.0 : 203.9 266.9 498.0 702.0 905.9 996.1 1200.0 905.9 : 63.0 294.1 498.0 702.0 792.2 996.1 1200.0 968.8 : 231.2 435.1 639.0 729.2 933.1 1137.0 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 : 171.88418 cents, oct.: 1203.18927 cents Scale is not proper Step pattern alph. order: AABAACD Step pattern size order : CCBCCAD 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 Scale contains a complete diamond : 1 3 Length of longest harmonic part : 2 at degree 6 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 42.8571% 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: 1 -- 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 : 0.261677 Specific harmonicity : 0.203174 Fundamental : 1/192, -7.5850 octaves, 1.3626 Hz. Guide tone : 2268, 11.1472 octaves, 593366.782 Hz. Exponens Consonantiae : 4.354560E+05, 18.73217 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 115.5, average 16.50000 Mersenne's string divisions : 24484845 Sum of van Prooijen's expressibility: 6.09343, average 0.87049 Sum of Tenney's harmonic distance : 11.81300, average 1.68757 Vogel's harmonic complexity : 12.00000 Wille's k value : 121 Wilson's harmonic complexity : 22 Rectangular lattice diameter : 6 Triangular lattice diameter : 5 Lattice compactness : 110.80130, average 3.95719 Lattice compactness (without 2's) : 60.34988, average 2.15535 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -6 .. 2 -1.85714 19 1 3: -1 .. 4 1.28571 11 5 7: 0 .. 1 0.14286 1 1 Average exponent except 2's : 10 / 7 = 1.42857 Average absolute exponent except 2's: 12 / 7 = 1.71429 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 1 1 1 1 SP B ME I SD: 40.9636 c. M: 64.9629 c. Lebeng 9: 2 1 1 1 2 0 2 N T3 SD: 34.8554 c. M:-62.7567 c. 10: 2 1 1 2 2 0 2 P D3 S SD: 32.1802 c. M:-54.1350 c. 11: 2 2 1 1 2 1 2 N D3 SD: 31.1234 c. M:-47.4095 c. 12: 2 2 1 2 2 1 2 P M ME S SD: 12.4803 c. M:-31.1741 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 17: 3 3 1 3 3 1 3 N M DE S SD: 11.0510 c. M:-19.4094 c. Safi al-Din's maqam `Ussaq 24: 4 4 2 4 4 1 5 N SD: 8.2193 c. M: 18.8259 c. 27: 5 4 2 5 4 2 5 N SD: 11.5417 c. M:-18.3122 c. 29: 5 5 2 5 5 1 6 N SD: 7.1873 c. M: 17.1018 c. 32: 5 6 2 6 5 2 6 N T3 SD: 9.1503 c. M: 16.4100 c. 33: 6 5 3 5 6 2 6 N SD: 9.9144 c. M:-14.2718 c. 36: 6 6 3 6 6 2 7 N SD: 4.1943 c. M: 7.8200 c. 41: 7 7 3 7 7 2 8 N SD: 1.5164 c. M: 2.9722 c. 77: 13 13 6 13 13 4 15 N SD: 1.6933 c. M: 2.6252 c. 94: 16 16 7 16 16 5 18 N SD: 0.6378 c. M:-1.3869 c. 135: 23 23 10 23 23 7 26 N SD: 0.5628 c. M:-1.0689 c. 171: 29 29 13 29 29 9 33 N SD: 0.4491 c. M: 0.8025 c. 212: 36 36 16 36 36 11 41 N SD: 0.3697 c. M: 0.9014 c. 265: 45 45 20 45 45 14 51 N SD: 0.1679 c. M: 0.2728 c. 306: 52 52 23 52 52 16 59 N SD: 0.0760 c. M: 0.1985 c. 400: 68 68 30 68 68 21 77 N SD: 0.1153 c. M:-0.1800 c. 571: 97 97 43 97 97 30 110 N SD: 0.0601 c. M: 0.1142 c. 706: 120 120 53 120 120 37 136 N SD: 0.0591 c. M:-0.1120 c. 877: 149 149 66 149 149 46 169 N SD: 0.0435 c. M: 0.0688 c. 971: 165 165 73 165 165 51 187 N SD: 0.0275 c. M:-0.0721 c. 1277: 217 217 96 217 217 67 246 N SD: 0.0063 c. M:-0.0109 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: 7.1688 cents 4 x 5 x 6 x 7:8 S SD: 5.3766 cents 5 x 6:7 x 8:9:10 S SD: 32.5620 cents 6:7 x 8:9:10:11:12 S SD: 17.4107 cents 7:8:9 x 11:12 x 14 SD: 18.6721 cents 8:9:10:11:12 x 14:16 S SD: 9.5750 cents 10:11 x 13:15:17:18:20 SD: 12.8848 cents 11:12:14:15:17 x 19:22 SD: 14.5571 cents 12:14:15:16:18:20:21:24 S SD: 9.9889 cents 14:16:18:19:21:24:25:28 SD: 9.4677 cents 15:17:19:20:23:25:26:30 SD: 6.9254 cents 16:18:20:21:24:27:28:32 S SD: 4.9608 cents 24:27:30:32:36:41:42:48 SD: 4.3184 cents 26:29:33:35:39:44:46:52 SD: 4.2900 cents 30:34:38:40:45:51:53:60 SD: 3.4929 cents 33:37:42:44:50:56:58:66 SD: 3.4419 cents 38:43:48:51:57:64:67:76 SD: 2.9339 cents 41:46:52:55:62:69:72:82 SD: 2.8606 cents 42:47:53:56:63:71:74:84 SD: 2.2919 cents 48:54:61:64:72:81:84:96 SD: 1.0157 cents 64:72:81:85:96:108:112:128 SD: 0.9680 cents 102:115:129:136:153:172:179:204 SD: 0.9126 cents 112:126:142:149:168:189:196:224 SD: 0.7038 cents 120:135:152:160:180:203:210:240 SD: 0.6430 cents 128:144:162:171:192:216:224:256 SD: 0.4826 cents 144:162:182:192:216:243:252:288 SD: 0.3395 cents 192:216:243:256:288:324:336:384 SD: 0.0000 cents