The standard tuning note is defined as 440Hz sine wave which is a pure A. However individual orchestras can use their own pitch, it is common to chose a higher pitch to make it easier to play, and choirs often chose a lower pitch for similar reasons. In practice there are often instruments that is hard to tune which everyone tunes to.
The 440Hz standard does actually have an interesting story behind it. The standard pitch used to be much lower. For example Handel’s tuning fork from 1740 was 422.5Hz. We have later forks as low as 409Hz. Then in the 1800s we got the pitch inflation war. By tuning instruments higher the same piece of music sounds better. But especially for the choir it can be hard to sing at very high pitch. As operas, cathedrals and music groups competed for attention the pitch standard increased over time. In the middle of the century the standard was already above 450Hz. The first official pitch standard came in 1859 and was set at 435Hz which was signed into French law. This standard spread to many other countries through a series of treaties. It was even one of the bargaining topics at the end of WWI which resulted in 435Hz being defined as a standard for the central powers who lost.
The British however settled on a higher standard of 452Hz. The Scottish did not even stop there and bagpipes are usually pitched over 470Hz. So eventually in 1939 there was a big international conference where they compromised on 440Hz for the entire world, obsoleting all older standards, even the 435Hz standard. Part of the reason that 440Hz was selected is because this have many factors so you can more easily compare it to a standard 1s pendulum.
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