If memory serves me right, the singing voice is an indefinite pitched instrument. However, with the amount of educational experiences that an opera singer has under his or her belt, it is very difficult to sing flat. Sharpness is nerves. Flatness is rather that the singer cannot hear what is going on in the room, acoustics. This is the problem of the conductor, the producer, the room, the recording.
The whole science and study of singing is adding and subtracting overtones. The true opera singer is trying to get as many overtones as they can possibly get. We sing on colour, not on volume.
No one hears every frequency. There is always one note that a person cannot hear.