Original Blog Entry: Equal Loudness

JADELottery — Thu, 27 Jul 2017 04:26:32 GMT

Been working on this one for a long while.

The following is the Equal Loudness Curves for a Base Line Frequency of 1000 Hz at a given dB.

The Equation is after the graph.

Ca0 = [ +584918276 / 6720025 -103831586233635427 / 2856403612062000 +794378430029096923 / 44344167963480000 -38790811232122019033 / 6917690202302880000 +37290541565009947 / 37059054655194000 -738665642886403 / 6829476135552000 +1647218534123999 / 232527401758080000 -17127252623983 / 62603531242560000 +870630168487 / 162769181230656000 -56221133 / 4340511499484160 -905135371 / 697582205274240000 +288653 / 18245186754795000 ]

Ca1 = [ -3148422351 / 73920275 +350719588425816859 / 3618111241945200 -2749900318774382348879 / 32859028460938680000 +184187318986680779843 / 4868004216435360000 -304469880071493491323 / 29573125614844812000 +4039288331398095383 / 2226682399235374080 -2846249053261467499 / 13254061900210560000 +21072389935899833 / 1220768859229920000 -453528524769713 / 488307543691968000 +1247486431379 / 39064603495357440 -9246037442197 / 14649226310759040000 +1459285789 / 269467373609280000 ]

Ca2 = [ +13775563019696468657 / 286514985900 -11370687841337045781409 / 447293972218500 +2623964381772455081232641 / 432355637643930000 -26195228365460186517092369 / 30331410887020320000 +19257428086889614312685471 / 236585004918758496000 -42429730168597174960451 / 7952437140126336000 +3289631551439307860611 / 13254061900210560000 -2858105252150952217 / 348791102637120000 +91886157892771247 / 488307543691968000 -186376057166539 / 65107672492262400 +380358058025653 / 14649226310759040000 -26618573567 / 250219704065760000 ]

Cb0 = [ +2440054313 / 66528247500 +15281212647019205947 / 23779560070416150000 -27090847859486093 / 72300273853500000 +183705368522726020559 / 1556480295518148000000 -13411492411525987063 / 622592118207259200000 +53014340147053 / 21587424566400000 -583193465228323 / 3170828205792000000 +43588562278253 / 4695264843192000000 -699757893089 / 2219579744054400000 +20335583869 / 2929845262151808000 -65705659541 / 732461315537952000000 +7542863 / 14596149403836000000 ]

Cb1 = [ -76491486421 / 133056495000 +30320926993346633617 / 19643984405995950000 -174734326454194660313 / 107149005850887000000 +1917876348523432946867 / 2112366115346058000000 -241931045702670842107 / 806539789495767600000 +1125460855949461513 / 17995816804165200000 -8442094840824031589 / 994054642515792000000 +555391994065074779 / 732461315537952000000 -1609256576101003 / 36623065776897600000 +14712087679 / 9301096070323200 -35046960646427 / 1098691973306928000000 +22035038441 / 80840212082784000000 ]

Cb2 = [ +3203642632288579763 / 1868575995000 -28134398538370546066702831 / 34754741641377450000 +35462675141771432481607843 / 205368927880866750000 -24985925347641185318078257 / 1137427908263262000000 +10953119633866074692074357 / 5914625122968962400000 -59241454935478259413 / 545327781944400000 +1499446630060632052277 / 331351547505264000000 -10894249571301009259 / 81384590615328000000 +33642484958483449 / 12207688592299200000 -550915346016881 / 14649226310759040000 +112128401223491 / 366230657768976000000 -394653897679 / 350307585692064000000 ]

Cc0 = [ +825637271 / 133056495000 -43616754460623251 / 5595190604803800000 +67105762471947743 / 13303250389044000000 -5242324777357478887 / 3112960591036296000000 +410491040596403969 / 1245184236414518400000 -50951052122581 / 1252070624851200000 +14407967694649 / 4359888782964000000 -6744609743791 / 37562118745536000000 +158004029551 / 24415377184598400000 -1087708261 / 7324613155379520000 +359545181 / 183115328884488000000 -71831 / 6311848390848000000 ]

