Tutorials and Topics - Peabody Computer Music

Elements of FM synthesisTutorial 11: Synthesis—Frequency modulationFrequency modulation (FM) has proved to be a very versatile and effective means ofsynthesizing a wide variety of musical tones. FM is very good for emulating acousticinstruments, and for producing complex and unusual tones in a computationally efficientmanner.Modulating the frequency of one wave with another wave generates many sidebands,resulting in many more frequencies in the output sound than were present in the carrierand modulator waves themselves. As was mentioned briefly in the previous chapter, thefrequencies of the sidebands are determined by the relationship between the carrierfrequency (Fc) and the modulator frequency (Fm); the relative strength of the differentsidebands (which affects the timbre) is determined by the relationship between themodulator amplitude (Am) and the modulator frequency (Fm).Because of these relationships, it’s possible to boil the control of FM synthesis down totwo crucial values, which are defined as ratios of the pertinent parameters. One importantvalue is the harmonicity ratio, defined as Fm/Fc; this will determine what frequencies arepresent in the output tone, and whether the frequencies have an harmonic or inharmonicrelationship. The second important value is the modulation index, defined as Am/Fm; thisvalue affects the “brightness” of the timbre by affecting the relative strength of thepartials.Technical detail: In John Chowning’s article “Synthesis of Complex AudioSpectra by Means of Frequency Modulation” and in Curtis Roads’Computer Music Tutorial, they write about the ratio Fc/Fm. However, inF.R. Moore’s Elements of Computer Music he defines the termharmonicity ratio as Fm/Fc. The idea in all cases is the same, to express therelationship between the carrier and modulator frequencies as a ratio. Inthis tutorial we use Moore’s definition because that way whenever theharmonicity ratio is an integer the result will be a harmonic tone with Fcas the fundamental.The frequencies of the sidebands are determined by the sum and difference of the carrierfrequency plus and minus integer multiples of the modulator frequency. Thus, thefrequencies present in an FM tone will be Fc, Fc+Fm, Fc-Fm, Fc+2Fm, Fc-2Fm, Fc+3Fm,Fc-3Fm, etc. This holds true even if the difference frequency turns out to be a negativenumber; the negative frequencies are heard as if they were positive. The number andstrength of sidebands present is determined by the modulation index; the greater theindex, the greater the number of sidebands of significant energy.114