Why is singing/playing an instrument off-key a thing? Why are some frequencies of the acoustic wave okay and some not okay?
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First, musicality is about the pitch relationships between notes. When we say an instrument is *out-of-tune*, we mean that a named note is different from the expected pitch of that note, relative to either a standard (concert A at 440Hz), to another instrument, or to itself (a string on a guitar that is not tuned correctly relative to the other strings).
Acoustic instruments produce sound by harmonic motion – a plucked/bowed string, a column of air oscillating in a tube, a vibrating reed. The mathematical formula that describe the resulting frequency have references to a large number of physical quantities – mass, tension, length, elasticity. Some of those properties have other dependencies – temperature and humidity being the main ones. Things like the tension of a guitar string change over time as the string stretches, but the elasticity decreases.
What this means is that most instruments change their tune over time. For some instruments (like a piano) this may take months if it is in a stable environment and not moved. For others (like guitars and wind/brass instruments) they may need tuning every time they are played. In fact, wind and brass instruments need to be **warmed up** to playing temperature and humidity and then tuned again just prior to performing.
Instruments that need regular tuning also have accessible tuning pegs. This means that the pegs can be knocked, putting it out of tune. Wind instruments are tuned by moving the mouthpiece in or out. Brass instruments have a small slide with a locking nut.
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