Scala analysis: yarman_ushaq
10-tone Ushaq/Huseyni by Ozan Yarman
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 13/12 138.572661 tridecimal 2/3-tone 2: 12/11 150.637059 undecimal neutral second, 3/4-tone 3: 32/27 294.134997 Pythagorean minor third 4: 4/3 498.044999 perfect fourth 5: 3/2 701.955001 perfect fifth 6: 128/81 792.179997 Pythagorean minor sixth 7: 13/8 840.527662 tridecimal neutral sixth 8: 18/11 852.592059 undecimal neutral sixth 9: 16/9 996.089998 Pythagorean minor seventh 10: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 1: 13/12 138.5727 tridecimal 2/3-tone 2: 144/143 12.0644 Grossma 3: 88/81 143.4979 2nd undecimal neutral second 4: 9/8 203.9100 major whole tone 5: 9/8 203.9100 major whole tone 6: 256/243 90.2250 limma, Pythagorean minor second 7: 1053/1024 48.3477 tridecimal major diesis 8: 144/143 12.0644 Grossma 9: 88/81 143.4979 2nd undecimal neutral second 10: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 144/143 12.064 cents Grossma 1: 1 1053/1024 48.348 cents tridecimal major diesis 1: 1 256/243 90.225 cents limma, Pythagorean minor second 1: 1 13/12 138.573 cents tridecimal 2/3-tone 1: 2 88/81 143.498 cents 2nd undecimal neutral second 1: 3 9/8 203.910 cents major whole tone 2: 1 729/704 60.412 cents undecimal major diesis 2: 1 13/12 138.573 cents tridecimal 2/3-tone 2: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 2: 2 128/117 155.562 cents 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 2: 2 11/9 347.408 cents undecimal neutral third 2: 1 81/64 407.820 cents Pythagorean major third 3: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 3: 1 9/8 203.910 cents major whole tone 3: 1 32/27 294.135 cents Pythagorean minor third 3: 1 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 3: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 3: 2 16/13 359.472 cents tridecimal neutral third 3: 1 143/108 485.981 cents 3: 1 4/3 498.045 cents perfect fourth 3: 1 11/8 551.318 cents undecimal semi-augmented fourth 4: 1 32/27 294.135 cents Pythagorean minor third 4: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 4: 1 81/64 407.820 cents Pythagorean major third 4: 4 4/3 498.045 cents perfect fourth 4: 1 351/256 546.393 cents 4: 1 18/13 563.382 cents tridecimal augmented fourth 4: 1 352/243 641.543 cents 5: 2 4/3 498.045 cents perfect fourth 5: 1 192/143 510.109 cents 5: 1 351/256 546.393 cents 5: 1 243/176 558.457 cents 5: 1 352/243 641.543 cents 5: 1 512/351 653.607 cents 5: 1 143/96 689.891 cents 5: 2 3/2 701.955 cents perfect fifth 6: 1 243/176 558.457 cents 6: 1 13/9 636.618 cents tridecimal diminished fifth 6: 1 512/351 653.607 cents 6: 4 3/2 701.955 cents perfect fifth 6: 1 128/81 792.180 cents Pythagorean minor sixth 6: 1 44/27 845.453 cents neutral sixth 6: 1 27/16 905.865 cents Pythagorean major sixth 7: 1 16/11 648.682 cents undecimal semi-diminished fifth 7: 1 3/2 701.955 cents perfect fifth 7: 1 216/143 714.019 cents 7: 2 13/8 840.528 cents tridecimal neutral sixth 7: 1 44/27 845.453 cents neutral sixth 7: 1 64/39 857.517 cents 39th subharmonic 7: 1 27/16 905.865 cents Pythagorean major sixth 7: 1 16/9 996.090 cents Pythagorean minor seventh 7: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 8: 1 128/81 792.180 cents Pythagorean minor sixth 8: 2 18/11 852.592 cents undecimal neutral sixth 8: 1 