In Schenker's monumental treatise Der freie Satz (1935), he presented a tonal scheme of major-third harmonic progression as an analysis of "Das Ständchen" from Gedichte von Eichendorff (1880-1888) by Hugo Wolf (1860-1903). His sketch is unusual because it has no structural dominant using symmetrical divisions of the octave by third. Even though some theorists have accepted to construct the chromatic third progression as a tonal scheme with the music of the late nineteenth century, a process of harmonic evolution in tonal structure has been overlooked. The general aim of the present study is to explore how the third harmonic scheme has been established. The first part of this paper examines a process of harmonic evolution from the diatonic third to the chromatic third presenting a model for the progressions. This examination leads to some analyses of music from Liszt, Beethoven, and Tchaikovsky, discussing how the third harmonic progression has been gradually changed as an overall tonal structure. In this paper, bass-line sketch and Tonnetz are used as analytical tools.