Piano tuner

Aural piano tuning is the art of making adjustments to the tensions in the strings of a piano so that the instrument is in tune. Image File history File links Download high resolution version (1428x952, 962 KB) Description: Piano tuner Source: photo taken by Barbara Mürdter Date: March 10, 2006 Author: Barbara Mürdter Permission: Barbara Mürdter put it under the CC-BY-SA File links The following pages link to this file... Image File history File links Download high resolution version (1428x952, 962 KB) Description: Piano tuner Source: photo taken by Barbara Mürdter Date: March 10, 2006 Author: Barbara Mürdter Permission: Barbara Mürdter put it under the CC-BY-SA File links The following pages link to this file... This article or section is not written in the formal tone expected of an encyclopedia article. ... A short grand piano, with the top up. ... In music, there are two common meanings for tuning: Tuning practice, the act of tuning an instrument or voice. ...

Introduction

The meaning of the term in tune in the context of piano tuning is not as straightforward as it might seem, as it does not refer to the assignment of particular fixed set of pitches as it may with other instruments. Fine piano tuning requires an assessment of the interaction between 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. In the case of piano tuning, A440 is the usual standard. Pitch is the perceived fundamental frequency of a sound. ... An equal temperament is a musical temperament — that is, a system of tuning intended to approximate some form of just intonation — in which an interval, usually the octave, is divided into a series of equal steps (equal frequency ratios). ... This is a virtual piano with 88 keys tuned to A440, showing the frequencies, in cycles per second (Hz), of each note (i. ... A440 is the 440 Hz tone that serves as the standard for musical pitch. ...

Piano tuning is distinct from repairs or other maintenance that may be carried out (e.g. regulation of the action). There are typically about 220 strings in a full-sized piano, which may have a combined tension of about 20 tonnes. Tuning involves making minute adjustments to the tensions of these strings, in order to properly align the intervals between their tones. The piano requires various forms of maintenance to produce its best sound. ...

Temperament and beating

The relationship between two pitches, called an interval, is the ratio of their absolute frequencies. Two different intervals are perceived to be the same when the pairs of pitches involved share the same frequency ratio. The easiest intervals to identify, and the easiest intervals to tune, are those that are just — which have a simple whole-number ratio. The term temperament refers to a tuning system which tempers the just intervals (usually the perfect fifth which has the ratio 3:2) in order to satisfy some other mathematical property; in equal temperament, to temper a fifth one slightly narrows it by flattening its upper pitch slightly, or raising its lower pitch slightly. A system of temperament can also be known as a set of bearings, a term derived from early treatises on temperament which asserted that a fifth could be flattened "as much as it can bear". In music theory, the term interval describes the difference in pitch between two notes. ... FreQuency is a music video game developed by Harmonix and published by SCEI. It was released in November 2001. ... In music, just intonation, also called rational intonation, is any musical tuning in which the frequencies of notes are related by ratios of whole numbers. ... In musical tuning, a temperament is a system of tuning which slightly compromises the pure intervals of just intonation in order to meet other requirements of the system. ... In music, just intonation, also called rational intonation, is any musical tuning in which the frequencies of notes are related by ratios of whole numbers. ... The perfect fifth or diapente is one of three musical intervals that span five diatonic scale degrees; the others being the diminished fifth, which is one semitone smaller, and the augmented fifth, which is one semitone larger. ...

Tempering an interval produces a beating, which is a fluctuation of the intensity of sound heard when an interval is played. The rate of beating is determined by the difference the frequencies of any harmonics that coincide (for a fifth this would be the third harmonic of the lower note and the second harmonic of the upper note) and is heard clearly when these two pitches are close enough together that this difference is small (less than 20 hertz (Hz)). 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 which are close to a simple harmonic ratio such as a perfect fifth will produce a beating at a higher pitch due to an interaction between their harmonic series. In the case of an interval that is close to a perfect fifth, the strongest beating will be heard at 3 times the fundamental frequency of the lower string (known to musicians as an octave plus a perfect fifth up), and 2 times the frequency of the higher string (an octave up). Where these frequencies can be calculated, a temperament may be tuned aurally by timing the beatings of tempered intervals. In acoustics, a beat is an interference between two sounds of slightly different frequencies, perceived as periodic variations in volume whose rate is the difference between the two frequencies. ... MHZ redirects here. ... Pitched musical instruments are usually based on a harmonic oscillator such as a string or a column of air. ... The fundamental tone, often referred to simply as the fundamental, is the lowest frequency in a harmonic series. ... In music, an octave (sometimes abbreviated 8ve or P8) is the interval between one musical note and another with half or double its frequency. ...

