The idea of synthesizing sounds by summing sinusoidal oscillations [Helmholtz
1863] has intrigued generations of musical instrument builders. Thaddeus
Cahill's electromechanical implementations [Nicholl 93] illustrate graphically the
basic challenge faced by these engineers--the creation of a large number of
oscillators with accurate frequency control. (...)
One hundred years after Cahill's work, despite rapid gains in computational
accuracy and performance, the state of the art in affordable single chip real-time
solutions to the problem of additive synthesis offers only 32 oscillators. Since
hundreds of sinusoids are required for a single low pitched note of the piano, for
example, current single chip solutions fall short by a factor of at least 20.
This paper describes a new technique for additive synthesis, FFT-1, that offers a
performance improvement of this order. This technique also provides an efficient
method for adding colored noise to sinusoidal partials, which is needed to
successfully synthesize speech and the Japanese Shakuhachi flute, for example.
Before describing the details of the FFT-1 method, additive synthesis will be
compared to the popular synthesis methods: frequency modulation
[Chowning 73] and digital sampling.