  We are looking for a mathematical model of monophonic sounds with independent
time and phase dimensions. With such a model we can resynthesise a sound with
arbitrarily modulated frequency and progress of the timbre. We propose such a
model and show that it exactly fulfils some natural properties, like a kind of
time-invariance, robustness against non-harmonic frequencies, envelope
preservation, and inclusion of plain resampling as a special case. The
resulting algorithm is efficient and allows to process data in a streaming
manner with phase and shape modulation at sample rate, what we demonstrate with
an implementation in the functional language Haskell. It allows a wide range of
applications, namely pitch shifting and time scaling, creative FM synthesis
effects, compression of monophonic sounds, generating loops for sampled sounds,
synthesise sounds similar to wavetable synthesis, or making ultrasound audible.
