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Piano Tuning involves adjusting tension on the strings to ensure that the intervals are tuned. In the context of tuning a piano, the meaning of 'in tune,' isn't just a fixed set of pitch. The standard tuning for pianos is equal temper. The theoretical tuning of the piano is described in Piano Key Frequencies.

The MIDI definition of middle C, 261.626 Hz, is C3. The MIDI standard definition for middle C (261.626 Hz) is C3. In reality, a MIDI program can display the C 3 to C 5. This can be confusing, particularly for beginners.

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Many people are involved in piano tuning, including independent technicians, piano builders, technical staff at piano stores, and even hobbyists. Organizations or guilds such as the Piano Technicians Guild offer professional training and certification. Most piano manufacturers suggest that the pianos are tuned at least twice per year.

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Frequency Conditions Background

The tuning lever, or "hammer", and the mutes are amongst the most essential tools for a piano tuner.

A diagram showing beating. As one wave increases in frequency, the sum of both waves is displayed (blue). Two waves start out identical. The frequency of the wave in green is then increased gradually by 25 percent. The result of constructive and destructive interference is a wave with a beating pattern.

Pianos can go out of pitch for a variety of reasons, including atmospheric conditions. The temperature of the piano can be affected by changes in . Newer pianos have strings that stretch over time and wood parts that compress. This causes the piano to become flat. Older pianos can lose their tuning pins, which hold the string in tune.

A piano that is out of tune can be recognized by its characteristic sound. The sound intensity fluctuation is caused by two or more tones being played at the same time. If a piano chord tuned at 442 Hz is played with a piano key tuned at 440 , then the resultant tone will beat out 2 Hz due to the constructive and destructive interference. If a 220 Hz string (with an harmonic of 440 Hz), is played with a 442 Hz string, then the 2 Hz is also heard.

For a vibrating string, the frequency is determined by its length and mass. The frequency of a string is determined by its length, weight and tension.

History

The first piano tuners were trained and employed in factories, often for a period of 5-7 years. The first piano tuners worked in factories and were often apprentices for 5-7 years. The challenges faced by early piano tuners were the wide variety of different pianos, non-standard pitches and new models.

Well temperament was developed to allow fixed-pitch instrument play well across all keys. Johann Sebastian Bach's "Well-Tempered Clavier", which includes preludes, fugues, and other pieces in all the 24 major keys and minor keys, took advantage of the new technology. However, even though unpleasant intervals, such as the wolf, were no longer used, there were differences between the keys regarding the size of the intervals. This variation in 1800s led to an increased use of "quasi-equal temper", where the ratio of frequency between adjacent keys on the keyboard was nearly equal.

Though A440 is generally the standard, some orchestras use a higher pitch standard such as A442. Although A440 is the general standard for piano tuning, certain orchestras in Europe use A442.

"Theory"

Harmonics and overtones

Diagram of the six modes and harmonics on a vibrating, two-sided string.

The first harmonic (or fundamental frequency) is usually the loudest and determines what pitch you hear. First harmonic or fundamental frequency is the loudest and is what determines pitch. In theory, higher harmonics vibrate as integer multiples to the fundamental frequency. (e.g. The overtones of a 100-Hz fundamental string would be 200 Hz and 300 Hz. The overtones' frequencies are actually shifted upwards due to disharmonicity, which is caused by stiffness in the strings.

The ratio between the absolute frequencies of two notes is called a interval. It is easiest to tune intervals where note frequencies are a whole number ratio. the octave has a ratio of 2:1, the perfect fifth is 3:2, and so on. Because the harmonics are in tune, they beat together. For a perfect five, the third harmonic of the bottom note is the same as the second harmonic of top note.

Temperament

The term temper is used to describe a tuning method that permits intervals instead of " only intervals". The term em>a href="https://en.wikipedia.org/wiki/Musical_temperament" title="Musical temperament">temperament/a> refers to ''just intervals/a>/em> instead of tuning pure or "a href="https://en.wikipedia.org/wiki/Just_intonation".

A beat is caused by adjusting an interval. Due to the fact that the tone of a piano string vibrating is not a single pitch but rather a complex arrangement of sounds arranged into a series of pitches, the pitch difference between two adjacent harmonics can cause a close harmonic ratio, such as the perfect fifth, to be achieved at higher pitch. A temperament can be tuned acoustically by timing the beats of tempered interspaced.

An A440 tuning fork

A practical way to tune a piano is by tuning all of the notes of the "temperament octave" in the middle lower range. Tuners start by tuning a starting pitch using an or A440 tuning fork (or more commonly, a C523.23 fork). They then use tempered interval relationships to tune the rest of the notes. It is normal to use tempered interval relationships to tune the other notes in a "temperament" using tempered fifths, sixths and thirds.

The tuner will then tune the remainder of the piano by working from the temperament and aligning each note using the octaves or other intervals.