64/39 857.517 cents 39th subharmonic 8: 1 27/16 905.865 cents Pythagorean major sixth 8: 2 117/64 1044.438 cents 8: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 8: 1 24/13 1061.427 cents tridecimal neutral seventh 8: 1 1408/729 1139.588 cents 9: 3 16/9 996.090 cents Pythagorean minor seventh 9: 2 81/44 1056.502 cents 2nd undecimal neutral seventh 9: 1 24/13 1061.427 cents tridecimal neutral seventh 9: 1 243/128 1109.775 cents Pythagorean major seventh 9: 1 2048/1053 1151.652 cents 9: 2 143/72 1187.936 cents Highest number of different intervals for one interval class: 9 Average number of different intervals per interval class: 7.55556 = 68/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 138.6 150.6 294.1 498.0 702.0 792.2 840.5 852.6 996.1 1200.0 138.6 : 12.1 155.6 359.5 563.4 653.6 702.0 714.0 857.5 1061.4 1200.0 150.6 : 143.5 347.4 551.3 641.5 689.9 702.0 845.5 1049.4 1187.9 1200.0 294.1 : 203.9 407.8 498.0 546.4 558.5 702.0 905.9 1044.4 1056.5 1200.0 498.0 : 203.9 294.1 342.5 354.5 498.0 702.0 840.5 852.6 996.1 1200.0 702.0 : 90.2 138.6 150.6 294.1 498.0 636.6 648.7 792.2 996.1 1200.0 792.2 : 48.3 60.4 203.9 407.8 546.4 558.5 702.0 905.9 1109.8 1200.0 840.5 : 12.1 155.6 359.5 498.0 510.1 653.6 857.5 1061.4 1151.7 1200.0 852.6 : 143.5 347.4 486.0 498.0 641.5 845.5 1049.4 1139.6 1187.9 1200.0 996.1 : 203.9 342.5 354.5 498.0 702.0 905.9 996.1 1044.4 1056.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 12.0644 .. 203.9100 cents 143/128, 191.8456 cents 144/143, 12.0644 cents 2: 60.4121 .. 407.8200 cents 11/9, 347.4079 cents 81/88,-143.4979 cents 3: 150.6371 .. 551.3179 cents 121/96, 400.6809 cents 256/297,-257.1829 cents 4: 294.1350 .. 641.5429 cents 11/9, 347.4079 cents 256/297,-257.1829 cents 5: 498.0450 .. 701.9550 cents 9/8, 203.9100 cents 81/88,-143.4979 cents 6: 558.4571 .. 905.8650 cents 11/9, 347.4079 cents 81/88,-143.4979 cents 7: 648.6821 .. 1049.3629 cents 121/96, 400.6809 cents 256/297,-257.1829 cents 8: 792.1800 .. 1139.5879 cents 11/9, 347.4079 cents 256/297,-257.1829 cents 9: 996.0900 .. 1187.9356 cents 143/128, 191.8456 cents 81/88,-143.4979 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 144/143, 12.0644 cents, class 1 Average step (divided formal octave): 120.0000 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 9.946622 Largest / Average step : 1.699250 Largest / Smallest step : 16.901797 Median interval of one step : 141.03530 cents, amount: 0 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 117.52345 cents, oct.: 1175.23446 cents Scale is not proper Step pattern alph. order: ABCDDEFBCD Step pattern size order : DAEFFCBAEF Scale is not a Constant Structure Scale diversity : 1.370424 Lumma stability : 0.020107 Lumma impropriety factor : 0.899313 Rothenberg efficiency : 0.397302 redundancy: 0.602698 Efficiency x scale size : 3.973016 Number of different interval sizes : 44 = 4.88889 / class Number of one step interval sizes : 6 Highest interval variety : 9 Mean interval variety : 7.55556 = 68/9 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 352/351, 4.9253 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 7 Most common triad is 0.0 498.045 701.955 cents, amount: 4 Number of recognisable fifths : 9, average 701.9550 cents 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 = 30.0000% Scale is