The Science behind Music
Harmonics, Frequency, Wavelength, and Piano Tuning
Music is deeply connected to physics, and learning about the science behind it has been both fun and fascinating. From wavelength and frequency to harmonics and tuning, understanding these concepts has given me a deeper appreciation for the sounds around us.
Harmonics
When a piano string vibrates, it does not oscillate at a single frequency but rather at multiple frequencies simultaneously. This phenomenon, known as harmonics or overtones, is fundamental to musical timbre and resonance.
The fundamental frequency, or first harmonic, determines the pitch of the note. It is the lowest frequency at which a system naturally vibrates and is typically the strongest. In musical instruments, this frequency is produced by the entire vibrating medium, such as a string or air column, moving together, resulting in a higher amplitude and making the fundamental frequency more easily perceived than other frequencies.
The additional harmonics, which are integer multiples of the fundamental frequency, contribute to the richness and character of the sound.
For example, if a piano A2 string is vibrating at 110 Hz (fundamental frequency), its harmonics will include:
Second harmonic (first overtone): 220 Hz (A3)
Third harmonic (second overtone): 330 Hz (E4)
Fourth harmonic: 440 Hz (A4), and so on.
The interesting double frequency
You might noticed in the above example, when you double the frequency, it creates an octave apart, 110 Hz (A2)-> 220 Hz (A3) -> 440 Hz (A4). The perception of octaves is largely due to the way our auditory system processes sound. When the frequency of a musical note is doubled, the resulting pitch is perceived as the same note but one octave higher. This is because our ears and brain recognize pitches that are related by a 2:1 frequency ratio as equivalent. This octave equivalence is fundamental to music theory and is reflected in the way musical scales and tuning systems are structured.
The Art and Science of Piano Tuning
The presence and relative strength of harmonics shape the unique tone of each instrument. Pianos, in particular, exhibit complex harmonic structures due to factors like the stiffness of their strings and the resonant properties of their soundboard. It's important to note that in real-world instruments like pianos, overtones deviate slightly from perfect integer multiples of the fundamental frequency—a phenomenon known as inharmonicity. This deviation influences the instrument's tuning and tonal quality. After establishing the initial tuning using equal temperament, tuners employ additional techniques to refine the piano's sound:
Stretch Tuning: To counteract inharmonicity, tuners adjust the tuning by slightly sharpening higher notes and slightly flattening lower notes. In the upper registers, the overtones of higher strings are slightly sharper than their theoretical values. To align these overtones with the fundamentals of lower notes, tuners slightly sharpen the higher notes. Conversely, in the lower registers, the overtones of lower strings tend to be slightly flatter. Tuners slightly flatten the lower notes to correct this and ensure their harmonics correspond appropriately with the fundamentals of higher notes. These adjustments help achieve a more consonant and unified sound across octaves.
Beating Phenomenon: Tuners listen for beats—periodic fluctuations in amplitude that occur when two slightly different frequencies interfere with each other. By adjusting the tuning of intervals so that the interference patterns between their overtones are reduced, tuners achieve a smoother and more harmonious sound. When two notes are played together, their overtones interact, and if these overtones are close but not identical in frequency, they produce beats. Beats manifest as periodic fluctuations in volume caused by the constructive and destructive interference of sound waves. Minimizing beats between reference notes helps achieve accurate tuning and contributes.
Isn't this a fascinating world? Next time maybe you will listen to overtones in the sounds around you?