One practical method of tuning the piano begins with tuning a set of strings in the middle range of the piano to a temperament octave. Once these strings are tuned, the tuner may proceed to tune all other pitches by comparing octave intervals against this temperament octave. This is convenient, because the octave is the most easy interval to tune (having the simplest ratio of 2:1) after the unison (1:1). (These octaves are tuned to have no beating.) For other uses, see Unison (disambiguation). ...

The following table lists the beat frequencies between notes in an equal temperament octave. The top row indicates absolute frequencies of the pitches; usually only A440 is determined aurally. Every other number indicates the beat rate between any two tones (which share the row and column with that number) in the temperament octave. Begin by tuning one note to the other so that the beating disappears, temper that interval in the appropriate direction (either making the interval wider or narrower, see further below) until the desired beat rate is achieved. 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 over the range of the piano.

This 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.

Stretched octaves

The tuning described by the above beating plan will give a good approximation of equal temperament across the range of the temperament octave. If it were extended further, however, the actual tuning of the instrument would become increasingly inaccurate. This is due to a factor known as inharmonicity, which is present in different amounts on all piano strings. The harmonic series of strings does not fall exactly into whole-number multiples of a fundamental frequency, but rather each harmonic is slightly sharper than a whole-number ratio, and this sharpness increases as higher tones in the harmonic series are reached. This means that an aurally tuned octave will be slightly wider than the just 2:1 ratio assumed above, known as a stretched octave. The amount of stretching depends on the style of piano and is determined mainly by the length of the strings: shorter pianos such as baby grands and spinets will have octaves that are stretched farther than concert grands. In music, inharmonicity is the degree to which the frequencies of the overtones of a fundamental differ from whole number multiples of the fundamentals frequency. ... A pseudo-octave is an interval whose frequency ratio is not 2:1, the definition of an octave, but is treated in some way or ways equivalent to this ratio. ... A short grand piano, with the top up. ... A spinet is a smaller type of harpsichord or other keyboard instrument, such as a piano or organ. ... The piano Piano is a common abbreviation for pianoforte, a large musical instrument with a keyboard (see keyboard instrument). ...

This has the effect that, on a piano, the notes in the higher register will end up slightly sharper than those in the lower octave. This is less apparent on longer pianos which have proportionally thinner strings (string inharmonicity is directly related to the ratio of string length to thickness). Despite this deviation from the simpler ideal equal temperament, this is considered the correct way to tune a piano because it maintains interval identity across the piano, which generally improves the sound of music played on it.

There are other factors, physical and psychoacoustic that affect the tuner's ability to achieve a temperament. Among physical factors are additional inharmonic effects due to soundboard resonance in the bass strings, and other effects such as poorly manufactured strings or peculiarities of resonance or bridge shape which can cause beatings in some notes that are unrelated to the tuning and that the piano tuner cannot correct. 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 oftentimes is not sufficient to overcome this phenomenon, so piano tuners oftentimes stretch the top octave or so of the piano even more. Psychoacoustics is the study of subjective human perception of sounds. ...

See also: Piano acoustics, Stretched octave and Stretched tuning.

Piano acoustics are those physical properties of the piano which affect its acoustics. ... A pseudo-octave is an interval whose frequency ratio is not 2:1, the definition of an octave, but is treated in some way or ways equivalent to this ratio. ... Stretched tuning is a detail of musical tuning, applied to wire-stringed musical instruments and older, non-digital electric pianos (such as the Fender Rhodes piano and Wurlitzer electric piano) to accommodate the natural inharmonicity of their vibrating elements. ...

References

1. Helmholtz, Hermann. On the Sensations of Tone. Trans: Alexander Ellis. Dover Publications. New York, 1954 (1885). ISBN 0-486-60753-4
2. Jorgensen, Owen. Tuning. Michigan State University Press, 1991. ISBN 0-87013-290-3

External links

• Piano Technicians Guild - Information on piano tuning and becoming a Registered Piano Technician.
• Piano tuning FAQ
• Piano tuning, music, mathematics and philosophy
• Fundamentals of Piano Practice, Chapter Two: Tuning Your Piano
• How to tune a piano yourself
• Frequency of every note; link to spreadsheet of beat rates for equally tempered intervals