n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 13 Odd number limit : 1053 (O: 1053 U: 1053) Highest odd numerator or denominator: 81 Scale harmonicity : 0.015075 Average absolute harmonicity : 0.188928 Specific harmonicity : 0.098264 Fundamental : 1/7128, -12.7993 octaves, 0.0367 Hz. Guide tone : 14976, 13.8704 octaves, 3918104.466 Hz. Exponens Consonantiae : 1.067489E+08, 26.66965 octaves Euler's gradus suavitatis : 45 Sum of Mann's harmonic distance : 203.0, average 20.30000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.55901, average 0.95590 Sum of Tenney's harmonic distance : 19.89633, average 1.98963 Vogel's harmonic complexity : 25.90000 Wille's k value : 5791 Wilson's harmonic complexity : 42 Rectangular lattice diameter : 8 Triangular lattice diameter : 6 Lattice compactness : 242.69234, average 4.41259 Lattice compactness (without 2's) : 127.97700, average 2.32685 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 7 1.60000 28 1 3: -4 .. 2 -0.70000 15 5 11: -1 .. 0 -0.20000 2 2 13: 0 .. 1 0.20000 2 2 Average exponent except 2's :-7 / 10 =-0.70000 Average absolute exponent except 2's: 19 / 10 = 1.90000 Scale is weakly epimorphic with val: <10 17 33 35|
FIT/MODE
10: 1 0 1 2 2 0 1 0 1 2 N SD: 33.9657 c. M: 72.1800 c. 11: 1 0 2 2 1 1 1 0 1 2 N SD: 32.6334 c. M:-47.4095 c. 12: 1 1 1 2 2 1 0 1 1 2 N SD: 28.1656 c. M:-49.3629 c. 14: 2 0 1 3 2 1 1 0 2 2 N SD: 22.7820 c. M: 36.9921 c. 16: 2 0 2 3 2 2 0 0 2 3 N SD: 20.3541 c. M:-32.8200 c. 17: 2 0 2 3 3 1 1 0 2 3 N G SD: 8.0480 c. M: 15.7094 c. 24: 3 0 3 4 4 2 1 0 3 4 N SD: 5.8815 c. M:-11.4273 c. 41: 5 0 5 7 7 3 2 0 5 7 N SD: 4.1074 c. M:-8.2528 c. 53: 6 1 6 9 9 4 2 1 6 9 N SD: 3.7101 c. M:-7.8535 c. 58: 7 0 7 10 10 4 3 0 7 10 N SD: 4.6975 c. M:-7.7482 c. 61: 7 1 7 10 11 4 3 0 8 10 N SD: 5.2759 c. M:-7.1887 c. 62: 7 1 7 11 10 5 2 1 7 11 N SD: 4.9750 c. M: 8.9932 c. 65: 8 0 8 11 11 5 3 0 8 11 N SD: 4.2926 c. M:-9.1196 c. 70: 8 1 8 12 12 5 3 1 8 12 N SD: 2.4814 c. M:-4.5508 c. 77: 9 1 9 13 13 6 3 1 9 13 N SD: 2.5512 c. M:-5.2071 c. 94: 11 1 11 16 16 7 4 1 11 16 N SD: 1.4974 c. M:-2.7271 c. 159: 18 2 19 27 27 12 6 2 19 27 N SD: 1.2453 c. M: 2.7918 c. 167: 19 2 20 28 29 12 7 2 20 28 N SD: 1.7668 c. M:-2.7124 c. 171: 20 1 21 29 29 13 7 2 20 29 N SD: 1.7370 c. M:-3.5483 c. 173: 20 2 20 30 29 13 7 2 21 29 N SD: 1.6434 c. M: 2.8055 c. 176: 20 2 21 30 30 13 7 2 21 30 N SD: 1.0997 c. M: 2.2090 c. 183: 21 2 22 31 31 14 7 2 22 31 N SD: 0.7275 c. M:-1.2626 c. 200: 23 2 24 34 34 15 8 2 24 34 N SD: 0.3776 c. M: 0.6371 c. 294: 34 3 35 50 50 22 12 3 35 50 N SD: 0.2683 c. M:-0.4692 c. 477: 55 5 57 81 81 36 19 5 57 81 N SD: 0.2035 c. M:-0.3063 c. 494: 57 5 59 84 84 37 20 5 59 84 N SD: 0.1286 c. M: 0.2772 c. 694: 80 7 83 118 118 52 28 7 83 118 N SD: 0.1659 c. M: 0.2492 c. 718: 83 7 86 122 122 54 29 7 86 122 N SD: 0.1185 c. M: 0.2244 c. 971: 112 10 116 165 165 73 39 10 116 165 N SD: 0.0933 c. M: 0.1587 c. 995: 115 10 119 169 169 75 40 10 119 169 N SD: 0.1015 c. M:-0.1818 c. 1012: 117 10 121 172 172 76 41 10 121 172 N SD: 0.0876 c. M:-0.1838 c. 1195: 138 12 143 203 203 90 48 12 143 203 N SD: 0.0555 c. M:-0.1213 c. 1395: 161 14 167 237 237 105 56 14 167 237 N SD: 0.0717 c. M: 0.1189 c. 1489: 172 15 178 253 253 112 60 15 178 253 N SD: 0.0364 c. M:-0.0681 c. 1689: 195 17 202 287 287 127 68 17 202 287 N SD: 0.0152 c. M: 0.0303 c.
