cloth / scarf
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cloth
A piece of fabric used for a specific purpose, for example for cleaning, drying, or covering something.
Kannst du mir bitte ein feuchtes Tuch geben, um den Tisch abzuwischen?
Could you please give me a damp cloth to wipe the table?
'Tuch' (cloth) is the base word for many useful nouns that describe a specific type of fabric. Examples include 'das Handtuch' (towel, for drying), 'das Geschirrtuch' (dish towel, for dishes), or 'das Halstuch' (neck scarf, as an accessory).
Reich mir bitte das saubere Handtuch aus dem Schrank.
Please hand me the clean towel from the cupboard.
The idiom 'auf Tuchfühlung gehen' is a fixed construction. It means to get very close to someone or something, often also in a figurative sense.
Bei dem Konzert ging der Sänger mit seinen Fans auf Tuchfühlung.
At the concert, the singer got up close with his fans.
You can recognize whether a cleaning cloth (meaning 1) or a fashion scarf (meaning 2) is meant from the verb. A cleaning cloth is used for 'Wischen' (wiping) or 'Putzen' (cleaning), while a fashion scarf is 'getragen' (worn) or 'umgebunden' (tied on).
Ich muss den Spiegel mit einem trockenen Tuch polieren.
I need to polish the mirror with a dry cloth.
When 'Tuch' (cloth) means material for clothing, it is often used in an elevated or specialized context, for example at a tailor's or in the fashion industry. It then describes a high-quality fabric.
Der Maßanzug wurde aus einem sehr feinen Tuch gefertigt.
The tailor-made suit was made from a very fine cloth.
fabric / material
'der Stoff' and 'das Tuch' both have to do with textiles. 'Stoff' usually means the material from which you sew or make something. 'Tuch' often means a concrete piece of fabric that you use, for example for cleaning, drying, covering something, or as an accessory. They can be confused because a Tuch is made of Stoff. The simple difference is: Stoff is more like material; Tuch is more like a finished piece with a purpose.
Nach dem Essen wischt Paul den Tisch mit einem feuchten Tuch ab.
After the meal, Paul wipes the table with a damp cloth.
Sie sucht im Laden einen weichen Stoff für neue Kissen.
She is looking in the shop for a soft fabric for new cushions.