The Art of Piano Tuning – Part Two
Last month I discussed the need to stabilize the piano strings when tuning a piano. This procedure ensures that the piano will remain in tune for an extended period of time. However, even an extremely stable piano will need to be re-tuned periodically, depending on how hard and how often it is played. Likewise, a piano that is never played will eventually go out of tune due to tension on the strings that cause them to stretch out over time.
As we look further into the art of piano tuning we examine the role of inharmonicity. No, this is not a topic on the Dr. Phil show. It actually describes the effect that even slight imperfections which exist in all piano strings have on the sound that they make. What follows may be a little technical but please bear with me.
When a piano string is struck by the piano hammer it starts to vibrate, producing sound waves. These sound waves are measured in hertz (hz), or cycles per second. The number of cycles per second is directly related to the length of the piano string. Longer strings vibrate more slowly and therefore produce fewer cycles and a lower tone. Shorter strings vibrate faster producing more cycles and a higher tone. The number of cycles per second for the A above middle C on the piano has been standardized at 440, which is why you will often see the term A-440 hz used to describe the desired pitch for setting the tuning of the piano.
However a piano string does not produce a single tone or pitch but rather a whole series of tones, called partials or overtones. These partials are theoretically whole multiples of the lowest tone, known as the fundamental. For example the A-440 fundamental would have partials of 880 (440X2), 1320 (440X3), 1760 (440X4) and so on. As you go up each partial is slightly softer than the previous one and the tone fades more rapidly.
A-440 – Fundamental
A-880 – Second Partial
E-1320 – Third Partial
A-1760 – Fourth Partial
C#-2200 – Fifth Partial
E-2640 – Sixth Partial
G-3080 – Seventh Partial
This is where inharmonicity comes in. Due to differences in tension, stiffness, length and other factors the partials are not exact multiples of the fundamental. They will typically beat a little faster as you go up. For example, A-440 might actually have partials of 882, 1324 and 1768. This is what creates the “warmth” often associated with true piano sound.
A further result of inharmonicity in piano tuning is the need to “stretch” the octaves. The octave above A-440 should be A-880. But as we see in the example above, the second partial of A-440 is actually 882. The difference between these two numbers creates unwanted noise, called beats. So this second octave must be tuned slightly sharp to eliminate this beat. However, since there are several different partial in each note, several different beats may be heard. A skilled piano technician will chose a tone that blends these competing beats to create a pleasing sound.
Pianos with longer strings typically have less inharmonicity than pianos with shorter strings. Therefore a spinet piano will need to have more stretch than a console which will need more than a full upright. Concert grand pianos, with their extra long strings, tend to have the least amount of stretch. Creating the proper amount of stretch to minimize inharmonicity is what helps to make the each piano sound its best.