Basic Information
The piano, a musical instrument with a manual keyboard actuating hammers that strike wire strings, producing sounds that may be softened or sustained by means of pedals. What makes the piano one of the greatest instruments of all is that it produces a greater range of musical sounds. With a piano, it is possible to play melody and harmony at the same time.
The first piano was made in 1709 by Bartolommeo Cristofori. He had named his instrument “gravicembalo col piano e forte” which means, harpsichord with soft and loud. It was later shortened to pianoforte. This instrument was the inspiration of the modern piano. In the late 1700’s, John Broadwood improved the piano to make louder and richer tones. In 1821, Sébastien Èrard designed the double escapement, which improved the action of the pianos hammers. Alpheus Babcock invented a large cast-iron frame in 1825. In 1855, Henry E. Steinway combined all theses inventions in one piano, making what closely resembles the grand pianos of today.
Parts of a Piano
A standard Piano consists of seven main parts:
1. Strings: In most cases, the strings are made from steel. There are usually 220 strings, each tuned to one of 88 pitches. The strings vary from 6 to 80 inches. They are ranged from left to right in semitones. The longer strings are lower in pitch and form the bass section. The shortest strings are the highest pitch and form the treble section.
2. Keyboard: The keyboard consists of 88 keys on a standard piano. 36 Keys are black and 52 are white. The black keys are shorter and thicker then the white ones.
3. Action: A system of levers which move a hammer to strike a string, which vibrates and produces a tone. The action consists of 4,000 parts, which are mostly made of wood.
4. Pedals: The pedals are to vary the quality of the tones played. Most pianos have a damper pedal on the right side soft pedal on the left. The damper pedal lifts all the damper, allowing the strings that are struck to vibrate freely. The soft pedal shifts the hammers, which in result strikes one less string then it normally does, which softens the done.
5. Frame: Made of cast iron, it withstands the strain of 220 strings exerting a total pull from 35,000 to 45,000 pounds.
6. Soundboard: A thin sheet of wood lying under the strings. It is made of a light wood, generally spurce. The wood vibrates with the strings, intensifying the sounds.
Case: Usually a wooden case which covers the strings,action,frame, and soundboard.
The Hammer
The actions of all grand pianos are identical in principle, the only difference are the designs.
Fig. 1. View of the action of a modern grand piano (Steinway & Sons). The shaded areas indicate felt and the broad lines indicate leather.
Principally, the action consists of four major parts: the key, the lever body with appurtenant parts, the hammer and the damper (see Fig. 1). The successive steps in the operation of the action during a blow is illustrated in Fig. 2.
2(a) Rest position. The hammer rests via the hammer roller on the spring-supported repetition lever, a part of the lever body. The lever body stands on the key, supported by the capstan screw. The weight of the hammer and the lever body holds the playing end of the key in its upper position. The damper rests on the string, pulled down by lead weights.
2(b) Acceleration. When the pianist depresses the key, the lever body is rotated upwards. The jack, mounted on the lever body, pushes the roller and accelerates the hammer. The damper is lifted off the string by the inner end of the key.
2(c) Let-off. The tail end of the jack is stopped by the escapement dolly, and the top of the jack is rotated away from the hammer roller. The hammer, which now is free, continues towards the string. The repetition lever is stopped in waiting position by the drop screw.
2(d) Check. The rebounding hammer falls with the hammer roller on the repetition lever, in front of the tripped jack, before it is captured at the tail of the hammer head by the check. The stroke may now be repeated, either by releasing the key as usual, or by using the double-repetition feature (see text).
The action of the grand piano features a special construction for fast repetitions, the double-repetition mechanism, not incorporated in the action of the upright piano. In order to use the double-repetition feature, the key is let up only about a third of its travel after a stroke. At this stage, the hammer has been released from the check and lifted slightly by the spring-supported repetition lever (cf. Fig. 2 d). This allows the spring-loaded jack to slip back into its initial position under the roller, and the action is set for a second blow. The double-repetition mechanism enables very fast repetitions on the same key, without the damper touching the string between notes.
A correct function of the action requires a careful regulation. Of crucial importance is the distance between the top of the hammer at rest and the string, in the following hammer-string distance (piano technicians term: "blow level"). This distance is adjusted with the capstan screw (typical value 45 - 47 mm). Of equal importance is the setting of the release of the jack ("let-off"). This is adjusted with the escapement dolly. The adjustment is made by observing the distance between the string and the top of the hammer at the highest point of its travel (let-off distance), when the key is depressed slowly. The let-off distance is typically set between 1 and 3 mm, the actual value depending on such factors as the diameter of the string, interval between regulations, and sometimes, the personal taste of the pianist.
In all contact points between moving parts, one of the surfaces is covered with felt or leather in order to ensure a smooth and silent motion, free from backlash. In particular, thin shafts with close tolerances, for example the shaft for the hammer shank in the flange, are mounted in bushings of high-quality felt. The combination of wood and felt parts means that the action will change condition not only because of wear, but also due to changes in temperature and humidity. Periodic regulation is thus necessary in order to keep the instrument in optimum condition
The String
The pitch of the note is determined by the number of vibrations in a second (also called frequency). The frequency of the piano strings is determined by the tension, length, and diameter of the string. The tenser, longer, and thicker the string, the lower the note. We hear the vibrations of the strings.
