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Lesson 161: "Negative Harmony"

What is "Negative Harmony"?

Lately, there has been some discussion on a concept referred to as "negative harmony". Other names, by which this concept goes, are:

  • "mirror harmony"
  • "symmetrical harmony"
  • "Otonality vs. Utonality = overtone tonality vs. undertone tonality"

The "Axis"

When transforming harmony into negative/ mirror/ symmetrical harmony, you need an axis. The axis can be

  • a single note, for example C
  • a two-note axis, often the tonic- dominant of a key, for example C-G

How Can the Concept of "Negative Harmony" Be Used?

  1. You can mirror just the roots of the chords of a cadence/ progression
  2. You can apply the concept of negative harmony to a single chord, using a pitch conversion table
  3. You can apply the concept of negative harmony to scales, using a pitch conversion table
  4. You can apply the concept of negative harmony to a single chord, using a single note as the axis

1) Mirroring Just the Roots of the Chords of a Cadence/ Progression

Functionally, using negative harmony can be thought of as converting a cadence or chord progression into a negative, mirror image, symmetrical one. In this case you use only a single note, the tonic of the key, for example C, as an axis.

For this the circle of fifths is an excellent tool. The tonic of the key is the center, the axis, in this case C. Then you just have to replace a note with the mirror note, the opposite note on the other side of the circle.

Example 1

Take the generic II - V - I cadence/ progression so common in jazz:
Dm7 - G7 - Cmaj7
The negative harmony, mirror image, symmetrical substitute is:
Bbmaj7 - Fmaj7 - Cmaj7

A progression by fifths II - V - I is changed into an equivalent, negative image progression by fourths bVII - IV - I. A chain of dominant relation cadences is transformed into a chain of plagal cadences.

Example 2

Now, let's take this idea a little further:
Em7 - A7 - Dm7 - G7 - Cmaj7
becomes
Abmaj7 - Ebmaj7 - Bbmaj7 - Fmaj7 - Cmaj7

Again, a progression by fifths III - VI - II - V - I is changed into an equivalent, negative image progression by fourths bVI - bIII - bVII - IV - I. A chain of dominant relation cadences is transformed into a chain of plagal cadences.

Comparable Progressions

The idea that the new progression is functionally comparable to the original one is the essence of negative harmony.

2) Applying the Concept of Negative Harmony to a Single Chord

You can also apply the concept of negative harmony to a single chord. This is done by flipping/ negating all the individual pitches of a chord across a two-note axis, which is the tonic- dominant axis of the key at the moment.

"The Axis" and a Table for Conversion of Pitches

If you want to make the conversion very easy, you can make a table like the one below.

  1. Choose the key center, in this case C.
  2. Locate the dominant, in this case G.
  3. "The axis" is therefore C-G ( tonic- dominant).
  4. Find the O, the origin. That is the note that is exactly halfway between C and G. This note is always halfway between two notes, in this case halfway between Eb and E.
  5. Map out all the notes of the chromatic scale with Eb/E as 0, like this:

Bb   B   C   C#   D  (Eb/E)  F   F#  G   Ab  A
-5  -4  -3   -2  -1     0    1   2   3   4   5

Tadaa! Now it is very easy to locate the mirror note or negative note of any note!

Example 3

Take a generic V - I cadence/ progression:
G7 - Cmaj7
Flip the individual pitches of the G7 chord across the C-G axis, using the table above. g becomes c, b becomes ab, d becomes f and f becomes d. So, the negative harmony equivalent of G7 is a chord with the notes c, ab, f and d: Fm6 ( or Dm7b5).
This means that the V - I cadence/ progression G7 - Cmaj7 is transformed into the IV - I cadence/ progression
Fm6 - Cmaj7

This happens to be a very common and interesting subdominant minor to tonic cadence/ progression.

It can also be interesting to look at the resolution of the single notes and compare the cadences/ progressions G7 - Cmaj7 and Fm6 - Cmaj7 to each other:
G7 - Cmaj7
g -> g
b -> b or c
d -> c or e
f -> e or g
Fm6 - Cmaj7
f -> e or g
ab -> g
c -> c or b
d -> e or c

Example 4

Now, take a Dm7 chord.
Flip the individual pitches of the Dm7 chord across the C-G axis, using the table above. d becomes f, f becomes d, a becomes bb and c becomes g. So, the negative harmony equivalent of Dm7 is a chord with the notes f, d, bb and g: Bb6 ( or Gm7).

Example 5 - Triads

Take a C major triad.
Flip the individual pitches of the C chord across the C-G axis, using the table above. c becomes g, e becomes eb and g becomes c. So, the mirror chord of C is a chord with the notes c, eb and g: Cm.

This automatically means that the mirror chord of Cm is C. So, a C major triad and a C minor triad are mirror chords of each other, with C-G as the axis.

3) Applying the Pitch Conversion Table to Scales

If you mirror every note of the C major scale over the C-G axis, i.e. using the table above, you get:
c -> g
d -> f
e -> eb
f -> d
g -> c
a -> bb
b -> ab
c -> g,
which turns out to be a descending G Phrygian mode, i.e. the third mode of the Eb major scale, which contains the same notes as a C natural minor scale! So, the mirror image of the major scale is the natural minor scale. This is a very surprising and interesting fact concerning major vs. minor.

You can also think about it like this:

  • the steps of a major scale are upwards w w h w w w h ( whole, whole, half, whole, whole, whole, half)
  • starting on the note you like, if you take the same steps downwards you will get a Phrygian scale

4) Applying the Concept of Negative Harmony to a Single Chord, Using a Single Note as the Axis

It can also be interesting to negate a single chord using a single note as the axis. Then you will be using the circle of fifths again.

Some Examples - Triads

If you use C as the axis:

The negation of C is Fm ( c e g -> c ab f)
The negation of F is Cm ( f a c -> g eb c)
The negation of G is Bbm ( g b d -> f db bb)
The negation of Am is Ab ( a c e -> eb c ab)
The negation of Em is Db ( e g b -> ab f db)
The negation of Dm is Eb ( d f a -> bb g eb)

The negation of Bb is Gm ( bb d f -> d bb g)
The negation of D is Ebm ( d f# a -> bb gb eb)
The negation of A is G#m ( a c# e -> d# b g#)
The negation of E is C#m ( e g# b -> g# e c#)
The negation of B is F#m ( b d# f# -> c# a f#)
The negation of F# is Bm ( f# a# c# -> f# d b)

The negation of a major chord is always a minor chord and the negation of a minor chord is always a major chord.

The most interesting result of this seems to be that the negation of C is Fm. This coincides with the fact that

  • if we use the first five notes of the overtone series of the note c ( c c g c e), we get a C major triad
  • if we use the first five notes of the undertone series of the note c ( downwards c c f c ab), we get an F minor triad
So, the mirror chord or negation of a tonic major triad is a subdominant minor triad ( when you use one note, the tonic, as the axis). Very interesting... :-)

What's the Point? How Do I Use This?

You may wonder what the point is. You can use the concept of negative harmony

  • when writing music - composing and arranging, for new and interesting chord progressions
  • as a tool for analyzing and understanding chord progressions that otherwise might seem strange and difficult to explain

Some Tunes to Listen to

Listen to the following tunes:

2017 Tomas Karlsson. All rights reserved.