Melodies are still there. However for the last 10 or 15 years almost everything I hear on radio a songs with fairly long introductions that are quite melodic and musically very well done followed by a segue into a cha-cha with disco drums added. Not really enough variety for dancing.
As well as the mathematics, the pitch of a note on a practical instrument is affected by several factors. The recorder is close to your "theoretical instrument" and is one I am very familiar with, so I will use it as an example.
Recorders have a 2 octave and a tone range. The bottom octave is the fundamental notes and the upper octave notes are "overblown" ...
It's a much simpler job to tune a drum which has one head. Timps are such. One head will produce one pitch (plus the complex overtones) when it's stretched regularly. When it's uneven, it'll try to produce several different pitches, resulting in a bit of a mess. Rototoms are similar, with just the one head. I don't think they'd do the job with two.
Some physical differences that result in a distinct pitch of an instrument may include but are not limited to, size of the drum, tightness of the drum, the type of material of the drum, etc. I hope that helps.