Inharmonicity

inharmonicinharmonic partialsodd-order overtones
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).wikipedia
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Harmonic series (music)

harmonic seriesovertone seriespartials
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).
Inharmonicity is a measure of the deviation of a partial from the closest ideal harmonic, typically measured in cents for each partial.

Overtone

overtonessuperharmonicpartials
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).
An overtone is a partial (a "partial wave" or "constituent frequency") that can be either a harmonic partial (a harmonic) other than the fundamental, or an inharmonic partial.

Pizzicato

pluckedbare fingerspizzicati
However, when a string is struck or plucked, as with a piano string that is struck by a hammer, a violin string played pizzicato, or a guitar string that is plucked by a finger or plectrum, the string will exhibit inharmonicity.
This complex timbre is called inharmonicity.

Piano

grand pianopianistacoustic piano
However, in stringed instruments such as the piano, violin, and guitar, or in some Indian drums such as tabla, the overtones are close to—or in some cases, quite exactly—whole number multiples of the fundamental frequency.
All else being equal, longer pianos with longer strings have larger, richer sound and lower inharmonicity of the strings.

Stretched tuning

stretchoctave stretchingstretches
In general, electronic instruments that duplicate acoustic instruments must duplicate both the inharmonicity and the resulting stretched tuning of the original instruments.
Stretched tuning is a detail of musical tuning, applied to wire-stringed musical instruments, older, non-digital electric pianos (such as the Fender Rhodes piano and Wurlitzer electric piano), and some sample-based synthesizers based on these instruments, to accommodate the natural inharmonicity of their vibrating elements.

Piano acoustics

Railsback curveacoustic pianoinharmonicity in pianos
For more information, see Piano acoustics and Piano tuning.
The frequency-raised overtones (above the harmonics), called 'partials', can produce an unpleasant effect called inharmonicity.

Tabla

tablastabltabla player
However, in stringed instruments such as the piano, violin, and guitar, or in some Indian drums such as tabla, the overtones are close to—or in some cases, quite exactly—whole number multiples of the fundamental frequency.
The precise construction and shaping of this area is responsible for modification of the drum's natural overtones, resulting in the clarity of pitch (see inharmonicity) and variety of tonal possibilities unique to this instrument which has a bell-like sound.

Piano tuning

piano tunerpiano technicianpiano tuners
For more information, see Piano acoustics and Piano tuning. The exact amount 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.
(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 caused by the stiffness of the strings.

Pseudo-octave

Stretched octavestretchedoctave
In piano tuning, stretched octaves are commonly encountered, where the inharmonicity caused by string thickness and tension makes it necessary to widen every interval very slightly.

Frequency

frequenciesperiodperiodic
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).

Integer

integersintegralZ
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).

Percussion instrument

percussionpercussionistpercussions
Many percussion instruments, such as cymbals, tam-tams, and chimes, create complex and inharmonic sounds.

Cymbal

cymbalsbellbowed cymbal
Many percussion instruments, such as cymbals, tam-tams, and chimes, create complex and inharmonic sounds.

Gong

tam-tamtamtamgongs
Many percussion instruments, such as cymbals, tam-tams, and chimes, create complex and inharmonic sounds.

Tubular bells

chimestubular bellbells
Many percussion instruments, such as cymbals, tam-tams, and chimes, create complex and inharmonic sounds.

Violin

violinsfiddleviolinist
However, in stringed instruments such as the piano, violin, and guitar, or in some Indian drums such as tabla, the overtones are close to—or in some cases, quite exactly—whole number multiples of the fundamental frequency.

Guitar

guitarslead guitarbass
However, in stringed instruments such as the piano, violin, and guitar, or in some Indian drums such as tabla, the overtones are close to—or in some cases, quite exactly—whole number multiples of the fundamental frequency.

Cylinder

cylindricalcylindersrod
For instance, a very thick string behaves less as an ideal string and more like a cylinder (a tube of mass), which has natural resonances that are not whole number multiples of the fundamental frequency.

Synthesizer

synthesizerssynthsynths
According to their research synthesized piano tones sounded more natural when some inharmonicity was introduced.

Piano Technicians Guild

piano tunersRegistered Piano Technician
When pianos are tuned by piano tuners, the technician sometimes listens for the sound of "beating" when two notes are played together, and tunes to the point that minimizes roughness between tones.

Beat (acoustics)

beatbinaural beatsbeating
When pianos are tuned by piano tuners, the technician sometimes listens for the sound of "beating" when two notes are played together, and tunes to the point that minimizes roughness between tones.

Roughness (psychophysics)

roughnessauditory roughnessmessy and indistinct
When pianos are tuned by piano tuners, the technician sometimes listens for the sound of "beating" when two notes are played together, and tunes to the point that minimizes roughness between tones.

Musical temperament

temperedtemperamenttemperaments
Piano tuning is a compromise—both in terms of choosing a temperament to minimize out-of-tuneness in the intervals and chords that will be played, and in terms of dealing with inharmonicity.