![André Studencki pianostämmare-1987](https://upload.wikimedia.org/wikipedia/commons/c/ce/Andr%C3%A9_Studencki_pianost%C3%A4mmare-1987.jpg)
Piano tuning is the act of adjusting the tension of the strings of an acoustic
piano
The piano is a stringed keyboard instrument in which the strings are struck by wooden hammers that are coated with a softer material (modern hammers are covered with dense wool felt; some early pianos used leather). It is played using a keyboa ...
so that the
musical intervals
In music theory, an interval is a difference in pitch between two sounds.
An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or ha ...
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
An equal temperament is a musical temperament or tuning system, which approximates just intervals by dividing an octave (or other interval) into equal steps. This means the ratio of the frequencies of any adjacent pair of notes is the same, wh ...
. (See
Piano key frequencies
This is a list of the fundamental frequencies in hertz (cycles per second) of the keys of a modern 88-key standard or 108-key extended piano in twelve-tone equal temperament, with the 49th key, the fifth A (called A4), tuned to 440 Hz (referr ...
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 A440 or A-440 may refer to:
* A440 (pitch standard)
* A440 highway (Australia), a road in Victoria, Australia
* Quebec Autoroute 440 (Laval)
* Quebec Autoroute 440 (Quebec City)
See also
* Apollo 440
Apollo 440 (also known as Apollo Four Fo ...
(440 Hz), the note A above middle C. Note that for a classical piano and musical theory, the middle C is usually labelled as C
4 (as in
scientific pitch notation
Scientific pitch notation (SPN), also known as American standard pitch notation (ASPN) and international pitch notation (IPN), is a method of specifying musical Pitch (music), pitch by combining a musical Note (music), note name (with accidental ...
); However, in the
MIDI
MIDI (; Musical Instrument Digital Interface) is a technical standard that describes a communications protocol, digital interface, and electrical connectors that connect a wide variety of electronic musical instruments, computers, and re ...
standard definition this middle C (261.626 Hz) is labelled C
3. In practice, a MIDI software can label middle C as C
3-C
5, 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
The Piano Technicians Guild (PTG) is an International organization for Registered Piano Technicians, headquartered in Kansas City, Kansas. The PTG was formed in 1957 from the merger of the American Society of Piano Technicians and the National As ...
. Many piano manufacturers recommend that pianos be tuned twice a year.
Background
![WaveInterference](https://upload.wikimedia.org/wikipedia/commons/e/eb/WaveInterference.gif)
Many factors cause pianos to go out of tune, particularly atmospheric changes. For instance, changes in
humidity
Humidity is the concentration of water vapor present in the air. Water vapor, the gaseous state of water, is generally invisible to the human eye. Humidity indicates the likelihood for precipitation, dew, or fog to be present.
Humidity depe ...
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
String or strings may refer to:
*String (structure), a long flexible structure made from threads twisted together, which is used to tie, bind, or hang other objects
Arts, entertainment, and media Films
* ''Strings'' (1991 film), a Canadian anim ...
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.
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
A honky-tonk (also called honkatonk, honkey-tonk, or tonk) is both a bar that provides country music for the entertainment of its patrons and the style of music played in such establishments. It can also refer to the type of piano ( tack piano) ...
" or
beating
Beat, beats or beating may refer to:
Common uses
* Patrol, or beat, a group of personnel assigned to monitor a specific area
** Beat (police), the territory that a police officer patrols
** Gay beat, an area frequented by gay men
* Battery ...
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
Interference is the act of interfering, invading, or poaching. Interference may also refer to:
Communications
* Interference (communication), anything which alters, modifies, or disrupts a message
* Adjacent-channel interference, caused by extra ...
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
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
of vibrations. For a vibrating string, the frequency is determined by the string's length,
mass
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different elementar ...
, and
tension
Tension may refer to:
Science
* Psychological stress
* Tension (physics), a force related to the stretching of an object (the opposite of compression)
* Tension (geology), a stress which stretches rocks in two opposite directions
* Voltage or el ...
