For example, the last two quavers of the Piano 1 phrase which concludes at the beginning of bar 14 reiterate dyads F[sharp], G and C, C[sharp] from the hexatonic tetrachords
preceding them in a vertical alignment that produces 4--9: [0,1,6,7], an octatonic tetrachord
Similarly, it would have been helpful for Simms to clarify his approach to pitch, such as in the presentation of the "triadic tetrachords
If we combine all the notes of both delayed symmetrical pairings ([D.sub.4]-[B.sub.5] and [E[flat].sub.6]-[B[flat].sub.3]) we form [TE23], another instance of (0145)--capable of surrounding the same axis as the  in measure 1 because the tetrachords
are [T.sub.6] trans poses of each other.
Since it occurs where the larger intervals of the series begin, it structurally demarcates the intervallic shift and bisects the series, producing two tetrachords
linked by a common pitch with a similar but not identical intervallic structure.
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.
 The sketches make clear what is not readily apparent from the score: the seventeen-tone row is constructed as a string of chromatic tetrachords
, each ordered such that its interval-class succession is [less than]2-1-2[greater than].
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.
Because of the adjustments, not only are there foreign pitch classes (an exact mirror around E[flat] would have yielded these also) but the ascending and descending tetrachords
4-2 (0124) and 4-3 (0134) in the tenor are foreign interval collections with respect to the diatonic collection.
Happily, these tetrachords
are conjunct rather than disjunct, for original physical form allows for reproduction, while reformatting includes physical reproduction.
For example, to complete his second exercise, "with C and F[sharp] sustaining, score seven different all-interval tetrachords
Even the simplest, pitch-class against pitch-class ("first species") statement of, for example, inversionally related lines yields, for instance, tetrachords
whose constituent dyads refer directly to the series and either to another dyad in the series of to one that is not a member of the series, or to a dyad of another so-derived tetrachord
which is, therefore, itself not a dyadic segment of the series.
With the final chapter, we come to the heart of Chalmers's treatise, a 40-page, annotated catalogue of 723 tetrachords
, systematically arranged, that the author believes exhausts the practical, musical possibilities of tetrachordal division.