Editing Inharmonicity (section)

==Pianos==
{{Main|Piano_acoustics#Inharmonicity_and_piano_size|l1=Piano acoustics – Inharmonicity and piano size}}

===Sound quality of inharmonicity===
In 1943, Schuck and Young were the first scientists to measure the spectral inharmonicity in piano tones. They found that the spectral partials in piano tones run progressively sharp—that is to say, the lowest partials are sharpened the least and higher partials are progressively sharpened further.

Inharmonicity is not necessarily unpleasant. In 1962, research by Harvey Fletcher and his collaborators indicated that the spectral inharmonicity is important for tones to sound piano-like. They proposed that inharmonicity is responsible for the "warmth" property common to real piano tones.<ref>[http://www.acoustics.org/press/134th/galembo.htm Acoustical Society of America - Large grand and small upright pianos] {{webarchive|url=https://web.archive.org/web/20120209050929/http://www.acoustics.org/press/134th/galembo.htm |date=2012-02-09 }} by Alexander Galembo and 
Lola L. Cuddy<!-- Bot generated title -->]</ref>  According to their research [[synthesizer|synthesized piano tones]] sounded more natural when some inharmonicity was introduced.<ref>Matti A. Karjalainen (1999). [https://www.researchgate.net/publication/228587669_Audibility_of_inharmonicity_in_string_instrument_sounds_and_implications_to_digital_sound_synthesis "Audibility of Inharmonicity in String Instrument Sounds, and Implications to Digital Sound Systems"]</ref>  In general, electronic instruments that duplicate acoustic instruments must duplicate both the inharmonicity and the resulting [[stretched tuning]] of the original instruments.

===Inharmonicity leads to stretched tuning===
When pianos are tuned by [[Piano tuning|piano tuners]], the technician sometimes listens for the sound of "[[beat (acoustics)|beating]]" when two notes are played together, and tunes to the point that minimizes [[Roughness (psychophysics)|roughness]] between tones. Piano tuners must deal with the inharmonicity of piano strings, which is present in different amounts in all of the ranges of the instrument, but especially in the bass and high treble registers. The result is that octaves are tuned slightly wider than the harmonic 2:1 ratio. The exact amount [[Piano tuning#Stretched octaves|octaves are stretched]] in a piano tuning varies from piano to piano and even from register to register within a single piano—depending on the exact inharmonicity of the strings involved.

Because of the problem of inharmonicity, electronic piano tuning devices used by piano technicians are not designed to tune according to a simple harmonic series.  Rather, the devices use various means to duplicate the stretched octaves and other adjustments a technician makes by ear.  The most sophisticated devices allow a technician to make custom inharmonicity measurements—simultaneously considering all partials for pitch and volume to determine  the most appropriate stretch to employ for a given instrument.  Some include an option to simply record a tuning that a technician has completed by ear; the technician can then duplicate that tuning on the same piano (or others of similar make and model) more easily and quickly.

The issues surrounding setting the stretch by ear vs machine have not been settled; machines are better at deriving the absolute placement of semitones within a given chromatic scale, whereas non-machine tuners prefer to adjust these locations preferentially due to their temptation to make intervals more sonorous.  The result is that pianos tuned by ear and immediately checked with a machine tend to vary from one degree to another from the purely theoretical semitone (mathematically the 12th root of two) due to human error and perception. (If pleasing the ear is the goal of an aural tuning, then pleasing the math is the goal of a machine tuning.)  This is thought to be because strings can vary somewhat from note to note and even from neighbors within a unison.  This non-linearity is different from true falseness where a string creates false harmonics and is more akin to minor variations in string thickness, string sounding length or minor bridge inconsistencies.

Piano tuning is a compromise—both in terms of choosing a [[Musical temperament|temperament]] to minimize out-of-tuneness in the intervals and chords that will be played, and in terms of dealing with inharmonicity.  For more information, ''see [[Piano acoustics]]'' and ''[[Piano tuning]]''.

Another factor that can cause problems is the presence of rust on the strings or dirt in the windings.<ref>Rowland, David (1998). [https://books.google.com/books?id=kEy1MRsnVHIC&dq=inharmonicity&pg=PA106 The Cambridge companion to the piano], p. 106. {{ISBN|0-521-47986-X}}.</ref> These factors can slightly raise the frequency of the higher modes, resulting in more inharmonicity.