Ladysmith Black Mambazo’s first new studio album in five years, Walking in the Footsteps of Our Fathers, marks a generational shift, both in the veteran a cappella band and their native South Africa. As the title indicates, the group are moving ahead while honoring the elders who paved the way: In the song “Vulani Amasango,” they honor those who sang with LBM over the last half-century, specifically founder Joseph Shabalala; in “Long Walk to Freedom,” they celebrate the people who struggled for apartheid-free S.A., specifically Nelson Mandela. Shabalala still records with the group, though his sons Msizi, Thulani, Sibongiseni, and Thamsanqa carry on his legacy live. Joseph derived LBM’s exquisite vocal harmonies from isicathamiya, traditional music by black miners. Already well-known in S.A., the group’s music spread around the world when Paul Simon asked them to sing on 1986’s Graceland. New versions of two of those songs — “Diamonds on the Soles of Her Shoes” and “Homeless” — appear on Walking, which recently received the group’s 17th Grammy nomination; LBM has won four. As uplifting as the harmonies, other themes discuss freedom, equality, love, and optimism.