Scala analysis: Thailand_Ranat_Thum_04
4 (Ranat Thum), Thailand
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 185.000 cents 185.000000 2: 365.000 cents 365.000000 3: 530.000 cents 530.000000 4: 700.000 cents 700.000000 5: 870.000 cents 870.000000 6: 1040.000 cents 1040.000000 7: 1210.000 cents 1210.000000 8: 1390.000 cents 1390.000000 9: 1570.000 cents 1570.000000 10: 1735.000 cents 1735.000000 11: 1905.000 cents 1905.000000 12: 2075.000 cents 2075.000000 13: 2245.000 cents 2245.000000 14: 2415.000 cents 2415.000000 15: 2595.000 cents 2595.000000 16: 2775.000 cents 2775.000000
SHOW/INTERVAL
0: 180.0000 cents 180.0000 1: 185.0000 cents 185.0000 2: 180.0000 cents 180.0000 3: 165.0000 cents 165.0000 4: 170.0000 cents 170.0000 5: 170.0000 cents 170.0000 6: 170.0000 cents 170.0000 7: 170.0000 cents 170.0000 8: 180.0000 cents 180.0000 9: 180.0000 cents 180.0000 10: 165.0000 cents 165.0000 11: 170.0000 cents 170.0000 12: 170.0000 cents 170.0000 13: 170.0000 cents 170.0000 14: 170.0000 cents 170.0000 15: 180.0000 cents 180.0000 16: 180.0000 cents 180.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 165.00000 cents 1: 8 170.00000 cents 1: 5 180.00000 cents 1: 1 185.00000 cents 2: 2 335.00000 cents 2: 6 340.00000 cents 2: 2 345.00000 cents 2: 2 350.00000 cents 2: 2 360.00000 cents 2: 2 365.00000 cents 3: 2 505.00000 cents 3: 4 510.00000 cents 3: 2 515.00000 cents 3: 2 520.00000 cents 3: 1 525.00000 cents 3: 3 530.00000 cents 3: 2 545.00000 cents 4: 2 675.00000 cents 4: 2 680.00000 cents 4: 2 685.00000 cents 4: 2 690.00000 cents 4: 2 695.00000 cents 4: 3 700.00000 cents 4: 1 710.00000 cents 4: 1 715.00000 cents 4: 1 725.00000 cents 5: 2 845.00000 cents 5: 2 855.00000 cents 5: 2 860.00000 cents 5: 3 865.00000 cents 5: 3 870.00000 cents 5: 1 880.00000 cents 5: 1 885.00000 cents 5: 1 890.00000 cents 5: 1 895.00000 cents 6: 4 1025.00000 cents 6: 4 1035.00000 cents 6: 3 1040.00000 cents 6: 1 1050.00000 cents 6: 1 1055.00000 cents 6: 2 1060.00000 cents 6: 1 1065.00000 cents 7: 9 1205.00000 cents 7: 1 1210.00000 cents 7: 1 1220.00000 cents 7: 1 1225.00000 cents 7: 3 1230.00000 cents 7: 1 1235.00000 cents 8: 1 1370.00000 cents 8: 4 1375.00000 cents 8: 3 1385.00000 cents 8: 3 1390.00000 cents 8: 4 1400.00000 cents 8: 1 1405.00000 cents 9: 1 1540.00000 cents 9: 3 1545.00000 cents 9: 1 1550.00000 cents 9: 1 1555.00000 cents 9: 1 1565.00000 cents 9: 9 1570.00000 cents 10: 1 1710.00000 cents 10: 2 1715.00000 cents 10: 1 1720.00000 cents 10: 1 1725.00000 cents 10: 3 1735.00000 cents 10: 4 1740.00000 cents 10: 4 1750.00000 cents 11: 1 1880.00000 cents 11: 1 1885.00000 cents 11: 1 1890.00000 cents 11: 1 1895.00000 cents 11: 3 1905.00000 cents 11: 3 1910.00000 cents 11: 2 1915.00000 cents 11: 2 1920.00000 cents 11: 2 1930.00000 cents 12: 