Why pianos don’t work too well

The nodal points at which a string vibrates at a harmonic

Pianos rely on the physics of harmonics.  No hang on. Sorry.  Let’s start again.  Pianos don’t rely on the physics of harmonics.  Yes that’s better.  Because it’s absolutely true.  And that is why they don’t work too well unless they are tuned and maintained regularly.

Harmonics is a pure science…when studied scientifically.  Let’s explore harmonics briefly.  When a string vibrates it produces a tone, a wave of sound that vibrates the air, which in turn vibrates the eardrum.  One would imagine that a string vibrates from one fixed end to the other when plucked or struck.  And indeed it does and this is known as the string’s speaking length.  The complete speaking length provides what is known as the fundamental frequency.  Interestingly the same string’s vibrations present themselves through dividing the string exactly in half and vibrating along that distance also. At the same time it also divides itself by three and vibrates along those three distances also. It will keep dividing itself by integers and vibrating along those lengths infinitely or until the tension and/or the thickness and/or the length of the string prevent it from doing so.  Each of these divisions is known as node. Each node produces its own overtone and these are known as harmonics.  In music these harmonics are called overtones because they exist over and above the fundamental tone produced by the string. (see the image above)

Most stringed instruments are harmonic.  Their strings are the same length and are stretched at roughly the same tension with a small variance in their thickness.  These instruments work well because they allow the strings to vibrate uniformly and so they behave in a reasonably consistent way.  However this consistency limits the range of the notes an instrument can play. Such instruments include the Guitar and the Violin family.  The piano has a range of musical notes that is capable of sounding notes lower in pitch than a double bassoon and higher in pitch than a piccolo, 88 in all (there is an exception, the Bösendorfer Imperial, but that is for another post)

Pianos have strings that are of different lengths, made of different materials that are stretched under different tensions and have a significant variance in thickness.  It is this lack of pragmatism that allows the piano to sound such a wide range of pitch.  But this inconsistency also means that the strings do not divide and vibrate in a uniform sequential fashion.  In fact the strings are deemed to be inharmonic (or not harmonic).  The overtones produced by the piano are a mathematically unruly, non-conformist bunch and for that reason these overtones cannot accurately be described as harmonics.  They are known as “partials”.  A piano string produces a fundamental frequency and then partial frequencies of that fundamental.  Couple the delinquent behaviour of the strings with the pianos dislike for humidity, heat, cold and being moved about and you have an instrument that doesn’t work too well if left to its own devices, without being tuned.

Piano tuners spend months if not years trying to identify, single out and match up partials with their own ear drum in order to tune them.  The inharmonicity of the strings make this task so much more difficult. The digital age has not passed the piano tuner by and software can be purchased that can identify and match the partials reasonably accurately and this takes the donkey work out of the piano tuning process.  However, the software cannot distinguish the finer points of piano tuning and string behaviour, so the human ear is and probably always will be necessary to finish the job to the highest standard.