Scala analysis: xen18-erlich-negripent-19
10L 9s MOS for Negripent, L=66.56, s=59.58
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 66.560 cents 66.560000 2: 126.140 cents 126.140000 3: 192.700 cents 192.700000 4: 252.280 cents 252.280000 5: 318.840 cents 318.840000 6: 378.420 cents 378.420000 7: 444.980 cents 444.980000 8: 504.560 cents 504.560000 9: 571.120 cents 571.120000 10: 630.700 cents 630.700000 11: 697.260 cents 697.260000 12: 756.840 cents 756.840000 13: 823.400 cents 823.400000 14: 882.980 cents 882.980000 15: 949.540 cents 949.540000 16: 1009.120 cents 1009.120000 17: 1075.680 cents 1075.680000 18: 1135.260 cents 1135.260000 19: 1201.820 cents 1201.820000
SHOW/INTERVAL
0: 66.5600 cents 66.5600 1: 66.5600 cents 66.5600 2: 59.5800 cents 59.5800 3: 66.5600 cents 66.5600 4: 59.5800 cents 59.5800 5: 66.5600 cents 66.5600 6: 59.5800 cents 59.5800 7: 66.5600 cents 66.5600 8: 59.5800 cents 59.5800 9: 66.5600 cents 66.5600 10: 59.5800 cents 59.5800 11: 66.5600 cents 66.5600 12: 59.5800 cents 59.5800 13: 66.5600 cents 66.5600 14: 59.5800 cents 59.5800 15: 66.5600 cents 66.5600 16: 59.5800 cents 59.5800 17: 66.5600 cents 66.5600 18: 59.5800 cents 59.5800 19: 66.5600 cents 66.5600
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 9 59.58000 cents 1: 10 66.56000 cents 2: 18 126.14000 cents 2: 1 133.12000 cents 3: 8 185.72000 cents 3: 11 192.70000 cents 4: 17 252.28000 cents 4: 2 259.26000 cents 5: 7 311.86000 cents 5: 12 318.84000 cents 6: 16 378.42000 cents 6: 3 385.40000 cents 7: 6 438.00000 cents 7: 13 444.98000 cents 8: 15 504.56000 cents 8: 4 511.54000 cents 9: 5 564.14000 cents 9: 14 571.12000 cents 10: 14 630.70000 cents 10: 5 637.68000 cents 11: 4 690.28000 cents 11: 15 697.26000 cents 12: 13 756.84000 cents 12: 6 763.82000 cents 13: 3 816.42000 cents 13: 16 823.40000 cents 14: 12 882.98000 cents 14: 7 889.96000 cents 15: 2 942.56000 cents 15: 17 949.54000 cents 16: 11 1009.12000 cents 16: 8 1016.10000 cents 17: 1 1068.70000 cents 17: 18 1075.68000 cents 18: 10 1135.26000 cents 18: 9 1142.24000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 0.0 : 66.6 126.1 192.7 252.3 318.8 378.4 445.0 504.6 571.1 630.7 697.3 756.8 823.4 883.0 949.5 1009.1 1075.7 1135.3 1201.8 66.6 : 59.6 126.1 185.7 252.3 311.9 378.4 438.0 504.6 564.1 630.7 690.3 756.8 816.4 883.0 942.6 1009.1 1068.7 1135.3 1201.8 126.1 : 66.6 126.1 192.7 252.3 318.8 378.4 445.0 504.6 571.1 630.7 697.3 756.8 823.4 883.0 949.5 1009.1 1075.7 1142.2 1201.8 192.7 : 59.6 126.1 185.7 252.3 311.9 378.4 438.0 504.6 564.1 630.7 690.3 756.8 816.4 883.0 942.6 1009.1 1075.7 1135.3 1201.8 252.3 : 66.6 126.1 192.7 252.3 318.8 378.4 445.0 504.6 571.1 630.7 697.3 756.8 823.4 883.0 949.5 1016.1 1075.7 1142.2 1201.8 318.8 : 59.6 126.1 185.7 252.3 311.9 378.4 438.0 504.6 564.1 630.7 690.3 756.8 816.4 883.0 949.5 1009.1 1075.7 