The beginnings and development of a New Zealand music: The life ...

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tonic of tone, semi tone , tone, tone, tone, semitone, and tone. Thus,
although the scale notes employed have remained the same, the change of
tonic has effected a change in property and function of each of these
scale notes. The tonic chord and the dominant chord, for example, are
now minor triads, rather than major triads as before. The subdominant
chord, though, remains as a major triad. Because of the change in
function for these scale notes, and because the tonic of the scale is
now D instead of C, the scale becomes D dorianrather than C major.
The converse of such a shift in the ordinal index of modality is
what Vincent calls a shift in the lateral index of modality. This occurs
when a particular set of scale notes is exchanged for a new set of scale
notes, whilst the tonic for both sets remains the same. C major becomes
C dorian when the third and seventh degrees of the scale are lowered
(thus altering the characteristic pattern of ordering of the scale notes
in interval steps away from the tonic).
According to Vincent, a shift in the lateral index of modality
represents an interchange of mode, and a shift in the ordinal index of
modality represents a modulation of the mode. What is meant by a change
of key (or modulation) in the traditional tonal sense, occurs with a
shift in both the ordinal and lateral indices of modality. (The
exceptions to this are, of course, a change of key to the relative major
or minor, or to the tonic major or minor. In the former of these, in
Vincent's terms, only a shift in the ordinal index has occurred, whilst
in the latter, only a shift in the lateral index has occurred.)
Vincent's analytical model helps explain the tonal ambiguity of
such passages as the introduction to Aotearoa Overture. Three ordinal
indices (sets of scale notes) are employed in the twenty-four bars that
comprise this introduction. These are that based on B-flat major (two
flats) bars 1-9; that based on C major (no flats or sharps) bars 10-20;
and that based on G major (one sharp) bars 21-4.
Throughout -this introduction, Lilburn makes frequent use of pedal
points. Where these are scored on degrees of the scale other than the
tonic, a change of tonic (or centre of gravity for the scale) occurs and
a shift in the ordinal index of modality is undertaken.
Thus, whilst bars 1-4 are based on B-flat major, bars 5-9 (by
virtue of the persistent and prolonged articulation of the note C in the
bass-line) are based on Cdorian.
A change of tonic to C does not coincide in bar 10 with the
cancellation of the two flats used in the opening nine bars. The tonic