The New Sacred Harp (or The New Sacred Harp: A Collection of Hymn-tunes, Anthems, and Popular Songs: for the Choir, Class, Convention and Home Circle) was a seven-shape note tune book released in 1884 through S.P.
The New Sacred Harp was 192 pages long, including rudiments, 206 songs, and an index.
The songs of the book tended towards the more "modern" gospel style of Kieffer-Showalter-Vaughan publications (7-shapes, closer subdued harmony, etc.).
About a dozen compositions were by J. L. White, though none were written by B. F., Jr. His contributions were apparently only editorial and financial.
These brothers probably hoped to profit from the name connection to their father's popular song book.