Cadences and Negative Harmony

     This is a technique that makes use of existing material, be it from chords or melodies. As you will see, it is not a simple inversion or mirroring technique because the harmonic functionality in the chord progression will be maintained when “flipped”. In other words, it will still make sense. To demonstrate this I will be using cadences examples, a device used in the end of chord progressions to confirm tonality.

     The authentic cadence resolves to the tonic with a descending perfect fifth movement (or ascending perfect fourth – see interval complementation), and it is quite common to hear music using chord progressions that move in a perfect fifths cycle:

vi – ii – V – I chord progression in C

     Or even in a chain of dominant chords:

Chain of dominant chords with a C major target chord – A⁷ – D⁷ – G⁷ – C

     As we saw in the harmonic candeces post, there is also a plagal cadence that consists in the movement of the subdominant chord to the tonic – see harmonic cadences. Compared with the authentic cadence movement, the plagal cadence sounds gentler, and less intense because it has less tensions when resolving to the tonic.

     In the circle of fifths represented below, you can see that the chord progression used in the previous example moves in a descending fifths cycle – from A to C:

     The idea behind negative harmony is that you can move towards the tonic but instead of doing it in perfect fifths, you can do it in descending perfect fourths, just like the plagal cadence – from Bb to C; and still maintain the functional quality of the chord progression towards the tonic (in this case).

     In terms of functional harmony, we would be converting a progression by fifths into a “negative” progression by fourths (a chain of plagal cadences) and still maintain the purpose of cadences, which is to reinforce or confirm the tonic or tonality.

     That said, in negative harmony you can have a “positive” chord, chord progression, note or melody and you can flip it over the axis of the tonality you are working on and create a “negative” version of that same musical content while maintaining the functional aspect of the material we are working with. The idea that this process is comparable in chord/cadence functionality is what makes negative harmony an interesting tool.

     Relative to any given key center, the axis of that tonality is defined by its tonic and the dominant – by axis, I mean the point from which the pitches are rotated, inverted or mirrored. In the case of the C major tonality, the axis is the middle point between C and G – a pitch that is in between Eb and E.

     Because we are working on a twelve-tone system, we will be chromatically inverting the next six pitches to the left of Eb, inclusively, and the result is seen on the right side of the vertical bar, as represented below:

In the tonality of C major, and using the representation above, a melody with the pitches C, D and B will have its negative counterpart with the pitches G, F and Ab, respectively

     There are other ways that can be used to figure out the “negative” pitches and chords from the “positive” material, but using the circle of fifths seems to be the most straightforward one.

     In this case you just have to draw a line that splits the tonality you are working on and the following fifth that you can find while moving clockwise. This line will represent the mentioned axis between the tonic and the dominant as previously mentioned. If we consider we are working on the C major tonality, then it would look something like this:

     This way the circle of fifths is divided in mirroring halves and for every pitch on one side of the axis, there exists its corresponding “negative” reflection. In the previous example, the notes C, D and B were mirrored and here too you can see that the negative pitches are G, F and Ab. This is good for melodies, but the same can be applied to any chord formation you wish to know its negative counterpart.

     As a general rule, any major chord will have a minor “negative” chord and vice-versa; and dominant chords will have a minor 6^th chord “negative” counterpart and vice-versa. For now, we will be picking up the previous chord progression examples and use the circle of fifths to find the negative counterparts of the “positive” chord tones that are being used:

The Am – Dm – G – C “positive” chord progression is transformed into the “negative” Eb – Bb – Fm – C;

while the A⁷ – D⁷ – G⁷ – C is transformed into Ebm⁶ – Bbm⁶ – Fm⁶ – C

     Generally, you wouldn’t want to change the tonic chord since the whole point is to use negative harmony as a way to provide harmonic functional equivalents of the chord progression we are using.

     In that sense, there is no point in changing the target chord itself. However, for other purposes like expanding the harmonic options or recycling the harmonic material of any given section, those may be good reasons to change whatever chords you see fit.

     Mind you that the negative harmony approach must not be confused with simply mirroring or inverting the intervals around a given axis – which destroys the chord’s contextual function. On the other hand, inverting chords using the negative harmony approach maintains their tonal function in the harmonic context.

     As a final note, if you look at the Fm⁶, the resulting negative chord of G⁷, it has the notes F, Ab, C and D. If inverted, the same chord can be spelled as a Dm⁷(b5). As seen, this is a dominant chord substitution of G⁷ and thus it confirms the validity of the negative harmony approach as a cadential alternative. Also, the leading tone B in the G⁷ chord resolves up to the tonic C, while F, the 7^th of the chord, resolves down to the mediant E.

     In comparison, all the chord tones of Fm⁶ resolve down. In terms of brightness, when comparing both cadences, the plagal cadence is less bright – coming from the flat side of the circle of fifths; but still maintains the harmonic functional purpose with a smooth cadence in terms of voice leading.

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     Now that you have come so far, it is time to test this approach in your music and discover new possibilities for your chords and melodies. The results might surprise and, even better, inspire you!

Happy composing!