Book Review – “On the Sensations of Tone as a Physiological Basis for the Theory of Music” by Hermann von Helmholtz

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Is a 150-year-old book that was to be the foundation for modern acoustics really still relevant today? You bet it is! Find out why.

by Dave Townsend, Mar. 2014

(Original title: “Die Lehre von den Tonempfindungen als physiologische Grundlage für die Theorie der Musik”)

SoundBytes endeavors to suggest essential resources for the serious student of audio, but none merit the adjective “essential” quite as literally as this book. Published in 1863 (translated into English in 1875), “Sensations of Tone” is no less than the foundation of modern acoustics. Is a 150-year-old book really still relevant today? You bet it is!

I once read an online forum thread in which the subject of a particular plugin’s response to sine wave test tones was being discussed. One poster indignantly interjected that “I deal with music, not sine waves!” I just sighed to myself, thinking “this guy really needs to read Helmholtz.” I refrained from replying that whether it offends your artistic sensibilities or not, music is indeed sine waves, as is all sound.

This, in a nutshell, is the knowledge Herr Helmholtz bestowed on the world: that all sound, no matter how complex, can be mathematically broken down into constituent sine waves. Whether you know it or not, you’re applying that principle every time you insert an equalizer, examine a spectrum analyzer or shape a waveform in a synthesizer.

In 1863, this was a new and fairly radical concept. Helmholtz therefore wrote his treatise using plain language for a broad, non-technical (but musically-knowledgeable) audience. That’s why it still works as a primer today. Even if you are completely new to the subject, just remember that in 1863 so was everybody else.

Now some really good news: Hermann von Helmholtz is dead. OK, not so great for Hermann himself, but for you and me it means his work is in the public domain and can be had for cheap or free – which happens to be right in this cheapskate’s price range! You can read it online here:, or download a pdf here:

Helmholtz was a professor of anatomy, and it was his interest in human physiology that led to studies of sensory perception, initially ophthalmology and then hearing.

In the mid-19th century, a lot of research was being dedicated to drawing lines between the mechanics of the universe and aesthetics. It was an attempt to reconcile two spheres of intellectual pursuit that had, since ancient times, been treated as completely separate and incompatible realms. But in the 19th century the hunt was on for physical explanations and scientific descriptions for everything, even the arts. Why, for example, are some sounds pleasant while others are irritating? What really distinguishes music from noise? (OK, we’re still struggling with that one!) Helmholtz believed that such questions could be answered via the scientific method, through experimentation and observation.

Now, if you want to study sound, it follows that you’ll first need to make some sound. Specifically, sound whose amplitude and frequency can be controlled. Helmholtz began by using hand-cranked mechanical sirens, similar to a WWII-era air-raid siren. That must have made him real popular on campus.

Later, he invented a more practical device that came to be called the “Helmholtz Resonator”. You’ve probably heard that term in reference to an acoustical treatment (more on that below), but the “resonator” described in his book wasn’t an acoustical device at all. It was actually an electronic tone generator, what we would today call an oscillator.

With this resonator, he was able to generate consistent sine waves whose frequency did not depend on a student’s tireless arm to turn a crank. After building a bunch of them, he discovered that he could make complex sounds by combining multiple frequencies. He was even able to mimic vowel sounds.  

A case could be made that Helmholtz was the father of additive synthesis! Sixty years later, Laurent Hammond would employ a similar technique in the invention of the tone wheel organ.

NOTE: One of Helmholtz’s students was Heinrich Hertz, who went on to make great contributions to the field of electromagnetic physics and for whom the standard unit for frequency is named. Max Planck, who originated quantum mechanics, was another famous student of Hermann von Helmholtz. Walter Schottky, who invented the pentodes that power your Marshall stack, was in turn a student of Max Planck. The reach of teachers can extend across generations and centuries. Just one reason I respect teachers far more than rock stars.

Right from Chapter One, the reader is gently eased into the notion that all sounds, even the most majestic musical compositions, are in fact comprised of sine waves and that they are broken down into their constituent frequencies by the inner ear. It was a tough sell in 1863, and remains a tough sell to some musicians and audio engineers to this day. Helmholtz, however, slowly and logically builds his case for a logical connection between physics and music.

The first two sections of the book deal primarily with mechanics and physics, or “natural philosophy” to use the term of his day for the “hard” sciences. He makes general observations about the sensation of sound and the nature of periodic vibrations, with extensive explanations of the workings of the human ear. Helmholtz, knowing it would be a challenge convincing readers to connect the dots between physics and music, carefully avoids anything too radical or controversial in the first two sections.

The connection to aesthetics is gradually sneaked in later, when he begins talking about musical scales and notes, the relationship between pitch and frequency, and the mathematical relationships of notes in a scale. By the time he gets into intervals, harmonies and intonation it all just seems like a perfectly logical progression of ideas. With the possible exception of a few references to obscure composers, you’ll have no trouble following along, even if you’re better versed in musical terminology than mathematics.

When “Sensations of Tone” was originally published, some musicians took offense to its mechanical explanations of music, a resistance that persists even now. Musicians don’t want to think of what they do as being equivalent to a mechanical engineer’s constructs.

There is some merit to that prejudice. There are indeed things that can be heard but not measured or quantitatively analyzed. However, no evidence exists to suggest that ignorance of the physics of music somehow promotes better music. Even non-techies can benefit from this knowledge, which is why I consider this book to be essential reading. Helmholtz’s book will help you to better understand filters, synthesis, acoustic treatments, speakers, acoustical instruments and most important, the ultimate terminus of the signal chain: ears.

Helmholtz Resonator


This term has come to have a different meaning today than it originally had in Helmholtz’s book. Nowadays, it refers to a resonating cavity that effectively isolates one particular frequency (and its harmonic series) from broadband sound. Modern resonators are based on designs by Helmholtz that came after the publication of “Sensations of Tone”. Those designs, by the way, are quite similar to devices dating back to ancient Greece, where large pots (amphora) were used as acoustical treatments in open-air theaters. Archeologists, however, did not know their purpose until Helmholtz explained it in 1863.


The specific term “Helmholtz Resonator” is most often used in the audio world today to describe a type of bass trap that can be tuned to a specific frequency for absorbing problematic bass. Google “DIY Helmholtz Resonator” for instructions and formulas for building your own!


Helmholtz resonators also have other applications beyond acoustics, from internal-combustion engines to airplane wings. Fun fact: the loud whistle you hear when you roll down your car window slightly, or the tone you get by blowing over the top of a soda bottle are both demonstrations of Helmholtz resonance.

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