I want to create in my house a simple glass harp using household glasses. (It will not be used for performance on stage in front of people, it will be used for my own entertainment). I want to know the length of water and the length of air in a glass needed to produce different pitches. To make it easy let us think that I have 8 glasses and I want to produce only 8 pitches. It will be nice and easy if the person who answers writes which pitch we will get if a glass is filled ½ with water, 1/3 with water ans 2/3 with water.
As topo says, actually plucking a string anywhere along its length won't make it change pitch - although often it will affect the overtones produced with that pluck.
If you mean touching the string at 1/3 (or 2/3, it's the same backwards) of its length, then the pitch produced is a harmonic. The second overtone. E.g. on a string pitched at A, the note produced is an octave and a P5 above - an E.
If indeed you do mean pressing on a fretboard (such as a guitar), then 1/3 along will produce a P5. 2/3 along will produce a P5 an octave above the former.
The tuning of a glass harp can't be compared with the tuning of a guitar where the tones of each string can be considered as the proportions and the pitches analogue the tuning of a mono chord: https://en.wikipedia.org/wiki/Monochord.
So far this question could be answered by taking 2 empty bottles of bear and comparing the pitch. Try it. Perhaps they might be the same pitch but just by accident: There are too many variables of shape, thickness, glass bottom and the composition of the material ...
Even if this were so that the volume of water would correlate with the different pitches - like the frets of a guitar (length of the string) - it wouldn't help you to have 8 glasses and you made marks that correlate to the pitches you couldn't play on this instrument, because you had always to change the pitch of each glass by filling water.
Of course if you once have tuned 8 glasses you can play a simple tune like "oh my darling clementine", "London bridge is falling down", "sur le pont d'Avignon" "happy birthday to you".
But the best for tuning 8 glasses (the best is they have all the same shape or are even the form of a cylinder) is a good trained ear or you use an app for pitch control like pitchronome:
tuning a glass harp: