In 1891 and 1901, Thomas Parker Rodgers was living at Fieldhead Road and
was a music seller.
in 1911, he was living at Asline Road and a music dealer.
He died in 1924 and is buried in Norton Cemetery, Derbyshire Lane, Sheffield.
In a newspaper advertisement in 1915, he was trading at 34 Haymarket and
5,25, 27 and 28 Norfolk Market Hall.
Richard,
Based on many reports in Sheffield newspapers it looks like Thomas P Rodgers inherited the music shop/warehouse business in Norfolk Market Hall from his father Henry, who likewise seems to have got from his father.
You can view search results in FMP without subscription, but you need subs to view the original articles.
Search surname Rodgers and put Music in the additional info box. You can restrict to Sheffield and to ever narrowing periods in time.
One article in 1858 refers to items handsomely bound in cloth.
One ref is to the same address in 1899 and the company is then Rodgers and Pilkington.
Thomas P Rodgers was born 1848 to Henry Rodgers and Mary nee Parkin. They married in Rotherham in 1835 (FMP)
There are 2 possible deaths for Henry , in 1860 and 1867. Census data should sort that out, or perhaps a will (Ancestry) and tell you when Thomas took over.
All this seems to indicate that your volumes were manufactured before 1899 and after 1860 (or perhaps 1867).
Dave