into sixteen parts. He could produce sixteen clearly different sounds within a whole tone. From then on, he immersed himself in the study of the physical and mathematical basis of music. In 1899, General Porfirio Díaz, President of Mexico, heard Carrillo as a violinist. Díaz was impressed, and gave him a special scholarship to study in Europe. Studies abroad Carrillo was admitted to the Leipzig Royal Conservatory, where he studied with Hans Becker (violin), Johann Merkel (piano), and Salomon Jadassohn (composition, harmony and counterpoint). He became first violin in two orchestras: the Conservatory's Orchestra, conducted by Hans Sitt; and the Gewandhaus Orchestra, conducted by Arthur Nikisch. Carrillo composed several works at Leipzig, including Sextet in G Major for two violins, two violas and two violoncellos (1900), and the First Symphony in D Major for Orchestra (1901). Carrillo conducted the Leipzig Royal Conservatory Orchestra in the premiere performance of his First Symphony. In 1900, Carrillo attended the International Congress of Music in Paris, presided by Camille Saint-Saëns. He presented a paper, which the Congress accepted and published, on the names of musical sounds. He proposed that, since each note is one sound, each note name (C, D flat, etc.) should be a single syllable. He proposed 35 monosyllabic names. He also befriended Romain Rolland. When he finished his studies in the Leipzig Conservatory, he went to Belgium to improve his skills as a violinist. There, he studied with Albert Zimmer (who had been Eugène Ysaÿe's student) and was admitted to the Ghent Royal Conservatory of Music. In 1903, he composed a Quartet in E minor, which he intended to give, "ideological unity, [and] tonal variety," to classical forms. Return to Mexico In 1904, he won the First Award Cum Laud and with Distinction in the Ghent Conservatory International Violin Competition. Later that year he returned to Mexico where President Díaz gave him an Amati violin "as a present from the Mexican Nation" for his excellent performance in foreign countries. In Mexico City, Carrillo began intense work as violinist, orchestra conductor, composer and teacher. He was appointed professor of history (1906), composition, counterpoint, fugue and orchestration in 1908 by the National Conservatory. Among his students was José Francisco Vázquez Cano who founded the Free School of Music and Declamation, the Faculty of Music of the National University (UNAM) and the National University Philharmonic Orchestra (OFUNAM). Other notable students were Antonio Gómezanda (pianist