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These principles, which are applied with remarkable consistency, may be easier to grasp from Table 9.1. It shows the formulae according to which notation symbols are chosen for the notes of any tetra-chord. Find in the left-hand column the scale degree corresponding to the lowest note of the tetrachord. In the right-hand columns the figures 1, 2, 3, 4 refer to successive triads of symbols, reading up the repertory on p. 256. The bare figure denotes the base note of the triad, the 'natural', and a/b denote the first and second sharps. |
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TABLE 9.1.
Formulae for choosing notation symbols of tetrachords |
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For each of the fifteen keys of post-Aristoxenian theory a selection of note-symbols was drawn up according to these formulae, one for each degree of the Unmodulating System. They are all set out in Fig. 9.2, using the identification numbers of the chart facing it (Fig. 9.1). The 'railway map' shows the forked structure of the Unmodulating System (cf. p. 222), triplicated at intervals of a fourth. The central line in heavy black represents the basic Dorian, Ionian, Phrygian, Aeolian, or Lydian, while the higher and lower ones represent respectively the associated Hyper- and Hypo- keys, which serve to provide a choice between conjunct and disjunct tetrachords throughout the middle register. Mese in each key is to be found at the point where the line forks, and the other standing notes of the system are shown as 'principal stations'. The note-series for the various keys are listed in five columns, each of which includes the Hyper- and Hypo- key together with the central one. The layout matches that of the diagram, with a double set of numbers where there is a |
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