The Nealon Equation |
y = (A*sin(B*x+C) + D*sin(E*x+F) + G*sin(H*x+I) + J*sin(K*x+L)) * (M + N*x + O*x^2 + P*x^3 + Q*x^4) * atan(R*x) * atan(S*(BL-x)) |
Nealon Resonator |
Calculated curve |
Graphed in Logger Pro |
y = (A*sin(B*x+C)+D*sin(E*x+F)+G*sin(H*x+I)+J*sin(K*x+L))*(M+N*x+O*x^2+P*x^3+Q*x^4)*atan(R*x)*atan(S*(20.1-x)) |
Front (lauan) and back (copper) of another thin body Nealon Resonator. |
Back (Honduran mahogany) of a non-resonator instrument with the same shape. |
Back of the instrument shown above. |
This outline is created by plotting +y(x) and –y(x) in Graph and removing the axes. |
Total length = 29.91 inches |
L |
x |
Length of the side around the perimeter. |
|
Nealon Resonator |
|
A |
.1957769 |
B |
-.9361852 |
C |
-3.203335 |
D |
.4075888 |
E |
.8057877 |
F |
5.039549 |
G |
4.322408 |
H |
.09507775 |
I |
3.699719 |
J |
2.170954 |
K |
.3080430 |
L |
-3.177518 |
M |
-.6046287 |
N |
-.06450537 |
O |
.04824956 |
P |
-.00597517 |
Q |
.0001856246 |
R |
16.00042 |
S |
8.550479 |
BL |
20.1 |
|
|
A B C D E F G H I J K L M N O P Q R S BL |
.1957769 -.9361852 -3.203335 .4075888 .8057877 5.039549 4.322408 .09507775 3.699719 2.170954 .3080430 -3.177518 -.6046287 -.06450537 .04824956 -.00597517 .0001856246 16.00042 8.550479 20.1 |
|
|
A = .1957769 |
|
B = -.9361852 |
|
C = -3.203335 |
|
D = .4075888 |
|
E = .8057877 |
|
F = 5.039549 |
|
G = 4.322408 |
|
H = .09507775 |
|
I = 3.699719 |
|
J = 2.170954 |
|
K = .3080430 |
|
L = -3.177518 |
|
M = -.6046287 |
|
N = -.06450537 |
|
O = .04824956 |
|
P = -.00597517 |
|
Q = .0001856246 |
|
R = 16.00042 |
|
S = 8.550479 |
|
BL = 20.1 |