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Negative Harmony

Discussion in 'General Instruction [BG]' started by Mark Wilson, Apr 7, 2009.


  1. Mark Wilson

    Mark Wilson Supporting Member

    Jan 12, 2005
    Toronto, Ontario
    Endorsing Artist: Elixir® Strings
    Alright, any of you advanced theory buffs turned on this?

    I heard about it recently, and am currently writing a song with Bartok as an inspiration for it.

    Discuss the ideas and rules for Negative Harmony.


    GO!
     
  2. HaVIC5

    HaVIC5

    Aug 22, 2003
    Brooklyn, NYC
    I'm not sure what you mean by this. Is that another term for mirror harmony?
     
  3. Mark Wilson

    Mark Wilson Supporting Member

    Jan 12, 2005
    Toronto, Ontario
    Endorsing Artist: Elixir® Strings
    Possibly?
     
  4. Tyler C.

    Tyler C.

    Jan 18, 2009
    Explaining what it is briefly may be a little bit helpful here.
     
  5. HaVIC5

    HaVIC5

    Aug 22, 2003
    Brooklyn, NYC
    Yeah ^. Not sure what you mean by negative harmony.
     
  6. Mark Wilson

    Mark Wilson Supporting Member

    Jan 12, 2005
    Toronto, Ontario
    Endorsing Artist: Elixir® Strings
    Oops!
    Sorry!
    I thought i did.

    It could be the same concept as "mirror Harmony"

    Say, you have a progression...Something simple like Cmajor7, Emi7, G7.

    you take the intervals between the chords, and do the exact opposite.

    C - E = Major 3rd ascending.
    E - G = Minor 3rd ascending.

    Therefore, in Negative Harmony, the progression would be...

    Cmajor7, Abmi7, F7

    C - Ab = Major 3rd DESCENDING.
    Ab - F = Minor 3rd DESCENDING.

    Dig?
     
  7. HaVIC5

    HaVIC5

    Aug 22, 2003
    Brooklyn, NYC
    Dig. (I call it mirror harmony)

    Hmm, where to get started with this. First all you did with that chord progress was invert the roots progression about the pitch axis C - it isn't mirror harmony in its purest sense because then all the intervals in in all the chords would have to be different. You just mirrors the roots, which I guess is a form of less strict mirror harmony. I would call this a much more literal mirror harmony of tertian structures:

    (progression I)

    Cmaj7 (C E G B)
    E-7 (E G B D)
    G7 (G B D F)

    (It's Mirror)

    Dbmaj7 (Db F Ab C)
    F#-7 (F# A C# E)
    A-7(b5) (A C Eb G)

    Notice how I got that? I started on the root of the first chord progression and spelled down new chords based upon the intervallic content of the first ones. C major 7 is C up a major third to E up a minor third to G up a major third to B. I took that same order of intervals, but used it going down instead of up. C down a major third is Ab, down a minor third is F down a major third is Db. This order of notes spelled a Db major 7 chord. You can do that with any quality of chord, and they will invert to some interesting things. Here's a basic list.

    Major 7 => Major 7 a half step up (Cmaj7 to Dbmaj7)
    Minor 7 => Minor 7 a whole step up (E-7 to F#-7)
    Dominant 7 => Minor 7(b5) a whole step up (G7 to A-7(b5))
    Minor7 (b5) => Dominant 7 a whole step up (C-7(b5) to D7)
    Diminished 7 => Diminished 7 a minor third up (inverts to itself, essentially)
    Minor major 7 => Augmented major 7 a half step up (C-(maj7) to Db+maj7)
    Augmented major 7 = Minor major 7 a half step up