This table shows the theoretical frequency of beats between two notes within an equal-tempered octave. The absolute pitches are listed in the top row; typically, only A440 can be determined by an external reference. The other numbers indicate the rate of beat between two notes (which are in the same row or column as that number). Metronomes or similar devices can help you time slower beat rates. It is hard to adjust the beats-per-second for the thirds of the temperament octave. However, after duplicating the temperament one octave lower, these frequencies will be present half as fast in this octave. This is a great way to verify that your temperament is accurate. Playing a series of major thirds each a half-tone higher than the previous one is a simple way to test for equal temperament. The beat rate should be increasing evenly across the entire temperament area if equal temperament is achieved.

The intervals are listed in terms of the pitch where the most intense beating occurs. When tuning a fifth perfect, as described earlier, you can hear the beat not in either key, but an octave above and a fifth above (the perfect twelfth), which is where their harmonic series intersects. The tuner will then adjust the tuning to either make it wider or smaller than if there were no beatings.

Beats are a constant occurrence the interval estimated frequency ratio Beats above lower pitch Tempering Octave

Stretch

Railsback curve - a measure of the difference between a normal piano tuning scale and an equal-tempered one.

If you extend the tuning further, however, the actual tuning of the instrument becomes increasingly inaccurate because of a href="https://en.wikipedia.org/wiki/Inharmonicity" title="Inharmonicity">inharmonicity/a>. This causes harmonics to run slightly'sharp (music)' as higher notes in the harmonic series are reached. As the harmonic series is raised, harmonics become more sharp. As one tunes higher (and, to a certain extent, lower) than the temperament range of the instrument's tuning region, can be used as a way to "stretch". The octaves that are stretched are not tuned to the second partial (lowest coincidental) but to an overtone higher (usually the fourth partial). The octaves are stretched to the same extent, maintaining both intervallic consistency and tone.

Western music in general, and western classical literature specifically, require this deviation from equal temperament theory because music is seldom played within an octave. The treble range must be stretched in order to match the overtones that are produced by the lower registers. This is because a pianist plays over four and three octaves. The tuner can tell which octave requires "more" or 'less" stretching because the octave stretch is not measured but is felt. Good tuning is a compromise between intonation, tonal brilliance and a sense of tone gradation throughout the instrument's compass. String scaling is used to determine the amount of stretching required. This complex calculation takes into account tension, length and diameter of each string. The railsback curve results from measuring fundamental frequencies and plotting deviations of unstretched Equal Temperament.

The inharmonicity of small pianos is extreme. When a stretch is set based on the triple octave, the single octaves will beat conspicuously, while the fast, wide intervals, especially the major 17ths, will be wildly beaten. The tuner must limit the stretching. Less inharmonicity is possible with large concert grand pianos, allowing for more string stretching without affecting the close octaves or other intervals. While it is true that the smaller keyboard receives more stretch in relation to its fundamental pitch, the concert grands octaves have the ability to be fully expanded so that triple-octaves remain beatless. Concert grands have a "singing", brilliant response.

Stretching octaves has the benefit of correcting dissonance in the perfect fifth. The slow and almost imperceptible beats of the fifths (from a little over one every two seconds up to one per second), in the temperament area, would be doubled for each ascending eighth without octave stretch. The theoretically and ideally pure fifth at the top of the piano would then be beating eight times a second. Western ears can tolerate fast tempos in intervals other than perfect fifths or octaves (seconds and sevens, thirds and sixs), but they cannot do so in perfect fifths. The concert grand's string length, which accommodates dissonance on the fifth note in a perfect harmony, also mitigates this accumulation.

The ability of the tuner to create a temperament is also affected by Psychoacoustic and other factors. Physical factors include inharmonic sounds due to resonances in the strings of the bass, poor quality strings or other peculiarities which can produce "false" beats (false, because these are not related to tuning manipulation). Psychoacoustic factors include the fact that people tend to hear higher notes as flatter than those in the middle range. This phenomenon is not always overcome by stretching the tuning of the piano to compensate for the inharmonicity of the strings.

Tool and Methods

A few common tools for tuning a piano: from top to bottom, there is a tuning knob, felt mute (left), rubber mute (right), felt temperament strip and Papps mute.

Tuning pianos is done with a number of tools, including the "hammer" or tuning lever, mute, tuning fork, or electronic device. The tuning lever turns the pins to increase or decrease the tension. The mutes used for tuning are to quiet the strings. While tuning for the temperament octave a felt piece is placed in the middle section of the keyboard. It is inserted into the trichords between the notes, muting the outer strings, so only the center string can vibrate. In an upright piano, a Papps mutes performs this function. It is used to mute the two left strings of a trichord or the two right strings in a similar way. The felt strip is removed one note at a time, after the center (or right strings if you are using a Papps mutes) strings have been tuned. The wedge-shaped mutes can be inserted in between the two strings and muted. Papps mutes, on the other hand, are commonly used to tune the higher notes of upright pianos as they slide more easily through the hammer shanks.

[16] After tuning the A4 note, the rest of the piano will be tuned using the temperament octave.

The temperament step can be skipped if you use an electronic tuning instrument, since the tuner is able to change the notes in the device directly.

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