A Harmonic Series Written as Notes on the Grand Staff and Treble Clef
Visualizing the Harmonic Series on the Staff
Below is a representation of the first 24 partials (or harmonic overtones) of the fundamental pitch C2, which vibrates at approximately 65.4 Hz. These overtones are shown in traditional musical staff notation across both the grand staff and treble clef. Between the staves, you’ll see the partial numbers, each representing a whole-number multiple of the fundamental frequency. 5 4 1
You’ll also notice symbols such as “–” and “+” placed next to some notes. These indicate that the pitch of that particular partial is slightly flatter (–) or sharper (+) than the same pitch in the equal temperament tuning system, the tuning system used by modern pianos.
Why Some Notes Sound “Out of Tune”
As you listen to the following audio clips, try comparing each pitch to the same note played on a well-tuned piano. You may notice that some intervals, even in the lower partials, do not align exactly. This is because the harmonic series is based on just intonation, a tuning system built on pure whole-number ratios between frequencies. In contrast, equal temperament slightly adjusts (or tempers) every interval so that instruments like the piano can play equally well in all keys.
These adjustments are generally subtle enough that they don’t sound out of tune on their own. However, when comparing natural harmonics directly with piano notes, the differences become audible.
Listen to the Harmonic Series
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Partials 1–12
These are the most musically relevant and closely aligned with the equal-tempered scale, though small deviations begin to appear.
- Partials 8–20
Partials 8-20
As you move higher, the intonation differences between just and equal-tempered tuning become more noticeable.
- Partials 16–24
Partials 16-24
Higher partials increasingly deviate from the equal-tempered scale and often sound sharper or flatter compared to their piano equivalents.
Tip: Listen for where the harmonic partials start to “drift” from what your ear expects based on piano tuning.
What Does the Full Harmonic Series Sound Like?
The sound clip below demonstrates what the fundamental pitch C2 (65.4 Hz) sounds like with all of its harmonics combined. Your ear perceives this layered sound as a single, coherent pitch — despite it being composed of many individual frequencies.
The waveform used here is a sawtooth wave, a type of electronically generated tone that includes both even and odd harmonics of the fundamental. Because it contains all integer harmonics, a sawtooth wave closely resembles the timbre of bowed string instruments such as violins and cellos
Summary: Why This Matters
Understanding how the harmonic series works, and how it differs from equal temperament, is essential for musicians, especially those working with instruments that either emphasize or deviate from harmonic norms (like timpani, gongs, or tuned percussion). The harmonic series not only shapes how we hear pitch and timbre, but also why some intervals sound more consonant or dissonant depending on tuning context.