Next: Speech Production
Up: Lectures
Previous: Percussion Instruments
Pianos and harpsichords are often considered percussion instruments (chordophones), given their striking and plucking excitation mechanisms, respectively. Together with the pipe organ, however, we have a group of instruments related by their user interface: the keyboard.
We have already studied the behavior of strings and acoustic pipes. Thus, this section will be concerned mainly with the particular excitation mechanisms, as well as any other distinguishing characteristics of these instruments.
- Aspects of Construction:
- All pianos have 88 keys.
- The soundboard is nearly always made of spruce and is the main source of radiated sound.
- The piano strings are held at high tensions to obtain the desired loudness.
- A sturdy cast iron frame is used to offset these high forces.
- Piano Strings:
- The high string tensions demand high-strength wires.
- To minimize inharmonicities due to string stiffness, the smallest string diameter possible should be used.
- The added stiffness due to string displacement provides an additional restoring force (besides tension) which slightly raises the frequency of all the modes.
- String bending is greater for the higher modes, resulting in greater frequency stretching.
- In order to maintain string mass but minimize stiffness, the lower strings are wrapped.
- Because of the inherent inharmonicity of the its strings, the piano is ``stretch-tuned''.
- Coupled Strings:
- Over most of its playing range, the piano has three strings per note.
- In order to maximize decay time, these strings are slightly mistuned by about one to two cents from each other.
- The initial ``in-phase'' excitation of all three strings produces a rapid initial decay of string energy into the sound board. Because of mistunings, however, the vibrations soon grow out of phase and result in a much longer secondary decay.
- Hammer-String Interaction:
- The hammer action of the piano produces a ``striking'' excitation.
- The hammer is typically ``thrown'' away from the string by the first reflected pulse on the string. Depending on its weight, however, the hammer may remain in contact with the string for longer or shorter periods of time.
- A small square piece of brass, called a tangent, is attached to the end of each key. When a key is depressed, the tangent strikes the string(s) and becomes a termination point for the string(s).
- Vibrato can be achieved by vibrating the key, thus varying the string tension.
- Depressing a key of a harpsichord results in the plucking of a string.
- Because the strings of the harpsichord have a much lower tension and diameter, inharmonicities due to stiffness are much less than those of the piano.
- Timbre variations due to changing pluck points and string dimensions are common over the range of the harpsichord.
- Aspects of Construction:
- Each division of an organ is controlled by a separate keyboard.
- Various means exist for controlling the key/windchest action. Direct mechanical controls are now rare. Direct electric and electropneumatic controls are used in most modern organs.
- One rank of pipes will include one pipe for each note (61 in a keyboard division, 32 in a pedal division). Each ``stop'' on the organ usually corresponds to one rank, though mixture stops exist with several ranks.
- Organ Pipes:
- Flue pipes produce sound by means of a vibrating air jet.
- Reed pipes produce sound by means of a vibrating brass reed.
- Flue pipes may be open or stopped at their far end and be made of wood or metal.
- Three families of flue pipes: diapasons, flutes, and strings. String pipes are slender and have the greatest overtone content. Flute pipes usually have the least overtone content.
- Reed pipes are cylindrical or conical. The reed is made to vibrate at its resonance frequency and the pipe length is adjusted to match this frequency.
- Sound Excitation in Flue Pipes:
- The air jet in organ pipes is almost completely turbulent.
- A wavelike disturbance is set up in the jet. The conditions necessary to set up a stable oscillatory regime between the jet and the flue pipe are dependent on the time necessary for a wave on the jet to travel from the flue slit to the upper lip (which in turn are determined by the mouth height and the blowing pressure).
- Tuning and Voicing:
- Reed pipes are tuned by adjusting the length of the vibrating reed, as well as the length of the pipe.
- Flue pipes are tuned by adjusting the effective length of the pipe.