. 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
harpsichord
A harpsichord ( it, clavicembalo; french: clavecin; german: Cembalo; es, clavecín; pt, cravo; nl, klavecimbel; pl, klawesyn) is a musical instrument played by means of a keyboard. This activates a row of levers that turn a trigger mechanism ...
s, 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
In music, just intonation or pure intonation is the tuning of musical intervals
Interval may refer to:
Mathematics and physics
* Interval (mathematics), a range of numbers
** Partially ordered set#Intervals, its generalization from numbers to ...
,
pythagorean tuning
Pythagorean tuning is a system of musical tuning in which the frequency ratios of all intervals are based on the ratio 3:2.Bruce Benward and Marilyn Nadine Saker (2003). ''Music: In Theory and Practice'', seventh edition, 2 vols. (Boston: Mc ...
and
meantone temperament
Meantone temperament is a musical temperament, that is a tuning system, obtained by narrowing the fifths so that their ratio is slightly less than 3:2 (making them ''narrower'' than a perfect fifth), in order to push the thirds closer to pure. Me ...
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
Well temperament (also good temperament, circular or circulating temperament) is a type of tempered tuning described in 20th-century music theory. The term is modeled on the German word ''wohltemperiert''. This word also appears in the title of J ...
allowed fixed-pitch instruments to play reasonably well in all of the keys. The famous "
Well-Tempered Clavier
''The Well-Tempered Clavier'', BWV 846–893, consists of two sets of preludes and fugues in all 24 major and minor keys for keyboard by Johann Sebastian Bach. In the composer's time, ''clavier'', meaning keyboard, referred to a variety of in ...
" by
Johann Sebastian Bach
Johann Sebastian Bach (28 July 1750) was a German composer and musician of the late Baroque period. He is known for his orchestral music such as the '' Brandenburg Concertos''; instrumental compositions such as the Cello Suites; keyboard w ...
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
In music theory, the wolf fifth (sometimes also called Procrustean fifth,
or imperfect fifth)
Paul, Oscar (1885). A manual of harmony for use in music-schools and seminaries and for self-instruction', p.165. Theodore Baker, trans. G. Schirmer. ...
) 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
An equal temperament is a musical temperament or tuning system, which approximates just intervals by dividing an octave (or other interval) into equal steps. This means the ratio of the frequencies of any adjacent pair of notes is the same, wh ...
, 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 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 A442.
Theory
Overtones and harmonics
![Standing waves on a string](https://upload.wikimedia.org/wikipedia/commons/5/5c/Standing_waves_on_a_string.gif)
A stretched string can vibrate in different modes, or
harmonics
A harmonic is a wave with a frequency that is a positive integer multiple of the ''fundamental frequency'', the frequency of the original periodic signal, such as a sinusoidal wave. The original signal is also called the ''1st harmonic'', the ...
, 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. (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
In music, inharmonicity is the degree to which the frequencies of overtones (also known as partials or partial tones) depart from whole multiples of the fundamental frequency ( harmonic series).
Acoustically, a note perceived to have a singl ...
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
In music, an octave ( la, octavus: eighth) or perfect octave (sometimes called the diapason) is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon that has been refer ...
with a 2:1 ratio,
perfect fifth
In music theory, a perfect fifth is the Interval (music), musical interval corresponding to a pair of pitch (music), pitches with a frequency ratio of 3:2, or very nearly so.
In classical music from Western culture, a fifth is the interval fro ...
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
The term ''
temperament
In psychology, temperament broadly refers to consistent individual differences in behavior that are biologically based and are relatively independent of learning, system of values and attitudes.
Some researchers point to association of temperam ...
'' refers to a tuning system that allows intervals to beat instead of tuning pure or "
just intervals". In
equal temperament
An equal temperament is a musical temperament or tuning system, which approximates just intervals by dividing an octave (or other interval) into equal steps. This means the ratio of the frequencies of any adjacent pair of notes is the same, wh ...
, 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.
![A440 Tuning Fork](https://upload.wikimedia.org/wikipedia/commons/5/5d/A440_Tuning_Fork.jpg)
One practical method of tuning the piano begins with tuning all the notes in the "temperament" octave in the lower middle range of the piano. A tuner starts by using an external reference, usually an
A440 A440 or A-440 may refer to:
* A440 (pitch standard)
* A440 highway (Australia), a road in Victoria, Australia
* Quebec Autoroute 440 (Laval)
* Quebec Autoroute 440 (Quebec City)
See also
* Apollo 440
Apollo 440 (also known as Apollo Four Fo ...
tuning fork
A tuning fork is an acoustic resonator in the form of a two-pronged fork with the prongs (tines) formed from a U-shaped bar of elastic metal (usually steel). It resonates at a specific constant pitch when set vibrating by striking it against ...
