The secret geometry of a symphony: How physics writes our favorite songs.
By Saachi Khemchandani
Introduction
Have you ever heard about the Stradivari’s miracle? Why is a 300 -year-old violin still priced above all others? For centuries, musicians and historians have whispered about the “Stradivarius Miracle”. People might think that it is Stradivari’s artistry that makes it so “magical”. While many attribute this to the “magic” varnish the reason lies in the physics that was used in the violin’s making.
A Stradivarius violin made in 1684 (from Capon, 2017). https://www.science.smith.edu/climatelit/stradivarius-violins/
While we often perceive listening to music as an emotional experience, it is fundamentally a physical phenomenon governed by air. Music isn’t simply an art it’s a series of longitudinal waves that travel at about 343 meters per second at standard temperature. The music we listen isn’t just a piece of art but the perfect balance of density, resonance and wave interference. To understand why a 300-year-old instrument remains the standard, we must understand the mechanics of the vibrations.
The difference between noise and a masterpiece lies in the mathematical patterns hidden in the sounds. Musicians create music by organizing various sounds together. When we listen to music carefully, it can be noticed that each song has its own noticeable pattern. To further understand the concept of how a Violin works and how a pattern in sound is created it is necessary to decode how a sound wave works.
Anatomy of a sound wave
To decode the nature of sound, one must understand how energy travels through a medium. In physics a wave is described as a disturbance due to which energy is transferred from one point to another through a medium like water or air. Waves are typically of two types - Transversal waves and longitudinal waves. While light waves are transversal waves sound waves are longitudinal waves. These waves travel through a medium like the spruce wood of a violin or the surrounding air.
Image displaying difference between Noise and Tone
(PDF) The Physics Behind Music
The movement of sound is characterized by “push and pull” movements of the molecules. These movements are called compressions and rarefactions. When we think about characteristics of sound waves, we think about amplitude, intensity i.e. how loud is it and its frequency i.e. the pitch of the sound being produced. We mainly look at three fundamental properties namely wavelength, amplitude and frequency.
Labelled Longitudinal Wave
https://www.geeksforgeeks.org/physics/longitudinal-waves/
Just like we use instruments to measure a physical object, we use wavelength and amplitude to quantify to dimensions of a sound. The distance between the tops of two waves is the same and can be measured. This distance is called the wavelength. Just like wavelength we have amplitude. Amplitude is the height of a wave which is consistent and can be measured. The frequency of a wave is the number of cycles a wave completes in a second.
The relation between these properties is not random but bound by a mathematical equation. While listening to music the “tone” is often talked about. The tone mainly depends on two factors the frequency of the wave and the amplitude. The frequency determines the pitch (degree of highness or lowness) of the tone. The amplitude affects the volume of a tone, higher the amplitude, the louder the volume. A mathematical connection between these properties is governed by the wave equation
Where is the speed of sound (343 m/s), is the frequency, and is the wavelength. This equation explains why, as a violinist moves their finger up the fingerboard (shortening the string and the wavelength), the frequency-and thus the pitch-must increase.
Timbre and Overtone
Even when two instruments play the exact same note, our brain can detect a “sonic fingerprint” that tells them apart. When we hear the same note being produced by a violin, guitar, piano or a human we can immediately differentiate between them. The quality of sound that distinguishes between these sounds is TIMBRE (pronounced as tam-Ber). Timber brings color, emotion, and individuality to musical sound.
What we might consider a single note is actually a complex compilation of hidden layers. Overtones are hidden layer of sound that accompanies every note and gives each instrument or voice its distinctive color and identity. Timbre is determined by overtones. Without overtones all instruments would sound identical, thus stripping music of its emotional depth and identity. When a musical instrument produces a note, it doesn’t emit a single frequency but a combination of one fundamental frequency and a series of overtones (also known as harmonics).
