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Consider a professional orchestra with a fairly wide repertoire. Obviously it will need players of all of the strings pretty much all of the time. However, for many of the other instruments, the need will vary a lot.

Consider the clarinet next. Many older pieces will need none. One, two, or three will be commonly required. Some pieces, e.g. Stravinsky's Rite of Spring, will need five. Does the orchestra retain five clarinet players but some sit idle a lot? Do they need to engage individuals to boost the numbers when required?

How about rarer instruments (in the classical repertoire). The saxophone appears occasionally but not often. So, I doubt that there will be a retained saxophone specialist. A clarinetist might double on the saxophone but pieces that need the saxophone often need a clarinet as well so there may be no spare retained clarinettist. Similar comments apply to other occasional instruments e.g. oboe d'amore and larger flutes.

It is not obvious what a harp player might double on but many pieces require nohe whereas others require one or two.

In a professional orchestra, they'll only retain the core players. For pieces that need additional instrumentalists, they'll hire them for just that concert. The managers of these orchestras maintain a network of the city's top players and usually use the same ones.

In a college or civic orchestra, there's usually not the same ability to bring in extra people for one specific piece, so they have to be more careful when programming a concert. Any piece with a lot of extra instruments (such as Rite of Spring) is a major planning effort, if it's even possible at all. But of course, even pieces with more typical personnel requirements do vary a bit. One piece will call for 2 clarinets, another for 3. These groups will maintain just enough people to cover the largest normal requirements, and they usually rotate chairs a bit to keep everyone involved. Harpists and pianists may be asked to cover easy percussion for pieces where they otherwise wouldn't be used.

It depends on the orchestra's schedule. Some orchestras hire all of their players on a "per service" basis. Others have a core on salary, but they will hire additional players per service as needed.

The Metropolitan Opera orchestra has a long list of "associate musicians" on their roster, for example, but no indication of who plays saxophone.