FM Synthesis
FM音響合成

FM synthesis, widely recognized as the foundation of the YAMAHA DX7, is a method that generates complex overtones by rapidly modulating the frequency of one sine wave with another. It is regarded as a major technological innovation in the history of electronic music. The birth of this technique is closely tied to the aesthetic vision and intellectual outlook of its inventor and composer, John Chowning.

John Chowning, born in 1934, is an American composer who studied musicology and composition at Stanford University before engaging in research on electronic and computer music. From the late 1960s, he began experimenting with FM sound synthesis, and in 1973, through a licensing agreement with YAMAHA, he laid the foundation for commercial synthesizers. At the same time, Chowning developed a unique methodology that connected technology with compositional theory through his research and compositional practice at IRCAM. Notably, Chowning did not create FM synthesis through mathematics or theory alone; rather, he discovered sounds by ear during experimentation and later substantiated them theoretically.

Twentieth century Western music often appears to be driven by technology, yet even the most technically oriented works carry the worldview of their composers and the atmosphere of their era. These elements have continually shaped the forms of sound. The FM synthesis invented by John Chowning is no exception. It was not a case in which composers simply supplied effective demonstrations for devices developed by manufacturers. Rather, manufacturers turned the sounds invented by a composer into actual products. This article approaches FM synthesis with that background in mind. Instead of limiting the discussion to equipment or theoretical mechanisms, it uses Stria, a work that embodies a new harmonic outlook of the twentieth century, as an entry point to explore the distinctive resonance and beauty FM can create. The aim is not to turn technical explanation into an end in itself, but to consider how technique becomes integrated into a work, and to look toward the creative processes that lie beneath that transformation.

Stria, created by John Chowning in 1977, is an electronic music work widely regarded as a landmark demonstration of the artistic potential of FM sound synthesis. The piece is neither a mere technical experiment nor a showcase of electronic sounds; by placing frequency ratios and spectral structures at the core of its composition, it produces sonorities that transcend traditional Western harmonic concepts. Its close integration of timbre and structure marks it as a masterpiece of contemporary music and a work that influenced the later spectral music movement.

What is particularly remarkable about this work is that FM sound synthesis functions not merely as a tool for generating new timbres, but as a compositional technique that shapes the very structure of the piece. In Stria, tuning, timbre, and temporal structure are integrated, allowing the sonic world to unfold like a vast wave. While it is possible to understand the technical mechanisms of FM in advance, listening to the work first and attending to how FM’s distinctive harmonic expressions shape our perception can provide an important key to grasping the technology itself.

A key element in understanding the resonance of Stria is the Stria scale, designed by Chowning himself. Rather than following conventional twelve tone equal temperament or just intonation, Chowning based the system on a nine tone equal temperament that divides the octave into nine equal steps. He then introduced the idea of a pseudo octave, a slight adjustment applied to each step to refine the basic frequencies.

The pseudo octave preserves the sense of an octave while subtly modifying the frequency ratios across the scale. This concept concerns pitch design rather than timbre. Through this adjustment, the overlapping of partials generates a more dimensional form of modulation.

In FM synthesis, the ratio between a carrier frequency and a modulator frequency is often described with specialized terminology. Chowning intentionally used noninteger ratios, symbolically including the golden ratio phi which is approximately 1.618. This approach creates complex interactions and graceful connections between partials that would not normally combine smoothly. As a result, the system produces a vivid and fluid resonance that cannot arise from simple integer based harmonic structures. Even a single note carries layers that shift in a spatial manner over time, forming an acoustic environment that recalls the spirit of spectral music.

A notable feature of the Stria scale is that partials are shared and connected across multiple notes. When some overtones overlap at different pitches, a single tone can produce a sense of multiple layers resonating simultaneously, and as the lines of sound intertwine and move gently, they are perceived by the ear as continuous frequency lines (Stria, meaning “lines” or “striae”).

The overlapping and interference of these partials create a temporal continuity resembling complex patterns drawn in sound, forming a rich and ambiguous sonic space that is neither a clear chord nor noise. One might even say that this bears a resemblance to nineteenth-century compositional practices in which modulation is carried out continuously around common tones.

The design of Stria is closely connected to the research Chowning carried out at IRCAM. In the late nineteen seventies he conducted a mathematical investigation of FM synthesis at IRCAM and linked these findings directly to compositional practice. Relationships among frequency ratios, modulation indices, and durations were organized into a coherent system, making it possible to treat subtle timbral variations as structural elements within a composition. As a result, the motion and layered architecture of sound in Stria are not merely technical demonstrations but are integrated into the overall form of the work.

