The Piano

The piano has 88 keys which span the frequency range 27.5 Hz (A0) to 4186 Hz (C8). The strings are sounded by hammer mechanisms which are activated by the keys. Held in a heavy cast iron frame, the strings pass over a bridge to a pin block by which the strings are tuned. The soundboard is a crucial element in the sound of the piano. Energy is coupled from the strings into the soundboard and from it into the air. The soundboard is usually made of spruce.

Three pedals afford the player some control over the sound of the instrument. The left pedal is the "soft pedal" or una corda. It shifts the keyboard beneath the strings so that the hammers strike fewer strings, giving a softer sound. The center pedal is the sustain or sustenuto pedal which disengages the dampers. The right pedal is the damper pedal to dampen the whole keyboard.

Some grand pianos have on the order of 7000 parts! Their function can be described in terms of six features: the keyboard, the hammers, the dampers, the bridge, the soundboard, and the strings. There are 52 white keys and 36 black keys (for the chromatic notes), bridging seven and a third octaves with 12 equal semitones per octave. The piano is the standard instrument for the equal tempered scale, yet both the high end and low end of the instrument are tuned so that they depart slightly from equal temperament because the sound has been judged to be more pleasing with that arrangement (see "stretched" tuning discussion below).

Depressing a key on the piano engages a complex mechanism called the "action" of the piano which causes the hammer to strike the string. Actually, the hammers are in sets for the keys which sound two or three strings. The striking point is about 1/7th of the way along the string to discriminate against the 7th harmonic resonance, which is significantly out of tune with the equal tempered scale. This "7th harmonic problem" can be illustrated by examining the musical intervals formed by a an exact harmonic sequence.

The grand piano has about 230 strings for the 88 keys. Generally, the ten lowest pitches have one wirewound string. The next 18 pitches have two, and the last 60 have three strings each. In the modern piano, the strings are mounted on a cast iron frame to provide the strength to main the required tension in all of these strings (about 30 tons for a grand). Working out combinations of lengths, masses and tensions for these strings within a compact instrument is a formidable problem. In order to maintain comparable tensions in the strings without inconvenient size for the instrument, the length is not halved with each octave but a ratio between 1.88 and 1.94:1 is used. The string mass is varied to constrain the frequencies to their proper values. For the lower pitches, the steel wire is wound with copper or brass, which adds mass without producing excessive stiffness.

Even with the windings of soft metal, the increased stiffness of the lower strings makes them depart from the "ideal string" necessary to produce exact harmonics. As you increase in harmonic number, the frequencies are increasingly sharp. This has led to the practice of tuning the lower strings of the piano up to about 30 cents flat, since that puts the upper harmonics more in tune with the midrange notes of the piano. This makes the piano sound better to most ears, partially because the low end of the piano at 27.5 Hz is in a frequency range where your hearing has dropped off considerably, so that the upper harmonics of these low strings are probably heard more prominently than the fundamental. The extreme upper end of the piano is tuned up to 30 cents sharp in a practice that is called "stretched" tuning.

Ranks of Organ Pipes

A complete set of organ pipes of the same type is called a rank. In a large modern organ, the keyboard span is typically five octaves from C2 to C7. With 12 semitones per octave, this gives 61 pipes for a rank. Five doublings of length means that the longest pipe in a rank is 32 times the length of the shortest pipe.

Since the idea of a rank is to produce a set of pipes with similar tone quality, it has been found to be necessary to scale the diameters in a different way than the lengths. In order to enhance the higher harmonic content of the longer pipes, it has been found desirable to make their diameters smaller in proportion to their lengths. In a rank, the diameter of the longest pipe will be 12 to 13 times the diameter of the shortest pipe, while the length has increased by a factor of 32.

Some History of the Piano

Harpsichord maker Bartholomeo Cristofori created the first version of the piano in 1709 by replacing the crow quills of the harpsichord with leather-covered wooden hammers. In addition to a richer tone quality, the hammers allowed for a large dymamic range that was subject to the sensitivity of the player's touch. The instrument was given the imposing name "gravecembalo col piano e forte", meaning "harpsichord with soft and loud". This was soon shortened to "pianoforte" and then finally to just "piano". So the final name emphasizes the possibility of a soft touch, although the piano is also capable of "forte".

We have few pianos from the early era because they had wooden frames for the strings. Some authors attribute the demise of the early pianos to the gradually rising pitch standard. The wooden frames could not stand the increase in tension necessary for tuning upward to the new standards. Since the introduction of iron frames into the construction of the piano in 1820, the design of the instrument has changed very little.