air / aura
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air
In music, a song-like, melodious instrumental piece that often has a calm and solemn character.
Bachs berühmte Air aus der Orchestersuite Nr. 3 wird oft bei feierlichen Anlässen gespielt.
Bach's famous Air from Orchestral Suite No. 3 is often played on ceremonial occasions.
'Die Air' does not mean 'Luft' (air) like the English word 'air'. It refers either to a piece of music or to a person's particular aura or manner.
Sie gab sich eine Air der Gleichgültigkeit, um ihre Unsicherheit zu verbergen.
She gave herself an air of indifference to hide her insecurity.
You can recognize the meaning from the context. If it is about music, composers, or instruments, a musical piece is meant. If it is about a person's behavior or aura, an affectation is meant.
Das Orchester spielte eine wunderschöne Air von Händel.
The orchestra played a beautiful air by Handel.
In the meaning 'Gehabe' (affectation/mannerism), the word is almost always used with the reflexive verb 'sich geben' (to give oneself). The expression 'sich eine Air geben' means that someone is pretending to have a certain attitude or aura.
Er gibt sich eine Air des Intellektuellen, liest aber nie ein Buch.
He gives himself an air of an intellectual, but he never reads a book.
song
'das Lied' and 'die Air' both belong to music and can be melodic. The important difference is that a song has lyrics and is sung. An air is a song-like, usually calm instrumental piece, meaning music without sung lyrics. 'Air' is also a special and rather technical word, while 'Lied' is very normal in everyday language. The words can be confused because both refer to something melodic. When people are singing, 'Lied' almost always fits. When an instrument plays a calm melody, 'Air' can fit.
Das Orchester spielt eine ruhige Air für Streicher.
The orchestra plays a calm air for strings.
Im Radio läuft gerade ein Lied, das alle mitsingen können.
There is a song on the radio right now that everyone can sing along to.