Frequencies of the audible range on a twelve and eight equal tempered scale

Hammers and mutes are basic tuning tools

Some common piano tuning tools:Top to bottom:Tuning Hammer, Felt Mute, Rubber Mute, Temperment Strip, Papps Mute.

Piano tuning

        From Wikipedia, the free encyclopedia

     Piano tuning is the act of making minute adjustments to the tensions of the strings of an acoustic piano to properly align the intervals between their tones so that the instrument is in tune. The meaning of the term 'in tune', in the context of piano tuning, is not simply a particular fixed set of pitches. Fine piano tuning requires an assessment of the vibration interaction among notes, which is different for every piano, thus in practice requiring slightly different pitches from any theoretical standard. Pianos are usually tuned to a modified version of the system called equal temperament. In all systems of tuning, every pitch may be derived from its relationship to a chosen fixed pitch, which is usually A440, above middle C  (pitch 261.626 hertz).

   Piano tuning is done by a wide range of independent piano technicians,

piano rebuilders, piano-store technical personnel, and hobbyists. Professional

training and certification is available from organizations or guilds, such as the Piano Technicians Guild. Many piano manufacturers recommend that pianos be tuned twice a year.

   Many factors cause pianos to go out of tune, particularly atmospheric changes. For instance, changes in humidity will affect the pitch of a piano; high humidity causes the sound board to swell, stretching the strings and causing the pitch to go sharp, while low humidity has the opposite effect. Changes in temperature can also affect the overall pitch of a piano. In newer pianos the strings gradually stretch and wooden parts compress, causing the piano to go
flat, while in older pianos the tuning pins (that hold the strings in tune) can become loose and don't hold the piano in tune as well. Frequent and hard playing can also cause a piano to go out of tune. For these reasons, many piano manufacturers recommend that new pianos be tuned four times during the first year and twice a year thereafter.

   An out-of-tune piano can often be identified by the characteristic "honky tonk" wah-wah or beating sound it produces. This fluctuation in the sound intensity is a result of two (or more) tones of similar frequencies being played together. For example, if a piano string tuned to 440 Hz(vibrations per second) is played together with a piano string tuned to
442 Hz, the resulting tone beats at a frequency of 2 Hz, due to the constructive and destructive interference
between the two tones. Likewise, if a string tuned to 220 Hz (with a harmonic at 440 Hz) is played together with a string tuned at 442 Hz, the same 2 Hz beat is heard. Because pianos typically have multiple strings for each piano key,
these strings must be tuned to the same frequency to eliminate beats.

   The pitch of a note is determined by the frequency of vibrations. For a vibrating string, the frequency is determined by the string's length, mass, and tension. Piano strings are wrapped around tuning pins, which are turned to adjust the tension of the strings.
   Piano tuning became a profession around the beginning of the 1800s, as the "pianoforte" became mainstream. Previously musicians owned harpsichords, which were much easier to tune, and which the musicians generally tuned
themselves. Early piano tuners were trained and employed in piano factories, and often underwent an apprenticeship of about 5–7 years. Early tuners faced challenges related to a large variety of new and changing pianos and non-standardized pitches.

   Historically, keyboard instruments were tuned using just intonation, pythagorean tuning and meantone temperament
meaning that such instruments could sound "in tune" in one key, or some keys, but would then have more dissonance in other keys. The development of well temperament allowed fixed-pitch instruments to play reasonably well in all of the keys. The famous "Well-Tempered Clavier" by Johann Sebastian Bach took advantage of this breakthrough, with preludes and fugues written for all 24 major and minor keys. However, while unpleasant intervals (such as the wolf interval)
were avoided, the sizes of intervals were still not consistent between keys, and so each key still had its own distinctive character. During the 1700s this variation led to an increase in the use of equal temperament, in which the frequency ratio between each pair of adjacent notes on the keyboard was made equal, allowing music to be transposed between keys without changing the relationship between notes.

   Pianos are generally tuned to an A440 pitch standard that was adopted during the early 1900s in response to widely varying standards. Previously the pitch standards had gradually risen from about A415 during the late 1700s and early 1800s to A435 during the late 1800s. Though A440 is generally the standard, some orchestras, particularly in Europe, use a higher pitch standard, such as A444.

Overtones and harmonics

   A stretched string vibrates in different modes, or harmonics. When a piano string vibrates, all the harmonic modes are excited simultaneously. The first harmonic (or fundamental frequency) is usually the loudest, and determines the pitch that is perceived. Theoretically the higher harmonics (also called overtones or partials) vibrate at integer multiples of the fundamental frequency. (e.g. a string with a fundamental frequency of 100 Hz would have overtones at 200 Hz, 300 Hz, 400 Hz, etc.) In reality, the frequencies of the overtones are shifted up slightly, due to inharmonicity caused by the stiffness of the strings.The relationship between two pitches, called an interval,is the ratio of their absolute frequencies. The easiest intervals to identify and tune are those where the note frequencies have a simple whole-number ratio (e.g. octave with a 1:2 ratio, perfect fifth with 2:3, etc.) because the harmonics of these intervals coincide and
beat when they are out of tune. (For a perfect fifth, the 3rd harmonic of the lower note coincides with the 2nd harmonic of the top note.)

   The term temperament refers to a tuning system that allows intervals to beat instead of tuning pure or "just intervals". In equal temperament, for instance, a fifth would be tempered by narrowing it slightly, achieved by flattening its upper pitch slightly, or raising its lower pitch slightly. Tempering an interval causes it to beat. Because the actual tone of a
vibrating piano string is not just one pitch, but a complex of tones arranged in a harmonic series, two strings that are close to a simple harmonic ratio such as a perfect fifth beat at higher pitches (at their coincident harmonics), because
of the difference in pitch between their coincident harmonics. Where these frequencies can be calculated, a temperament may be tuned aurally by timing the beatings of tempered intervals.

Common tools for tuning pianos include the tuning hammer or lever,

a variety of mutes, and a tuning fork or electronic tuning device.
The tuning hammer is used to turn the tuning pins, increasing or
decreasing the tension of the string. Mutes are used to mute strings
that are not being tuned. While tuning the temperament octave, a felt
strip is often placed over the temperament (middle) section of the
piano, and inserted between each note, muting the outer two strings of
each note, but leaving the middle string free to vibrate. After the
center strings are all tuned, the felt strip can be removed note by note, tuning the outer strings to the center strings. Wedge-shaped mutes are inserted between two strings to mute them, while a Papps mute is
sometimes used for tuning the high notes in upright pianos because it slides easily between hammer shanks.
In an aural tuning a tuning fork is used to tune the first note (generally A4) of the piano, and then a temperament octave is tuned, using a variety of intervals and checks, until the tuner is satisfied
that all the notes in the octave are correctly tuned. The rest of the piano is then tuned to the temperament octave, working up and down the piano using octaves, fifths, fourths, etc. Alternatively, if an electronic tuning device is used, the temperament step is skipped, and the tuner may tune many or all of the notes directly with the tuning device.