, (or commonly a C523.23 tuning fork) to tune a beginning pitch, and then tunes the other notes in the "temperament" using tempered interval relationships. During tuning it is common to assess fifths, fourths, thirds (both major and minor) and sixths (also major and minor), often playing the intervals in an ascending or descending pattern to hear whether an even progression of beat rates has been achieved.
Once the temperament octave is finished the tuner tunes the rest of the piano, working outward from the temperament, and using octaves and other intervals to align each note with notes that have already been tuned.
The following table lists theoretical beat frequencies between notes in an equal temperament octave. The top row indicates absolute frequencies of the pitches; usually only A440 is determined from an external reference. Every other number indicates the beat rate between any two tones (which share the row and column with that number) in the temperament octave. Slower beat rates can be carefully timed with a metronome, or other such device. For the thirds in the temperament octave, it is difficult to tune so many beats per second, but after setting the temperament and duplicating it one octave below, all of these beat frequencies are present at half the indicated rate in this lower octave, which are excellent for verification that the temperament is correct. One of the easiest tests of equal temperament is to play a succession of major thirds, each one a semitone higher than the last. If equal temperament has been achieved, the beat rate of these thirds should increase evenly in the temperament region.
The next table indicates the pitch at which the strongest beating should occur for useful intervals. As described above, when tuning a perfect fifth, for instance, the beating can be heard not at either of the fundamental pitches of the keys played, but rather an octave and fifth (perfect twelfth) above the lower of the two keys, which is the lowest pitch at which their harmonic series overlap. Once the beating can be heard, the tuner must temper the interval either wide or narrow from a tuning that has no beatings.
Stretch
The tuning described by the above beating plan provides a good approximation of equal temperament across the range of the temperament octave. If extended further, however, the actual tuning of the instrument becomes increasingly inaccurate because of
inharmonicity
In music, inharmonicity is the degree to which the frequencies of overtones (also known as partials or partial tones) depart from whole multiples of the fundamental frequency ( harmonic series).
Acoustically, a note perceived to have a singl ...
, which causes harmonics to run slightly
sharp
Sharp or SHARP may refer to:
Acronyms
* SHARP (helmet ratings) (Safety Helmet Assessment and Rating Programme), a British motorcycle helmet safety rating scheme
* Self Help Addiction Recovery Program, a charitable organisation founded in 199 ...
, as increasingly higher tones in the harmonic series are reached. This problem is mitigated by
"stretching" the octaves as one tunes above (and to an extent below) the temperament region. When octaves are stretched, they are tuned, not to the lowest coincidental overtone (second partial) of the note below, but to a higher one (often the 4th partial). This widens all intervals equally, thereby maintaining intervallic and tonal consistency.
All western music, but western classical literature in particular, requires this deviation from the theoretical equal temperament because the music is rarely played within a single octave. A pianist constantly plays notes spread over three and four octaves, so it is critical that the mid and upper range of the treble be stretched to conform to the inharmonic overtones of the lower registers. Since the stretch of octaves is perceived and not measured, the tuner is aware of which octave needs "more" or "less" stretching. A good tuning requires compromise between tonal brilliance, intonation and an awareness of gradation of tone through the compass of the instrument. The amount of stretching necessary to achieve this is a function of string scaling, a complex determination based on the string's tension, length, and diameter. The
Railsback curve
Piano acoustics is the set of physical properties of the piano that affect its acoustics, sound. It is an area of study within musical acoustics.
String length, mass and tension
The piano wire, strings of a piano vary in thickness, and therefore ...
is the result of measuring the fundamental frequencies of stretched tunings and plotting their deviations from unstretched equal temperament.
In small pianos the inharmonicity is so extreme that establishing a stretch based on a triple octave makes the single octaves beat noticeably, and the wide, fast beating intervals in the upper treble—especially major 17ths—beat wildly. By necessity the tuner will attempt to limit the stretch. In large pianos like concert grands, less inharmonicity allows for a more complete string stretch without negatively affecting close octaves and other intervals. So while it may be true that the smaller piano receives a greater stretch relative to the fundamental pitch, only the concert grand's octaves can be fully widened so that triple octaves are beatless. This contributes to the response, brilliance and "singing" quality that concert grands offer.
