In this article I wish to explore the music theory subject of negative harmony. It is not a widely discussed topic, but it does have practical applications and in learning about one uncovers a great deal about harmony. The structure of the article will be as follows.
Set forth a melody.
Harmonize that melody, using basic rules of counterpoint.
Harmonize using negative equivalent.
Compose using negative harmony.
1. Set forth Melody
Let’s note that we are in the key of C major, when we look near the treble clef, we see no accidental markings, so if we do in fact come across any note that is non-diatonic1 it will need to be marked with an accidental (# or b). 4/4 is the time signature which is apparent by measure 1; there are simply 4 quarter notes in a bar.
Melodies follow a progression of tension and release, and our minds, without active effort pick up on which notes have the sense of rest and which notes are tense (keys colors)2. Each mode, (in our case we are in A aeolian) has its own unique sequence of notes that pattern varying levels of tension and release. If you are familiar with solfege, you’ll understand by singing scales beginning from different syllables (do, re, mi, etc.) the scale takes on a completely different sensation.
Notice how the first and last note are A, when you listened to the melody at which points did you feel the sense of rest or resolution, and, at which points did you feel the melody was at is most unstable? Most people would say the resolution came at the end, for this was the point of rest. In this particular melody, to me, the tension seemed to be mounting all the way up until the end.
2. Harmonize Melody
Now it is time to harmonize this melody. But before we do that, we need to know a few rules of counterpoint3.
From one perfect consonance to another perfect consonance, one must proceed in contrary or oblique motion.
From a perfect consonance to an imperfect consonance, one may proceed in any of the three motions (direct, contrary, and oblique).
From an imperfect consonance to a perfect consonance, one must proceed in contrary or oblique motion.
From one imperfect consonance to another imperfect consonance on may proceed in any of the three motions.
To help us stay on track, let’s define a few more terms. Two notes are in perfect consonance when they are unison, perfect fourth and fifth, or an octave apart. An imperfect consonance is major/minor sixths, and major/minor thirds. Every other interval can be classified as a dissonance4. For our sake, we are only going to deal with perfect and imperfect consonances5.
Next thing to understand is motion. The four rules dictate that when we move from either a perfect or imperfect consonance to a perfect or imperfect consonance, we must use a specified motion. Motion is the direction notes take in a melody, either up or down or unchanged. The three types of motion are direct, contrary, and oblique. Direct motion is when the two notes move equilaterally, that is when one moves up, the other moves up the same rate. Contrary motion is the opposite of direct motion, when one note moves up, the other has to move down, or vice versa. Oblique motion is when one note stays in the same spot and the other note moves either up or down.
Alright, let’s take a look at how this melody was harmonized. Remember that the initial melody is still preserved, all we have done has added another voice6. In the first bar, we see that the new voice is playing 4 quarter notes at E. Can you recall what type of motion has one voice unchanging while the other voice is free to move either up or down? That would be oblique motion. Now, look at what type of consonances are formed and how they follow the four rules of first species counterpoint. Well chord #1 consists of E and A, which makes up a perfect 4th, chord #2 is E and B which is a perfect 5th. The first rule states that moving from a perfect consonance to another perfect consonance one must use either contrary or oblique motion. This checks out because the lower voice remains motionless in both chords as the upper voice ascends. Let us then look at chord #2 to #3. This is a perfect fifth to a major sixth, or a perfect consonance to an imperfect consonance. Rule two states that when moving from a perfect to imperfect consonance we are free to use any of the three motions. It looks like oblique motion was used again. Take a look at the rest of the chords, first identify if they are perfect or imperfect, then consult the four rules of counterpoint. Harmonizing a melody using counterpoint requires one to pay attention to not only the motion used, whether it be direct, contrary, or oblique, and also the type of intervals formed whether they be perfect or imperfect.
Negative Harmony
The next step in our little journey is to convert the harmony to its negative version. But once again before we do that lets look at some of the prerequisite knowledge. Earlier it was mentioned that melody and harmony is a sequence of notes traveling through points of tension and resolution. We also know that in any given key the tonic will invariably produce a sense of resolution since our minds adapt that to be the point in which all other notes gravitate towards7.
Negative harmony is the theory that every note in a key has a note of equal tension to the tonic but of opposite quality. The best way to explain this is with the circle of fifths.
At the top of the circle of fifths we see our key center C. The circle of fifths lets us visualize moving towards the key center from two different directions. From the right side (counterclockwise), the distance from note to note is a fifth apart. This movement of fifths is known as a perfect cadence. From the left side (clockwise), the distance is a fourth part. This is known as a plagal cadence. Perfect cadences have a brighter more confident sound to them, and plagal cadences seem more timid and less resolute.
Take a listen to chord progression cadences approaching the key center from the right and left side of the circle of fifths and hear the different qualities.
Next step to convert a melody to its negative version is to draw a line splitting the circle of fifths between the tonic (C) and dominant (G) fifth degree.
This line will be the axis of reflection that we will use to convert a note to the negative version of itself. For instance, C would become G, F would become D, Bb is now D.
This harmony is the negative version of the one we played earlier. By using the circle of fifths, we translated each note to the negative version of itself. The perfect fourth that we began with (chord #1); E and A, translated to Eb and Bb, a perfect 5th. Chord #2 went from a perfect fifth; E and B, to Eb and Ab, a perfect 4th. The major sixth, E and C, turned into minor third chord, Eb and G. I think it’s apparent that the harmony now sounds darker more ominous than the original one.
The key point of negative harmony is that we are approaching the key center from a different direction, and as a result the chord and note qualities changed.
A cheat sheet for flipping chords to their negative version is a helpful time-saver.
I - i
V7 - iv6
IV - v
ii7 - bVII6
vi - bIII
Chord labeling8
Composition
Now I thought I would put together a little composition that plays through this cheat sheet featuring each chords negative version within a bar (i.e. in each bar the initial chord and then negative version will play). I’ve labeled each chord above so it should be easy to follow. Overtop I have created a flute melody that will consist of notes within the given chord. Cello is providing the bass, and a drum beat to help us keep time.
I hope this article was enjoyable and clear to read, the topic of negative harmony is no doubt complicated so if you have any questions please don’t hesitate to comment. If you did enjoyed this, please consider subscribing for more content. Thank you!
Non-Diatonic refers to any note or chord that does not belong the music’s key. Non-diatonic notes can be thought of as chromatic notes, as there are 8 diatonic notes to a key but a total of 12 chromatic notes in music.
Key’s Color refers to the specific sensation a note assumes relative to the tonic. These sensations or qualities have descriptors like perfect, imperfect, major, minor, dissonant, etc.
The Study of Counterpoint by Johann Joseph Fux, pg 21-2
Major/minor second, diminished fifth, tritone, and major/minor seventh are dissonant.
First species of counterpoint deals only with perfect and imperfect consonances.
Voice refers to a musical line (it does not have to be a voice necessarily). In 4 part harmony or SATB, each section (soprano, alto, tenor, and bass) has its own range and its own melody line.
In our case in the key of C major, the melody begins on A, which is the sixth degree of the key. Aeolian is the relative minor to Ionian. In the melody we hear the resolution point on the note A which gives the melody a ‘minor’ feel.
Upper-case letters symbolize major chords, as lower-case letters symbolize minor chords. Chords are identified using roman numerals. Any number that follows a roman numeral (IV6) is a scale degree that must be added to the chord (F-A-C-D), an accidental before chord number adjusts the chord just as a sharp or flat would, (IVb6) F-A-C-Db.
Negative Harmony
This is a great explanation of negative harmony, thank you!