In the introduction to the piano-vocal score, JensenMoulton describes how Gideon created principal motives for the opera by employing subsets of these collections (many of which contain an intervallic overlap), particularly on the trichordal and tetrachordal
Portillo (2006) has further applied this notion to post-tonal multi-part dictation by exploring approaches to sequencing trichordal and tetrachordal
13) In relatively complex cases like Example 7d, Rae proceeds by parsing a twelve-note chord into three tetrachordal
segments, which he finds to be often types based on various arrangements of pitch class intervals 3, 4, and 5.
From this it is apparent that the system was dominated by structures derivable, like the various Western modes, from a single scale within which each has its own finalis and intermediate prominent and cadence notes, usually at a 4th or a 5th from the finalist Modes utilizing different scale structures occupied a position of lesser importance, while yet others--mostly those that cannot be related to a tetrachordal
base--were relegated to the exotic fringes.
This BACH motive, as he explains, is one of several chromatic tetrachordal
lines that combine to form the aggregate.
Instead of hexachordal, tetrachordal
, or other divisions that only satisfy claims for symmetrical correspondences or for reductions in the number of intervallic cells within the series, the reproductive, combinatorial activity is applied to zones--that is, half of the serial area is, for example, dynamic and progressive, the other half is stagnant, repetitive, and fixed.
In the end, in spite of Kahan's meticulous and thorough research, she is unable to pinpoint the cause behind Polignac's discovery; his adventurous nature combined with a thorough mathematical training and exposure to Greek tetrachordal
theory are cited as the most likely catalysts.
With a tetrachordal
invariance, the two pentatonic scales constitute a pair of maximum-intersecting pentatonic scales.
Thus, the tetrachordal
segments of row P are reflected by the horizontal lines of X1.
As the movement continues to gain vital force, this drone is transformed into the pizzicato foundation of a minimalist passage that gradually unfolds an imitative tetrachordal
cluster and expands to a maestoso conclusion.
This feature explains both why this extended transitive tuple is so large (in comparison with Forte's transitive tuples) and why this is the largest tetrachordal
transitive tuple under [R.
Meanwhile, the tetrachord of Example 10d is the only instance in the third piece of tetrachordal
p-space symmetry, amidst many other inversional pairings surrounding other axes.