Piano tuning is the process of adjusting the tension of the strings of an acoustic piano so that the musical intervals between strings are 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. (See Piano key frequencies for the theoretical piano tuning.) In all systems of tuning, every pitch may be derived from its relationship to a chosen fixed pitch, which is usually A440 (440 Hz), the note A above middle C. For a classical piano and musical theory, the middle C is usually labelled as C4 (as in scientific pitch notation); However, in the MIDI standard definition this middle C (261.626 Hz) is labelled C3. In practice, a MIDI software can label middle C as C3-C5, which can cause confusion, especially for beginners. 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.
Background
Many factors cause pianos to go out of tune, particularly atmospheric changes. Changes in humidity will significantly affect the pitch of a piano. High humidity causes the sound board, crowned upward, to swell, crowning it further and pushing upward on the strings, causing the pitch to rise. Low humidity has the opposite effect. To a lesser degree, changes in temperature will 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 not hold the piano in tune as well. Frequent and hard playing can also cause a piano to go out of tune. Many piano manufacturers recommend that new pianos be tuned four times during the first year, mostly owing to string stretch, and twice a year thereafter. An out-of-tune piano can often be identified by the characteristic "honky tonk", warbling, 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 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 sound waves. 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.
History 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. 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 1800s this variation led to an increase in the use of quasi- equal temperament, in which the frequency ratio between each pair of adjacent notes on the keyboard were nearly 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 20th century in response to widely varying standards. Previously the pitch standards had gradually risen from about A415 during the late 18th century and early 19th century to A435 during the late 19th century. Though A440 is generally the standard, some orchestras, particularly in Europe, use a higher pitch standard, such as A442.
Theory
Overtones and harmonics
A stretched string can vibrate in different modes, or harmonics, and when a piano hammer strikes a string it excites multiple harmonics at the same time. The first harmonic, or fundamental frequency, is usually the loudest, and determines the pitch that is perceived. In theory, the higher harmonics, also called overtones or partials, vibrate at integer multiples of the fundamental frequency. For example, 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 2:1 ratio, perfect fifth with 3:2, 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.
Temperament
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