What would extended periods on Mars do to musical instruments? I'm assuming these instruments would be in habitats similar to ISS or similar, but how might they degrade?
Generally the first question is: What causes instruments to degrade over time here on Earth?
Multiple factors play into it:
Temperature and humidity variations: Temperature change causes materials to expand and contract, so extended periods of extreme temperature cycles can work materials apart like the glue, welds, or solder joints holding together the instrument. Similarly, humidity can enter the wood of a wooden instrument and can cause it to expand, also leading to mechanical stresses.
Corrosion: Materials interact with the oxygen in the atmosphere and this can cause chemical reactions to occur in the materials. In metals, this is usually called corrosion or rust, but even organic materials can develop a patina or discoloration when exposed to the atmosphere for a long time and not maintained regularly.
Gravity and storage direction: Generally, supportive hard cases for instruments are recommended when storing them long term. This is because if they are just lying around--unsupported--some materials can slowly flex or warp on long time scales
Water damage: This one is a bit obvious, but ties into "humidity" and corrosion. An instrument that was submerged in water or has had liquid water drip onto it suffers from all sorts of problems.
Life: Mold and insects are also a danger to instruments, particularly the more edible ones like string instruments which are often composed of organic material.
Now, how would these factors change in a space habitat on Mars (or habitat generally)?
Climate Control: Controlling the air temperature and humidity is vital to the survival and health of the people inside the habitat. Unless something has gone seriously wrong, the inside temperature of a habitat should not swing to any extremes that would cause undue thermal stress on the instrument (On Earth, you wouldn't want to store an instrument in an attic that gets very hot in the summer and cold in the winter)
Corrosion: If anything, less of an issue in a habitat than on Earth. Humidity can be tightly controlled and things that cause undue corrosion here on Earth like salt-laden ocean air would not be a factor in a habitat.
Gravity: Due to the lower gravity and stresses of the instrument's own mass being reduced, instruments would probably actually store better than on Earth.
Water damage: If your habitat floods, you have bigger issues than instrument health.
Life: Generally, a habitat should have less insect life than somewhere on Earth because there is (presumably!) no robust biosphere of native life that can attack the organic materials in the instruments. That said, the International Space Station is notorious for having mold problems and a generally peculiar smell that presumably comes from lots of people of people living in close proximity and working hard.
Instruments of all types should keep rather well in a space habitat, because the primary factors that cause instrument degradation (temperature and humidity) are already carefully monitored and controlled in the closed environment. Musicians just need to make sure to properly clean their instruments, and they will be fine!
It now has more mat finish but generally nothing much happened to it. As I expect trumpet do be made from comparable materials, I expect it to stay playable and even in tune over many years, at least a bugle with no valves. There may be corrosive brines on the surface but all you need is to place the trumped somewhere on a rock away from these. All you need is to shake the sand out of it that may be blown in by Martian storms.
A classic violin made from the wood would do worse because of the extreme changes of the temperature. I still expect to survive it longer than on Earth where the first rain likely would significantly damage it, and then wood-eating life (fungi, insects) could finish. There are violins made from metal and even stone, if you are building a plot for the story it could be one of these. I do not think that strings would survive well however, they are usually not even metal.
The question was later narrowed to ask only how would the instruments survive inside the closed habitat module. I assume, likely the same as anywhere in the Earth building, unless there are problems with the climate control in the habitat.