The String Vibrations
The string motion on each side of a hammer in the middle section of the piano is illustrated in Fig. 1. On the side facing the bridge (upper panel) one sees the following.
First the initial pulse, or hump (I) passes on its way to the bridge. Then nothing happens for a period of time, while the string is at rest a little displaced relative to its equilibrium position. After some delay, corresponding to the travelling time to the bridge and back again, the pulse returns (II), now turned upside down (inverted) on reflection at the bridge. The pulse continues to the agraffe where it is reflected once more and turned right side up. Shortly after this reflection, the pulse returns to the observation point (III). (Because of the short distance between the hammer and the agraffe, the travelling time from the hammer and back again is very short, and the incoming pulse (II) and reflected pulse (III) partly merge.) The first period of the string motion is now completed, and the pulse continues towards the bridge for the next round trip, and the process repeats.
The curve displaying the string velocity may be somewhat more difficult to interpret, but is in fact more informative on the very details of the process. A hump passing the magnet, which is observed as a single pulse in the displacement curve, corresponds to a positive and a negative peak in the velocity curve. This is so since the string moves in the opposite direction during the latter half of hump when the string is restored to its initial position. Remember also that the velocity is high where the slope of the displacement curve is steep.
On the other side of the hammer, towards the agraffe (Fig. 1 lower panel), the picture is entirely different during the initial moment when the hammer is still in contact with the string. During that period, the hammer acts as a temporary string termination and the initial pulse is reflected back and forth on the short string segment between the hammer and the agraffe. This causes repeated impulses on the hammer, and after about four or five such impulses the hammer is released from the string. In fact, this motion of the trapped pulse on the short string segment is the major mechanism of hammer release for most notes on the piano.
Fig. 1 String motions close to the hammer; bridge side, observation point B (upper panel), and agraffe side, observation point A (lower panel) fro a C4 note atfortelevel.In the displacement curve (I) denotes the initial outgoing pulse, (II) the same pulse after the first reflection (at the bridge), and (III) the same pulse after the second reflection (at the agraffe). The corresponding pulses in the velocity curve are denoted by 1, 2 and 3. Note that each passing displacement pulse corresponds to a positive velocity wave (up) as well as a negative (down). The round-trip time for a pulse on the string (period time) is indicated by T. Observe that the string motion on the agraffe side is entirely different from the motion on the bridge side during the hammer-string contact.
Because the piano string is fixed at both ends, vibrations traveling along the string will create a standing wave. The natural modes of the string create longitudinal waves that reach our ears detect as musical tones. The resonating capabilities of the piano can increase the tone and richness of these sounds. The equation:
Because the piano string is fixed at both ends, vibrations traveling along the string will create a standing wave. The natural modes of the string create longitudinal waves that reach our ears detect as musical tones. The resonating capabilities of the piano can increase the tone and richness of these sounds. The equation:
Lambda n = 2L/n
Can be used to find wavelength where n is the specified standing wave and lambda is wavelength. You can use this equation to find resonance points on a string.
Tone
When the hammer strikes the string, a combination of sounds are produced! These sounds overlap, but a trained ear can distinguish them (to most people it sounds like just one note). These tones begin first with a fundamental tone and second with harmonics. The fundamental tone is when the entire string vibrates as a whole. The harmonics happen when the string divides into two independently vibrating halves that create a higher tone. This combination of sounds adds to the richness and depth of string instruments.
Fundamental wave :
First Harmonic:
Frequency
Frequency is the number of cycles an object makes divided by the total time. A cycle is one complete vibration. The SI unit for frequency is Hertz (Hz). Period is the time divided by the number of cycles per second or the time required for one complete vibration. Period is measured in seconds (s). Frequency and period are reciprocals of each other. The speed of vibration in a stringed instrument is determined by the length of the string. The shorter the string, the higher frequency of the vibration.
Musical notes are measured on a scale from A - G. This scale is repeated over all eighty-eight keys on a piano, all six strings on a guitar, etc. The distance, for example, from one C to the next C is called an octave. In each octave the higher C has a frequency that is twice the frequency of the lower C. When two notes that are an octave apart are played together, they form a euphonious combination.
Beat frequency has to be understood in order to tune a musical instrument. The waves coming from the instrument and the waves coming from what it is being tuned to must be at the same frequency. Beat frequency is the number of beats heard per second. It is found by subtracting the lower frequency from the higher one. When two instruments are in tune, the beat frequency should be zero.
Frequencies higher than humans can hear which is twenty kHz are called ultrasonic. Frequencies lower than twenty Hz or lower than humans can hear are called infrasonic. The lowest note on a piano has a frequency of twenty-seven Hz while the highest note is a little more than four kHz. Frequency - modulation (FM) radio stations broadcast at up to fifteen kHz. They are heard through hi - fi receivers.
Conclusion
The human ear can "hear" sounds in the frequency range of about 20 to 20,000 hertz. Using the equation: , it can be determined that the lowest audible note, at 20 hertz, would arise from a 17 meter wavelength. The highest note, at 20,000 hertz, would come from a wavelength of 0.017 m. The sound reaches our ear from the piano through vibrations of the string passing through the air. When the key on the piano is depressed, a hammer pinches the string inside the piano which begins to vibrate. These vibrations form wave’s which then travel through the air and to our ear allowing us to hear the sound.