A benefit of stretching octaves is the correction of dissonance that equal temperament imparts to the perfect fifth. Without octave stretching, the slow, nearly imperceptible beating of fifths in the temperament region (ranging from little more than one beat every two seconds to about one per second) would double each ascending octave. At the top of the keyboard, then, the theoretically (and ideally) pure fifth would be beating more than eight times per second. Modern western ears easily tolerate fast beating in non-just intervals (seconds and sevenths, thirds and sixths), but not in perfect octaves or fifths. Happily for pianists, the string stretch that accommodates inharmonicity on a concert grand also nearly exactly mitigates the accumulation of dissonance in the perfect fifth.
Other factors, physical and
psychoacoustic
Psychoacoustics is the branch of psychophysics involving the scientific study of sound perception and audiology—how humans perceive various sounds. More specifically, it is the branch of science studying the psychological responses associated wit ...
, affect the tuner's ability to achieve a temperament. Among physical factors are inharmonic effects due to soundboard resonance in the bass strings, poorly manufactured strings, or peculiarities that can cause "false beats" (false because they are unrelated to the manipulation of beats during tuning). The principal psychoacoustic factor is that the human ear tends to perceive the higher notes as being flat when compared to those in the midrange. Stretching the tuning to account for string inharmonicity is often not sufficient to overcome this phenomenon, so piano tuners may stretch the top octave or so of the piano even more.
Tools and methods
![Piano tuning tools](https://upload.wikimedia.org/wikipedia/commons/5/5d/Piano_tuning_tools.jpg)
Common tools for tuning pianos include the
tuning lever
A tuning wrench (also called a tuning lever or tuning hammer) is a specialized socket wrench used to tune string instruments, such as the piano, harp, and hammer dulcimer, that have strings wrapped around tuning pins. Other string instruments do ...
or "hammer", a variety of
mutes, and a
tuning fork
A tuning fork is an acoustic resonator in the form of a two-pronged fork with the prongs (tines) formed from a U-shaped bar of elastic metal (usually steel). It resonates at a specific constant pitch when set vibrating by striking it against ...
or
electronic tuning device. The tuning lever is used to turn and 'set' the tuning pins, increasing or decreasing the tension of the string. Mutes are used to silence strings that are not being tuned. While tuning the temperament octave, a felt strip is typically placed within the temperament (middle) section of the piano; it is inserted between each note's trichord, muting its outer two strings so that only the middle string is free to vibrate. A Papps mute performs the same function in an upright piano and is placed through the piano action to mute either the 2 left strings (of a trichord), or the 2 right strings similarly. After the center strings are all tuned (or right if a Papps mute is used) 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, and the Papps mute is commonly used for tuning the high notes in upright pianos because it slides more 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 between F3 and F4 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, using octaves and other intervals as checks.
If an electronic tuning device is used, the temperament step might be skipped, as it is possible for the tuner to adjust notes directly with the tuning device in any reasonable order.
See also
*
Piano acoustics
Piano acoustics is the set of physical properties of the piano that affect its sound. It is an area of study within musical acoustics.
String length, mass and tension
The strings of a piano vary in thickness, and therefore in mass per length, w ...
*
Institute of Musical Instrument Technology
*
Pseudo-octave
A pseudo-octave, pseudooctave,"Interview with Max Mathews", p.21. Author(s): C. Roads and Max Mathews. Source: ''Computer Music Journal'', Vol. 4, No. 4, (Winter, 1980), pp. 15–22. Published by: The MIT Press. or paradoxical octave"The Parado ...
*
Stretched tuning
Stretching is a form of physical exercise in which a specific muscle or tendon (or muscle group) is deliberately flexed or stretched in order to improve the muscle's felt elasticity and achieve comfortable muscle tone. The result is a feeling ...
Notes
References
* . 1954, 1885. .
*
*
*
External links
How to tune a pianoMidrange Piano Tuning, Octave Types and DistributionGill Green MA
How often should a piano be tuned
{{DEFAULTSORT:Piano tuning
Musical tuning
Piano
Articles containing video clips