Béla Bartók (1881-1945)
Z-Cells
While it has taken some time to filter into the general literature, the existence of Z-cells in the music of Bartók has been accepted for some time now by most serious scholars.
The term "Z-cell" was coined by Leo Treitler, as an extension of the work of George Perle. Perle had identified X- and Y-cells in Bartók's music, specifically in the Fourth String Quartet. Z-cells have been found in a large number of Bartók's works from all periods of his life. The concept of Z-cells has been enlarged and extended by Elliot Antokoletz, especially in his book "The Music of Bela Bartók". Other scholars, such as Benjamin Suchoff, have also found these cells to be fundamental to Bartók's style.
What are Z-cells?
Basically, a Z-cell is a pitch collection of pitch-classes (0,1,6,7). Its designation as a cell or set signifies that the pitches may occur in vertical (harmonic) or horizontal (melodic) configurations, or both. Bartók often uses the cell as a fifth (e.g. C-G) enclosing two 'tendency tones' that push outward to the fifth (e.g. Db-F#). This usage is documented in Charles Morrison's article in Music Theory Spectrum.
How Characteristic are Z-cells in Bartók's Music?
Bartók's use of these cells varies from piece to piece, as you might expect. Scholars are divided on whether Z-cells are fundamentally important to Bartók in their own right, or whether they are by-products of other processes. In any case, they certainly appear in a large number of important Bartók works, often in significant places.
It is interesting to note that when Witold Lutoslawski wrote Musique Funebre ("a la memoire de Bela Bartók") he based the opening section on Z-cells, as an obvious recognition of their importance in Bartók's work. (Lutoslawski was also careful in his treatment of these cells so that the impression is one of reference, but not direct quotation.)
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