Before delving into one of the pivotal figures in the history of music theory, it’s important to acknowledge the complexity surrounding Pythagoras's contributions. His name is often used as a shorthand for early advances in the mathematical understanding of music. However, the "discovery" of these principles was likely far more nuanced, involving the accumulated knowledge of earlier civilizations. Rather than originating these ideas from scratch, Pythagoras may have inherited and systematized pre-existing insights about the harmonic series and numerical ratios. In this research, I will reference Pythagoras with an awareness of this historical context, embracing his legendary status not as a purely factual figure but as an inspiring, poetic, and spiritual symbol guiding my exploration. Pythagoras is traditionally credited with discovering the relationship between musical intervals and mathematical ratios. Ancient accounts tell us he observed that strings of varying lengths produced harmonious sounds when their lengths were in simple ratios—such as 2:1 for an octave, 3:2 for a perfect fifth, and 4:3 for a perfect fourth. According to legend, he conducted experiments using a monochord, a single-string instrument, to systematically study these relationships. By dividing the string into whole-number ratios, Pythagoras demonstrated how these divisions created consonant intervals.
One of the first devices able to visualise Pythagoras' ratios, an ancestor of the oscilloscope, the harmonograph is a mechanical device that creates intricate geometric patterns by translating motion into visual art. It was invented in the mid-19th century by a professor Blackburn. Blackburn designed it to illustrate the principles of harmonic motion using pendulums, captivating both scientists and artists with its ability to generate mesmerising designs. Anthony Ashton in his book about the harmonograph states that “the instrument draws pictures of musical harmonies, linking sight and sound.”1 In a lateral harmonograph, two pendulums swing in perpendicular directions—one controlling horizontal motion and the other vertical. Their combined oscillations create patterns influenced by frequency, amplitude, and phase, ranging from simple ellipses to intricate spirals. A rotary harmonograph introduces rotational motion, often using a spinning platform or pendulums with rotational attachments. These mechanisms create more symmetrical and complex designs, resembling floral or mandala-like patterns. The harmonograph gained popularity during the Victorian era, blending scientific exploration with artistic expression. Exactly like the oscilloscope, it beautifully demonstrates the interplay of physics and mathematics, particularly harmonic motion and resonance. I will take a closer look on how to recreate the lateral and rotary technique on the oscilloscope in the practical part of this research (see paragraphs 10.1 and 11). It is relevant to mention here the Kaleidophone and the Chladni patterns (or Cymatics) for the reader further curiosity.
The shapes created by a harmonograph are known as Lissajous figures. In the mid-nineteenth century, French mathematician Jules Antoine Lissajous devised an experiment to visualize harmonic motion. He discovered that if a small mirror was attached to the tip of a vibrating tuning fork and a beam of light was directed at it, the vibration could be projected as a pattern onto a dark screen. Striking the tuning fork produced a simple vertical line, and when the light beam was cast sideways, it formed a sine wave. Curious about the results of combining motions, Lissajous placed a second tuning fork at a right angle to the first, introducing lateral movement. He found that tuning forks vibrating at simple frequency ratios created intricate and beautiful shapes2. These patterns, now called Lissajous figures, are formed by the interplay of two perpendicular harmonic oscillations. Their appearance depends on the relative frequencies, amplitudes, and phase differences of the oscillations. They range from circles, ellipses, and figure-eights to highly complex, symmetric designs at specific frequency ratios. I will explore the figures created by specific intervals in a later chapter, let’s now get back to the main character of the story, and let’s understand its history and its functioning (see 10.2 Music intervals)
We have already introduced the oscilloscope, but to refresh our understanding, it is a device that displays how the voltage between two points in a circuit varies over time. For instance, when connected to a sinusoidal voltage source, the oscilloscope displays a wave-like pattern (fig. 1, 2). One of the earliest attempts to automate the conversion of electrical signals into a visual display was the Hospitalier Ondograph, developed in the early 1900s (fig. 3). This device used a capacitor to drive a galvanometer with a pen attached. As voltage varied, the pen traced a waveform on scrolling paper. However, the Ondograph's mechanical system was too slow to keep up with rapidly changing electrical signals, requiring multiple samples to accurately record them. In the late 19th century, scientists studying cathode rays (electrons traveling in straight lines in a Crookes tube) discovered that these rays could be deflected by electric or magnetic fields. In 1897, German physicist Karl Ferdinand Braun built the first oscilloscope using a cathode ray tube (CRT). By applying voltage to vertical plates, he directed an electron beam to strike a phosphor-coated screen, producing a visible dot that moved vertically with voltage changes (fig. 4). In 1899, physicist Jonathan Zenneck added horizontal plates, enabling the beam to sweep side-to-side. This innovation allowed the oscilloscope to display real-time graphs of electrical signals (fig. 5).
Having briefly explored the history of the oscilloscope, let us now delve into the artistic part. In this section, I will highlight key references—both significant to the field and particularly relevant to my research—while touching on the broader historical relationship between sound and image. The term visual music refers to an artistic movement that explores the interplay between sound and image, aiming to create compositions where the two elements are equally integral. While its formal origins date back to the late 19th and early 20th centuries, the connection between sound and image seems as old as music itself, recognized and celebrated even in ancient times. For example, cave art from 40,000 years ago is thought to have a sonic dimension3. Whether these spaces were used for ritualistic sound performances or if the acoustics held special meaning for the painters remains unknown. However, these environments combined images, light (fire), and a highly resonant sonic experience4 (fig. 6). Historically, one of the earliest foundations of sound-image correspondence comes from Pythagoras' study of musical harmony, which influenced the aesthetic theories of artists, sculptors, and architects.
