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After we have analyzed the simpler examples, this page discusses the various complications we can encounter in tonality analysis.
A musical piece does not necessarily begin with its theme. Here is the example of F. Chopin's Ballade n° 1:
The very beginning of the ballade introduces the key of A flat major, until we encounter an F sharp. Chopin insists on that F sharp by extending it with a rest. He could make us believe that our tonal compass is going to rotate towards D flat major, but further notes prove that that extraneous note is an F sharp (and not a G flat, indeed) and that our compass is rotating towards G minor, the key of the theme further on.
At first, in order to simplify, we told that musical interval extents were meaningless in perceiving a tonality. That approximation is insufficient to take ascending or descending chromatic scales into account. To constitute a true chromatic progression, intervals have to be semitones (half steps).
The same is true in the specific case of the leading (sensible) note. The leading note and the tonic must constitute a chromatic progression and form an interval of a minor second.
In order to analyze chromatic progressions or leading → tonic relationships, the cycle of fifths is no longer enough. Analyzing the note pitches and the intervals they form is essential.
Scores (especially older scores) often contain ornaments (for instance, trill, mordent, appoggiatura, acciaccatura, gruppetto, etc.) that complicate tonality analysis.
An ornament is a series of short notes that render the trailing note of the series more significant. As is the case of chromatism and leading notes, all notes in the series form intervals of a (major or minor) second. Here too, the minor second somehow plays the role of a leading note by emphasizing the tonal importance of the upper note.
Previously, the theme of J. S. Bach's toccata in D minor and that of F. Schubert's serenata have shown how the mordent (or its inverse) emphasize the role of certain notes.
For the purpose of tonality analysis, after identifiying certain ornaments, we can disregard them and only retain the trailing note of the series that constitutes the ornament. When they make part of an ornament, short notes take less tonal importance, indeed. Conversely, discarding all short notes would lead to incorrect tonality analysis.
At first, in order to simplify, we told that the order in which we hear the notes is meaningless in perceiving a tonality. That approximation is insufficient for a precise tonality analysis.
In the theme of G Mahler's adagietto, the initial notes set forth a perfect cadence. That is true only because we hear the notes in the order of the C → F triad. The limits of the triad emphasize the impression of a perfect cadence.
Let us transpose that triad two whole tones (whole steps) above and compare it with the theme of the second movement (adagio sostenuto) of S. Rachmaninov's second piano concerto:
Here is the theme of the second movement (adagio sostenuto) of S. Rachmaninov's second concerto:
and here is the transposed triad B → E, from the beginning of the theme of G Mahler's adagietto:
Except for an octave, both examples contain the same notes, but the notes are presented in a quite different order. In his adagio sostenuto, Rachmaninov insists on G sharp, and the limits of the phrase emphasize the impression of an interval between E (lower note) and G sharp (thus emphasized), which implies a tonic chord of E major (or maybe C sharp minor, as long as further analyzing the theme has not enabled us to choose between the two relative keys).
Heard in a different order, the same notes do not lead to the same tonality.
Major and minor chords, or even chords of a (major or minor) third, are often enough to state a key, but for that they must be emphasized, for instance at the beginning or the end of a phrase. When they are merged into the context of a larger phrase, they lose their tonal importance and can therefore become misleading.
In a major scale, there are three degree combinations that hide minor chords. These are the [II, IV, VI], [III, V, VII] and [III, VI, I] combinations. Here is the example of C major (click to listen):
In a minor scale, considering certain degrees varying, there are four degree combinations that hide major chords. These are the [III, V, VII] [IV, VI, I], [V, VII, II] and [VI, I, III] combinations. Here is the example of C minor (click to listen):
In both previous examples, only chords emphasized at the start or end of a phrase can possibly state a key.
As for chords or intervals of a (major or minor) third, where a dominant is missing, they are yet more ambiguous. Here are two examples of intervals of major and minor thirds:
In the first example, successive intervals state a C major chord, confirmed by the trailing C. In the second example, the same intervals, presented in the reverse order, state a C minor chord. In both examples, the pitches of the upper note (G) and lower note (C) delimit the perfect cadence and hence state the key of C. The major or minor mode then depends upon the mediant.
Here is another example, excerpted from the first movement (allegro con brio) of L. v. Beethoven's 5th symphony, of the ambiguity inherent in major and minor thirds:
The first five bars do not precisely state the key. The major and minor thirds are ambiguous. By not accompanying his theme with any harmony that could help us solve the ambiguity, Beethoven keep us in suspense. We have to wait for a few more bars before hearing the arpeggio of C minor, in sustained notes. The trailing part of the theme enforces our analysis.
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Jean-Pierre Vial January 2021 |
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