joint / fugue
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joint
The narrow gap between two building components, such as tiles, bricks, or floorboards, which is often filled with mortar or a sealant.
Der Handwerker hat die Fugen im Badezimmer neu gemacht.
The craftsman redid the joints in the bathroom.
You can easily recognize the meaning of 'Fuge' from the context. In connection with construction, trades, or words like 'Fliesen' (tiles) and 'Badezimmer' (bathroom), it refers to the gap. In the context of music, composers, or instruments, it refers to the musical form.
Die Fugen zwischen den Steinen müssen erneuert werden.
The joints between the stones need to be renewed.
When it refers to the gap, typical verbs are 'Fugen füllen' (to fill joints), 'reinigen' (to clean), or 'erneuern' (to renew). The word is often used in the plural.
Nach dem Fliesenlegen müssen die Fugen noch gefüllt werden.
After laying the tiles, the joints still need to be filled.
In a musical context, typical combinations are 'eine Fuge komponieren' (to compose a fugue), 'eine Fuge spielen' (to play a fugue), or referring to a person as a 'Meister der Fuge' (master of the fugue).
Der Pianist spielte eine komplexe Fuge von Bach.
The pianist played a complex fugue by Bach.
The idiom 'aus den Fugen geraten' (to fall apart) is a fixed unit. It means that an order collapses. The noun is always plural here ('Fugen'), and the verb is 'geraten'.
Nach der unerwarteten Nachricht schien sein ganzes Leben aus den Fugen zu geraten.
After the unexpected news, his whole life seemed to be falling apart.
gap
'die Lücke' and 'die Fuge' can both refer to a space in between. 'Lücke' is more general: it is an open spot where something should actually be continuous or closed. 'Fuge' is used especially in building or renovation, for example between tiles, stones, or wooden boards. A 'Fuge' is often narrow and planned, and sometimes it is filled with material. Learners may confuse the words because both refer to a space between things. As a practical rule: between tiles, you usually say 'Fuge'; for a missing spot in general, you say 'Lücke'.
Nach dem Duschen putzt Lena die Fugen zwischen den Fliesen.
After showering, Lena cleans the joints between the tiles.
In der Mauer ist eine Lücke, durch die man den Garten sehen kann.
There is a gap in the wall through which you can see the garden.