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Instruments are not all in the same key due to historical design constraints, ease for players switching between different instrument sizes, and to simplify sheet music reading.
You might think that when different instruments play a note written as C on sheet music, it'd sound the same across the board. Not always! Some instruments are what we call "transposing instruments". This means they read notes in one key, but sound in another.
For instance, when a trumpet (which is commonly in the key of Bβ, or B-flat) plays a written C, it produces a Bβ note. Similarly, a French horn (commonly in the key of F) playing a written C produces an F note. Check out this video to get a better sense of what this means sound-wise.
This is confusing, to say the least! So, let's break this question down into a few parts:
A key is a range of notes that form a harmonic foundation of a piece of music. If a song is said to be in C Major, it primarily consists of notes from the C Major scale: C, D, E, F, G, A, and B.
When we say that a trumpet is in the key of Bβ, it's another way of saying that the trumpet most naturally emits sounds from a Bβ scale. For instance, if you were to play a trumpet without adjusting any of the valves, the sound produced would be a Bβ.
There are a lot reasons why transposing instruments exist, but here are three key reasons:
When instruments were originally invented, there were limitations to design. For example, horns were first built without any valves, so the sounds were inherently limited to the natural key of the instrument. Over time, innovations in design have allowed for instruments to tap into a wider array of tones, but now we're most familiar and comfortable with hearing an instrument in its original key.
Take saxophones for example. There are different types of saxophones that range in size. Larger ones produce lower sounds, smaller ones produce higher sounds.
If all saxophones played in the same key, it would mean that a player would have to relearn an entirely new set of fingerings to play the same notes. Having instruments in different keys allows musicians to more easily play different sizes of instrument.
Reason #3: It's easier to read sheet music.
Sheet music is designed to comfortably accommodate around 20 notes within and around the ledger lines.
Instruments with natural keys outside of this range would require their sheet music to have an excessive amount of lines. This would make reading and writing sheet music incredibly difficult.
Transposing repositions the notes to fit comfortably within the ledger lines making life easier for composers and musicians alike.
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