XI) Summary of Metric Organization
Our discussion of metric structures leads to an easily understood and heard taxonomy of two meters: duple and triple. Tempo and the number of heard pulse streams will be a significant determinant of notation. Regarding notation: if we recognize that tuplet notation is coequal to the dotted note to show triple meter, we find that a triple metric structure can be notated in several ways.
Concerning the 9/8 type: In the whole population of time signatures used in the 18th to 21th centuries, the triple meter with two triple pulse streams occurs infrequently. We have recognized that a measure of 9/8 can’t be expressed by a single note value, as with duple and triple measures, and also that it is the only metric structure included in the traditional taxonomy (simple and compound versions of duple, triple, and quadruple meters) with two triple streams. In these three respects, 9/8 lies outside our system. However, we can accommodate 9/8 as a component of our organization the same way we accommodate the letter 'y' when reciting our vowels: “a, e, i, o, u, and sometimes y.” Thus our taxonomy is complete—it’s:
duple, triple, and sometimes 9/8. [or the 98 type]