Music is the mathematics of sound, an A 440 is going to be an A 440 cycles per second. An octave above is going to be 880, and an octave below is going to be 220.
Since math and physics don't change, the required design of musical instruments is going to have to adhere to the physics behind producing sound. The length, tension, and thickness of strings is going to be consistent, as will the distance between holes on flutes and other similar instruments. Same thing with percussion, skins on drums will have to conform, as will shapes, and other designs.
The math and physics of sound are constant, and will therefore restrict the design of instruments.
The exception would be as with some instruments in Asia which follow different musical rules and don't use the octal or chromatic scales, so if you had music that followed different rules, the instruments may take on a slightly different appearance, but the basic rules would still apply. Regardless of the tone, the only thing that would change from a microtone string instrument, would be the length and tension on the strings, and perhaps the number of strings, however, the limitations on the human body would also dictate the design.
For example, a guitar could not exceed the length for a human to play it. A keyboard would retain the same basic design, as it would have to accommodate the reach of a human hand, Schumann tried to extend his reach, but ended up crippling himself.
The same applies for amplification, you need an opening or openings behind the strings to amplify the sound.
Then of course different materials make different sounds based on their materials, and the materials are also restricted by physics. Glass is rarely used due to it's fragility and the difficulties that resonance brings to the table. (ever see an opera singer shatter a glass?)
Math, physics, and the limitations of the human body are constants and will severely limit what musical instruments can look like.
Now, if you had an alien physiology, then some interesting designs could occur, and that would overcome the limitations of the human body, but the same physical limitations would apply to what actually makes the sound, and amplification of the sound (assuming no power to amplify by other means)