I will recommend also:

Parsegh Ganatchian

 he died in 1967...

His songs are directly from eden garden as persian ancient music... He is armenian ... here his complete songs...Direct from Eden garden or near it ...

I lost my box of Minoo Javan an Iranian singer mastering old Persian songs ...

For me this is contemporary...She died in 1978... And it remind me on a past persian reincarnation for sure ...😁

His box i lost i retrieved it on youtube :

The litterature of Piano will not be complete without the great Samuil Feinberg ...he died in 1962... This interpretation is the best over the colder Hamelin ...

I love Simpson, but I was just noting that the OP had made an arbitrary cut off that he wanted currently living composers.  I would be more than happy to have a separate thread devoted to composers active after 1920

Oups! i must delete all my posts then....

😁