In 1818, he composed a concerto for flute, extraordinarily and curiously similar to the second concerto that Saverio Mercadante wrote for the same instrument in 1819. In 1825, he won (tied with Luigi Ferdinando Casamorata) a competition by the Accademia di Belle Arti di Firenze centered around the putting to music of the cantata "Il Ciclope" by Pietro Metastasio. In 1828, the fame of Giorgetti as a composer, teacher, and publicist was established in Florence because of the fact that he most furiously participated in a written debate regarding German influence in the didactics of Italian music. In the periodicals, space was given to the prevalent idea that there was an excessive penetration of German taste inside the classrooms of the conservatories, while Giorgetti, on the contrary, affirmed that the study of Germans of the Classical period (Mozart, Haydn and Beethoven) was instead essential in acquiring the necessary knowledge that permitted Italian singability to be expressed well. Giorgetti proposed a sort of union between German and Italian style, which in this era were considered to be incompatible. He pointed to Gioachino Rossini as the ultimate example of that union. Rossini was taught through German examples during his education in Bologna; indeed, he was given the nickname “"il tedeschino" (the little German). Giorgetti was given the nickname “il tedescone" (the big German) for his fondness of Teutonic artistry. That fondness found fertile ground in the "Germanophile" Tuscany, ruled by Habsburg-Lorraine. In 1827, on the frontispiece of "Tre trj di una difficoltà progressiva" (dedicated to Paganini) he indicates «first violin of the court of the Grand Duke of Tuscany», and thanks to the support of the court (members to which Giorgetti dedicated numerous compositions), he began promoting instrumental music and cultured European musical language, an activity to which he dedicated all of his energy as a composer, teacher and orchestral conductor. The quartet was a privileged object of interest in his work, and was, at that time, used infrequently by Italian composers. He considered the quartet to be the maximum expression of the art of music (and believes to be heir of the great European approach to the quartet, which at the time a myth considered created in Italy).