Scala analysis: CD03_08_rast_Egypt
Suite - Aziz 'Uthmân (rast, Egypt)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 207.890 cents 207.889832 2: 354.940 cents 354.940070 3: 502.193 cents 502.192678 4: 697.875 cents 697.875174 5: 838.296 cents 838.295610 6: 995.718 cents 995.718438 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 204.2816 cents 204.2816 1: 207.8898 cents 207.8898 2: 147.0502 cents 147.0502 3: 147.2526 cents 147.2526 4: 195.6825 cents 195.6825 5: 140.4204 cents 140.4204 6: 157.4228 cents 157.4228 7: 204.2816 cents 204.2816
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 140.42044 cents 1: 1 147.05024 cents 1: 1 147.25261 cents 1: 1 157.42283 cents 1: 1 195.68250 cents 1: 1 204.28156 cents 1: 1 207.88983 cents 2: 1 294.30285 cents 2: 1 297.84326 cents 2: 1 336.10293 cents 2: 1 342.93510 cents 2: 1 354.94007 cents 2: 1 361.70439 cents 2: 1 412.17139 cents 3: 1 483.35554 cents 3: 1 489.98534 cents 3: 1 493.52576 cents 3: 1 502.12483 cents 3: 1 502.19268 cents 3: 1 559.22163 cents 3: 1 569.59422 cents 4: 1 630.40578 cents 4: 1 640.77837 cents 4: 1 697.80732 cents 4: 1 697.87517 cents 4: 1 706.47424 cents 4: 1 710.01466 cents 4: 1 716.64446 cents 5: 1 787.82861 cents 5: 1 838.29561 cents 5: 1 845.05993 cents 5: 1 857.06490 cents 5: 1 863.89707 cents 5: 1 902.15674 cents 5: 1 905.69715 cents 6: 1 992.11017 cents 6: 1 995.71844 cents 6: 1 1004.31750 cents 6: 1 1042.57717 cents 6: 1 1052.74739 cents 6: 1 1052.94976 cents 6: 1 1059.57956 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 7.00000 = 7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 207.9 354.9 502.2 697.9 838.3 995.7 1200.0 207.9 : 147.1 294.3 490.0 630.4 787.8 992.1 1200.0 354.9 : 147.3 342.9 483.4 640.8 845.1 1052.9 1200.0 502.2 : 195.7 336.1 493.5 697.8 905.7 1052.7 1200.0 697.9 : 140.4 297.8 502.1 710.0 857.1 1004.3 1200.0 838.3 : 157.4 361.7 569.6 716.6 863.9 1059.6 1200.0 995.7 : 204.3 412.2 559.2 706.5 902.2 1042.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 140.4204 .. 207.8898 cents 67.46940 cents 140.42044 cents 2: 294.3028 .. 412.1714 cents 117.86855 cents 86.41301 cents 3: 483.3555 .. 569.5942 cents 86.23868 cents 71.18415 cents 4: 630.4058 .. 716.6445 cents 86.23868 cents 60.81156 cents 5: 787.8286 .. 905.6972 cents 117.86855 cents 71.18415 cents 6: 992.1102 .. 