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Showing my lack of knowledge of classical music here but I would like to get an answer to this . I saw on Demondre Thurmonds Facebook page that he will be playing this piece with the New York Phil. . Will he be playing a part written for tenor tuba and will he likely be playing a tenor tuba rather than euph?

I would think he will play his Miraphone euphonium on the Strauss Tenor Tuba part with NY....

There really isn't such a thing as tenor tuba, other than the one meant for french horn players.

I would rather suspect the part was originally played on an instrument similar to a Kaiser Baritone, with rotary valves and curved bell, although maybe a Bb Wagner Tuba (with French horn mouthpiece) was intended? Are they not labelled tenor tuba in some music by Wagner and Bruckner? A euphonium would unlikely to have been used in Germany at that time.

Although today it seems to usually be played by euphonium.