Building on Pythagoras’ ideas, Aristotle theorized a connection between color harmonies and musical proportions, which I will discuss in the chapter on colors in visual music. Similarly, Roman architect Vitruvius emphasized the need for architects to understand music to comprehendcanonical and mathematical relations. Leon Battista Alberti, the Renaissance polymath, famously wrote: The same numbers, by means of which the agreement of sounds affects our ears with delight, are the very same which please our eyes and mind. We shall therefore borrow all our rules for the finishing of our proportions from the musicians, who are the greatest masters of this sort of numbers5. A fascinating modern example of this connection is Jan Hoogstad’s work inspired by Bach’s music (figure 7). The visual arts also reflect this relationship. Italian painter Arcimboldo’s (1527–1593) works have been interpreted as inspired by Pythagorean harmony6. Michelangelo’s Sistine Chapel frescoes incorporate a 5:4 ratio, corresponding to the Miserere Mei by Gregorio Allegri, a piece composed for exclusive use in the chapel7 (figure 8). In the concept of the "harmony of the spheres," this correspondence is extended to the cosmos, as seen in the works of Robert Fludd8 (figure 9), Athanasius Kircher9, or Johannes Kepler10 (figure 9b).
In music, Louis Bertrand Castel, an 18th-century French Jesuit, envisioned a "color organ" that paired musical notes with specific colors, inspiring later inventions like Alexander Wallace Rimington’s working color organ (fig.10). Aleksandr Skryabin’s Prométhée also featured a part for such an instrument, projecting colors tied to his synesthetic experiences. The advent of cinema in the early 20th century introduced new possibilities for visual music. Artists like Wassily Kandinsky explored abstract shapes and sound, while filmmakers such as Oskar Fischinger and Len Lye created synchronized audiovisual animations. Walt Disney’s Fantasia fused visuals and music in groundbreaking ways, earning recognition as one of the most universal harmonic artistic achievements of the 20th century11. Technological advancements revolutionized visual music. Oscilloscopes, light projection systems, and computer graphics gave rise to immersive audiovisual art. Pioneers such as John Whitney, Bill Alves, and Stephen Malinowski (creator of the Music Animation Machine) pushed the boundaries of this art form12. A connection to oscilloscopes and early attempts to visualize soundwaves can be seen in several historical inventions. For instance, Eduard Leon Scott de Martinville’s Phonautograph (1857), which drew waveforms as a method for recording voice (fig. 11). Rudolph Koenig’s Metronomic Flame (1862) visualized sound vibrations (fig. 12). Around 1930, Soviet artist Arseny Avraamov created hand-drawn motion picture soundtracks (fig. 13), and Oskar Fischinger used drawn waveforms to produce optical soundtracks in 1932, often synchronized with classical music. One final, often-overlooked example is music notation itself. While not always considered a standalone art form, its visual elements hold immense artistic and cultural significance, from Tibetan chant notation to the experimental scores of the 20th century (figs. 14, 15, 16). Although I won’t expand further on historical references here, I encourage readers to explore the mentioned figures and works if intrigued.
After exploring the historical connections between sound and image, we now narrow our focus to oscilloscope music, a captivating art form that transforms sound waves into visual patterns using an oscilloscope. This unique medium bridges the gap between auditory and visual experiences by directly displaying sound as moving, luminous shapes on a screen. Oscilloscope music relies on stereo audio signals fed into the oscilloscope’s X and Y inputs, creating dynamic visuals as the sound determines the dot’s position. Artists manipulate these waveforms to generate mesmerizing animations that are both heard and seen. Early explorations of oscilloscope art emerged in the mid-20th century, with pioneers like Ben Laposky creating oscillons by photographing patterns generated on cathode ray oscilloscopes. Later, the medium inspired experimental works like the audiovisual performances of Jerobeam Fenderson, whose intricate shapes and animations pushed the creative boundaries of this art form13. Alberto Novello (a.k.a. Jestern) is also a source of inspiration about oscilloscope art14.While Jerobeam Fenderson’s work is a major contemporary reference for oscilloscope music and undeniably remarkable and inspiring, his technique—generating 3D shapes first and then converting them into sound signals—differs from my artistic perspective. In my work and this research, I aim to distance myself from this more artificial approach and remain faithful to the oscilloscope's pure, abstract representation of sound. This approach aligns with my artistic vision and the spiritual and philosophical concepts that underpin my exploration of sound and visual connection.
For Pythagoras, the empirical evidence of musical harmony served as proof of a profound metaphysical and cosmological principle: that numbers are the fundamental essence of reality, and that abstract numerical relationships shape our perception of the world15. To the Pythagoreans, musical harmony became the quintessential example of a universal order, a higher harmony governing the cosmos itself. The creation of the universe from primordial chaos, they believed, could be understood through the lens of numerical relationships16. This research, along with many of the topics and references it encompasses, is a direct or indirect descendant of the Pythagorean harmonic system. Countless artists throughout history have drawn inspiration from these principles, whether implicitly or explicitly. As Tatarkiewicz notes, the Pythagorean foundation of musical harmony influenced the aesthetic theories of visual artists, sculptors, and architects17.This influence extended into the modern era, as exemplified by John Whitney’s 1980 book Digital Harmony: On the Complementarity of Music and Visual Art. Whitney hypothesized that Pythagorean principles of harmony could extend beyond music into visual art: “This hypothesis assumes the existence of a new foundation for a new art... that the attractive and repulsive forces of harmony’s consonant/dissonant patterns function outside the dominion of music.”18 With Whitney’s hypothesis as a guide, we step into the realms of multimedia, multisensory, or cross-modal art—domains where Pythagorean principles continue to resonate in new and innovative ways.