1 2050.00000 cents 12: 1 2060.00000 cents 12: 1 2065.00000 cents 12: 3 2075.00000 cents 12: 2 2080.00000 cents 12: 2 2085.00000 cents 12: 2 2090.00000 cents 12: 2 2095.00000 cents 12: 2 2100.00000 cents 13: 2 2230.00000 cents 13: 3 2245.00000 cents 13: 1 2250.00000 cents 13: 2 2255.00000 cents 13: 2 2260.00000 cents 13: 4 2265.00000 cents 13: 2 2270.00000 cents 14: 2 2410.00000 cents 14: 2 2415.00000 cents 14: 2 2425.00000 cents 14: 2 2430.00000 cents 14: 6 2435.00000 cents 14: 2 2440.00000 cents 15: 1 2590.00000 cents 15: 5 2595.00000 cents 15: 8 2605.00000 cents 15: 2 2610.00000 cents Highest number of different intervals for one interval class: 9 Average number of different intervals per interval class: 6.80000 = 34/5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 0.0 : 185.0 365.0 530.0 700.0 870.0 1040.0 1210.0 1390.0 1570.0 1735.0 1905.0 2075.0 2245.0 2415.0 2595.0 2775.0 185.0 : 180.0 345.0 515.0 685.0 855.0 1025.0 1205.0 1385.0 1550.0 1720.0 1890.0 2060.0 2230.0 2410.0 2590.0 2775.0 365.0 : 165.0 335.0 505.0 675.0 845.0 1025.0 1205.0 1370.0 1540.0 1710.0 1880.0 2050.0 2230.0 2410.0 2595.0 2775.0 530.0 : 170.0 340.0 510.0 680.0 860.0 1040.0 1205.0 1375.0 1545.0 1715.0 1885.0 2065.0 2245.0 2430.0 2610.0 2775.0 700.0 : 170.0 340.0 510.0 690.0 870.0 1035.0 1205.0 1375.0 1545.0 1715.0 1895.0 2075.0 2260.0 2440.0 2605.0 2775.0 870.0 : 170.0 340.0 520.0 700.0 865.0 1035.0 1205.0 1375.0 1545.0 1725.0 1905.0 2090.0 2270.0 2435.0 2605.0 2775.0 1040.0: 170.0 350.0 530.0 695.0 865.0 1035.0 1205.0 1375.0 1555.0 1735.0 1920.0 2100.0 2265.0 2435.0 2605.0 2775.0 1210.0: 180.0 360.0 525.0 695.0 865.0 1035.0 1205.0 1385.0 1565.0 1750.0 1930.0 2095.0 2265.0 2435.0 2605.0 2775.0 1390.0: 180.0 345.0 515.0 685.0 855.0 1025.0 1205.0 1385.0 1570.0 1750.0 1915.0 2085.0 2255.0 2425.0 2595.0 2775.0 1570.0: 165.0 335.0 505.0 675.0 845.0 1025.0 1205.0 1390.0 1570.0 1735.0 1905.0 2075.0 2245.0 2415.0 2595.0 2775.0 1735.0: 170.0 340.0 510.0 680.0 860.0 1040.0 1225.0 1405.0 1570.0 1740.0 1910.0 2080.0 2250.0 2430.0 2610.0 2775.0 1905.0: 170.0 340.0 510.0 690.0 870.0 1055.0 1235.0 1400.0 1570.0 1740.0 1910.0 2080.0 2260.0 2440.0 2605.0 2775.0 2075.0: 170.0 340.0 520.0 700.0 885.0 1065.0 1230.0 1400.0 1570.0 1740.0 1910.0 2090.0 2270.0 2435.0 2605.0 2775.0 2245.0: 170.0 350.0 530.0 715.0 895.0 1060.0 1230.0 1400.0 1570.0 1740.0 1920.0 2100.0 2265.0 2435.0 2605.0 2775.0 2415.0: 180.0 360.0 545.0 725.0 890.0 1060.0 1230.0 1400.0 1570.0 1750.0 1930.0 2095.0 2265.0 2435.0 2605.0 2775.0 2595.0: 180.0 365.0 545.0 710.0 880.0 1050.0 1220.0 1390.0 1570.0 1750.0 1915.0 2085.0 2255.0 2425.0 2595.0 2775.0 2775.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 165.0000 .. 185.0000 cents 20.00000 cents 165.00000 cents 2: 335.0000 .. 