On the Spectrum...

We know that the pitch of a musical note (how high or low the tone sounds) is almost entirely determined by the frequency of vibration of the sound. Frequencies in the range between about 27.5 Hz and 4,186 Hz (you might recognise this as the pitch range of a standard piano) sound essentially “musical” to the human ear.

The most "verifiable" and elegant fact in music science is that our perception of pitch is logarithmic, not linear. The musical note identified as A2 has a frequency of 110 Hz, and its next octave relative A3 has a frequency of 220 Hz – double the frequency. Each additional octave note has double the frequency of the previous pitch, and so mathematical ratios are at the heart of music perception.

The harmonic series: Concept

Each note we play as wind musicians is formed by a complex column of vibrating air, with a mixture of frequencies that are whole-number multiples of the fundamental (the first harmonic) – the note you actually hear. In addition to the octaves, there are perfect fifths (3 times the ƒ of the fundamental), perfect fourths, major thirds, etc…effectively forming a natural chord. Even monophonic instruments actually play chords!

You can reveal this pattern of sound frequencies as a colour spectrogram, a topographical map where the complexity of a musical pitch can be “seen”. The parallel series of horizontal lines is best seen with a steady single tone, and each spectrograph is typical for the instrument type.

A comparative spectrogram for three of our familiar instruments: Trombone (left), Flute (middle) and Oboe (right). The bars represent specific frequencies, and the brightness indicates intensity (loudness) of that particular overtone/harmonic.

Why do individual instruments have such unique patterns of harmonic proportions?

It’s all about the physics of cylinders vs. cones. 

The physical shape of an instrument's bore dictates which harmonics are allowed to exist. Most wind instruments act as “open” pipes or cones, which produce a full set of harmonics. The clarinet is an exception, with its cylindrical pipe closed at the reed/mouthpiece. Physics determine that the even-numbered harmonics are suppressed. Result: A clarinet's spectrum is dominated by odd harmonics (1 ƒ, 3 ƒ, 5 ƒ...). This is why a clarinet "overblows" to a twelfth (the 3rd harmonic) instead of an octave (the 2nd harmonic) when the register key is pressed.

Brass instruments like the Trumpet or Trombone are technically closed at one end (the lips), which should mean they only play odd harmonics. However, through centuries of "engineering evolution," the flare of the bell and the mouthpiece shift the air's resonance. This "stretches" the frequencies, so they align into a complete, usable harmonic series (1 ƒ, 2 ƒ, 3 ƒ, 4 ƒ...), allowing brass players to play melodies using only their lips.

Find out more about your own instrument’s unique spectral peculiarities with the help of your mobile phone, tablet or PC. Download and open an audio spectrum analyser app (e.g. Spectroid (Android OS), WavePad (iPadOS), Audacity (Windows, macOS and Linux), Audio/Spectrum Analyzer for iPhone) and record long tones with display set to Spectrogram. The easiest way is to open a web-based app, like this one: https://lnadi17.github.io/spectrogram-live/.

Why does it matter?

When we tune (and play) as individual instruments within the band, we are not simply trying to “line up” our fundamentals, and it is the variation of the harmonic strengths of individual players and instruments that can create harmony or dissonance.

Want to see how this concept has been used by composers? Follow this link to learn how Ravel used his understanding in Bolero! Have your headphones handy!