David von Augsburg's treatise De exterioris et interioris hominis compositions, discussed in the fourth chapter, contains a section with a primer on Guido d'Arezzo's gamut and the associated syllables of the three hexachords
And it's not too difficult to see his frequent use of tetrachords containing all intervals and hexachords
containing all triads--and most recently, twelve-note chords--repeated without transposition and in key positions as an acknowledgment of tonality.
3) The all-combinatorial hexachords
are six hexachords
that are capable of forming an aggregate with any of its transposed forms: prime, retrograde, inversion, and retrograde inversion.
48, Divina is further dignified through the acquisition of an exordium that not only serves as an introduction but treats letters and hexachords
(arrangements of the syllables ut-re-mi-fa- sol-la) and thus gives information prerequisite to an understanding of Divina.
After 1950, Finney's works incorporated a serial technique involving symmetrical hexachords
Example 3a shows measures 27-9 of Form, the transition from the original pair of 6-3/6-36 hexachords
to their transpositions by [T.
Additionally, the pitch collections are meticulously, if not serially, arranged: six pitch collections (pentachords with a repeated pitch) or hexachords
occur every five bars (in bars 1, 6, 11, 16 and 21 - the first bar of each staff).
Cicada, cricket, we were drilled by insect hexachords
, the quarry garbled and transumed whatever sentence we passed upon the dark, upon the rushes that swayed in the far shallows, and the throb - monotonous, incessant - that was the quarry's breathing: who needed words?
The second book briefly discusses the hexachords
arid the third addresses the ratios of the intervals via the monochord.
And while Wolpe uses the technique of a continuous development of material through the use of highly contrapuntal textures and the alternation of the two hexachords
that freely circulate and gradually interface and merge with one another, Shapey employs a more traditional format, variation form.
The ut-fa-re motif appears as C-G-D in the natural hexachord
, and is also transposed into the hard and soft hexachords
, as G-C-A and F-B [flat]-G respectively, maintaining the interval structure of ascending 4th-descending minor 3rd.
He argues that a diminished seventh produced by the framing tritones of the row's two hexachords
acts as a deep, or background, symmetrical structure against which the row forms unfold.