The USSR would be severely at a disadvantage here. Funk originated from early African American slave music and without that culture or history, you aren't going to get anything remotely resembling what we call funk.
Just for fun though: The Union of Soviet Socialist Republics is established after World War I. Despite some early authoritarian leanings, the state reforms by 1930 into a representative socialist state with a self-styled "soviet democracy". Many of the revolutionary reforms put in place by Lenin remain, and many are aghast and bewildered by the dangerously progressive nature of the world's first communist state. Though industrialization is slow to develop and many have a hard time adjusting to such a different society (which Stalin OTL helped curb), by 1940, a stable economy and consumer industry begins to grow. World War II becomes a limited conflict when Germany is stopped at Czechoslovakia, thus the Soviet Union never enters the conflict and is allowed the grace of peace.
OTL, the Soviet Union invited several black students from the United States to come and study in their country. This TL would be no different, except in that the less repressive and more liberal nature of the Union would kickstart a load of immigration from the United States, which bungles Civil Rights and has given too much leeway to Southern Democrats. An expatriate community of African Americans is established in Moscow, mostly of artists and musicians from urban areas. Not long after, Moscow is revered in the music world as a rival city to Manchester and New York City (which has stagnated a bit), giving birth to such music genres as funk, a Russian analogue to krautrock, and what would come to be known as industrial music, developed alongside of British artists during the 70's. The 60's and 70's would be the most experimental and dramatic years of musical innovation ever.