Which instrument sets the pitch that is used to 'tune' an orchestra? Why is that instrument used, and how does the player know they have the correct pitch?

...By the 1800s, the size and instrumentation were much like the modern orchestra. An order was added to the tuning ritual, with each "family" of instruments taking its turn to tune with the oboe.

When a fixed-pitch instrument, such as an organ, was included with the orchestra, the oboe would be tuned to it before the ritual began.

These tuning traditions continue today.

The traditional tuning note is A. This stems from the open A string being common to all orchestral string instruments.

The oboist plays a long A when instructed by the concert master - usually the lead violinist - who stands and indicates to the oboist and then to each section of the orchestra when it's time to tune.

The string players tune their A strings, from which they can tune their other strings. In turn, other sections of the orchestra also tune to A. When the tuning ends and the instruments are silent, the orchestra is ready to perform.

Stable in Pitch: The oboe's double reed and cylindrical bore design make it less susceptible to pitch fluctuations caused by temperature or humidity changes compared to other instruments. This stability is critical when setting the standard pitch for an entire orchestra.
Easily Heard: The oboe's timbre, often described as "bright" or "penetrating," cuts through the textures of other instruments. Even in a large orchestra, the oboe's A is easy to distinguish, making it an ideal reference point.
Rich in Overtones: The oboe produces a spectrum of overtones that contribute to its distinctive tone. These overtones make the oboe's pitch easier to match across a range of instruments.