Cc1 = [ +41556109 / 133056495000 -1078949069560794073 / 903623282675813700000 +126983827110067897 / 88015254806085750000 -2901994967663087941 / 4224732230692116000000 +7024221150843994039 / 70975501475627548800000 +113120648593443731 / 4175029498566326400000 -53386943636210971 / 3976218570063168000000 +886614309148877 / 366230657768976000000 -4967137318061 / 20927466158227200000 +9301008757 / 697582205274240000 -1774350301453 / 4394767893227712000000 +5591609 / 1092435298416000000 ]

Cc2 = [ -1579116737978502889 / 42977247885000 +113157235346395245101563 / 6319043934795900000 -1060494490076383381193 / 268543874313000000 +1183363080962496121637519 / 2274855816526524000000 -1076007134249986807202713 / 23658500491875849600000 +3856888720151962529819 / 1391676499522108800000 -8378559335141774357 / 69758220527424000000 +25109372899822447 / 6782049217944000000 -554936413978513 / 6975822052742400000 +302255378387 / 266349569286528000 -14170081917209 / 1464922631075904000000 +2007857 / 53794162422000000 ]

x is the Linear Frequency with a nominal range of 1 to 31, however it can be extended.

f is the Frequency in Hz.

d is the Decibel level at 1000 Hz.

f0(x) - f5(x) are special Low and High pass filters and operate with the -2/ .