1059.5796 cents 67.46940 cents 86.41301 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 140.42044 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 207.88983 cents Average / Smallest step : 1.220824 Largest / Average step : 1.212691 Largest / Smallest step : 1.480481 Median interval of one step : 157.42283 cents, amount: 1 Least squares average step : 169.86884 cents, oct.: 1189.08187 cents Scale is strictly proper Step pattern alph. order: ABCDEFG Step pattern size order : GBCEADF Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 60.81156 cents Scale diversity : 1.441665 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.547372 Rothenberg efficiency : 0.285714 redundancy: 0.714286 Efficiency x scale size : 2.000000 Number of different interval sizes : 42 = 7.00000 / class Number of one step interval sizes : 7 Highest interval variety : 7 Mean interval variety : 7.00000 = 7 Median interval variety : 7 Lowest interval variety : 7 Smallest interval difference : 0.06785 cents Number of recognisable fifths : 5, average 705.7632 cents Number of appreciable fifths : 4, average 703.0428 cents 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% -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 21.3945 c. M: 36.4613 c. Lebeng 10: 2 1 1 2 1 1 2 P D3 I SD: 21.7696 c. M: 35.7184 c. 16: 3 2 2 2 2 2 3 P D3 I SD: 18.3016 c. M: 22.8752 c. 17: 3 2 2 3 2 2 3 SP D3 I SD: 6.3372 c. M:-8.7632 c. Safi al-Din's maqam Rast 24: 4 3 3 4 3 3 4 SP D3 I SD: 5.9917 c. M:-11.7044 c. Miha'il Musaqa's mode: Egypt, Neutral Diatonic Hypodorian, Dastgah-e Sehgah, Maqam Nairuz 40: 7 5 5 6 5 5 7 SP I SD: 5.1911 c. M: 7.8752 c. 41: 7 5 5 7 5 5 7 SP D3 I SD: 5.0069 c. M:-10.4849 c. 50: 9 6 6 8 6 7 8 SP SD: 5.9988 c. M:-12.2816 c. 52: 9 6 7 8 6 7 9 SP SD: 5.4348 c. M: 8.7862 c. 53: 9 7 6 9 6 7 9 SP I SD: 3.8525 c. M:-7.3241 c. 57: 10 7 7 9 7 7 10 SP I SD: 3.5550 c. M: 6.2448 c. 64: 11 8 8 10 8 8 11 SP I SD: 3.1962 c. M:-5.4544 c. 70: 12 9 8 12 8 9 12 SP I SD: 3.4972 c. M:-5.0599 c. 74: 13 9 9 12 9 9 13 SP I SD: 3.3708 c. M: 6.5292 c. 77: 13 10 9 13 9 10 13 SP I SD: 3.3309 c. M: 5.2924 c. 81: 14 10 10 13 10 10 14 SP I SD: 2.7508 c. M:-6.1488 c. 82: 14 10 10 14 9 11 14 SP SD: 3.4386 c. M: 4.6317 c. 84: 15 10 10 14 10 11 14 SP SD: 3.6688 c. M:-6.3959 c. 86: 15 10 11 14 10 11 15 SP SD: 3.0633 c. M: 6.1029 c. 88: 15 11 11 14 10 12 15 SP SD: 3.0417 c. M: 6.4774 c. 93: 16 12 11 15 11 12 16 SP I SD: 2.6607 c. M:-6.3503 c. 94: 16 12 11 16 11 12 16 SP I SD: 3.2595 c. M: 4.3203 c. 96: 17 11 12 16 11 13 16 SP SD: 3.2502 c. M: 4.9401 c. 98: 17 12 12 16 11 13 17 SP SD: 2.5922 c. M: 5.6425 c. 105: 18 13 13 17 12 14 18 SP SD: 1.8621 c. M: 4.0099 c. 119: 21 14 15 19 14 16 20 SP SD: 2.2637 c. M:-3.8749 c. 122: 21 15 15 20 14 16 21 SP SD: 1.3721 c. M: 2.2758 c. 146: 25 18 18 24 17 19 25 SP SD: 1.2417 c. M: 2.4104 c. 163: 28 20 20 27 19 21 28 SP SD: 1.4482 c. M: 