Asymmetrical shawl in the shape of biased triangle is quite simple. The shape is achieved through a certain rhythm of increases and decreases.
A particular kind of yarn is not critical. Yarns that give good drape are all fine (country wool, linen, rayon, cotton and blend thereof). If you are using wool, fingering weight (100 g/400-450 m) is suitable. Linen can be 100 g/300-450 m.
My sample is from leftovers. I used linen 100 g/600 m (held double) and a very thin cotton 100 g/1600 m (in order to get a certain shade). The black part is from Bodrum (linen-polyamide blend, 100 g/280 m).
A sample knitted by Ruth Loorits (her daughter Kristel is the model) for the test is from Aade Lõng Artistic 8/2 (pure wool, 100 g/400 m), 160 g.