Is there an equation to relate a glass's frequency to its mass when it's struck with a spoon? The mass therefore would be changing because I am pouring in water and testing the frequency at different volumes. Obviously as the volume increases the mass increases and the frequency decreases.
How would I exactly model this with an equation?
Perhaps using the equation for a simple harmonic oscillator:
$$
\left[\text{frequency}\right] ~=~ 2 \pi \sqrt{\frac{\left[\text{stiffness constant}\right]}{\left[\text{mass}\right]}}
\,.$$
But can the stiffness constant really be applied to a material like glass, since its so rigid and brittle and not like a spring?
So does anyone have any suggestions?
 A: The normal modes frequencies will indeed depend on the elasticity of the glass, measured by Young's modulus and shear modulus and the mass of the vibrating body. Adding water increases the mass and decreases the frequencies. The glass does has elastic properties but it is much stiffer than rubber, for example. This translates into much higher values of the elasticity modulus. 
As for a formula, there is no analytic formula. The actual dependence of frequencies on the elasticity and mass will depend on the specific geometry of the glass. Even then you may find a "half'analytic " formula, including some coefficients obtained by numerically solving the differential equations for a given, simple, geometry.
All these considerations apply to the vibration of the glass body. There may be also vibrations in the air contained in the glass. But when you hot the glass you excite mostly the vibration of the body. If you blow across the top you may excite the vibrations of the air which have different laws.   
