6.4 Pitch Shifting
Transposition is one of the basic tools of musicians. When we think about providing this effect by signal-processing means, we need to think about the various aspects of it. For a musician, transposing means repeating a melody after pitch shifting it by a fixed interval. Each time the performer transposes the melody, he makes use of a different register of his instrument. By doing so, not only is the pitch of the sound modified, but also the timbre is affected.
In the realm of DAFX, it is a matter of choice to transpose without taking into account the timbre modification or whether the characteristic timbre of the instrument has to be maintained in each of its registers. The first method could be called “variable timbre transposition,” whereas the second approach would be called “constant timbre transposition.” To get an insight into the problem we have to consider the physical origins of the audio signal.
The timbre of a sound heavily depends on the organization of its spectrum. A model can be derived from the study of the singing voice. The pitch of a singing voice is determined by the vocal chords and it can be correlated with the set of frequencies available in the spectrum. The timbre of the voice is mainly determined by the vocal cavities. Their effect is to emphasize some parts of the spectrum, which are called formants. A signal model can be derived where an excitation part is modified by a resonance part. In the case of the voice, the excitation ...