Crystal structures of the metals mentioned:
18/8 (300-series) stainless is an austenitic steel and therefore has a face-centered cubic crystal structure
alpha-brass is Cu+Zn (I don't know which brass specifically is used and therefore what the other additives are, but alpha-brass is very common) has a body-centered cubic crystal structure. It is single phase and in the unworked state has a microstructure of smaller or larger equiaxed grains depending on heat treatment cycle.
alpha-titanium has an HCP crystal structure, but the most common Ti-alloy is Ti-6Al-4V which is an "alpha-beta" alloy. the beta phase has a BCC crystal structure and so the microstructure contains both phases. Specifics as to the microstructure are dependent on specific content of additives and heat treatment cycle.
alpha-zinc also has an HCP crystal structure, but I don't know which zinc alloy you might be using specifically. However, the most common diecast zinc alloys are Zn-Al and are described in ASTM B240 with the most common being Zamak 2, 3, and 5. IIRC, this is still almost entirely HCP and section thickness during casting was the primary determinant in whether it had a primarily fine or coarse microstructure. (Fine-grained skin and coarse-grained bulk)
I'm not so sure it's an issue of the crystal structure per se, but possibly an issue relating to transmissibility due to different speeds of sound in the metal. Different metals will have different speeds of sound for both compression and shear waves. The generalized equation for this is V = sqrt(Cij/rho). Cij being the lattice constants and rho being density. The impedance is described by Z = V*rho. Fractional reflection at an interface is determined by R = [(Z2-Z1)/(Z2+Z1)]2. This means that steel-core bronze-wrapped wires are in general going to have worse transmissibility at the interface with light-metal tremolos (aluminum being the most common) than with those of transition metals. Titanium however has a larger elastic modulus and density than aluminum, and so has an impedance closer to that of both the steel and the bronze and therefore a better transmissibility. For nylon core, silver-plated copper-wrapped strings, similar should apply as both copper and silver are transition metals and fall into a somewhat different regime than aluminum. Now, the lattice constants are in fact partly related to crystal structure, but this is a a fairly complicated topic which I'm not going to get into. They may also be influenced by processing history. When something is worked it produces a preferred orientation for grains in the metal and this creates anisotropic lattice constants which therefore creates anisotropies in the speed of sound. So, it may also be as prosaic as whether the material was rolled into sheets or cast near-net into its present shape in terms of how well it transmits sounds from a given material.