1135.3 1201.8 378.4 : 66.6 126.1 192.7 252.3 318.8 378.4 445.0 504.6 571.1 630.7 697.3 756.8 823.4 890.0 949.5 1016.1 1075.7 1142.2 1201.8 445.0 : 59.6 126.1 185.7 252.3 311.9 378.4 438.0 504.6 564.1 630.7 690.3 756.8 823.4 883.0 949.5 1009.1 1075.7 1135.3 1201.8 504.6 : 66.6 126.1 192.7 252.3 318.8 378.4 445.0 504.6 571.1 630.7 697.3 763.8 823.4 890.0 949.5 1016.1 1075.7 1142.2 1201.8 571.1 : 59.6 126.1 185.7 252.3 311.9 378.4 438.0 504.6 564.1 630.7 697.3 756.8 823.4 883.0 949.5 1009.1 1075.7 1135.3 1201.8 630.7 : 66.6 126.1 192.7 252.3 318.8 378.4 445.0 504.6 571.1 637.7 697.3 763.8 823.4 890.0 949.5 1016.1 1075.7 1142.2 1201.8 697.3 : 59.6 126.1 185.7 252.3 311.9 378.4 438.0 504.6 571.1 630.7 697.3 756.8 823.4 883.0 949.5 1009.1 1075.7 1135.3 1201.8 756.8 : 66.6 126.1 192.7 252.3 318.8 378.4 445.0 511.5 571.1 637.7 697.3 763.8 823.4 890.0 949.5 1016.1 1075.7 1142.2 1201.8 823.4 : 59.6 126.1 185.7 252.3 311.9 378.4 445.0 504.6 571.1 630.7 697.3 756.8 823.4 883.0 949.5 1009.1 1075.7 1135.3 1201.8 883.0 : 66.6 126.1 192.7 252.3 318.8 385.4 445.0 511.5 571.1 637.7 697.3 763.8 823.4 890.0 949.5 1016.1 1075.7 1142.2 1201.8 949.5 : 59.6 126.1 185.7 252.3 318.8 378.4 445.0 504.6 571.1 630.7 697.3 756.8 823.4 883.0 949.5 1009.1 1075.7 1135.3 1201.8 1009.1: 66.6 126.1 192.7 259.3 318.8 385.4 445.0 511.5 571.1 637.7 697.3 763.8 823.4 890.0 949.5 1016.1 1075.7 1142.2 1201.8 1075.7: 59.6 126.1 192.7 252.3 318.8 378.4 445.0 504.6 571.1 630.7 697.3 756.8 823.4 883.0 949.5 1009.1 1075.7 1135.3 1201.8 1135.3: 66.6 133.1 192.7 259.3 318.8 385.4 445.0 511.5 571.1 637.7 697.3 763.8 823.4 890.0 949.5 1016.1 1075.7 1142.2 1201.8 1201.8
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 59.5800 .. 66.5600 cents 6.98000 cents 59.58000 cents 2: 126.1400 .. 133.1200 cents 6.98000 cents 59.58000 cents 3: 185.7200 .. 192.7000 cents 6.98000 cents 52.60000 cents 4: 252.2800 .. 259.2600 cents 6.98000 cents 59.58000 cents 5: 311.8600 .. 318.8400 cents 6.98000 cents 52.60000 cents 6: 378.4200 .. 385.4000 cents 6.98000 cents 59.58000 cents 7: 438.0000 .. 444.9800 cents 6.98000 cents 52.60000 cents 8: 504.5600 .. 511.5400 cents 6.98000 cents 59.58000 cents 9: 564.1400 .. 571.1200 cents 6.98000 cents 52.60000 cents 10: 630.7000 .. 637.6800 cents 6.98000 cents 59.58000 cents 11: 690.2800 .. 697.2600 cents 6.98000 cents 52.60000 cents 12: 756.8400 .. 763.8200 cents 6.98000 cents 59.58000 cents 13: 816.4200 .. 823.4000 cents 6.98000 cents 52.60000 cents 14: 882.9800 .. 889.9600 cents 6.98000 cents 59.58000 cents 15: 942.5600 .. 949.5400 cents 6.98000 cents 52.60000 cents 16: 1009.1200 .. 1016.1000 cents 6.98000 cents 59.58000 cents 17: 1068.7000 .. 1075.6800 cents 6.98000 cents 52.60000 cents 18: 1135.2600 .. 1142.2400 cents 6.98000 cents 59.58000 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 59.58000 cents, class 1 Average step (divided formal octave): 63.2537 cents Largest one step interval : 66.56000 cents Average / Smallest step : 1.061660 Largest / Average step : 1.052271 Largest / Smallest step : 1.117153 Median interval of one step : 66.56000 cents, amount: 10 Most common interval of one step : 66.56000 cents, amount: 10 Least squares average step : 63.21130 cents, oct.: 1201.01462 cents Scale is strictly proper Scale has Myhill's property chromas: 6.98000 cents and 52.60000 cents, ratio: 7.535817 generators: 2 of 126.14000 cents and 17 of 1075.68000 cents ET pair of linear temperament : 10&19 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 1896-tone equal temperament with octave 1201.820 cents degrees: 105 199 304 398 503 597 702 796 901 995 1100 1194 1299 1393 1498 1592 1697 1791 1896 generators: 199 and 1697 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABABABABABABABABA Step pattern size order : LSLSLSLSLSLSLSLSLSL Scale is a Constant Structure, by a margin of 52.60000 cents Scale diversity : 1.067709 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.895459 Rothenberg efficiency : 0.701754 redundancy: 0.298246 Efficiency x scale size : 13.333333 Number of different interval sizes : 36 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 6.98000 cents Most common intervals : 126.14000 cents & inv., amount: 18 Scale is a chain of 9 triads 0.0 126.140 252.280 cents Most common triad is 0.0 126.140 1075.680 cents, amount: 17 Number of recognisable fifths : 19, average 695.7905 cents Number of recognisable fourths : 19, average 506.0295 cents Number of appreciable fourths : 15, average 504.5600 cents Scale contains two identical disjunct "tetrachords" of 9 notes Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 19 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions with margin 6.9800 cents: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Limited inverse transpositions with margin 6.9800 cents: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 9-10 -- Rational properties --
FIT/MODE
19: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 2.0122 c. M: 3.3063 c. 105: 6 5 6 5 6 5 6 5 6 5 6 5 6 5 6 5 6 5 6 SP M ME I SD: 1.2874 c. M:-2.1154 c. 124: 7 6 7 6 7 6 7 6 7 6 7 6 7 6 7 6 7 6 7 SP M ME I SD: 0.7818 c. M: 1.2847 c. 143: 8 7 8 7 8 7 8 7 8 7 8 7 8 7 8 7 8 7 8 SP M ME I SD: 0.4106 c. M: 0.6747 c. 162: 9 8 9 8 9 8 9 8 9 8 9 8 9 8 9 8 9 8 9 SP M ME I SD: 0.1264 c. M: 0.2078 c. 181: 10 9 10 9 10 9 10 9 10 9 10 9 10 9 10 9 10 9 10 SP M ME I SD: 0.0980 c. M: 0.1611 c. 343: 19 17 19 17 19 17 19 17 19 17 19 17 19 17 19 17 19 17 19 SP M DE I SD: 0.0080 c. M: 0.0131 c. 1210: 67 60 67 60 67 60 67 60 67 60 67 60 67 60 67 60 67 60 67 SP M DE I SD: 0.0079 c. M: 0.0129 c. 1553: 86 77 86 77 86 77 86 77 86 77 86 77 86 77 86 77 86 77 86 SP M DE I SD: 0.0044 c. M: 0.0072 c. 1896: 105 94 105 94 105 94 105 94 105 94 105 94 105 94 105 94 105 94 105 SP M DE I SD: 0.0021 c. M: 0.0035 c. 2239: 124 111 124 111 124 111 124 111 124 111 124 111 124 111 124 111 124 111 124 SP M DE I SD: 0.0006 c. M: 0.0010 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 1.8200 cents 2 .. 