That Negative Harmony Talk Unravelled

Photo: Tatiana Gorilovsky (Peter King's 75th Birthday, 606 Club, 2015)

   I was delighted that my lecture on Negative Harmony in France a couple of weeks ago drew a great deal of interest, many probing questions and a not a little controversy. The subject came up because a number of my students, enthused by Jacob Collier, had asked me about Negative Harmony, so I thought I ought to get up to speed with the kids! In order to find a way to work with this system, I set two musical criteria: (i) The chords could always be tweaked, extended or inverted, just as regular jazz chords would be in a reharmonisation. (ii) The goal would be to always to create musically satisfying sounds rather than awkward chords in order to be true to the 'rules'.

   Negative Harmony is offers a darker, more thoughtful, minor or Subdominant alternative to the extravert, bright Tonic-Dominant relationships of classical music. The main problem with Negative Harmony is that it is supposed to be derived by an reversing polarities inherent in the natural harmonic overtone series, while at the same time applying mathematical ideas using equal temperament, which is an artificial creation. The idea of an upside-down 'undertone' series below the tonic, which cannot be heard, is pure hokum. This does not mean that it is not possible to use some of the ideas from Negative Harmony to find new sounds and make interesting music.

   The idea of a pull between the the root and the fifth, the first natural harmonic that produces a different note, is fundamental to a lot of music theory. The first melody ever blown on an animal horn (in Greenland allegedly) would have been a fifth, and we are hard-wired to recognise the primacy of this interval. Negative Harmony creator Ernst Levi used 19th century analyst Hugo Riemann's reversed major triad (C major: C-E-G becomes C minor: G-Eb-C, built from the G downwards using the same intervals) and built a scale of triads coming downwards from the Dominant G, starting with G-Eb-C and using the same intervals as the regular major scale. This produces 'Negative C major', a Phrygian scale of G, with chord I being Cm and chord V being Fm or Fm6 if the chord is extended down to include the 7th. Moving from Fm6 to Cm creates a minor Plagal cadence in place of the regular Perfect one, and this is one of the characteristic sounds of Negative harmony. Some theorists argue about whether the F in the Fm6 should be the bass note, or whether the chord is Dm7b5. The problem here is that we are used to hearing the lowest note as the bass note, not the top note as the generating root. Anyone familiar with Bill Evans however will be aware of the concept of rootless voicings - the chord could be Fm6, Dm7b5 or even Bb9 to him. As jazz musicians therefore, we need not be overly concerned about this, nor bound to the rules at the expense of good sounds. II-V-I in Negative C could therefore be Gm7 to Dm7b5 to Ab major7, or even Eb major7 to Bb9 to Fm9 if all the chords are extended (down) to the 9ths.

 
   In applying this reverse, or 'reciprocal' principle to jazz standard harmony, all sorts of fascinating possibilities are occur. One of the most interesting questions concerns polarity. For example: is the first chord of an F blues a tonic chord, (F minor in Negative) or, as an F7, does it belong to its destination key in bar 5: Negative Bb major, making it a Cm7b5? The end of the blues sequence would have to have a II-V heading towards Negative F in any case. Another question is, should the Bb chord be a Cm, chord IV of Negative F, or should the harmony move in the opposite direction, to Negative C major? In a more complex jazz standard with many changes of key, these relationships and choices become more and more interesting.

This interpretation of an F blues (below) supposes that the first chord is a tonic chord, a 6th/9th in fact, as it was often played during the 30s and 40s. With all the intervals inverted, this gives a Bb7sus chord as the the first chord. In bar 4, when the chord becomes F7 for the modulation, the chord is Dm7b5, or Bb9 here, which is Chord V in Negative C major, since we are modulating in the reverse direction to a normal blues. From bar 8 we have a simple Negative Harmony VI-II-V-I progression to complete the structure.

This is not really that interesting as a chord progression, but it does serve to demonstrate the principles involved. The idea of slipping down from the Bb7 onto the F7 conveys the relaxing Plagal feeling of Negative Harmony. At the end of the sequence the root movement Db-Abmj7-Eb-Bb again shows the negative 4ths cycle.

In a future post I am going to present a Negative Harmony interpretation of one of the most complex and tonally interesting jazz standards, Victor Young's Stella by Starlight.