Some Values Table

Decibels

Linear - Frequency

0

10

20

30

40

50

60

70

80

90

100

110

120

-1.0 - 12.40

134.32

122.54

115.03

111.80

112.85

118.16

127.75

141.61

159.74

182.15

208.83

239.78

275.01

-0.5 - 13.92

102.66

98.48

96.65

97.17

100.04

105.27

112.85

122.78

135.07

149.71

166.70

186.04

207.74

0.0 - 15.63

82.88

83.15

84.69

87.49

91.56

96.88

103.47

111.32

120.43

130.81

142.45

155.35

169.51

0.5 - 17.54

70.75

73.51

76.96

81.10

85.93

91.45

97.66

104.57

112.16

120.45

129.42

139.09

149.44

1.0 - 19.69

63.82

67.92

72.43

77.38

82.75

88.55

94.77

101.42

108.50

116.01

123.94

132.30

141.08

1.5 - 22.10

59.65

64.35

69.39

74.76

80.47

86.52

92.90

99.62

106.68

114.07

121.80

129.86

138.26

2.0 - 24.80

54.92

59.80

65.01

70.53

76.38

82.54

89.03

95.83

102.96

110.41

118.17

126.26

134.67

2.5 - 27.84

50.54

55.55

60.89

66.55

72.54

78.85

85.49

92.45

99.73

107.34

115.28

123.54

132.13

3.0 - 31.25

46.87

52.05

57.55

63.38

69.55

76.05

82.87

90.03

97.52

105.35

113.50

121.98

130.80

3.5 - 35.08

43.73

49.08

54.76

60.78

67.14

73.82

80.85

88.21

95.90

103.93

112.29

120.99

130.02

4.0 - 39.37

40.81

46.33

52.19

58.38

64.91

71.78

78.98

86.52

94.40

102.61

111.16

120.05

129.28

4.5 - 44.19

37.90

43.58

49.60

55.96

62.65

69.68

77.05

84.76

92.81

101.19

109.92

118.98

128.38

5.0 - 49.61

34.93

40.77

46.94

53.46

60.32

67.51

75.05

82.92

91.13

99.69

108.58

117.80

127.37

5.5 - 55.68

31.90

37.91

44.27

50.96

57.99

65.35

73.06

81.09

89.47

98.18

107.23

116.62

126.34

6.0 - 62.50

28.90

35.11

41.66

48.54

55.75

63.29

71.16

79.37

87.90

96.77

105.97

115.50

125.37

6.5 - 70.15

26.04

32.45

39.19

46.26

53.65

61.36

69.40

77.77

86.46

95.48

104.82

114.49

124.48

7.0 - 78.75

23.39

29.99

36.90

44.14

51.70

59.58

67.77

76.29

85.13

94.28

103.76

113.55

123.67

7.5 - 88.39

21.00

27.73

34.79

42.17

49.87

57.88

66.22

74.88

83.86

93.15

102.77

112.71

122.96

8.0 - 99.21

18.88

25.69

32.83

40.30

48.11

56.24

64.70

73.50

82.62

92.07

101.86

111.97

122.42

8.5 - 111.36

17.02

23.83

31.00

38.52

46.40

54.62

63.20

72.14

81.42

91.07

101.06

111.41

122.11

9.0 - 125.00

15.37

22.13

29.28

36.82

44.74

53.05

61.75

70.83

80.30

90.17

100.41

111.05

122.07

9.5 - 140.31

13.90

20.57

27.68

35.21

43.17

51.56

60.38

69.63

79.30

89.41

99.94

110.90

122.29

10.0 - 157.49

12.54

19.14

26.21

33.74

41.75

50.22

59.16

68.57

78.45

88.79

99.61

110.89

122.64

10.5 - 176.78

11.25

17.82

24.88

32.44

40.50

49.06

58.12

67.67

77.73

88.28

99.33

110.88

122.93

11.0 - 198.43

9.99

16.59

23.70

31.32

39.45

48.10

57.25

66.92

77.09

87.78

98.98

110.70

122.92

11.5 - 222.72

8.74

15.44

22.64

30.35

38.57

47.29

56.52

66.25

76.49

87.23

98.47

110.23

122.48

12.0 - 250.00

7.46

14.32

21.66

29.49

37.80

46.60

55.87

65.63

75.87

86.59

97.80

109.49

121.66

12.5 - 280.62

6.16

13.21

20.72

28.68

37.09

45.95

55.27

65.04

75.27

85.95

97.08

108.66

120.70

13.0 - 314.98

4.90

12.12

19.78

27.87

36.39

45.34

54.72

64.53

74.77

85.45

96.55

108.08

120.05

13.5 - 353.55

3.73

11.10

18.89

27.11

35.74

44.80

54.29

64.19

74.52

85.27

96.45

108.05

120.07

14.0 - 396.85

2.77

10.25

18.15

26.48

35.25

44.44

54.06

64.10

74.58

85.49

96.82

108.59

120.78

14.5 - 445.45

2.12

9.70

17.71

26.15

35.02

44.33

54.07

64.24

74.84

85.88

97.34

109.24

121.58

15.0 - 500.00

1.75

9.47

17.60

26.13

35.06

44.39

54.13

64.27

74.81

85.75

97.10

108.84

120.99

15.5 - 561.23

1.15

9.11

17.40