Above image showcases the timbre and various overtones of a sound
https://jews-harps.com/the-art-of-sound-coloration/
However, this is not the simplest form of music. Music in its simplest form is monotonous that is it is only composed of pure tones. Monotonic music is usually considered dull and lifeless like a 1990’s ringtone. Real music on the other hand is polytonic that is a mixture of pure tones played together in a manner that sounds harmonious. Sound with multiple frequencies like that of an instrument or the human voice would still be periodic but more complex than just a simple curve. The human voice and musical instruments produce sounds by vibration. What vibrates determines the type of instrument.
Classification of instruments
Music and Noise – The Physics Hypertextbook
Physics of the Violin body
The violin acts as an amplifier, turning the almost silent vibration of a string into a room-filling performance. The study of the physics of the violin gives us a fascinating insight into how the instrument converts the player’s intricate movements into musical sounds. The strings themselves hardly make any noise by themselves they are thin and slip through air with barely making any noise.
Every component of the instrument is precisely engineered so as to manipulate the airs pressure and tension. The thicker more massive strings vibrate more slowly, so the strings on the violin get thicker as you go down from the E to A to D to G strings. The tension is adjusted by tuning pegs: tighter gives higher pitch. The frequency of the sound being produced also depends on the length of the string that is free to vibrate. The body consists of the front and back plates, the sides and the air inside. All these serve to transmit the vibration of the bridge into the air around the instrument.
The bridge and body of the violin transmit some of the energy of vibration of the strings into sound in the air. The bridge itself is very effective at transmitting power to the body at frequencies from about 4Hz, which is where the human ear is very sensitive.
Cross section at the bridge, seen from the tailpiece end. At low frequencies, the bridge oscillation approximates rotation around a point near the treble foot.
Violin acoustics: an introduction
Human voice as an Instrument
The most versatile instrument is not made of wood or metal but of bones and muscles. The human voice is one of the most overtones rich instruments. With the human voice we can shape timbre through articulation, breath control, and resonance. Singers possess the specialized technique of amplifying specific overtones creating the illusion of two pitches being sung simultaneously.
Showcases how the structure of voice box supports various overtones
https://www.phys.unsw.edu.au/jw/voice.html
How do our ears work
Our biological hardware is the final stage in the journey from a vibrating string to a conscious thought. The way we hear music also depends on the way our biological hardware works. First, the sound waves are focused into the ear canal via the ear flap also known as the pinnacle. These waves impinge on the ear drum. The ossicles in middle ear- hammer/anvil/stirrup-transfer vibrations into Cochlea.
Cochlea is filled with perilymph fluid, which transfers sound vibrations into Cochlea. Cochlea also contains basilar membrane which holds~30,000 hair cells in organ of Corti. Sensitive hairs respond to the sound vibrations-send signals to brain via auditory nerve. Brain finally processes audio as “music”.
Showing the inner anatomy of the human ear
https://courses.physics.illinois.edu/phys406/sp2017/POM_Talks/2012_UIUC_POM_Talk/2012_UIUC_POM_Talk.pdf
Conclusion
While the geometry and anatomy of the wave explain how sound moves, the "Stradivarius Miracle" may actually be a result of climate change. During the late 17th century, Europe experienced a "Little Ice Age." The prolonged cold winters caused the spruce and maple trees of the era to grow slowly and uniformly. This resulted in wood with a unique acoustic density and a higher modulus of elasticity (stiffness).
In physics, the resonance of a body is heavily dependent on its density. These specific wood properties allow the violin’s front and back plates to vibrate with a "purity" that modern wood cannot replicate. When the bridge transfers energy to this high-density wood, it creates a specific harmonic profile-a "Stradivarius Timbre"-that perfectly balances the fundamental frequency with its overtones.
References
· Violin acoustics: an introduction
· Kurdish Academy | Overtones and Timbre
· (PDF) The Physics Behind Music
· Music and Noise – The Physics Hypertextbook
· How a Violin Produces Music – The Masters Music School