We love the positive and the negative
Negative Harmony is a harmonic tool which can be used for improvisation.
Ernst Levy was a Swiss musicologist, composer, pianist
and conductor (1895-1981). The harmonic considerations he made (in his book 'A Theory in Harmony') are a part of the theoretical basis for this improvisational concept. Even though he did not use the term 'negative harmony', nor did he write his concept as a basis for improvising.
Steve Coleman has made a great and valuable contribution to the use of this concept in jazz since the 1980s.
A YouTube interview with Jacob Collier gave the concept a new input and generated great enthusiasm for this idea. For improvising this tool is interesting, because it helps creating new sounds.
[Keep in mind: this website just wants to give a brief overview of negative harmony. For more detailed information see the links at the end of this website]
The negative counterpart of the ascending C major scale is a descending G Phrygian Scale:
The ascending C-Major scale is wholetone, wholetone, semitone, wholetone, wholetone, wholetone, semitone.
The descending G-phrygian scale has the same intervallic structure and is therefore called negative G-Major Scale.
In C the tonic is C and the fifth is G. This perfect fifth is a very important interval for the C-tonality. This interval is also found in the negative G Major Scale. The G is called the 'generator' and C is also a perfect 5th below. And C is still the tonic.
To get negative melodies you only have to position the positive melody down the negative G-Major Scale. E.g. the melody c d f g e is 1 2 4 5 3 in C-major. To get its negative counterpart, go down the negative G-Major Scale with the same intervallic structure: -1 -2 -4 -5 -3. This will be: g f d c eь.
The same procedure you can do with chords. The C-Major Triad is c e g or 1 3 5. Put this intervallic structure down the negative G-Major Scale and you get g eь c. It is a major triad generated from top to bottom. G is the "generator", a major third down is EЬ and a minor third down is C. So the new chord has the same intervallic structure as its original chord, but in inverted direction. [Our ear can't be trained to hear this chord as a major triad inverted. We will hear a C-Minor Triad. But we can think in this way]
Triads in the key of C:
C-major becomes g eь c. That's a negative G-major. Adapted to the positive world (that's what you will hear:) a C-minor chord.
G-major becomes c aь f. That's a negative C-major. You will hear it as F-minor.
For complex chords the extra notes are added to the basic triad:
Cmaj7 becomes g eь c aь. You will hear it as Cm(Ь6). [It's not AЬmaj. Keep in mind: you add the extra notes to the basic triad. So you first have the Cm, the b6 is added]
Dmin7 becomes f d bь g. You will hear it as BЬ6.
G7 becomes c aЬ f d. You will hear it as Fm6. [Also not Dm7(b5). You add the 6th to the basic Fm-chord]
The cadence Dm7 G7 Cmaj7 will become a negative II V I. The resulting sounds are: Bb6 Fm6 Cm(b6).
Note: Working with negative harmonies leads us to use IVm6 chords instead of the classical dominants. This leads to the increased use of plagal chord connections and sounds.
In his viral Youtube Video, Jacob Collier is using an axis between Ь3 and 3 to mirror melodies and harmonies. This is the axis he talks about as 'converting perfect to plagal' and maintaining equivalent 'tonal gravity' between the original and mirror chords.
(Have also a look into Steve Coleman's Essay about 'symmetrical movement concept'. You find the link at the end of this site).
Using the Ь3/3 axis to mirror melodies and harmonies leads to the same results as using the negative MajorScale as outlined above.
E.g. in the key of C, the axis would be drawn between eь and e. If you mirror the note c you get g.
Look at the table for the related negative solution in the key of C:
As you can see, in the key of C the f becomes negative d.
This procedure can be used for rotating the melody to its negative.
The same procedure you can use to create the negative chords for a progression:
In the key of C, we create the negative of a C-Chord: c becomes g, e becomes eЬ and g becomes c. The C-Chord in C has the same negative G chord, back in the positive world it sounds like a Cm-Chord.
For example: the first bars of "All the Things", AЬ, could be transformed like this:
If you use the Levy-Method, you achieve the same goal:
The first 8 bars of the composition "All the Things" will become this:
The discussion is also about replacing only
the harmonic progression to its negative, but not the solution. In this
case, our II-V-I in C - progression would sound like this:
BЬ6 - Fm6 - C.
As you see, this way of using negative harmony produces IV-6 sounds instead of dominant sounds, which is very close to modal interchange.
Another way of using negative harmony flavoured sounds is to change only specific chords in the chart.
For example in the first 8 bars of "All the Things" change only the Dominant-7 Chords to their negatives:
| F-7 | BЬ-7 | DЬ-6 | AЬmaj7 | DЬmaj7 | F-6 | Cmaj7 | Cmaj7 ||
Another way to create new sounds is to move the axis to a different position. But keep in mind: The most important thing:
Have fun to check out new sounds!
Ernst Levy - A Theory of Harmony
Steve Coleman's thoughts about his 'symmetrical movement concept' and 'negative harmony'
Harmonic Dualism or Harmonic Polarity
Wikipedia about the Undertone Series
Wikipedia about the Riemann dualist system
Essential Neo-Riemannian Theory for Today's Musician"