3), while providing the opening melodic
tetrachords, seems to play no more important a role than the other two.
11: the occurrence, recurrence, and association of primary
tetrachords and their attendant constellations create an overall transformational narrative.
Example 6 shows that, eventually, a decision was taken to use the ordered pc dyad [less than]G[MUSICAL NOTES NOT REPRODUCIBLE IN ASCII]-F[MUSICAL NOTES NOT REPRODUCIBLE IN ASCII] at the boundaries between each of the row's component
tetrachords. At the top left of Example 5, an early version of the row begins (as do several previous sketches for this material) with a jumbled spelling of the name "BACH." The import of this fact will become clear in time.
Almost immediately, Rinds introduces a chromatic
tetrachord on the word "grave," which is pitch-symmetrical around [C.sub.4] and [D[flat].sup.4].
Parts of the book are intended for beginning students of atonal music, particularly Appendix 2, "Set-Classes Listed in Ascending Order by Cardinality." This is a list of all possible trichords,
tetrachords, pentachords, and hexachords.
The
tetrachord of this book's title - literally, four strings of a lyre or harp - is that of the ancient Greek theory of music, a series of four neighboring notes (A-G-F-E, for example) that fill in the interval of a perfect fourth.
Set classes 8-15 [01234689] and 8-29 [01235679], the complements of the all-interval
tetrachords, have pentachord representations of thirty-five, the highest of all 3/5 partitioned octachords.
Homs explains that, for example, in order to free his compositions from the strict dodecaphonic method, he would break a series into two hexachords or three
tetrachords, allowing thus a greater malleability of the row without leaving the system altogether.
My first computer piece used combinatorial
tetrachords. I had the spectrum of each
tetrachord tuned in major thirds, which are excluded in a combinatorial
tetrachord, with the result that the timbre would always uniquely define the
tetrachord.
The all-interval
tetrachords (4-15[0146] and 4-29 [0137]) are a hallmark of Carter's music from circa 1950-65.
different pitches) - result in figures that sometimes overlap with other structural configurations, such as tonalities (as is often the case on the Diamond Marimba or the Kithara), scales (as on the Harmonic Canon or the Boo),
tetrachords, harmonic formulae or suchlike, and at other times do not.
Here the seven-pitch cluster is formed by two 0167
tetrachords, with one note, the B, missing.
