One of the most difficult issues to tackle in harmonic analysis is determining which pitches are functional.
Now that we understand how circle-of-fifths progressions within a key create a basic harmonic “outline”, we can use that pattern to begin analyzing harmony. The framework of these progressions can be used to organize any piece of music in this tradition and allows us to ask the two fundamental questions of all harmonic analysis:
Regardless of the complexity or era of a composition, if a theorist can answer these questions about a piece, they can analyze the qualities that define that style of composition.
Look at the following chorale. Provide an analysis of this music by analyzing each chord and writing a Roman numeral and an inversion figure below every new harmony. As you go through this process, keep track of the questions that you solve as well as what makes this difficult. Start by looking at the big picture, and do not get bogged down in trying to figure out every pitch and chord at first glance. If you get stuck, keep moving and return to the difficult sections after you have a feel for the piece as a whole. This is a great opportunity to begin with leadsheet notation, and then return to add Roman numerals once you have some context.
Before you can even begin to analyze the chords within a piece, you need to figure out a number of major concepts.
As you answered each of these questions, you began understanding how harmony functions. Even without much guidance, you can use your knowledge of musical fundamentals – intervals, chords, melodic lines, Roman numeral labeling, etc. – to create a sketch of the harmonic underpinnings of this chorale.
We use chorales to begin studying analysis because of the vertical nature of the writing. Every chord in this composition is aligned to where it can be easily parsed by sight, and almost every tone is functional. In the final measure of the piece, did every note belong to the chord? If not, how did you decide which notes did not?
Analyze the following chorale-style progression. Pay particular attention to the how your decision process as you decide how analyze the third beat. Are there any non-chord tones there? If you are struggling to determine whether it belongs or not, try referring to your the harmonic outline that you built in the previous topic Unit 7a. Does the voice-leading–i.e. how each chordal member resolves–work with the rules that you established in Unit 7a if you do not have a non-chord tone?
There is one more type of cadence classification that is commonly used, although this is more of a sub-category of a half-cadence: the phrygian half-cadence. It only occurs in minor, and the approach to the half-cadence is the defining feature. Look at the following cadence and study the final two chords.
Students often confuse harmonic analysis with identifying each of the harmonies. While finding chords is a part of harmonic analysis, the actual goal of harmonic analysis is to explain how the listener hears the music. To do this, we must figure out which pitches are functional and which pitches are embellishments. The essential pitches of any harmony are those that if removed, would noticeably alter the way the listener hears the harmony.
To move toward this goal, music theorists use a number of tools, most of which are designed to look at contextual clues and draw conclusions based on their general knowledge. We created one of these tools in Unit 7a with the diatonic harmonic flowchart.
| (unnamed) | (unnamed) | pre-dominant | dominant | tonic |
|---|---|---|---|---|
| iii | vi | ii | V | I |
| IV | viio |
By employing the progressions from this flowchart, a theorist can look at a given harmony and decide which pitches support a harmonic progression that is likely to be heard by a listener. For an example of how this would work, refer to the third example under Examples 7a.
With nothing more than this, the students attempted a basic harmonic analysis of The Old Hundredth, a classic hymn with a standard SATB harmonization. I asked them to provide not only provide the chords in both leadsheet notation and Roman numerals, but also to take notes on questions that arose as they workeed through this process. They came up with three primary questions:
The first question was obvious to most, but difficult to tackle. How often does the harmony change? The rate at which harmonies change is called harmonic rhythm. This is often a chicken-or-the-egg question: you need to know how often the chord changes to determine which pitches to include in the chord, but you also need to look at which pitches create chords to figure out how often the chord changes. Chorales are an easy place to start, because most often, they change chords every quarter note; this creates an easy-to-see visual cue as each chord is stacked vertically and mostly homorhythmic. For more complicated textures, studying melodic patterns and bass-lines is often enough to provide enough context for an educated guess. Bass-lines in particular will often sustain pitches and/or outline chords until the harmony changes, and this gives a clear indicator of probable harmonic rhythm. This becomes much easier as the student gains experience.
Understanding the question of which pitches are functional means determining which pitches belong to the chord (chord tones) and which pitches are decoration for these chord tones. To this point, we have only looked at passing tones, neighbor tones, and suspensions. All of these require stepwise movement only, so any skip in our beginning examples will be a chordal skip. We will expand this as we begin looking at all of the classes of NCTs.
Much like determining the harmonic rhythm, finding NCTs can be difficult because it requires working through all possible combinations of the pitches within a given harmony and then choosing the most likely combination. Even if you know that the harmony includes only two beats, if there are many pitches within those two beats, it can be difficult to sort through all the possible combinations. Fortunately, the same strategies that work for looking at harmonic rhythm work for determining NCTs. Looking at melodic patterns and bass-lines is a great start, but it is also helpful to be aware of whether a note occurs in a strong or weak position. It is unusual for the functional tones to occur only on offbeats, as the ear is drawn to pitches when the occur on the beat.
Even for one experienced in finding patterns within the music, this still sometimes requires trial-and-error. For beginning students, I suggested that they try copying the pitches to another staff (or lightly next to the chord if there is room,) and begin rearranging the pitches to see what triads and seventh chords are even possible. Usually this is enough to limit the possibilities to one or two chords. When it is not, they should refer to their harmonic flowchart to see if there is some context that could provide a probable chord.
To nontate non-chord tones, you should place parentheses around the note head of each non-chord tone. You must also label the NCT with its abbreviation. Currently, we only have three possible NCTs:
The students had an excellent question regarding non-chord tones.
Regardless of whether you include the pitch as functional, the NCTs must always match the Roman numeral. In this scenario, if you choose to include the chordal seventh in your harmony, you only need to write the proper Roman numeral and inversion figure. If, however, you decide that the chordal seventh is just a passing tone, you must label it as a non-chord tone and write only V for the Roman numeral.
This was a brief discussion. Refer to the voicing guidelines under Unit 6b for likely doublings and omissions in four-part writing.