    OK, cool, so what use is this kind of thing? To be honest, in the way that I've been talking about it so far, I don't see it being very useful in any kind of tertian-based context simply because tertain harmony is so limiting. Bartok used it as a method of counterpoint where he was mainly worried about two voices moving in exact contrary (mirror) motion. If you did this with entire block tertian chords, the result would be rather...modern, shall we say. In other words, you'd be dealing with this ridiculously tall and dissonant polychords like Cmaj7/Dbmaj7, E-7/F#-7, and C-(maj7)/D+maj7 (the first one is probably my favorite, especially when put into a wide spread voicing). Some of them, though, "fit" with normal sounds, like C-7(b5)/D7 is just a voicing of D7(b9,b13). I supposed you could do some interesting things like write out standards in "inversion", by re-writing all the chords as their inverted counterparts and playing through them that way. That actually might be a fun exercise to see how they would sound.

    OK, so what about mirror counterpoint and mirrored melodies? This concept holds a lot more promise, IMO, than mirror tertian structures (although quartal/mixed interval structures are a wide open field for study). If you look at the modes of the major scale, you'll see that only one of them mirrors to itself - that is, when you write out the mirrored form of all the notes in the scale you end up with the same scale. That is the scale Dorian, and you can actually see how this ends up working by simply looking at a alphabetic representation of the whole/half pattern: whwwwhw. All the others invert to different scales all together. Bartok liked this about mirror counterpoint - it was a way to juxtapose two very different sounds together in a logical way.

    After learning this fact about Dorian, I looked into the whole symmetrical scale things and came to some interesting conclusions. There are only four 7-note scales which are symmetrical this way - that mirror to themselves. Dorian, Mixolydian b6, Nepolitain Minor (Melodic Minor b2) and the Double Harmonic Minor. The really wild thing is then looking at all of the modes of each of those scales and then seeing that all of them have exactly one perfect mirror at an interval besides the unison. In other words, say we take Ionian, which is a mode of the Dorian scale (usually we think of it the other way around, but for our purposes here we'll think this way). If you start the mirror process at the major third instead of at the unison, you'll end up with the major scale again. A major scale's intervallic makeup is wwhwwwh, which, when inverted and started on a pitch a major third above the tonic, inverts to the tonic's major scale. Check it out.

    C D E F G A B C
    w w h w w w h
    E D C B A G F E

    Cool huh? I won't bore you with the intervals with all the mirrors of all 28 different scales, but when I was looking into this, a interesting pattern arouse. The only intervals that occurred as intervallic mirrors (Ionian's intervallic mirror being a major third) were intervals that spelled the whole tone scale. Major 2, Major 3, TT, Minor 6, Minor 7. And, if you didn't already tacitly know this, the whole tone scale is the most symmetrical scale there is - wwwww - doesn't get any more mirror-friendly than that. So, basically, buried deep within these 7-note scales is actually a grand "whole tone" scale that governs how they invert and how all of the intervals relate to one another.

    Cool stuff, no? I thought so when I figured it all out.
     
  8. Zombbg4

    Zombbg4

    Jul 15, 2008
    Olympia,Wa
    Havic...please warn us before the barrage of theory, or better yet make a video :)
     
  9. Mark Wilson

    Mark Wilson Supporting Member

    Jan 12, 2005
    Toronto, Ontario
    Endorsing Artist: Elixir® Strings
    Cool :)

    I'll read deeper into it once I"m more awake, but I Understand it now!
    I didn't know much about the concept, just that you do it's mirror opposite. It never clued in to do it do the chords.

    Polychords here I come!
     
  10. Audiophage

    Audiophage

    Jan 9, 2005
    This is giving me some interesting ideas. I particularly like the concept of an underlying whole tone scale. I think I'm going to explore some of these later.
     
  11. JimmyM

    JimmyM

    Apr 11, 2005
    Apopka, FL
    Endorsing: Ampeg Amps, EMG Pickups
    Know what's a cool song that uses that type of harmony? The ending chorus of "Blockhead" by Devo. It's a simple version of it, but effective. The chords are E-D-C-Bb, and the synth plays E-F#-G#-A#. So it starts out going negative then syncs up at the end of the phrase.
     

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