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x x x x 4 S SD: 0.0000 cents 3 x x x 4 x x x 5 x 6 S SD: 10.5889 cents 4 x x 5 x 6 x x x 7:8 S SD: 24.0316 cents 5 x x 6:7 x 8 x x 9:10 S SD: 18.4632 cents 6 x x 7:8:9 x x 10:11:12 S SD: 11.2922 cents 7 x x 8:9 x 11 x x 12:14 SD: 21.8962 cents 8 x 9 x 11:12 x 13 x 14:16 SD: 13.3535 cents 9 x 10:11:12 x 14 x 15:16:18 S SD: 10.6900 cents 10 x 11:12:13:15:16 x x 18:20 SD: 8.4698 cents 11 x 12:13:15 x 17 x 18:20:22 SD: 9.6226 cents 12:13 x 14:16:18:19 x 20:21:24 S SD: 6.2590 cents 13:14 x 15:17:20 x 21 x 23:26 SD: 10.5795 cents 14:15 x 17:19:21:22 x 23:25:28 SD: 7.1466 cents 15:16 x 18:20:23:24 x 25:27:30 SD: 8.4456 cents 16:17 x 19:21:24:25:26 x 28:32 SD: 6.8585 cents 17:18:19:20:23:26:27 x 28:30:34 SD: 8.3339 cents 18 x 20:21:24:27:28:29 x 32:36 SD: 6.5151 cents 19 x 21:23:25:29:30 x 31:34:38 SD: 7.3342 cents 20 x 22:24:27:30:32 x 33:36:40 S SD: 5.9463 cents 21 x 23:25:28:32:33:34 x 37:42 SD: 4.3752 cents 22 x 24:26:29:33:35 x 36:39:44 SD: 2.9988 cents 23:25 x 27:31:35:36:37:38:41:46 SD: 5.1587 cents 24:26 x 28:32:36:38:39 x 43:48 SD: 3.8248 cents 25:27 x 30:33:38:40 x 41:44:50 SD: 5.7276 cents 26:28 x 31:35:39:41:42:43:46:52 SD: 3.5392 cents 27:29 x 32:36:41:43:44 x 48:54 SD: 3.7036 cents 28:30:31:33:37:42:44 x 46:50:56 SD: 4.3818 cents 29:31:32:34:39:44:46:47 x 52:58 SD: 5.1811 cents 30 x 33:36:40:45:47 x 49:53:60 SD: 3.9928 cents 31 x 34:37:41:47:49:50:51:55:62 SD: 3.5826 cents 32 x 35:38:43:48:51:52 x 57:64 SD: 2.6268 cents 33 x 36:39:44:50:52 x 54:59:66 SD: 2.6442 cents 34 x 37:40:45:51:54:55:56:60:68 SD: 3.0889 cents 35:38 x 41:47:53:55:57 x 62:70 SD: 3.9346 cents 36:39 x 43:48:54:57 x 59:64:72 SD: 1.7680 cents 37:40 x 44:49:56:58:60:61:66:74 SD: 3.2110 cents 38:41 x 45:51:57:60 x 62:68:76 SD: 2.2941 cents 40:43:44:47:53:60:63:65 x 71:80 SD: 3.0766 cents 41:44:45:49:55:62:65 x 67:73:82 SD: 3.4012 cents 42 x 46:50:56:63:66:68:69:75:84 SD: 2.0703 cents 43 x 47:51:57:65:68:70 x 76:86 SD: 2.5202 cents 44 x 48:52:59:66:70 x 72:78:88 SD: 2.0926 cents 45 x 49:53:60:68:71:73:74:80:90 SD: 2.1665 cents 46:50 x 55:61:69:73:75 x 82:92 SD: 2.6909 cents 47:51 x 56:63:71:74:76:77:84:94 SD: 2.5526 cents 48:52 x 57:64:72:76:78:79:85:96 SD: 1.4424 cents 49:53 x 58:65:74:77 x 80:87:98 SD: 2.3138 cents 50:54:55:59:67:75:79:81:82:89:100 SD: 2.0372 cents 51:55:56:60:68:77:81:83 x 91:102 SD: 2.7277 cents 52:56:57:62:69:78:82 x 85:92:104 SD: 2.3255 cents 53:57:58:63:71:80:84:86:87:94:106 SD: 2.1846 cents 54 x 59:64:72:81:85:88 x 96:108 SD: 1.0990 cents 55 x 60:65:73:83:87:89:90:98:110 SD: 1.8165 cents 56 x 61:66:75:84:88:91:92:100:112 SD: 2.1091 cents 57 x 62:68:76:86:90 x 93:101:114 SD: 2.2247 cents 58:63 x 69:77:87:92:94:95:103:116 SD: 1.5287 cents 59:64 x 70:79:89:93:96:97:105:118 SD: 1.7595 cents 60:65 x 71:80:90:95 x 98:107:120 SD: 0.9537 cents 62:67:68:73:83:93:98:101 x 110:124 SD: 1.9675 cents 63:68:69:75:84:95:100:102:103:112:126 SD: 1.8234 cents 