Scala analysis: xen18-schulter-zalzal
Zalzal's scale
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: 27/22 354.547060 neutral third, Zalzal wosta of al-Farabi 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 18/11 852.592059 undecimal neutral 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: 9/8 203.9100 major whole tone 2: 12/11 150.6371 undecimal neutral second, 3/4-tone 3: 88/81 143.4979 2nd undecimal neutral second 4: 9/8 203.9100 major whole tone 5: 12/11 150.6371 undecimal neutral second, 3/4-tone 6: 88/81 143.4979 2nd undecimal neutral second 7: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 88/81 143.498 cents 2nd undecimal neutral second 1: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 3 9/8 203.910 cents major whole tone 2: 2 32/27 294.135 cents Pythagorean minor third 2: 2 11/9 347.408 cents undecimal neutral third 2: 2 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 2: 1 81/64 407.820 cents Pythagorean major third 3: 5 4/3 498.045 cents perfect fourth 3: 1 11/8 551.318 cents undecimal semi-augmented fourth 3: 1 243/176 558.457 cents 4: 1 352/243 641.543 cents 4: 1 16/11 648.682 cents undecimal semi-diminished fifth 4: 5 3/2 701.955 cents perfect fifth 5: 1 128/81 792.180 cents Pythagorean minor sixth 5: 2 44/27 845.453 cents neutral sixth 5: 2 18/11 852.592 cents undecimal neutral sixth 5: 2 27/16 905.865 cents Pythagorean major sixth 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 2 81/44 1056.502 cents 2nd undecimal neutral 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 : 203.9 354.5 498.0 702.0 852.6 996.1 1200.0 203.9 : 150.6 294.1 498.0 648.7 792.2 996.1 1200.0 354.5 : 143.5 347.4 498.0 641.5 845.5 1049.4 1200.0 498.0 : 203.9 354.5 498.0 702.0 905.9 1056.5 1200.0 702.0 : 150.6 294.1 498.0 702.0 852.6 996.1 1200.0 852.6 : 143.5 347.4 551.3 702.0 845.5 1049.4 1200.0 996.1 : 203.9 407.8 558.5 702.0 905.9 1056.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 143.4979 .. 203.9100 cents 729/704, 60.4121 cents 88/81, 143.4979 cents 2: 294.1350 .. 407.8200 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 3: 498.0450 .. 558.4571 cents 729/704, 60.4121 cents 256/243, 90.2250 cents 4: 641.5429 .. 701.9550 cents 729/704, 60.4121 cents 61952/59049, 83.0859 cents 5: 792.1800 .. 905.8650 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 6: 996.0900 .. 1056.5021 cents 729/704, 60.4121 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 88/81, 143.4979 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.194641 Largest / Average step : 1.189475 Largest / Smallest step : 1.420996 Median interval of one step : 12/11, 150.6371 cents, amount: 2 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 170.38900 cents, oct.: 1192.72297 cents Scale is strictly proper Step pattern alph. order: ABCABCA Step pattern size order : LMSLMSL Scale is a Constant Structure, by a margin of 83.08588 cents Scale diversity : 1.352218 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.609151 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 : 243/242, 7.1391 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 Mixolydian octave species of abstract tetrachord Scale is Hypodorian octave species of abstract tetrachord Scale contains two identical conjunct tetrachords Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 1 3 9 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 5 = 71.4286% Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval class 3 -- Rational properties -- Prime limit : 11 Odd number limit : 243 (O: 243 U: 243) Highest odd numerator or denominator: 27 Scale