He received his first music lessons in piano, organ and counterpoint from his father Heinrich IV, himself a dilettante and composition student of Carl Gottlieb Reissiger.
Heinrich XXIV received formal music instruction in Dresden, and continued his studies at the Universities, first in Bonn, then in Leipzig where he was a pupil of Wilhelm Rust.
Heinrich XXIV's compositions display a masterful command of musical form and technique, especially in contrapuntal voice leading.
As with Brahms, Dvořák and Herzogenberg, chamber music was his main field of creativity; he contributed numerous works in various genres.
Even in the years after his death, his compositions were warmly recommended by various musical authorities, as expressed, for example, by the musicologist Wilhelm Altmann in the third volume of his Handbook for String Quartet Players published in 1929.