Tonality is a natural outgrowth of the transition from the intervallic concepts of mode to a harmonic concept. Each Church mode was distinguished by a specific order of whole and half steps which would then generate typical melodic patterns. By and large, the traditional formation of triads has its roots in the division of the harmonic series (2:1, 3:2, 4:3, etc.). In actuality, the fifth generated by 3:2 would be slightly different from the equal-temperament fifth of today's tonality.
Gioseffo Zarlino, whose theoretical writings come from the 16th century, gives a complete explanation of the modes and intervals. In addition, there is some reference to the sounding of intervals above one another, implying the beginnings of harmonic theory. However, it is really Rameau in his 1720 Treatise on Harmony
that formulates the notion of the invertibility of triads and their common identity and function, based on a concept of fundamental bass (root of the chord), as opposed to the real bass note.
We can imagine a hierarchy of scale degrees and functions in which each scale degree in the major (or minor) mode has a characteristic triad associated with it. Then, consequently, that triad is a template for a specific kind of harmonic function. For example, V is a major triad and it describes the traditional authentic cadence which may go to I, the tonic. V-I is the template, but that root motion (up a fourth or down a fifth) may be replicated on any scale degree, so that a cadence can be made to any note, with the appropriate accidentals adjusting the quality (major, minor, diminished) of the triads. This, ii in major mode may be a minor triad, but if its third becomes major and it proceeds to V, it is no longer ii but V of V, replicating the V-I
template on that fifth scale degree.
Harmonic motion can be characterized by three general types: substtution, pre-cadential motion, and cadential motion. Any chord in the tonal matrix will describe one of these three types of motion when proceeding to another chord. Likewise, the chord itself may have an identity based on its position in that matrix.
I characterizes the tonic and is a tonal resting place. iii and vi may substitute for the tonic and have a similar (although weaker) function.
V characterizes the dominant triad and is a cadential generator. vii may substitute for V and may have a similar (but more ambiguous) function.
IV characterizes the subdominant triad and is a pre-cadential generator: it prepares the V-I cadence. ii has a similar function and may substitute for IV.
In the selection of the various elements of the matrix the composer is able to produce an almost endless variety of contrast using the two concepts. For example: if in stead of going from V-I the composer substitutes vi for I (creating what is called a "deceptive cadence," V-vi) the cadential function is fulfilled, but the sense of complete rest implied by the arrival of the tonic is withheld.
The concept of relative strength and the implied ambiguity of harmonic progressions is also related to three other elements: the inversion of the triad(s), the spacing of that harmony, and the doubling (which note is reinforced). Using the harmonic series as a guide, any triad that has intervals above the bass that are low down on the harmonic series (like the fifth or major third) are going to be stronger that those that contain intervals that are higher or not present at all (like the sixth). Thus the first inversion of the tonic triad (sixth and third above bass) is weaker that the root position (primary note on the bottom), which contains a fifth and major third. Subtle effects can be achieved by varying spacing: the distance of the three upper voices relative to each other. In closed spacing, every note of the upper three voices is the closest it can be with no space for an inserted chord tone.k In open spacing there is one open space between each note, and in mixed spacing there is a mixture of elements. This procedure correlates the harmony with the appropriate note in the melody. For example: a C major triad in closed spacing may have C,E,G as the melody, but the other two notes will follow below in close order (from the top: C,G,E, or G, E, C, or E, C, G). The choice of spacing is intertwined with doubling as can be seen from the previous examples. CEG and other closed spacing triads above a C bass note have a doubling of the root (C) and would be the strongest; while, mixed and open spacings of GEG or EGE above a C bass note would be weaker.
It is imperative to understand the concept of weakness versus strength in the tonal context: strength implies a greater tendency to reinforce the harmonic function that is present, while weakness implies a more ambiguous tendency. This technique allows the composer flexibility in the global control of the tonal matrix. For example, if Bach is creating a harmonized chorale that has five phrases, he may hold off using strong cadences until the very end so that part of the chorale has greater finality than previous phrases.
What may seem to be a very straightforward chorale harmonization may contain untold complexities because of the intersection of the various parameters and function described in general above. When considerations of modal borrowing (taking a chord from the parallel minor) and the use of non-chord tones (like suspension dissonance or passing tones) are brought into play, the levels of subtlety become seemingly endless. In future chapters we will explore al the functions of the major and minor modes and deal with the enlargement of harmonic functions to include umbrella concepts of temporary tonicization and modulation. If a harmonic function can be defined by the motion of one chord to another, then attaching more than one chord to the sequence would further strengthen the function attached to that scale degree; and, if the sequence of chords is long enough, the whole tonal matrix may be shifted to another scale degree (modulation: a new note becomes tonic).
This introduction to the hierarchy of tonality should generate a healthy respect for the process of harmonization. Like nature, in which the simplest plant may be appreciated by anyone, but it biological secrets may take years of study, the world of music may have a surface familiarity that is betrayed by underlying complexities.