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Here the melody finally reaches the top of the scale, breaking free of its eternal pentachord.
The tag "secundum Guidonem" may have signaled for the Bergamo 21 redactor simply a theory of mode more conventional than Marchetto's, and he here sets up a dialogue between old and new: modal theory based on final and range on the one hand ("Guido"), or on species of pentachord and tetrachord on the other (Marchetto).
His use of pentatonicism is unabashedly obvious at times, yet he avoids the disadvantage of a monotonic effect through the ample use of minimum and maximum-intersecting pentachord pairs.
The final 'progression' in the work is from an octatonic pentachord, C, E[flat], E, G, B[flat] (6-32, from the same collection as 4-17 in bar 42), to a D major scale, a successive rather than simultaneous presentation of the movement's octatonic and diatonic materials.
Example 18 displays the results of cluster analysis of the pentachord classes under three other similarity relations, IcVSIM (Isaacson 1990), SATSIM (Buchler 1997), and REL (Lewin 1980).
He describes relations between several forms of the pentachord (01236) in the work but then notes the inability of conventional analytic tools to highlight the structural relationships that he finds most meaningful.
As shown in Example 22, Stravinsky's row begins with an ordered pentachord from the Boulez row, including the highly favored F-G[MUSICAL NOTES NOT REPRODUCIBLE IN ASCII]dyad.
5] These two writers disagree principally over the question of whether the piece is constructed from a chromatic tetrachord or an (0,1,2,3,6) pentachord, and von Blumroder's analysis demonstrates conclusively that Maconie is correct on this point, even if on other matters he falls short: "Robin Maconie has indeed deciphered the three tetrachordal groups of the first metrical section, but not, however, their subsequent modification, on account of which he describes the notes C and D-flat as 'free radicals' and the pitch composition from measure 8 onward as 'difficult to follow'" (page 126).
The left-over pentachord at the end is used to fill out row one of column zero; in this way the twelve-link chain is turned into a two-row, six-column matrix.
The pitch materials of paragraph 2 are all pentachords or tetrachords, and the interval contents of all the pentachords are identical, as are those of the hexachords.
Similarly, Example 14b is more readily classified as recurring chromatic pentachords than as five interlaced chains of major sixths.
This is a list of all possible trichords, tetrachords, pentachords, and hexachords.
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