Scala analysis: segah_rat
Rationalized Arabic Segh
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: 11/9 347.407941 undecimal neutral third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 27/16 905.865003 Pythagorean major 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: 9/8 203.9100 major whole tone 2: 88/81 143.4979 2nd undecimal neutral second 3: 12/11 150.6371 undecimal neutral second, 3/4-tone 4: 9/8 203.9100 major whole tone 5: 9/8 203.9100 major whole tone 6: 88/81 143.4979 2nd undecimal neutral second 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 : 203.9 347.4 498.0 702.0 905.9 1049.4 1200.0 203.9 : 143.5 294.1 498.0 702.0 845.5 996.1 1200.0 347.4 : 150.6 354.5 558.5 702.0 852.6 1056.5 1200.0 498.0 : 203.9 407.8 551.3 702.0 905.9 1049.4 1200.0 702.0 : 203.9 347.4 498.0 702.0 845.5 996.1 1200.0 905.9 : 143.5 294.1 498.0 641.5 792.2 996.1 1200.0 1049.4: 150.6 354.5 498.0 648.7 852.6 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 : 174.47274 cents, oct.: 1221.30918 cents Scale is strictly proper Step pattern alph. order: ABCAABC Step pattern size order : LSMLLSM 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 Phrygian octave species of abstract tetrachord Scale is Dorian octave species of abstract tetrachord Scale contains two identical disjunct 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 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 42.8571% 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 113.6850 cents: 1 -- Rational properties -- Prime limit : 11 Odd number limit : 243 (O: 243 U: 243) Highest odd numerator or denominator: 27 Scale harmonicity : 0.026656 Average absolute harmonicity : 0.254091 Specific harmonicity : 0.147630 Fundamental : 1/144, -7.1699 octaves, 1.8168 Hz. Guide tone : 1188, 10.2143 octaves, 310811.172 Hz. Exponens Consonantiae : 1.710720E+05, 17.38424 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 56.0, average 8.00000 Mersenne's string divisions : 307020 Sum of van Prooijen's expressibility: 5.42263, average 0.77466 Sum of Tenney's harmonic distance : 10.46636, average 1.49519 Vogel's harmonic complexity : 13.14286 Wille's k value : 121 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 6 Triangular lattice diameter : 5 Lattice compactness : 92.97885, average 3.32067 Lattice compactness (without 2's) : 59.62063, average 2.12931 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -0.85714 12 1 3: -2 .. 3 0.28571 10 4 11: 0 .. 1 0.28571 2 2 Average exponent except 2's : 4 / 7 = 0.57143 Average absolute exponent except 2's: 12 / 7 = 1.71429 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: 25.0981 c. M: 48.7221 c. Lebeng 13: 2 2 1 3 2 1 2 P D3 SD: 26.6317 c. M:-36.5065 c. 15: 2 2 2 3 2 2 2 SP M ME I SD: 24.1637 c. M: 43.9100 c. Miller's Porcupine-7 16: 3 2 2 2 3 2 2 SP M ME S SD: 19.6180 c. M:-27.5921 c. Antiphrygian 17: 3 2 2 3 3 2 2 SP D3 S SD: 7.0860 c. M:-11.7821 c. Pseudo Rast 24: 4 3 3 4 4 3 3 SP D3 S SD: 3.0344 c. M: 5.8650 c. Arabic Diatonic, Maqam Rast, Quasi-equal Heptatonic, Neutral Diatonic Phrygian 41: 7 5 5 7 7 5 5 SP D3 S SD: 2.2833 c. M:-4.2956 c. 65: 11 8 8 11 11 8 8 SP D3 S SD: 1.7957 c. M:-3.3613 c. 89: 15 11 11 15 15 11 11 SP D3 S SD: 1.9164 c. M:-3.1539 c. 94: 16 11 12 16 16 11 12 SP SD: 1.4347 c. M: 2.7271 c. 111: 19 13 14 19 19 13 14 SP SD: 1.2555 c. M:-2.2431 c. 118: 20 14 15 20 20 14 15 SP SD: 1.0248 c. M: 1.9053 c. 135: 23 16 17 23 23 16 17 SP SD: 0.5134 c. M:-0.8017 c. 159: 27 19 20 27 27 19 20 SP SD: 0.1774 c. M: 0.3063 c. 359: 61 43 45 61 61 43 45 SP SD: 0.1188 c. M:-0.2244 c. 494: 84 59 62 84 84 59 62 SP SD: 0.1031 c. M:-0.2079 c. 518: 88 62 65 88 88 62 65 SP SD: 0.0523 c. M:-0.0824 c. 677: 115 81 85 115 115 81 85 SP SD: 0.0520 c. M: 0.1043 c. 1012: 172 121 127 172 172 121 127 SP SD: 0.0364 c. M:-0.0639 c. 1171: 199 140 147 199 199 140 147 SP SD: 0.0142 c. M:-0.0274 c. 1689: 287 202 212 287 287 202 212 SP SD: 0.0087 c. M:-0.0166 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 6:7 x 8 S SD: 18.5029 cents 5 x 6:7 x 8:9:10 S SD: 26.5706 cents 6:7 x 8:9:10:11:12 S SD: 11.0888 cents 7:8 x 9:11:12:13:14 SD: 18.5861 cents 8:9:10:11:12:14:15:16 S SD: 14.1633 cents 9:10:11:12:14:15:17:18 SD: 12.4213 cents 10:11:12:13:15:17:18:20 SD: 10.7060 cents 13:15:16:17:20:22:24:26 SD: 10.3882 cents 14:16:17:19:21:24:26:28 SD: 7.8919 cents 16:18:20:21:24:27:29:32 SD: 7.3519 cents 18:20:22:24:27:30:33:36 S SD: 4.3449 cents 24:27:29:32:36:41:44:48 SD: 4.1471 cents 26:29:32:35:39:44:48:52 SD: 4.0674 cents 30:34:37:40:45:51:55:60 SD: 3.4165 cents 32:36:39:43:48:54:59:64 SD: 2.4825 cents 42:47:51:56:63:71:77:84 SD: 2.1231 cents 48:54:59:64:72:81:88:96 SD: 1.4012 cents 54:61:66:72:81:91:99:108 SD: 1.0709 cents 72:81:88:96:108:122:132:144 SD: 1.0157 cents 90:101:110:120:135:152:165:180 SD: 0.6444 cents 126:142:154:168:189:213:231:252 SD: 0.6163 cents 144:162:176:192:216:243:264:288 SD: 0.0000 cents