Born in the city of Kayseri (Caesarea) in the Ottoman Empire, Gudenian attended the Turkish University of Constantinople, then moved to Brussels in 1904, where he studied violin under César Thomson and Mathieu Crickboom. In Prague, he studied violin under Otakar Sevcik and composition with Vítězslav Novák. After finishing his studies, he traveled for several years in Czechoslovakia, Turkey, the Caucasus, Persia, and Egypt, collecting and assimilating the traditional music of folk songs and dances in those countries, followed by two years in the Balkans. He gave recitals in the principal cities and towns of Bulgaria and Romania, where he was under royal patronage; accompanied by Romanian violnist George Enescu, he performed for Queen Elisabeth (Carmen Sylva) in her palace at Bucharest. He played in Budapest, Munich, Geneva, Marseilles, Paris and other major cities in Continental Europe, coming from France to New York in January 1918 during World War I. Sent as a messenger under the authorization of the French minister, he devoted much time to Red Cross and Armenian relief work in the United States. Soon after his arrival in the United States, he secretly married Olive Peabody in St. Charles, Missouri; they had met at the Odeon Theatre in St. Louis when Gudenian performed in a benefit appearance on behalf of the Syrian-Armenian Relief Fund.