26.05

35.03

44.35

54.02

64.03

74.39

85.08

96.12

107.50

119.23

16.0 - 629.96

1.01

9.22

17.74

26.56

35.68

45.10

54.83

64.85

75.18

85.80

96.73

107.96

119.49

16.5 - 707.11

1.16

9.80

18.69

27.83

37.23

46.89

56.80

66.97

77.40

88.08

99.01

110.21

121.65

17.0 - 793.70

0.54

9.58

18.82

28.27

37.94

47.81

57.89

68.19

78.69

89.41

100.33

111.47

122.81

17.5 - 890.90

0.09

9.82

19.60

29.44

39.34

49.30

59.32

69.40

79.54

89.74

99.99

110.31

120.69

18.0 - 1000.00

0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

80.00

90.00

100.00

110.00

120.00

18.5 - 1122.46

0.08

10.00

19.94

29.89

39.86

49.84

59.84

69.85

79.87

89.91

99.97

110.03

120.12

19.0 - 1259.92

0.09

9.89

19.73

29.59

39.49

49.42

59.37

69.36

79.37

89.42

99.49

109.60

119.73

19.5 - 1414.21

-0.14

9.63

19.42

29.24

39.07

48.93

58.80

68.70

78.61

88.55

98.51

108.49

118.49

20.0 - 1587.40

-0.63

9.22

19.05

28.87

38.67

48.46

58.24

68.00

77.75

87.48

97.20

106.91

116.60

20.5 - 1781.80

-1.33

8.66

18.59

28.46

38.26

48.00

57.68

67.29

76.84

86.33

95.76

105.12

114.42

21.0 - 2000.00

-2.16

7.98

18.02

27.94

37.75

47.44

57.03

66.50

75.85

85.10

94.23

103.24

112.15

21.5 - 2244.92

-3.10

7.16

17.27

27.22

37.02

46.67

56.16

65.49

74.67

83.70

92.57

101.28

109.84

22.0 - 2519.84

-4.15

6.17

16.30

26.25

36.02

45.60

55.00

64.21

73.24

82.09

90.75

99.23

107.53

22.5 - 2828.43

-5.31

5.01

15.12

25.04

34.75

44.27

53.58

62.70

71.61

80.33

88.84

97.16

105.27

23.0 - 3174.80

-6.52

3.75

13.83

23.70

33.37

42.83

52.10

61.16

70.02

78.68

87.13

95.38

103.43

23.5 - 3563.59

-7.61

2.61

12.65

22.48

32.13

41.58

50.85

59.92

68.79

77.48

85.97

94.28

102.39

24.0 - 4000.00

-8.25

1.92

11.91

21.74

31.41

40.90

50.23

59.39

68.38

77.21

85.86

94.35

102.68

24.5 - 4489.85

-8.02

2.08

12.04

21.88

31.59

41.17

50.62

59.94

69.13

78.19

87.12

95.92

104.59

25.0 - 5039.68

-6.57

3.44

13.36

23.20

32.96

42.63

52.22

61.73

71.15

80.49

89.75

98.93

108.02

25.5 - 5656.85

-3.71

6.15

15.98

25.78

35.54

45.28

54.98

64.65

74.30

83.91

93.48

103.03

112.55

26.0 - 6349.60

0.32

9.96

19.62

29.31

39.02

48.75

58.50

68.28

78.08

87.90

97.74

107.61

117.50

26.5 - 7127.19

4.83

14.17

23.58

33.07

42.64

52.28

62.00

71.80

81.67

91.62

101.65

111.75

121.93

27.0 - 8000.00

8.73

17.68

26.77

36.00

45.36

54.87

64.51

74.29

84.21

94.26

104.46

114.79

125.26

27.5 - 8979.70

10.85

19.35

28.07

37.01

46.18

55.58

65.19

75.03

85.10

95.39

105.91

116.65

127.61

28.0 - 10079.37

10.50

18.47

26.80

35.47

44.51

53.90

63.64

73.74

84.19

94.99

106.15

117.67

129.54

28.5 - 11313.71

8.08

15.44

23.34

31.78

40.76

50.27

60.33

70.92

82.05

93.71

105.92

118.66

131.94

29.0 - 12699.21

5.66

12.30

19.71

27.88

36.81

46.50

56.95

68.16

80.13

92.87

106.36

120.62

135.63

29.5 - 14254.38

6.61

12.43

19.21

26.97

35.69

45.38

56.04

67.67

80.26

93.82

108.36

123.86

140.32

30.0 - 16000.00

12.76

17.74

23.82

30.98

39.23

48.58

59.01

70.53

83.15

96.85

111.64

127.52

144.49

30.5 - 17959.39

17.59

22.17

27.90

34.77

42.78

51.93

62.23

73.67

86.25

99.97

114.84

130.85

148.00

31.0 - 20158.74

25.47

30.40

36.40

43.47

51.61

60.81

71.09

82.43

94.84

108.32

122.87

138.48

155.17

31.5 - 22627.42

42.83

49.34

56.57

64.52

73.19

82.59

92.70

103.54

115.09

127.37

140.37

154.09

168.53

32.0 - 25398.42

74.83

84.93

94.98

104.97

114.91

124.79

134.61

144.38

154.09

163.74

173.34

182.88

192.36

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