During this process Chowning also developed a compositional theory that expanded traditional Western concepts of harmony and melody. In conventional music, melody, harmony, and rhythm form the core materials. In Stria, however, the internal structure of the spectrum, namely the partials themselves, assumes the role of harmony.

The introduction of the golden ratio, non integer ratios, nine tone equal temperament, and pseudo octaves, along with the delicate interference patterns produced by the overlap and connection of partials, allows timbre to function as a generator of motion and stratification along the temporal axis. In this way Stria elevates FM synthesis beyond a technique for producing timbre and turns FM into the very basis of musical form.

Download Max Patch BasicFMSynthesis.maxpat

FM sound synthesis is a technique in which the frequency of a carrier tone is rapidly varied by the frequency of a modulator tone. As a result, the ear perceives new frequency components called sidebands that are different from the carrier itself. A simple sine wave is transformed into a waveform that contains many partials and produces a richer timbre.

The principle can be understood as an extreme acceleration of vibrato. A slow vibrato that might occur only a few times per second is pushed to hundreds or thousands of cycles per second, and the range of pitch deviation is expanded across several octaves. The vibrato motion itself is no longer heard. Instead, new partials appear at mathematically predictable frequencies and strengths, and these partials are perceived as the resulting sound. This principle forms the basis of the synthesis method.

• Carrier - The fundamental frequency that serves as the central pitch. It is perceived as the pitch of the sound.
• Modulator - A signal that periodically modulates the frequency of the carrier. When applied at very high speed it produces sidebands and increases the complexity of the partial structure.
• Modulation Index - The depth of frequency deviation that the modulator imparts to the carrier. A large index generates many complex partials. A small index yields gentler partial structures. An index of zero produces no additional partials.
• Frequency Ratio - The ratio between the modulator frequency and the carrier frequency. Integer ratios create regularly aligned harmonic partials. Non integer ratios produce slightly displaced and complex inharmonic partials.
• Sidebands - New partials generated around the carrier frequency. Their positions and strengths depend on the modulation index and the frequency ratio.

Download Max Patch BasicFMSynthesis.maxpat

In this demo, you can understand both aurally and visually how changing the frequency ratio between the carrier and the modulator affects the harmonic structure, how increasing the modulation index increases the number of partials, and how the waveform remains unchanged as long as the ratio is constant, even if the carrier frequency changes. The fundamentals of FM synthesis are created with these two oscillators. FM synthesizers produced by YAMAHA or KORG with six oscillators are designed so that the sound generated by a pair of oscillators can act as a modulator for another oscillator, or multiple differently configured pairs can be arranged in parallel to produce more complex partials.

By varying the modulation index over time with an envelope or other means, it is also possible to create sounds in which the amount of partials changes dynamically. One of the defining features of FM synthesis is that even with a small number of oscillators, careful combinations can produce extremely complex and diverse sounds. The potential of this sound design approach is far from being fully explored.

Download Max Patch
StriaFM.maxpat

It is a simple two operator FM synthesis piece, yet it follows the inspiration of Stria by adopting the golden ratio and its powers as frequency ratios together with nine tone equal temperament. Inharmonic partials often produce dissonant colors even in single tones. However, because partials at different pitches can share certain frequency components, there are moments in which the harmony connects smoothly, similar to sustained common tones or pivot like modulations. This can be heard and also seen in the spectrogram. The example may offer one approach to working with dense and murky sonorities that are often difficult to use as musical material.

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FM synthesis completely transformed the music of the 1980s, which had been dominated by analog electronic sounds, with its dazzling and complex partials. The timbres used at that time are now often perceived with a sense of nostalgia. Meanwhile, from the 1990s onward, UK artists gradually explored new terrain by creating wobble basses with FM. This approach differs fundamentally from the web table synthesis popular in the 2010s, which typically controls aggressive partials through modulation and creates melodies by manipulating pitch. FM also pairs well with approaches that alter sound in ways other than directly shaping pitch. This video is a demo of a two oscillator FM synthesizer designed specifically for such bass music applications.

By modulating the depth of the FM index with geometric patterns synced to BPM, the partials appear to dance. Despite the simple two oscillator interface, both the carrier and modulator can use waveforms other than sine waves. This achieves complexity in a different way from the YAMAHA DX7, which combined six oscillators to generate rich partials. Designing interfaces and parameters that allow the maximum variety of sounds with minimal operation remains a key focus in modern FM synthesizer development.