64:69:70:76:85:96:101:104:105:114:128 SD: 1.3576 cents 65:70:71:77:87:98:103 x 106:116:130 SD: 2.0365 cents 66 x 72:78:88:99:104:107:108:117:132 SD: 1.0488 cents 67 x 73:79:89:101:106:109:110:119:134 SD: 1.7325 cents 68 x 74:81:91:102:107 x 111:121:136 SD: 1.8096 cents 69:75 x 82:92:104:109:112:113:123:138 SD: 1.3752 cents 70:76 x 83:93:105:111:114:115:124:140 SD: 1.5275 cents 71:77 x 84:95:107:112:115:116:126:142 SD: 1.4628 cents 72:78:79:85:96:108:114:117:118:128:144 SD: 1.2816 cents 73:79:80:87:97:110:115:119 x 130:146 SD: 1.9967 cents 74:80:81:88:99:111:117:120:121:132:148 SD: 1.2840 cents 76:82:83:90:101:114:120 x 124:135:152 SD: 1.2031 cents 78 x 85:92:104:117:123:127:128:139:156 SD: 1.3123 cents 79 x 86:94:105:119:125:128:129:140:158 SD: 1.6383 cents 80 x 87:95:107:120:126:130:131:142:160 SD: 1.1752 cents 81:88 x 96:108:122:128:132:133:144:162 SD: 1.2871 cents 82:89 x 97:109:123:130:133:134:146:164 SD: 1.1318 cents 84:91:92:100:112:126:133 x 137:149:168 SD: 1.4304 cents 85:92:93:101:113:128:134:138:139:151:170 SD: 1.1939 cents 86:93:94:102:115:129:136:140:141:153:172 SD: 0.8465 cents 90 x 98:107:120:135:142:146:147:160:180 SD: 0.9018 cents 91 x 99:108:121:137:144:148:149:162:182 SD: 1.1420 cents 92:100 x 109:123:138:145:150:151:164:184 SD: 1.4027 cents 93:101 x 110:124:140:147:151:152:165:186 SD: 1.0406 cents 96:104:105:114:128:144:152:156:157:171:192 SD: 0.7451 cents 102 x 111:121:136:153:161:166:167:181:204 SD: 0.7234 cents 103 x 112:122:137:155:163:167:169:183:206 SD: 1.2459 cents 104:113 x 123:139:156:164:169:170:185:208 SD: 0.9591 cents 107:116:117:127:143:161:169:174:175:190:214 SD: 0.8764 cents 108:117:118:128:144:162:171:176:177:192:216 SD: 0.7066 cents 114 x 124:135:152:171:180:185:187:203:228 SD: 0.8683 cents 115:125 x 136:153:173:182:187:188:204:230 SD: 1.1755 cents 117:127:128:139:156:176:185:190:191:208:234 SD: 0.9836 cents 118:128:129:140:157:177:186:192:193:210:236 SD: 0.7968 cents 120:130:131:142:160:180:190:195:196:213:240 SD: 0.6149 cents 126 x 137:149:168:189:199:205:206:224:252 SD: 0.8284 cents 129:140:141:153:172:194:204:210:211:229:258 SD: 0.7772 cents 130:141:142:154:173:195:205:211:213:231:260 SD: 0.6634 cents 134:145:146:159:179:201:212:218:219:238:268 SD: 0.6193 cents 144:156:157:171:192:216:228:234:236:256:288 SD: 0.5564 cents 166:180:181:197:221:249:262:270:272:295:332 SD: 0.5309 cents 168:182:183:199:224:252:265:273:275:299:336 SD: 0.4638 cents 190:206:207:225:253:285:300:309:311:338:380 SD: 0.4464 cents 216:234:236:256:288:324:341:351:353:384:432 SD: 0.3867 cents 240:260:262:284:320:360:379:390:393:427:480 SD: 0.3667 cents 242:262:264:287:323:363:382:393:396:430:484 SD: 0.3359 cents 253:274:276:300:337:380:400:411:414:450:506 SD: 0.3297 cents 264:286:288:313:352:396:417:429:432:469:528 SD: 0.1575 cents 384:416:419:455:512:576:607:624:628:683:768 SD: 0.1522 cents 432:468:471:512:576:648:683:702:707:768:864 SD: 0.1330 cents 528:572:576:626:704:792:834:858:864:939:1056 SD: 0.1160 cents