Documentary evidence exists in the famous postcard Carter wrote to a Boston music critic; both tetrachords
are notated, their "all-interval" properties demonstrated, and Carter states that both tetrachords
were used in both the First and Second Quartets.
Two aspects in particular set the style of De musica apart from other treatises: his long digression and commentary on part of Guido of Arezzo's influential treatise Micrologus, and his discussion of a diagram that purported to show the relationship between the tetrachords
and the modes in conjunction with the monochord.
Combinations of these tetrachords
, either in conjunction or disjunction, resulted in the formulation of a system of scales or tropoi, which can be purely diatonic, purely chromatic or mixed (Example 3) (6)
A more favorable learning sequence, preceding traditional fingering, hands-together, scales might be: tetrachord
scales, hands-alone scales and, finally, contrary motion for mirror image scales such as E major and E-flat major.
The alto line in question is simply moving in parallel thirds above an ascending Fmajor tetrachord
in the second violin part.
The interpolation of the "Dies irae" takes the form of a fifty-six-measure fortissimo mensuration canon for the full ensemble with patterned entrances on each step of a descending A-E tetrachord
Nonetheless, careful reading of Kurtzman's analyses reveals sound reasons for his reliance on older modal traditions, with their emphasis on the range or ambitus of melodies, the positions of the pentachord and tetrachord
in relation to the finalis, and the melodic emphasis on the reciting tone.
The best-known characteristic is the opening tear motive: the descending tetrachord
, "a standard emblem of grief" (p.
7-10, for example) recalls the end of Fantasia II, in which the opening motif of a descending fourth is transmuted in the course of the work into a slow descending chromatic tetrachord
that brings the work to a magisterial conclusion.
I have but one quibble with the glossary: the synemmenon tetrachord
would be better described as being conjunct with the meson tetrachord
- its lowest pitch coinciding with the highest of the meson - than as being situated a half step above it [pp.
The quartet opens with a held chromatic tetrachord
, C[sharp]-D-D[sharp]-E, based on an axis of symmetry, D-D[sharp].
The major and melodic minor scales are printed as whole notes, eighth and sixteenth notes, tetrachords
, modes and in thirds.