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Storage
Early samplers stored their samples in RAM as, indeed, do many software samplers. This obviously limits the number and size of the samples you can store and play at any one time. However, increases in computer power have lead enterprising companies to develop software samplers such as Nemesys' GigaSampler and Steinberg's HALion that can read samples directly from hard disk. At last, size is not obstacle.
Going loopy
The memory limitations of early samplers meant you could not store samples of any great length and, therefore, you could not hold a note for very long. The solution was the loop. You'd find a central portion of the sample and simply repeat it for as long as the key was held down and then jump to the end of the sample when the key was released.
Finding good loop points was an art, and a difficult one at that. The problem has been alleviated somewhat by samplers' and computers' ability to hold more RAM, cheaper RAM prices, the ability to store samples on hard disk, and by better looping facilities in the form of audio editors and dedicated loop-finding software.
Root of the problem
The first stage in preparing a sample for playback is to assign it to a root note. This does not necessarily have to be the pitch at which it plays. This is obvious in the case of drums, for example, but it's also useful when creating layers and key splits as it means you can play the same pitch from two or more sections of a keyboard.
To play an instrument sample in a realistic manner, you need to be able to play a range of pitches and different volume levels. The simplest way to do this is to assign a single sample to a root note and then pitchshift it to other pitches. However, this makes the note duration shorter or longer than the original sample and the attack phase will be shorter or longer, too. This can be acceptable for pitches say three or four semitones away from the root but you don't have to transpose a sample very far from its original pitch before it starts to sound unnatural.
Multisamples
The way around this is to use more than one sample, a process known, helpfully, as multisampling. In an ideal world, each individual note would have its own sample but, as you can imagine, the sampling process would require a lot of time and effort, and the sampler itself would need a lot of resources to store and play all those samples
But that has not prevented several enterprising companies producing gargantuan sample sets such as Steinberg's The Grand which includes 1.3Gb of samples! However, depending on the instrument, you can often get realistic playback using a different sample for only every three or four notes.
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