1.8534 c. 169: 29 21 21 27 20 22 29 SP SD: 1.4454 c. M: 2.0172 c. 172: 30 21 21 28 20 23 29 SP SD: 1.0571 c. M:-1.9560 c. 189: 33 23 23 31 22 25 32 SP SD: 0.8426 c. M:-1.6340 c. 213: 37 26 26 35 25 28 36 SP SD: 0.8358 c. M:-1.4647 c. 236: 41 29 29 38 28 31 40 SP SD: 0.8966 c. M: 1.2650 c. 253: 44 31 31 41 30 33 43 SP SD: 0.7209 c. M:-1.2301 c. 282: 49 34 35 46 33 37 48 SP SD: 0.7018 c. M: 1.7486 c. 294: 51 36 36 48 34 39 50 SP SD: 0.6103 c. M: 1.5609 c. 301: 52 37 37 49 35 40 51 SP SD: 0.5989 c. M: 1.0863 c. 311: 54 38 38 51 36 41 53 SP SD: 0.5174 c. M: 0.9966 c. 318: 55 39 39 52 37 42 54 SP SD: 0.3563 c. M: 0.5598 c. 375: 65 46 46 61 44 49 64 SP SD: 0.2613 c. M: 0.5184 c. 564: 98 69 69 92 66 74 96 SP SD: 0.2762 c. M:-0.6208 c. 571: 99 70 70 93 67 75 97 SP SD: 0.2227 c. M:-0.4287 c. 676: 117 83 83 110 79 89 115 SP SD: 0.2193 c. M: 0.4258 c. 686: 119 84 84 112 80 90 117 SP SD: 0.2489 c. M: 0.3947 c. 693: 120 85 85 113 81 91 118 SP SD: 0.0893 c. M: 0.2004 c. 1092: 189 134 134 178 128 143 186 SP SD: 0.1101 c. M: 0.1975 c. 1264: 219 155 155 206 148 166 215 SP SD: 0.0866 c. M:-0.1676 c. 1281: 222 157 157 209 150 168 218 SP SD: 0.0744 c. M:-0.1119 c. 1785: 309 219 219 291 209 234 304 SP SD: 0.0732 c. M: 0.1587 c. 1957: 339 240 240 319 229 257 333 SP SD: 0.0635 c. M:-0.0931 c. 1974: 342 242 242 322 231 259 336 SP SD: 0.0392 c. M:-0.0751 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: 2.0399 cents 3 x x 4 x 5 x 6 S SD: 15.4165 cents 4 x 5 x 6 x 7:8 S SD: 10.3807 cents 5 x 6:7 x 8:9:10 S SD: 19.0577 cents 6:7 x 8:9:10:11:12 S SD: 15.3769 cents 7:8 x 9:10:11:12:14 S SD: 22.6932 cents 8:9:10:11:12:13:14:16 S SD: 9.2121 cents 14:16:17:19:21:23:25:28 SD: 6.5891 cents 18:20:22:24:27:29:32:36 SD: 4.2851 cents 26:29:32:35:39:42:46:52 SD: 3.7105 cents 30:34:37:40:45:49:53:60 SD: 2.8935 cents 32:36:39:43:48:52:57:64 SD: 2.4481 cents 39:44:48:52:58:63:69:78 SD: 2.4036 cents 40:45:49:53:60:65:71:80 SD: 2.3945 cents 45:51:55:60:67:73:80:90 SD: 2.1632 cents 48:54:59:64:72:78:85:96 SD: 1.4348 cents 62:70:76:83:93:101:110:124 SD: 1.3390 cents 71:80:87:95:106:115:126:142 SD: 1.0134 cents 93:105:114:124:139:151:165:186 SD: 0.9381 cents 101:114:124:135:151:164:180:202 SD: 0.7589 cents 119:134:146:159:178:193:212:238 SD: 0.7091 cents 127:143:156:170:190:206:226:254 SD: 0.6349 cents 149:168:183:199:223:242:265:298 SD: 0.3321 cents 220:248:270:294:329:357:391:440 SD: 0.1952 cents 369:416:453:493:552:599:656:738 SD: 0.1585 cents 493:556:605:659:738:800:876:986 SD: 0.1456 cents 562:634:690:751:841:912:999:1124 SD: 0.1338 cents 580:654:712:775:868:941:1031:1160 SD: 0.1009 cents