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.
William of Hirsau fully endorsed the principle of conjunct tetrachords
within the octave as first outlined by Herman of Reichenau, and devoted the four chapters of his Musica following the introduction of cribrum monochordi to a discussion of the necessity for conjunction around D and d (in the process openly criticizing both Boethius and Guido of Arezzo for failing to recognize the double function of these pitches).
In this short passage, three descending (0 1 3 4) tetrachords
from as many different octatonic collections are presented with two other lines in first species counterpoint.
In an attempt to reconcile their findings with contemporary practices of equal temperament, two genera of tetrachords
were identified: diatonic and chromatic (Examples 1 and 2).
They are, of course, not pentatonic at all, as they are formed by addition of tetrachords
to form heptatonic scales.
Under the Sea" asks students to spell the two tetrachords
in major scales.
Roberto Airoldi's "The Intonation of the Greek Tetrachords
according to Aristoxenos" argues that a rigorous mathematical perspective is incommensurate with the empirical Aristoxenian approach to tuning theory.
Unlike Forte, Gilbert does not mention Gershwin's distinctive treatment of Richard Wagner's famous "Tristan" chord, the importance of two ubiquitous overlapping tetrachords
(E-F[sharp]-G-A and A-B-C-D), and the anticipation and climactic uses of E[flat], a note virtually ignored by Gilbert as non-Schenkerian, both as a harmonic force and as melodic apex (the latter on the "-brace-" in "embraceable," m.
Happily, these tetrachords
are conjunct rather than disjunct, for original physical form allows for reproduction, while reformatting includes physical reproduction.
This is a list of all possible trichords, tetrachords
, pentachords, and hexachords.
are here, too, generated by the various procedures given in earlier chapters, some created by Chalmers specifically to fill "gaps in the tetrachordal space" (pp.
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.