365.0000 cents 30.00000 cents 150.00000 cents 3: 505.0000 .. 545.0000 cents 40.00000 cents 140.00000 cents 4: 675.0000 .. 725.0000 cents 50.00000 cents 130.00000 cents 5: 845.0000 .. 895.0000 cents 50.00000 cents 120.00000 cents 6: 1025.0000 .. 1065.0000 cents 40.00000 cents 130.00000 cents 7: 1205.0000 .. 1235.0000 cents 30.00000 cents 140.00000 cents 8: 1370.0000 .. 1405.0000 cents 35.00000 cents 135.00000 cents 9: 1540.0000 .. 1570.0000 cents 30.00000 cents 135.00000 cents 10: 1710.0000 .. 1750.0000 cents 40.00000 cents 140.00000 cents 11: 1880.0000 .. 1930.0000 cents 50.00000 cents 130.00000 cents 12: 2050.0000 .. 2100.0000 cents 50.00000 cents 120.00000 cents 13: 2230.0000 .. 2270.0000 cents 40.00000 cents 130.00000 cents 14: 2410.0000 .. 2440.0000 cents 30.00000 cents 140.00000 cents 15: 2590.0000 .. 2610.0000 cents 20.00000 cents 150.00000 cents
SHOW DATA
Number of notes : 16 -- Interval properties -- Smallest interval : 165.00000 cents, class 1 Average step (divided formal octave): 173.4375 cents Largest one step interval : 185.00000 cents Average / Smallest step : 1.051136 Largest / Average step : 1.066667 Largest / Smallest step : 1.121212 Median interval of one step : 170.00000 cents, amount: 8 Most common interval of one step : 170.00000 cents, amount: 8 Least squares average step : 173.22193 cents, oct.: 2771.55080 cents Scale is strictly proper Scale is a mode of a 555-tone equal temperament with octave 2775.000 cents degrees: 37 73 106 140 174 208 242 278 314 347 381 415 449 483 519 555 Least number of segments generator : 278 of 1390.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 451 of 2255.000 cents and inv. generated superset size: 101 = 85 more = 631.250% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDDDDBBCDDDDBB Step pattern size order : DCABBBBCCABBBBCC Scale is a Constant Structure, by a margin of 120.00000 cents Scale diversity :-0.235204 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.800000 Number of different interval sizes : 102 = 6.80000 / class Number of one step interval sizes : 4 Highest interval variety : 9 Mean interval variety : 6.80000 = 34/5 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 5.00000 cents Most common intervals : 1205.00000 cents & inv., amount: 9 Number of recognisable fifths : 9, average 699.4444 cents Number of appreciable fifths : 8, average 697.5000 cents Number of recognisable fourths : 6, average 508.3333 cents Formal octave complements present : 9 = 56.2500% 2/1 octave complements present : 0 = 0.0000% Limited transpositions with margin 30.0000 cents: 1 3 4 5 6 7 8 10 11 12 13 14 15 Limited inverse transpositions with margin 30.0000 cents: 1 2 3 5 6 7 8 9 10 12 13 14 15 -- Rational properties --
FIT/MODE