4 match: 2 H SD: 2.5177 cents 3 .. 6 match: 3 H SD: 2.3012 cents 4 .. 8 match: 4 H SD: 5.3596 cents 5 .. 10 match: 5 H SD: 3.5187 cents 6 .. 12 match: 6 H SD: 5.2047 cents 7 .. 14 match: 7 H SD: 5.8282 cents 8 .. 16 match: 8 H SD: 4.7256 cents 9 .. 18 match: 9 H SD: 4.8218 cents 10 .. 20 match: 10 H SD: 5.2130 cents 11 .. 22 match: 11 H SD: 6.6812 cents 12 .. 24 match: 12 H SD: 4.7040 cents 13 .. 26 match: 13 H SD: 4.3030 cents 14 .. 28 match: 14 H SD: 4.0391 cents 15 .. 30 match: 15 H SD: 3.9354 cents 16 .. 32 match: 16 H SD: 4.0943 cents 17 .. 34 match: 16 S SD: 5.1544 cents 18 .. 36 match: 17 S SD: 3.5349 cents 19 .. 38 match: 17 SD: 4.8562 cents 20 .. 40 match: 18 SD: 3.1616 cents 21 .. 42 match: 18 SD: 3.8280 cents 22 .. 44 match: 18 SD: 4.4969 cents 23 .. 46 match: 19 SD: 3.3802 cents 24 .. 48 match: 19 SD: 2.6733 cents 25 .. 50 match: 19 SD: 2.6327 cents 26 .. 52 match: 19 SD: 2.5470 cents 30 .. 60 match: 19 SD: 2.4659 cents 33 .. 66 match: 19 SD: 2.4458 cents 36 .. 72 match: 19 SD: 2.2363 cents 38 .. 76 match: 19 SD: 2.0513 cents 41 .. 82 match: 19 SD: 1.7939 cents 44 .. 88 match: 19 SD: 1.3632 cents 51 .. 102 match: 19 SD: 1.2303 cents 66 .. 132 match: 19 SD: 1.1166 cents 69 .. 138 match: 19 SD: 0.9582 cents 75 .. 150 match: 19 SD: 0.9522 cents 77 .. 154 match: 19 SD: 0.8109 cents 82 .. 164 match: 19 SD: 0.8011 cents 95 .. 190 match: 19 SD: 0.5846 cents 123 .. 246 match: 19 SD: 0.5775 cents 130 .. 260 match: 19 SD: 0.5733 cents 133 .. 266 match: 19 SD: 0.5402 cents 135 .. 270 match: 19 SD: 0.5213 cents 144 .. 288 match: 19 SD: 0.5103 cents 148 .. 296 match: 19 SD: 0.4941 cents 153 .. 306 match: 19 SD: 0.4051 cents 159 .. 318 match: 19 SD: 0.3671 cents 177 .. 354 match: 19 SD: 0.3642 cents 197 .. 394 match: 19 SD: 0.3318 cents 204 .. 408 match: 19 SD: 0.3230 cents 212 .. 424 match: 19 SD: 0.2925 cents 228 .. 456 match: 19 SD: 0.2845 cents 248 .. 497 match: 19 SD: 0.2582 cents 281 .. 563 match: 19 SD: 0.2483 cents 282 .. 565 match: 19 SD: 0.2467 cents 286 .. 573 match: 19 SD: 0.2436 cents 287 .. 575 match: 19 SD: 0.2101 cents 307 .. 615 match: 19 SD: 0.1806 cents 332 .. 665 match: 19 SD: 0.1782 cents 355 .. 711 match: 19 SD: 0.1656 cents 407 .. 815 match: 19 SD: 0.1595 cents 409 .. 819 match: 19 SD: 0.1384 cents 434 .. 869 match: 19 SD: 0.1285 cents 460 .. 921 match: 19 SD: 0.1233 cents 478 .. 957 match: 19 SD: 0.1171 cents 535 .. 1071 match: 19 SD: 0.1156 cents 553 .. 1107 match: 19 SD: 0.1119 cents 593 .. 1187 match: 19 SD: 0.1113 cents 594 .. 1189 match: 19 SD: 0.0960 cents