Negative Harmony Cadences and Voice Leading Concepts by Ernst Levy/Steve Coleman/Miles Okazaki/Barry Harris Transcribed by Marco Fiorini
G7
-C7
F‹6 G7(b9/11)
4w w &4 w w
b˙˙˙ ˙
b˙˙˙˙
bw w w w w w
G7 is degree V of C Major scale: C D E F G A B -C7 is degree V of Negative G Major scale: G F Eb D C Bb Ab
The Root of a negative chord is a fifth below it's Generator. In this case, the Generator is C so the Root is F. The resulting chord is Fm6, not Dm7b5, eventhough their notes are the same. Each of these two chords can be used to resolve to C Major or C minor. The resulting cadences, in the Telluric Adaptation, are V to I and IVm to I (Negative V to I in Absolute Conception). Notice how Fm6 is an upper structure of G7 and the two chords combined together are nothing but a G7(b9/11). Another way to understand this relation is by looking at diminished chords. Let's take an F diminished 7 chord: F - Ab - C - D (enharmonic notation). This chord is completely simmetrical, as the distance between any of its notes is a minor third and any of those can be considered the Root. Lowering by an half-step a note of this chord we obtain a Dominant 7 chord. Raising up by an half-step a note we have a minor 6 chord. Each of the related dominant chord can substitute the others. These 4 related dominant chords are directly related to 4 Major and minor keys. The same is true speaking about the minor 6 chords. Notice how we've found relative negative minor 6 chords of positive Dominant 7 chords. Fm6 (-C7) is the negative of G7, they both resolve to C Major or minor. Abm6 (-Eb7) is the negative of Bb7, they both resolve to Eb Major or minor. Bm6 (-Gb7) is the negative of Db7, they both resolve to Gb Major or minor. Dm6 (-A7) is the negative of E7, they both resolve to A Major or minor. Another curious fact to look at is that each of these chord families generates a diminished chords, considering their roots. minor 6: F - Ab- B - D Dominant 7: G - Bb - Db - E Major/minor key: C - Eb - Gb - A We've completed the chromatic scale; Barry Harris calls this "playing with your sisters and brothers" since all these chords share a family.
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Diminished to Dominant 2 Fº7
w & bw ww
Related Tonal Centers Major/minor
G7
w w ww
C
B¨7
D¨7
E7
bbw w ww
bbw w ww
w #w w w
Eb
Gb
A
A¨‹6
B‹6
D‹6
ww ##w w
ww nnw w
Diminished to minor 6 Fº7
w & bw ww
F‹6
w bw w w
bbbw w w w
Another important concept to keep in mind is that negative chords reverse also chord qualities. Major becomes minor, minor becomes Major, Dominant becomes minor 6 etc. So if we want to reverse a IIm V7 IM cadence we should expect a -IIM -Vm6 -Im. Let's look at a II V I cadence in C Major. The II chord is Dm7; to find its negative we go to the II degree of the Negative G Major scale (F) and descend using the same intervals of a m7 chord. The resulting notes, from top to bottom, are F D Bb G. Remember that this chord has a Generator (F) and a Root (Bb), a fifht below the Generator. Hence the right Telluric disposition of the chord is Bb D F G: Bb6; this chord is also called -Fm7 in Absolute Conception. As we've seen before, the V chord G7 becomes Fm6. Here a few reasons why this chord is not to be considered Dm7b5. If you start harmonizing the negative scale in triads, as we've seen in the previous lesson, the notes of the V chord G (G B D) become, from top to bottom, C Ab F, an Fm triad. The note D only comes when we add the 7th F to the positive G7 chord. So, since adding a 7th to a chord should not alter its quality, its Root should always be F; otherwise we would have Fm in triads and Dm7b5 in tetrads (4 note chords) but this is not correct. Another reason is that mirroring chord progressions we should mirror also their root movement. So if G goes to C as an ascending 4th (or descending 5th), in the negative world F goes to C in descending 4th (or ascending 5th), the same interval, but backwards. Notice, infact, how the root movements of the Negative II V I cadence are polar opposites of the positive ones; this is true also looking at their guide tones, as their chromatic movement has the same gravity, but opposite direction. Once you apply these concepts to your own chord progressions you can even go the a positive I chord (C Major). Remember that negative harmony lives together with positive one, therefore one of its more interesting applications is to switch between positive and negative chords, focusing on movement and voiceleading between those.
© Marco Fiorini 2017 marco.fi
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Positive II V I 3 D‹7
˙ & ˙˙
G7
C
˙˙ ˙
w w w
Negative II V I or Telluric bVII IV I B¨6
˙ & ˙ b˙
F‹6
C‹
b˙˙ ˙
bw w w
If we apply the same concepts to a Dominant Cycle Movement (VI7 II7 V7 I7) the result will be a Cycle of m6 chords, with root movement opposite in polarity. It's important to focus on the arrival point (C7) as we want to move towards the same key center. So C7 becomes Cm6, then we move backwards, mirroring every root interval movement. An ascending 4th (or descending 5th) movement, like this one, becomes a descending 4th (or ascending 5th) movement. Notice how every chord voiceleads into the next one with chromatic movement of guide tones. In the positive cadence this movement is descending, while in the negative one is ascending, but every guide tones has the same polar value and the same gravity to the next one. The same is true for Tritone Substitution cadence.
Positive Cycle Movement A7
D7
G7
C7
˙˙ # & ˙
n#˙˙ ˙
n˙˙ ˙
b˙˙ n˙
F‹6
C‹6
Negative Cycle Movement E¨‹6
B¨‹6
nb˙˙ b˙
& b˙˙ b˙
nb˙˙ ˙
bn˙˙ ˙
Positive Tritone Substitution Negative Tritone Substitution D7
D¨7
C7
#œœ & œ
nœœ bœ
bn˙˙ ˙
B¨‹6
bœœ bœ © Marco Fiorini 2017 marco.fi
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B‹6
bnœœ nœ
C‹6
b˙˙ ˙