16: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 8.1580 c. M: 18.1250 c. 72: 5 4 5 4 5 4 4 5 5 4 4 5 4 5 4 5 SP D3 I SD: 10.8045 c. M: 18.1250 c. 74: 5 5 4 5 4 5 4 5 5 4 5 4 5 4 5 5 SP D3 I SD: 8.6377 c. M: 15.0000 c. 80: 5 6 4 5 5 5 5 5 5 5 5 5 5 5 5 5 SP T3 SD: 7.9477 c. M:-16.5625 c. 83: 6 5 5 5 5 5 5 6 5 5 5 5 5 5 6 5 SP D3 SD: 7.0930 c. M:-15.6024 c. 87: 6 5 6 5 5 6 5 6 5 5 6 5 5 6 5 6 SP D3 SD: 9.5714 c. M: 14.1379 c. 88: 6 6 5 5 6 5 5 6 6 5 5 6 5 6 5 6 SP SD: 8.4081 c. M:-13.4091 c. 90: 6 6 5 6 5 6 5 6 6 5 6 5 6 5 6 6 SP D3 I SD: 6.5318 c. M: 10.0000 c. 99: 7 6 6 6 6 6 6 7 6 6 6 6 6 6 7 6 SP D3 SD: 5.4374 c. M:-11.8182 c. 106: 7 7 6 7 6 7 6 7 7 6 7 6 7 6 7 7 SP D3 I SD: 5.3089 c. M: 7.1698 c. 115: 8 7 7 7 7 7 7 8 7 7 7 7 7 7 8 7 SP D3 SD: 4.4935 c. M:-11.0870 c. 122: 8 8 7 8 7 8 7 8 8 7 8 7 8 7 8 8 SP D3 I SD: 4.6502 c. M: 6.8443 c. 131: 9 8 8 8 8 8 8 9 8 8 8 8 8 8 9 8 SP D3 SD: 4.0275 c. M:-10.5344 c. 147: 10 9 9 9 9 9 9 10 9 9 9 9 9 9 9 10 SP D3 SD: 3.6631 c. M: 8.7755 c. 152: 10 10 9 9 10 9 9 10 10 9 9 10 9 9 10 10 SP I SD: 3.7921 c. M:-6.3158 c. 163: 11 10 10 10 10 10 10 11 10 10 10 10 10 10 10 11 SP D3 SD: 3.5403 c. M: 7.4847 c. 168: 11 11 10 10 11 10 10 11 11 10 10 11 10 10 11 11 SP I SD: 3.4884 c. M: 6.2500 c. 179: 12 12 10 11 11 11 11 12 11 11 11 11 11 11 11 12 SP SD: 3.3874 c. M:-7.0670 c. 182: 12 12 11 11 11 11 11 12 12 11 11 11 11 11 12 12 SP I SD: 2.9348 c. M: 5.9341 c. 185: 12 12 11 12 11 11 12 12 12 11 11 11 12 11 12 12 SP SD: 4.1458 c. M: 5.0000 c. 189: 13 12 11 12 11 12 11 13 12 11 12 11 12 12 12 12 SP SD: 4.0432 c. M:-7.6190 c. 192: 13 12 12 11 12 12 12 12 13 11 12 12 11 12 13 12 SP SD: 4.0205 c. M:-6.5625 c. 194: 13 13 11 12 12 12 12 12 13 11 12 12 12 12 12 13 SP SD: 3.4756 c. M:-6.9072 c. 195: 13 13 11 12 12 12 12 13 12 12 12 12 12 12 12 13 SP SD: 3.1541 c. M: 5.0000 c. 198: 13 13 12 12 12 12 12 13 13 12 12 12 12 12 13 13 SP I SD: 2.4239 c. M: 4.6970 c. 214: 14 14 13 13 13 13 13 14 14 13 13 13 13 13 14 14 SP I SD: 2.1385 c. M: 4.0421 c. 230: 15 15 14 14 14 14 14 15 15 14 14 14 14 14 15 15 SP I SD: 2.0514 c. M: 4.0217 c. 283: 19 18 17 17 18 17 17 19 18 17 17 18 17 17 19 18 SP SD: 2.4179 c. M: 3.9046 c. 288: 19 19 17 18 17 18 18 18 19 17 18 17 18 18 18 19 SP SD: 2.3619 c. M:-4.0625 c. 293: 20 19 17 18 18 18 18 19 19 17 18 18 18 18 19 19 SP SD: 2.0226 c. M:-4.4198 c. 294: 20 19 17 18 18 18 18 19 19 18 18 18 18 18 19 19 SP SD: 2.0293 c. M:-3.7755 c. 302: 20 20 18 18 19 18 19 19 20 18 18 19 18 19 19 20 SP SD: 2.3308 c. M: 3.7748 c. 304: 20 20 18 19 18 19 19 19 20 18 19 18 19 19 19 20 SP SD: 2.3056 c. M:-4.0625 c. 309: 21 20 18 19 19 19 19 20 20 18 19 19 19 19 20 20 SP SD: 1.6812 c. M:-3.5922 c. 310: 21 20 18 19 19 19 19 20 20 19 19 19 19 19 20 20 SP SD: 1.9747 c. M: 3.4677 c. 318: 21 21 19 19 20 19 20 20 21 19 19 20 19 20 20 21 SP SD: 2.1373 c. M: 3.2547 