brucec@orca.UUCP (10/03/84)
[start with white noise and subtract the sounds you DON'T want] Could someone out there please point me towards a good book or article on the theory of FM music synthesis? A thumbnail sketch of the technique would be appreciated too. Thanks in the proverbial advance, Bruce Cohen UUCP: ...!tektronix!orca!brucec CSNET: orca!brucec@tektronix ARPA: orca!brucec.tektronix@rand-relay USMail: M/S 61-183 Tektronix, Inc. P.O. Box 1000 Wilsonville, OR 97070
rlr@pyuxn.UUCP (Rich Rosen) (10/05/84)
> Could someone out there please point me towards a good book or article on > the theory of FM music synthesis? A thumbnail sketch of the technique > would be appreciated too. > Bruce Cohen FM synthesis is just what the name implies: frequency modulation to produce exotic timbres. Vibrato is a simple form of frequency modulation, where the modulating oscillator has a slow subaudio rate (about 8 Hz) and "modulates" the frequency of a program tone (sound source oscillator) by a bit less than a semitone up and down. Usually a sine wave is used in the modulating oscillator. (Note that this is an electronic simulation of vibrato in voice and acoustic musical instruments, which imparts a slightly more random and slowly building "frequency modulation" to a musical tone. True vibrato is generally considered more pleasing to the ear, partially because the regularity of sine wave vibrato in organs and synthesizers becomes annoying due to its monotonous regularity, especially if used in excess.) FM synthesis involves modulating a sound source's frequency at an audio rate, meaning that the modulating oscillator has a frequency in the audible range. Rather than a relatively slow oscillator moving the pitch of a note up and down just a little eight or so times a second, the rate of up/down frequency offset, and the degree of offset, is much greater. I can't explain mathematically what happens, but it produces very exotic timbres. Many bell sounds on synthesizers are produced with this method, resulting in bizarre non-hramonic timbres reminiscent of bells. Synthesizers use exponential FM, meaning that if a sine wave oscillator is used as a modulator, it will shift the PITCH up/down by equal amounts (e.g., if calibrated properly, a semitone up and a semitone down. Linear FM shifts the FREQUENCY up/down by equal amounts (e.g, 100 Hz up and 100 Hz down). John Chowning of Stanford did a great deal of research into uses of linear FM, and uncovered some principles for interesting harmonic syntheses. Parameters in his FM synthesis scheme, involving a sound source and (possibly) mutliple modulators, make use of (usually) integer ratios for carrier and modulator tones (frequency ratios 1:1 - same note, 2:1 - carrier one octave up, etc.), as well as an index (how deep the modulation go, usually also involving integer ratios of the frequencies). By changing the indexes of the modulators over the course of a note, the timbres become very exotic, though quite harmonic, yet not feasible through "standard" synthesis techniques. I recall one person at Stanford emulated a piano sound with this method by using slightly offset non-integer carrier:modulator ratios (1:1.1 ???). Stanford's CCRMA (Center for Computer Research of Music and Acoustics ???) in their Music Department probably can send you copies of Chowning's original paper on linear FM, and the way his methods emulates Bessel functions. Other papers are (or were at last check) also available. Remember that linear FM is rare in analog synthesizers (I know Serge Modular Music synthesizers have an option to make use of a linear FM input), so most of the work in linear FM is done with digital synthesizers. I believe most modern digital synthesizers provide some program to allow the user to specify C:M ratios and indexes to perform what gets called Chowning FM synthesis. Exponential FM in analog synthesizers still offers interesting timbres, but due to the difference in the mathematical results of such modulation the output is rarely "harmonic" or "tonal" (in a standard sense) in nature. Hope this was of some help. I don't know the address of Stanford University or the CCRMA, but it should be accessible. -- Occam's Razor: I liked it so much, I bought the company! Rich Rosen pyuxn!rlr
ron@brl-tgr.ARPA (Ron Natalie <ron>) (10/06/84)
I found out the hardway, I bought a Yamaha DX-7. Still don't understand everything yet. -Ron