What Is a Partial in Piano Tuning?
A partial, in the context of piano tuning, refers to one of the individual frequency components that make up the sound produced by a single piano string. When a key is pressed, the string vibrates in several ways at once, not just at its fundamental frequency. These multiple vibrations, called partials, combine to create the unique tone color, or timbre, of the piano.
Why Partials Matter in Piano Tuning
Piano strings are naturally stiff, which causes their partials to be slightly sharp compared to perfect mathematical harmonics—a phenomenon known as inharmonicity. Because of this, piano tuners do not tune strictly to equal temperament by frequency. Instead, they listen for how partials align between different notes. This approach leads to stretch tuning, where bass notes are tuned flatter and treble notes sharper than their theoretical values.
How Partials Are Produced
Partials are generated when a piano string vibrates at its fractional lengths. Each partial corresponds to a specific frequency:
- 1st Partial: The fundamental note itself
- 2nd Partial: One octave above the fundamental
- 3rd Partial: An octave plus a fifth above
- 4th Partial: Two octaves above
- 5th Partial: Two octaves plus a major third
- 6th Partial: Two octaves plus a fifth
- 7th Partial: Two octaves plus a minor seventh
- 8th Partial: Three octaves above
- …and so on
Partials and Tuning Technique
When tuning an octave, a piano tuner may match several different partials octave combinations to achieve the desired amount of stretch. The process relies heavily on comparing partials between notes rather than just aligning fundamental frequencies. This method ensures a stable and musical tuning across the keyboard.
Inharmonicity and Stretch Tuning
Because piano strings are stiff, their partials are inharmonic—meaning the higher partials are sharper than their “ideal” harmonics. The effect of inharmonicity is especially strong in the shorter and thicker strings found in the bass and treble ranges. If a piano were tuned strictly to equal temperament, the octaves would sound narrow and dull. Stretch tuning addresses this by aligning partials instead of fundamentals, adjusting notes so their important partials line up smoothly across the keyboard. As a result, the fundamental frequencies drift sharp in the treble and flat in the bass, but the overall sound is more pleasing and musical.
Summary
In summary, a partial is any individual vibration frequency of a piano string, including the fundamental. Piano tuning depends greatly on comparing partials between notes to achieve a consistent and musical tuning. Partials are sometimes referred to as “harmonics,” and understanding their behavior is essential for stretch tuning and for producing the rich sound characteristic of the piano.