Review of Harmony (previously studied)
Here is a basic review of harmony, loosely based around the concept of Harmonic Polarity. Please re-read Chapter 5 of Book 1 for details and musical examples of all these concepts.
I have expressed all of the following in chart form. Here it is. (LINK TO BE ADDED LATER).
- Harmony is based on the triads of Tonic (T), Dominant (D) and Subdominant (S). These are also labelled with Roman numerals as I, V and IV.
- The tendency is for triads to move T S D T. But the reciprocal movement, T D S T, is also possible, especially in blues-influenced popular music.
- T D S have relative counterparts, Tonic Relative (T-R), Dominant Relative (D-R) and Subdominant relative (S-r), which correspond to the vi, iii and ii chords in a major key.
- T-R (vi) often serves as a substitute or modal replacement for Tonic.
- The S-R (ii) quite often serves as a substitute for the Subdominant, especially when it is voiced in first inverstion, which preserves the F in the bass. Both S and Sr typically move to the Dominant triad.
- D-R (iii) does not function in same way, as a substitution for V, since V so strongly moves towards the tonic. Rater, it functions as a kind of prolongation, especially in a sequence of descending fifths (vii-iii-vi-ii-V-I for example).
- D-R (III) is more important when altered and transformed into a major triad. Then it becomes a secondary triad and a direct pointer to T-R (vi). It also then serves to move a passage of music into the relative minor key, either permanently or as a temporary tonicization.
- This is the other important aspect to the secondary or relative triads. T-R, D-R and S-R functions as Tº, Dº an Sº in a minor key. (In this system, the superscript circle º refers to the minor versions of TDS). Thus C, G and F in C major are functionally identical to Am, E and Dm in the relative minor of A minor.
- Minor triads, although functional sounding from the bottom up, are conceptually and philosophically/emotionally built from the top down, as a result of the reciprocal series of tones.
- Just as the overtone series (in C) gives us C E G as the 4-5-6 in the series, so two does the reciprocal series, beginning on high C, give is C Ab F, which is the F minor triad.
- Thus one common and expressive chromatic alteration in the key of C is the minor subdominant, which is in many ways the more natural and expressive of the subdominants, even if it is not a part of the key.
- Another common alteration is when the relative triads, naturally minor
in a major key, as expressed above, are changed in major triads.
- This was mentioned already as regards the E major triad, transforming it into the dominant of the relative minor. In C major, this is expressed as the V of vi. It's altered tone forms the leading tone to the relative minor (G# if we are in the key of C) .Hear in your mind the opening of the jazz standard "Georgia" to capture the movement of I going to the V of vi going to vi.
- Since the supertonic is found by going up to fifths from the tonic, it naturally forms a triad a fifth above the dominant. When this minor triad is made major, it becomes a V of V or a Dominant of the Dominant. It's altered tone forms the leading tone to the dominant (F# if we are in the key of C). Hear the opening of the "Star Spangeled Banner" (by the dawn's early light) to hear the movement from I to V/V to V.
- Finally, you can always precede this chord with its dominant, the V/ii. This is accomplished by turning the realtive tonic, the vi chord, into a major triad, thus creating the leading tone to the ii (C# in the key of C).
- Dissonant seventh chords are created with the addition of the tone
two fifths below a chord's root, which is analogous to the addition of
a tone a minor seventh above the root.
We'll call this the double reciprocal fifth.
- The Tonic triad's natural tendency to move down a fifth to the subdominant is reinforced by adding this tone, which in C is the Bb. This chord, C E G Bb, functioning as a V of IV, pulls the chord even more strongly to IV, as in the opening of Amazing Grace or the opening to Back in the Saddle Again.
- The dominant triad, when receiving the double reciprocal fifth,
has its tedency to move to I powerfully reinforced with the addition
of the F below the tonic. Both point in opposite directions to the
tonic note and the tonic chord.
- This Dominant Seventh Chord, as it's generically called, can be applied to all secondary dominant chords, turning them into secondary dominant sevenths.
- When the seventh (the double reciprocal fifth) is added to a minor triad, we find the minor seventh chord. This commonly occurs on the relative harmonies (ii, iii and vi) in all tonal music, from Bach onwards.
- The leading tone triad is a special case, as it is a triad with a diminished
fifth and thus is very unstable. It naturally resolves upwards to the
tonic triad.
(It is the diminished triad, normally abbreviated viiº).
- This is the chord most often thought of as a variant of the dominant seventh chord, but lacking the root (the G in the key of C).
- This chord my also be given the addition of the extra seventh, making it a diminished seventh chord. The note is taken from the minor version of the subdominant chord (the natural, reciprocal subdominant).
- There remain a few more chromatic chords, the Neapolitan sixth and the family of Augmented Sixth chords, which we will cover in this semester.
- Harmonic progression is defined by root movement. Root movement down a fifth (up a fourth), down a third or up a step are considered primary progressions. Root movement down a fourth (up a fifth), up a third or down a step are considered retrogressive or reciprocal progressions. In tonal classical music, primary progressions are by far the most occuring. In some rock and blues-influenced jazz music, more reciprocal progressions are heard, favoring the movement of IV to I rather than always V to I.
- Modulation is one of the great driving forces of tonal music. By re-establishing new key centers throughout the course of a composition, composers are able to construct complex and dramatic musical structures. Modulation will be studied in this and in the next semester.
- Finally, all theories of harmony must be brought together with an understanding of musical form, which gives structure and expressive implications to harmonic movement. This too will be studied at the end of the semester. We have already had a glimpse of this through our exploration of the 5th Symphony of Beethoven.
IN GENERAL:
Harmony as conceived above and as traditionally explained in theory texts is an abstract concept, based on a notion of blocks of harmonies moving from place to place. In reality, and as we will learn this semester, this harmonies grow out of a linear expression of simulataneous melody. That is the essence of four-part writing, the purpose of the next chapters in this text.
NEXT: 2A Composing with Ground Basses