harmonicity : 0.025964 Average absolute harmonicity : 0.255962 Specific harmonicity : 0.145064 Fundamental : 1/792, -9.6294 octaves, 0.3303 Hz. Guide tone : 432, 8.7549 octaves, 113022.244 Hz. Exponens Consonantiae : 3.421440E+05, 18.38424 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 67.5, average 9.64286 Mersenne's string divisions : 1811775 Sum of van Prooijen's expressibility: 5.33548, average 0.76221 Sum of Tenney's harmonic distance : 11.24451, average 1.60636 Vogel's harmonic complexity : 19.42857 Wille's k value : 445 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 6 Triangular lattice diameter : 5 Lattice compactness : 98.15194, average 3.50543 Lattice compactness (without 2's) : 60.36869, average 2.15602 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 4 0.42857 13 1 3: -2 .. 3 0.71429 11 4 11: -1 .. 0 -0.28571 2 2 Average exponent except 2's : 3 / 7 = 0.42857 Average absolute exponent except 2's: 13 / 7 = 1.85714 Scale is weakly epimorphic with val: <7 10 25| Scale is JI-epimorphic with val: <7 11 24| = patent Scale is weakly epimorphic with val: <7 12 23|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 19.9820 c. M:-32.4814 c. Lebeng 16: 3 2 2 2 2 2 3 P D3 I SD: 22.4320 c. M: 27.5921 c. 17: 3 2 2 3 2 2 3 SP D3 I SD: 5.1746 c. M:-7.8547 c. Safi al-Din's maqam Rast 24: 4 3 3 4 3 3 4 SP D3 I SD: 3.0616 c. M: 4.5471 c. Miha'il Musaqa's mode: Egypt, Neutral Diatonic Hypodorian, Dastgah-e Sehgah, Maqam Nairuz 41: 7 5 5 7 5 5 7 SP D3 I SD: 1.9980 c. M: 3.8116 c. 65: 11 8 8 11 8 8 11 SP D3 I SD: 1.9750 c. M: 3.7778 c. 94: 16 12 11 16 12 11 16 SP SD: 1.5186 c. M:-2.8997 c. 101: 17 13 12 17 13 12 17 SP SD: 1.7329 c. M:-2.8535 c. 111: 19 14 13 19 14 13 19 SP SD: 1.3422 c. M:-2.2097 c. 118: 20 15 14 20 15 14 20 SP SD: 0.8703 c. M:-1.6452 c. 135: 23 17 16 23 17 16 23 SP SD: 0.5708 c. M:-1.0085 c. 159: 27 20 19 27 20 19 27 SP SD: 0.1374 c. M:-0.2381 c. 359: 61 45 43 61 45 43 61 SP SD: 0.1215 c. M: 0.2295 c. 494: 84 62 59 84 62 59 84 SP SD: 0.0937 c. M:-0.1386 c. 518: 88 65 62 88 65 62 88 SP SD: 0.0588 c. M: 0.1069 c. 677: 115 85 81 115 85 81 115 SP SD: 0.0445 c. M:-0.0695 c. 1012: 172 127 121 172 127 121 172 SP SD: 0.0269 c. M:-0.0426 c. 1171: 199 147 140 199 147 140 199 SP SD: 0.0145 c. M:-0.0217 c. 1689: 287 212 202 287 212 202 287 SP SD: 0.0093 c. M: 0.0178 c. 1848: 314 232 221 314 232 221 314 SP SD: 0.0086 c. M:-0.0139 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: 10.5889 cents 4 x 5 x 6 x 7:8 S SD: 10.4656 cents 5 x 6:7 x 8:9:10 S SD: 20.6151 cents 6:7 x 8:9:10:11:12 S SD: 14.7302 cents 7:8 x 9 x 11:12:14 SD: 23.3114 cents 8:9:10:11:12:13:14:16 S SD: 9.8312 cents 14:16:17:19:21:23:25:28 SD: 6.5900 cents 18:20:22:24:27:29:32:36 SD: 5.0273 cents 22:25:27:29:33:36:39:44 SD: 3.8292 cents 30:34:37:40:45:49:53:60 SD: 2.7259 cents 39:44:48:52:59:64:69:78 SD: 2.7086 cents 40:45:49:53:60:65:71:80 SD: 2.3947 cents 48:54:59:64:72:79:85:96 SD: 1.7661 cents 54:61:66:72:81:88:96:108 SD: 1.7641 cents 58:65:71:77:87:95:103:116 SD: 1.6031 cents 66:74:81:88:99:108:117:132 SD: 1.0913 cents 72:81:88:96:108:118:128:144 SD: 1.0888 cents 80:90:98:107:120:131:142:160 SD: 0.9923 cents 96:108:118:128:144:157:171:192 SD: 0.6315 cents 144:162:177:192:216:236:256:288 SD: 0.5393 cents 162:182:199:216:243:265:288:324 SD: 0.4166 cents 168:189:206:224:252:275:299:336 SD: 0.3611 cents 198:223:243:264:297:324:352:396 SD: 0.2774 cents 264:297:324:352:396:432:469:528 SD: 0.1757 cents 360:405:442:480:540:589:640:720 SD: 0.1087 cents 432:486:530:576:648:707:768:864 SD: 0.0906 cents 528:594:648:704:792:864:939:1056 SD: 0.0878 cents