Mixing the musical instruments as opposed to the rhythmic instruments, the information will vary quite drastically in terms of the amplitude envelopes of the two instrument types. Drums are fast and transiential, while a lot of musical tracks such as a piano, guitar, strings and vocals, tend to have longer amplitude envelopes and sustained notes that hold for a prolonged period of time. This difference alone will prompt you to utilize a compressor in a slightly less responsive way like that of a drum compressor.
The need for compression shouldn’t come from a sound that is lacking in volume, it should come from a sound that needs to be controlled and kept at a more consistent, average volume over time. Take for instance, a vocalist like Adele. She will practically whisper in some of her tracks and later down the line, borderline yelling into the microphone, this dictates a sound with a lot of dynamic range, or difference in volume between the loudest part of the vocal track and the quietest part. While dynamic range is desirable for character and movement, some compression will simply draw the extreme high amplitude and extreme low amplitude information closer together.
Another classic case of standard compression is that of a live guitarist, with sub-professional performers, the velocity (strength) at which strings are plucked may be fairly inconsistent. Some strings may get lost in the music, while some of the harder plucks seemingly hit too hard, potentially burying another instrument creating a loss of clarity.
A compressor will control the loud parts, bringing them down in amplitude as they exceed the threshold. Once the signal has been attenuated, the output control must be used to regain any significant loss in overall volume. When using the output control to level the sound off again, this will also bring up the low amplitude signal that gets lost in the mix at times. With this type of compression, we have dealt with two issues, the parts that are too loud and the parts that are too quiet.
One compressor will often take care of most of the dynamic range corrections, however, two compressors are commonly chained together as to not overload one device with too much work. The first compressor should typically be faster reacting to catch the transient information, while the secondary compressor can be a little slower, allowing control over the body of a sound.