Inharmonicity

Inharmonicity

In music, inharmonicity is how much the frequencies of overtones (also called partials or partial tones) differ from whole multiples of the main frequency, called the harmonic series. When we hear a note, it actually includes many extra sounds called overtones. Many percussion instruments, like cymbals, tam-tams, and chimes, make complex and inharmonic sounds.

Music harmony and tuning depend on how harmonic the tones are. In real musical instruments, the part that makes the sound—like a string, wire, or air column—is not perfect and has some inharmonicity. For example, a thick string acts more like a cylinder and its resonances are not perfect multiples of the main frequency.

In string instruments such as the violin and guitar, or in some Indian drums like tabla, the overtones are often close to whole number multiples of the main frequency. But when a string is struck or plucked, like a piano string hit by a hammer, it shows inharmonicity. The inharmonicity of a string depends on its tension, stiffness, and length.

Pianos

Main article: Piano acoustics – Inharmonicity and piano size

In 1943, scientists found that piano tones have a special quality called inharmonicity. This means higher tones sound a little sharper than we might think. This inharmonicity helps piano tones sound warm and natural. Electronic instruments try to copy this to sound like real pianos.

Piano tuners need to think about inharmonicity, especially for low and high notes. Because of this, octaves—the notes that sound the same but at double the pitch—are tuned a little wider than normal. Tuning machines try to copy what a tuner does, but tuning by ear is an art that thinks about how nice the notes sound together. Rust or dirt on piano strings can also change how inharmonicity sounds.

Guitar

Guitars, like acoustic and electric guitars, are often tuned by the players. When tuning by ear, guitarists need to think about string inharmonicity. This can make notes sound a little higher than they should. Even with a perfectly made guitar, inharmonicity can affect tuning. This means some octaves might need small changes to sound right.

Electronic tuners became popular in the 1970s and 1980s. But they don’t always fix tuning problems. A guitar might look perfectly in tune on an electronic tuner, but some chords can still sound off because of inharmonicity. This can happen from worn strings, frets that are not in the right place, or other issues. Cleaning the strings can help tuning sound better. Some performers tune their guitars to fit the main key of a piece, but they might need to make bigger changes to keep all chords sounding good.

Mode-locking

Other stringed instruments like the violin, viola, cello, and double bass show inharmonicity when notes are plucked using the pizzicato technique. But this inharmonicity stops when the strings are played with a bow. The bow moves in a steady way, keeping all the string’s resonances at exact ratios, even if they shake a little above or below their normal note. This process, called mode locking, also happens in the human voice and in reed instruments such as the clarinet.

List of instruments

Some instruments create perfectly harmonic sounds. These include bowed string instruments like the violin and cello, as well as brass instruments such as the trumpet and horn. Other perfectly harmonic instruments are reed aerophones like the oboe and clarinet.

Other instruments, such as plucked string instruments including the guitar and harp, are nearly harmonic. Tuned percussion is approximately harmonic, while untuned percussion does not produce harmonic sounds.