Malicki Piano Tech Notes

The Science and Art of Piano Tuning

Piano tuning is a precise and specialized skill that goes far beyond simply adjusting the strings. My goal is to create a harmonious and beautiful sound that is unique to your specific instrument.

You might assume that "in tune" means a fixed set of pitches, like an exact A440 Hz. While we do use a theoretical standard, the true art of tuning lies in assessing the subtle interactions between all the notes on your piano. This is because every piano is a unique instrument, and what sounds "in tune" on one may not on another.

Understanding Equal Temperament

At the heart of modern piano tuning is a system called equal temperament. This system distributes the musical scale in a mathematically precise way, ensuring that every key sounds good in relation to all the others.

For instance, the pitch of each note is calculated by multiplying the previous note's frequency by the twelfth root of two. This ensures a consistent relationship between all the notes, allowing music to be played in any key without sounding out of tune.

The Role of Inharmonicity

While equal temperament provides a perfect theoretical starting point, a real piano is a physical object. The thickness and stiffness of the steel strings cause a phenomenon called inharmonicity. This means that a note's overtones are slightly sharper than a perfect harmonic ideal.

To compensate for this, a professional tuner uses a technique called stretched octaves. This involves making the intervals, especially in the high and low registers, slightly wider than their theoretical values. This slight adjustment ensures that the piano sounds perfectly in tune to the human ear. This is why a short piano, like a baby grand, may require more "stretching" than a long concert grand.

The Tuner's Experience

Ultimately, fine tuning a piano is a blend of scientific knowledge and a trained ear. I listen for subtle "beating" or wavering sounds that occur when two notes are slightly out of tune. By carefully timing these beats, I can precisely adjust the strings to achieve the perfect temperament for your piano. This includes accounting for your instrument's unique physical characteristics, from the soundboard to the bridge, to ensure a stable and beautiful sound.

I'm committed to providing a fine-tuned experience that will bring your piano to life. If you're interested in hearing the difference a professional tuning can make, please contact me.

"Technical"  Nerd Notes

The following table lists the beat frequencies between notes in an equal temperament octave. The top row indicates absolute frequencies of the pitches; usually only A440 is determined aurally. Every other number indicates the beat rate between any two tones (which share the row and column with that number) in the temperament octave. Begin by tuning one note to the other so that the beating disappears, temper that interval in the appropriate direction (either making the interval wider or narrower, see further below) until the desired beat rate is achieved. Slower beat rates can be carefully timed with a metronome, or other such device. For the thirds in the temperament octave, it is difficult to tune so many beats per second, but after setting the temperament and duplicating it one octave below, all of these beat frequencies are present at half the indicated rate in this lower octave, which are excellent for verification that the temperament is correct. One of the easiest tests of equal temperament is to play a succession of major thirds, each one a semitone higher than the last. If equal temperament has been achieved, the beat rate of these thirds should increase evenly over the range of the piano.

Equal temperament beatings (all figures in Hz)

The tuning described by the above beating plan will give a good approximation of equal temperament across the range of the temperament octave. If it were extended further, however, the actual tuning of the instrument would become increasingly inaccurate. This is due to a factor known as inharmonicity, which is present in different amounts on all piano strings. The harmonic series of strings does not fall exactly into whole-number multiples of a fundamental frequency, but rather each harmonic is slightly sharper than a whole-number ratio, and this sharpness increases as higher tones in the harmonic series are reached. (Or, more strictly speaking, the overtones of the strings are not exactly harmonic.) This means that an aurally tuned octave will be slightly wider than the just 2:1 ratio assumed above, known as a stretched octave. The amount of stretching depends on the style of piano and is determined mainly by the length of the strings: shorter pianos such as baby grands and spinets will have octaves that are stretched farther than concert grands.

This has the effect that, on a piano, the notes in the higher register will end up slightly sharper than those in the lower octave. This is less apparent on longer pianos which have proportionally thinner strings (string inharmonicity is directly related to the ratio of string thickness to length). Despite this deviation from the simpler ideal equal temperament, this is considered the correct way to tune a piano because it maintains interval identity across the piano, which generally improves the sound of music played on it.

There are other factors, physical and psychoacoustic, that affect the tuner's ability to achieve a temperament. Among physical factors are additional inharmonic effects due to soundboard resonance in the bass strings, and other effects such as poorly manufactured strings or peculiarities of resonance or bridge shape which can cause beatings in some notes that are unrelated to the tuning and that the piano tuner cannot correct. The principal psychoacoustic factor is that the human ear tends to perceive the higher notes as being flat when compared to those in the midrange. Stretching the tuning to account for string inharmonicity is often not sufficient to overcome this phenomenon, so piano tuners may stretch the top octave or so of the piano even more.