20th-century music engages with the diatonic collection in new and fascinating ways. While some composers abandon it completely, others find new ways to embrace it, however, coming to specific terms with the 20th-century use of the diatonic collection is challenging. I will show how several 20th-century melodies employ tri- and tetra-chordal subsets of the diatonic scale. I call this trait melodic micro-diatonicism. After comparing the use of melodic micro-diatonicism in these compositions, I will argue that melodic micro-diatonicism can be an indicator of formal structure.
Of the 12 tri-chordal set classes, 9 are subsets of sc 7-35, the diatonic collection. Of the 29 tetra-chordal set classes, 13 are subsets of 7-35. Therefore, in an average of randomly generated melodies, we would expect 75% of the tri-chords and 44.83% of the tetra-chords to belong to subsets of set class 7-35. These percentages will be used as a baseline to describe the level of micro-diatonicism in a melody. For example, taking a sampling of four 12-tone rows from various Webern works, the average tri-chordal micro-diatonicism is 57.5%, and the average tetra-chordal micro-diatonicism is 13.9%, both well below baseline. By contrast, diatonic tunes are 100% tri- and tetra-chordal micro-diatonicism. I am using the programing language Python and the Music21 library in order to assist in the gathering and analysis of data.
When examining the diverse music of the 20th-century, the micro-diatonic lens can lead to new insights into the design of melodies that fall comfortably into neither tonality, nor atonality.