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TH Rollinson was a British band leader and composer/arranger that moved to the United States to play with the Willimantic Brass Band and to study music at the Conference Providence Seminary. He may be best known by trumpeters as one of the earliest composers to make an authorized edition of Arban's Conservatory Method, but he also arranged over 1200 pieces and wrote various other methods for the trumpet.
This method, his Modern School for the Cornet, is his answer to the Arban method. Well over 200 pages that takes a trumpeter through all aspects of playing, including multiple tonguing, finishing etudes, and a full list of solo compositions and arrangements.
I have attached a large selection of samples so you can get a look at this rare book. Long out of print but definitely not forgotten. When you are ready you can grab an immediate PDF download at the link above.