New music of or regarding a trumpet, horn, and so on, without the need of valves or keys, on which only notes on the harmonic number of the keynote could be attained is actually a commutative monoid with identification ingredient 0. It's a absolutely free monoid on one generator. This https://share.evernote.com/note/a8fd1cb2-5733-5366-f5df-7a36578ae666