It is a motif that can be divided into two parts, A and B, and each of these parts can be included within the range of a descending tetrachord
, the second sequence being transposed one step down.
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).
"The Descending Tetrachord
: An Emblem of Lament." The Musical Quarterly 65: 346-59.
At about this time, Zaragoza continues, Falco reached Madrid with his tetrachord
and informed the Jesuit that it had been used very successfully the previous year (1674) in Valencia to divide the octave into 12 equal parts.
I like to explain the intervals by using the tetrachord
system (Figure 1).
164-166), Schneider describes the material as a "stormy, octatonically inflected G minor" in the orchestra, while the piano "pounds out dissonant tone clusters." But G minor simply doesn't exist here (a G-A-B[??]-C tetrachord
is embedded in the octatonic scale being used, but D, the dominant of G, never appears); the orchestral writing is purely octatonic.
But the primary function of Carter's twelve-note chords is to serve, in Mead's words, "as a background grid against which collections of smaller cardinality are projected." (8) Jonathan Bernard relates this function to the composer's "deliberately global" use of smaller pitch sets--for instance, the systematic inclusion of all possible trichord types in the Piano Concerto, all possible tetrachord
types in String Quartet No.
The chromatic tetrachord
contains the essence of both major and minor tonalities in any particular key (it is a combination of 'melodic-' and 'harmonic-minor'), and its outer notes emphasize the tonic and dominant of the key: the [flat]VI-V movement is the ideal preparation for a dominant pedal, and is often used to set up the overall progression [flat]VI-V-I.
In two-thirds of these eight-bar periods the fourbar bass line ostinato consists of the descending tetrachord
G-F-E-D, first plain, then varied in harmony, melody, rhythm and register.
The word (one unconvertible word in Greek Character) appears the papyrus remnants provide little intelligible context for it we can be confident that musical technicalities are still in play, in view of the indubitable reference to a tetrachord
in the next line (the surviving letters are (one unconvertible word in Gre
The task, however, is simplified by Caplin's choice of a topic linked to a fixed harmonic schema (the descending tetrachord
), which therefore manifests intrinsic formal functionality.
A major tetrachord
is one symmetric half of a major scale, either "do re mi fa" or "so la ti do." This pattern may be hummed or sung on the vowel sequences outlined in exercise A (Figure 1b).