Scala analysis: segah-zalzalian
Arabic Segah (or Sikah) based on zalzal.scl (step 5 = 1/1)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 88/81 143.497939 2nd undecimal neutral second 2: 11/9 347.407941 undecimal neutral third 3: 11/8 551.317942 undecimal semi-augmented fourth 4: 3/2 701.955001 perfect fifth 5: 44/27 845.452940 neutral sixth 6: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-tone 1: 88/81 143.4979 2nd undecimal neutral second 2: 9/8 203.9100 major whole tone 3: 9/8 203.9100 major whole tone 4: 12/11 150.6371 undecimal neutral second, 3/4-tone 5: 88/81 143.4979 2nd undecimal neutral second 6: 9/8 203.9100 major whole tone 7: 12/11 150.6371 undecimal neutral second, 3/4-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 : 143.5 347.4 551.3 702.0 845.5 1049.4 1200.0 143.5 : 203.9 407.8 558.5 702.0 905.9 1056.5 1200.0 347.4 : 203.9 354.5 498.0 702.0 852.6 996.1 1200.0 551.3 : 150.6 294.1 498.0 648.7 792.2 996.1 1200.0 702.0 : 143.5 347.4 498.0 641.5 845.5 1049.4 1200.0 845.5 : 203.9 354.5 498.0 702.0 905.9 1056.5 1200.0 1049.4: 150.6 294.1 498.0 702.0 852.6 996.1 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 : 173.02521 cents, oct.: 1211.17650 cents Scale is strictly proper Step pattern alph. order: ABBCABC Step pattern size order : SLLMSLM 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 Hypolydian octave species of abstract tetrachord Scale is Hypophrygian octave species of abstract tetrachord Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle 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 Limited inverse transpositions with margin 60.4121 cents: 4 -- Rational properties -- Prime limit : 11 Odd number limit : 243 (O: 243 U: 243) Highest odd numerator or denominator: 81 Scale harmonicity : 0.026656 Average absolute harmonicity : 0.210730 Specific harmonicity : 0.131220 Fundamental : 1/648, -9.3399 octaves, 0.4037 Hz. Guide tone : 264, 8.0444 octaves, 69069.149 Hz. Exponens Consonantiae : 1.710720E+05, 17.38424 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 152.0, average 21.71429 Mersenne's string divisions : 232540620 Sum of van Prooijen's expressibility: 6.94115, average 0.99159 Sum of Tenney's harmonic distance : 13.76663, average 1.96666 Vogel's harmonic complexity : 19.14286 Wille's k value : 445 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 6 Triangular lattice diameter : 5 Lattice compactness : 93.28385, average 3.33157 Lattice compactness (without 2's) : 61.90601, average 2.21093 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 3 0.14286 11 1 3: -4 .. 1 -1.28571 11 1 11: 0 .. 1 0.71429 5 5 Average exponent except 2's :-4 / 7 =-0.57143 Average absolute exponent except 2's: 16 / 7 = 2.28571 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: 20.7189 c. M: 37.0322 c. Lebeng 15: 2 2 3 2 2 2 2 SP M ME S SD: 19.6602 c. M:-34.5471 c. 17: 2 3 3 2 2 3 2 SP D3 S SD: 6.7902 c. M:-13.3879 c. 24: 3 4 4 3 3 4 3 SP D3 S SD: 3.2871 c. M:-6.5021 c. Maqam Sikah (Segah), Neutral Diatonic Hypolydian 41: 5 7 7 5 5 7 5 SP D3 S SD: 3.2780 c. M:-4.7796 c. 65: 8 11 11 8 8 11 8 SP D3 S SD: 2.8884 c. M:-4.1944 c. 87: 10 15 15 11 10 15 11 SP SD: 2.8740 c. M: 5.5669 c. 89: 11 15 15 11 11 15 11 SP D3 S SD: 2.8620 c. M:-4.8167 c. 94: 11 16 16 12 11 16 12 SP SD: 2.3150 c. M: 3.0724 c. 111: 13 19 19 14 13 19 14 SP SD: 1.5509 c. M: 2.9574 c. 118: 14 20 20 15 14 20 15 SP SD: 1.4282 c. M: 2.1654 c. 135: 16 23 23 17 16 23 17 SP SD: 0.7104 c. M: 1.2757 c. 159: 19 27 27 20 19 27 20 SP SD: 0.2187 c. M: 0.3745 c. 335: 40 57 57 42 40 57 42 SP SD: 0.1749 c. M:-0.3238 c. 359: 43 61 61 45 43 61 45 SP SD: 0.1897 c. M:-0.2347 c. 494: 59 84 84 62 59 84 62 SP SD: 0.0931 c. M: 0.1781 c. 518: 62 88 88 65 62 88 65 SP SD: 0.0761 c. M:-0.1314 c. 677: 81 115 115 85 81 115 85 SP SD: 0.0440 c. M:-0.0767 c. 1012: 121 172 172 127 121 172 127 SP SD: 0.0330 c. M:-0.0655 c. 1171: 140 199 199 147 140 199 147 SP SD: 0.0156 c. M: 0.0308 c. 1689: 202 287 287 212 202 287 212 SP SD: 0.0141 c. M:-0.0189 c. 1848: 221 314 314 232 221 314 232 SP SD: 0.0098 c. M: 0.0192 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: 21.9891 cents 4 x 5 x 6 x 7:8 S SD: 22.3605 cents 5 x 6:7 x 8:9:10 S SD: 12.6498 cents 6 x 7:8:9:10:11:12 S SD: 17.3509 cents 7:8:9:10 x 11:13:14 SD: 25.9357 cents 8:9:10:11:12:13:15:16 SD: 11.6944 cents 10:11:12:14:15:16:18:20 S SD: 9.5436 cents 13:14:16:18:20:21:24:26 S SD: 7.5861 cents 14:15:17:19:21:23:26:28 SD: 6.2481 cents 22:24:27:30:33:36:40:44 S SD: 3.3979 cents 24:26:29:33:36:39:44:48 SD: 2.9966 cents 32:35:39:44:48:52:59:64 SD: 2.3916 cents 46:50:56:63:69:75:84:92 SD: 1.7053 cents 54:59:66:74:81:88:99:108 SD: 1.6307 cents 67:73:82:92:101:109:123:134 SD: 1.5898 cents 70:76:86:96:105:114:128:140 SD: 1.5878 cents 72:78:88:99:108:117:132:144 SD: 0.9951 cents 90:98:110:124:135:147:165:180 SD: 0.9379 cents 94:102:115:129:141:153:172:188 SD: 0.8335 cents 114:124:139:157:171:186:209:228 SD: 0.8253 cents 126:137:154:173:189:205:231:252 SD: 0.5738 cents 152:165:186:209:228:248:279:304 SD: 0.5510 cents 162:176:198:223:243:264:297:324 SD: 0.2774 cents 256:278:313:352:384:417:469:512 SD: 0.2504 cents 288:313:352:396:432:469:528:576 SD: 0.1964 cents 360:391:440:495:540:587:660:720 SD: 0.1571 cents 440:478:538:605:660:717:807:880 SD: 0.1456 cents 464:504:567:638:696:756:851:928 SD: 0.1282 cents 486:528:594:668:729:792:891:972 SD: 0.0925 cents