The sound of bells

This activity helps students understand the difference between harmonic and inharmonic sounds. It develops the ability to analyze the frequency spectrum and recognize the unique characteristics of instrumental timbre.

Why does a bell sound so different from a violin, even when both play the same note? The answer lies in a fundamental distinction in acoustics: harmonic versus inharmonic sounds. When a violin string vibrates, it produces a fundamental frequency and a series of overtones that are exact integer multiples of the fundamental (2f, 3f, 4f, ...). This harmonic series gives string and wind instruments their characteristic musical quality. A bell, however, vibrates in complex three-dimensional modes that produce overtones at frequencies that are not integer multiples of the fundamental. These inharmonic overtones give bells their distinctive shimmering, sometimes clashing quality that makes them instantly recognizable but also difficult to tune precisely. Church bell founders have spent centuries perfecting bell shapes to bring the most prominent overtones as close to harmonic ratios as possible. Using FizziQ's spectrum analyzer, students can directly compare the harmonic spectrum of an oboe with the inharmonic spectrum of a bell and discover what makes each sound unique.

Activity overview:

The student analyzes and compares the frequency spectra of a bell and an oboe using FizziQ. By identifying the fundamental frequency and harmonics in each spectrum, the student discovers that the sound of an oboe is harmonic (integer multiple frequencies of the fundamental) while that of a bell is inharmonic, then explores other everyday objects to classify their sounds.

Level:

Middle school

FizziQ

Author:

Duration (minutes) :

30

What students will do :

- Analyze and compare the frequency spectra of a bell and an oboe using FizziQ
- Identify the fundamental frequency and overtones in each spectrum
- Determine whether the overtones are harmonic (integer multiples) or inharmonic (non-integer multiples)
- Understand the concept of musical timbre and its relationship to spectral content
- Classify everyday sounds as harmonic or inharmonic based on spectral analysis

Scientific concepts:

- Harmonic and inharmonic sounds
- Spectral analysis
- Musical timbre
- Vibration modes
- Music theory

Sensors:

- Microphone (frequency analysis)
- FizziQ spectrum analyzer (FFT)

Material needed:

- Smartphone with the FizziQ application
- Bell and oboe sound recordings from the Sound Library
- Optional: various everyday sound objects
- FizziQ experience notebook

Experimental procedure:

Open FizziQ and load the oboe recording from the Sound Library.
Play the recording and open the Spectrum Analyzer. Observe the spectrum: you should see a series of distinct peaks.
Record the frequencies of all visible peaks in a table. Label them as f₁ (fundamental), f₂, f₃, f₄, etc.
Calculate the ratio of each overtone to the fundamental: f₂/f₁, f₃/f₁, f₄/f₁, etc. For the oboe, these should be approximately 2, 3, 4, 5... (integer multiples).
Now load the bell recording from the Sound Library.
Play it and observe the spectrum. Again record the frequencies of all visible peaks.
Calculate the ratios of the bell overtones to its fundamental. These should NOT be simple integers.
Create a comparison table with columns: peak number, oboe frequency, oboe ratio, bell frequency, bell ratio.
Highlight the contrast: the oboe ratios are approximately 1, 2, 3, 4... while the bell ratios are irregular (e.g., 1, 2.0, 2.5, 3.0, 3.7...).
Listen to both sounds again. Can you now hear the difference in quality that corresponds to the harmonic versus inharmonic spectra?
Test other sounds from everyday objects: tap a glass, a metal pot, a wooden table. Classify each as harmonic or inharmonic.
Discuss why harmonic sounds are perceived as musical notes while inharmonic sounds are perceived as metallic or noisy.

Expected results:

The oboe spectrum should show clearly harmonic overtones: if the fundamental is at approximately 440 Hz (A4), the overtones should appear near 880, 1320, 1760, 2200 Hz, etc. (ratios of 2, 3, 4, 5). The bell spectrum should show overtones at non-integer ratios, typically: 1, ~2.0 (octave, roughly tuned), ~2.4 (minor third above the octave), ~3.0, ~3.7, etc. The exact ratios depend on the specific bell. Students should observe that the bell's overtone pattern is distinctly different from the oboe's, explaining the qualitative difference in sound character. Everyday objects like glasses and metal pots typically produce inharmonic spectra, while wind and string instruments produce harmonic spectra.

Scientific questions:

- Why do string and wind instruments produce harmonic overtones while bells and drums do not?
- What physical property of a vibrating string ensures that its overtones are exact integer multiples?
- How do bell founders attempt to make bells sound more musical despite their inharmonic nature?
- What is the relationship between harmonic content and the perception of a clear musical pitch?
- Why do some instruments (like the piano) have slightly inharmonic overtones at very high frequencies?
- Can a sound be both inharmonic and still perceived as having a definite pitch?

Scientific explanations:

The difference between harmonic and inharmonic sounds is fundamental in musical acoustics and organology (study of instruments). A harmonic sound, such as that produced by an oboe, a flute or a guitar string, is characterized by a frequency spectrum following the harmonic series: f, 2f, 3f, 4f...

where f is the fundamental frequency. This regular structure results from the mode of vibration of the instrument: a column of air or a vibrating string naturally generates standing waves whose frequencies are integer multiples of the fundamental.

In contrast, an inharmonic sound, typical of bells, gongs or metal plates, presents a spectrum where the higher frequencies are not integer multiples of the fundamental. This irregularity is explained by the complex geometry of these objects which can vibrate simultaneously in several independent modes.

In a bell, the vibration modes depend on its precise shape and the distribution of masses. Frequencies typically present include the "hum" (fundamental), the "third" (about 1.2 times the fundamental), the "fifth" (1.5 times), and the "octave" (2 times), but their exact ratio varies depending on the bell.

It is this inharmonic structure that gives bells their distinctive and recognizable sound. FizziQ's frequency spectrum uses the Fast Fourier Transform (FFT) to decompose the sound signal and visualize these spectral components.

The tool allows you to precisely identify the frequencies present in each sound and to directly observe this fundamental difference between harmonic and inharmonic instruments.

Extension activities:

Frequently asked questions:

Q: I cannot identify clear peaks in the bell spectrum. What should I do?
R: Bell sounds often have many closely spaced overtones. Increase the FFT resolution in FizziQ settings if possible, and analyze the recording during the sustained ring phase (not the initial strike, which contains noise).

Q: The oboe overtone ratios are not exactly 2, 3, 4. Is this normal?
R: Ratios within ±2% of the integer values are normal due to measurement precision. The oboe also has slight deviations from perfect harmonicity due to its bore shape.

Q: Why does the bell sound dissonant compared to the oboe?
R: Inharmonic overtones create frequency combinations that the ear perceives as beating or roughness. When overtones are in exact harmonic ratios, they reinforce each other and the brain fuses them into a single smooth percept.

Q: Can I use a real bell instead of the recording?
R: Yes, any bell will work. Strike it and record the sustained ring with FizziQ. Avoid recording the initial impact noise; analyze the decaying ring instead.