c. 325: 22 21 19 20 20 20 20 21 21 19 20 20 20 20 21 21 SP SD: 1.4518 c. M:-2.8462 c. 341: 23 22 20 21 21 21 21 22 22 20 21 21 21 21 22 22 SP SD: 1.3421 c. M:-2.5367 c. 403: 27 26 24 25 24 25 25 26 26 24 25 24 25 25 26 26 SP SD: 1.4303 c. M: 2.3821 c. 408: 27 27 24 25 25 25 25 26 27 24 25 25 25 25 27 26 SP SD: 1.3198 c. M:-3.1618 c. 417: 28 27 25 25 26 25 26 27 27 25 25 26 25 26 27 27 SP SD: 1.4411 c. M: 2.3741 c. 419: 28 27 25 26 25 26 26 27 27 25 26 25 26 26 27 27 SP SD: 1.4222 c. M: 2.3986 c. 424: 28 28 25 26 26 26 26 27 28 25 26 26 26 26 27 28 SP SD: 1.2443 c. M: 3.2547 c. 433: 29 28 26 26 27 26 27 28 28 26 26 27 26 27 28 28 SP SD: 1.3102 c. M: 1.9284 c. 440: 29 29 26 27 27 27 27 28 29 26 27 27 27 27 28 29 SP SD: 1.1744 c. M: 2.8977 c. 449: 30 29 27 27 28 27 28 29 29 27 27 28 27 28 29 29 SP SD: 1.2533 c. M: 1.6927 c. 456: 30 30 27 28 28 28 28 29 30 27 28 28 28 28 29 30 SP SD: 1.1805 c. M: 2.5658 c. 491: 33 32 29 30 30 30 30 32 32 29 30 30 30 30 32 32 SP SD: 1.0634 c. M:-2.3625 c. 507: 34 33 30 31 31 31 31 33 33 30 31 31 31 31 33 33 SP SD: 0.7724 c. M:-1.7160 c. 523: 35 34 31 32 32 32 32 34 34 31 32 32 32 32 34 34 SP SD: 0.4992 c. M:-1.1090 c. 539: 36 35 32 33 33 33 33 35 35 32 33 33 33 33 35 35 SP SD: 0.2422 c. M:-0.5380 c. 555: 37 36 33 34 34 34 34 36 36 33 34 34 34 34 36 36 SP SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 .. 5 match: 4 H SD: 5.3751 cents 2 .. 10 match: 8 H SD: 10.1659 cents 3 .. 15 match: 11 SD: 10.0639 cents 4 .. 20 match: 13 SD: 7.6351 cents 5 .. 25 match: 14 SD: 9.7734 cents 6 .. 30 match: 15 SD: 7.5855 cents 7 .. 35 match: 15 SD: 10.2180 cents 8 .. 40 match: 16 SD: 5.2017 cents 12 .. 60 match: 16 SD: 4.5512 cents 16 .. 79 match: 16 SD: 3.7577 cents 17 .. 84 match: 16 SD: 2.6506 cents 25 .. 124 match: 16 SD: 2.2669 cents 26 .. 129 match: 16 SD: 1.7828 cents 34 .. 169 match: 16 SD: 1.2207 cents 51 .. 253 match: 16 SD: 1.1599 cents 52 .. 258 match: 16 SD: 0.9960 cents 61 .. 303 match: 16 SD: 0.8640 cents 64 .. 318 match: 16 SD: 0.7565 cents 72 .. 358 match: 16 SD: 0.6287 cents 81 .. 402 match: 16 SD: 0.6194 cents 86 .. 427 match: 16 SD: 0.5584 cents 90 .. 447 match: 16 SD: 0.4577 cents 98 .. 487 match: 16 SD: 0.4076 cents 142 .. 705 match: 16 SD: 0.3595 cents 153 .. 760 match: 16 SD: 0.3219 cents 159 .. 790 match: 16 SD: 0.2783 cents 170 .. 844 match: 16 SD: 0.2410 cents 187 .. 929 match: 16 SD: 0.1944 cents 251 .. 1247 match: 16 SD: 0.1891 cents 265 .. 1316 match: 16 SD: 0.1684 cents 277 .. 1376 match: 16 SD: 0.1623 cents 285 .. 1416 match: 16 SD: 0.1494 cents 319 .. 1585 match: 16 SD: 0.1393 cents 329 .. 1634 match: 16 SD: 0.1293 cents 363 .. 1803 match: 16 SD: 0.0939 cents 435 .. 2161 match: 16 SD: 0.0819 cents 516 .. 2563 match: 16 SD: 0.0737 cents 550 .. 2732 match: 16 SD: 0.0720 cents