A Reverse ii-V-I (or a reverse anything)

In Ernst Levy's book, "A Theory of Harmony," he describes a way to "invert" notes in a key center. Everything Major becomes Minor, everything Perfect becomes Plagal. And so every inverted progression has the same gravity toward the key center, but with a completely new sound/feeling. His system involves inverting notes around an axis that is located between the root and the fifth. In C Major, this is exactly in between E and Eb. 

So, to invert the note A in the key of C Major, you would find the distance from A to the axis from a direction. I'll go with from above. Count downwards from A to the axis, and you get 5.5 half steps. Now, to invert the A, start at the axis between E and Eb and count downwards by 5.5 half steps. This gives us Bb.

If we apply this to the ii-V-I, this gives us a bVII-iv-i, or in the key of C Major, Bb, Fm and Cm. You may have noticed that a ii-V-I goes to the key center counterclockwise from the circle of fifths. D is a fifth away from G, is a fifth away from C. This bVII-iv-i, it approaches the key center from the opposite direction, clockwise on the circle of fifths. B flat is a fourth away fro, F, F is a fourth away from C

If we apply this to a Dm7 G7 C progression, we get Bb6 Fm6 Cm. But obviously if you're in a major key you're generally gonna want to resolve to the Major I, so you could change this to Bb6 Fm6 C. If you have a piano, try playing this with the Bb6 in 2nd inversion and the Fm6 voiced as a D half diminished, and you'll see what I mean when I say it has the same gravity as a ii-V-I.

Here's a chart that shows you what notes are inverted to what in the key of C Major. 

Interesting. I'm semi lost at the 5.5 steps part but I think I got it.

You said ii - V - i maps to bVii - v - i.  I thought this would be IV - v - i

Like I said, a ii-V-I approaches a key center from the circle of fifths. In C Major, a ii-V-I is Dm G C. D is a fifth away from G, G is a fifth away from C. The inverse version approaches the key center from the circle of fourths. In C major, bVII-iv-i is Bb Fm Cm. Bb is a fourth away from F, F is a fourth away from C. All of the minor chords become major, the major chords become minor.

What we are doing is flipping notes around an axis. This axis is located between the root and the fifth of a key center. In C major, this axis is located exactly between E and Eb, the notes that determine whether it is major or minor.

I gave a chart, but it only applies to C major.

This is the easier way to do it: Lets say we're in Eb. Play the root and the fifth of your key center. In Eb, this is Eb and Bb. Then, move the top note up a half step, and the bottom note down a half step. This gives you D and B, so those notes are opposites in Eb major. Do it again, and you get Db and C, so those two notes are opposites in Eb. Etc. 

2 hours ago, marsbars said:

Interesting. I'm semi lost at the 5.5 steps part but I think I got it.

You said ii - V - i maps to bVii - v - i.  I thought this would be IV - v - i

 

 

Like I said, a ii-V-I approaches a key center from the circle of fifths. In C Major, a ii-V-I is Dm G C. D is a fifth away from G, G is a fifth away from C. The inverse version approaches the key center from the circle of fourths. In C major, bVII-iv-i is Bb Fm Cm. Bb is a fourth away from F, F is a fourth away from C. All of the minor chords become major, the major chords become minor.

What we are doing is flipping notes around an axis. This axis is located between the root and the fifth of a key center, the most important in western music. In C major, this axis is located exactly between E and Eb, the notes that determine whether it is major or minor.

I gave a chart, but it only applies to C major.

This is the easier way to do it: Lets say we're in Eb. Play the root and the fifth of your key center. In Eb, this is Eb and Bb. Then, move the top note up a half step, and the bottom note down a half step. This gives you D and B, so those notes are opposites in Eb major. Do it again, and you get Db and C, so those two notes are opposites in Eb. Etc. 

2 hours ago, marsbars said:

Interesting. I'm semi lost at the 5.5 steps part but I think I got it.

You said ii - V - i maps to bVii - v - i.  I thought this would be IV - v - i

 

 

Any chord progression you play using this method will have the same amount of gravity to the key center as the original progression, just from the opposite direction. 

4 hours ago, jejrekmek said:

I gave a chart, but it only applies to C major.

This is the easier way to do it: Lets say we're in Eb. Play the root and the fifth of your key center. In Eb, this is Eb and Bb. Then, move the top note up a half step, and the bottom note down a half step. This gives you D and B, so those notes are opposites in Eb major. Do it again, and you get Db and C, so those two notes are opposites in Eb. Etc. 

Hey - this is a really helpful way of thinking about it!  I have been trying to understand negative harmony for a while and could never quite wrap my head around which tone to "flip" over.  Apparently it does work if you think of the axis as being half way between A and Bb or E and Eb like you said.  Thanks for clarifying things for me!

On 4/13/2021 at 11:24 PM, PeterthePapercomPoser said:

Hey - this is a really helpful way of thinking about it!  I have been trying to understand negative harmony for a while and could never quite wrap my head around which tone to "flip" over.  Apparently it does work if you think of the axis as being half way between A and Bb or E and Eb like you said.  Thanks for clarifying things for me!

 

You're welcome, and yeah this is a way easier way to do it than counting out the distances. Just play the root and fifth of the key center simultaneously, and move each note in half steps in opposite directions. Whatever two notes you play at once while doing this are opposites. 

11 hours ago, jejrekmek said:

 

This is the easier way to do it: Lets say we're in Eb. Play the root and the fifth of your key center. In Eb, this is Eb and Bb. Then, move the top note up a half step, and the bottom note down a half step. This gives you D and B, so those notes are opposites in Eb major. Do it again, and you get Db and C, so those two notes are opposites in Eb. Etc. 

 

Interesting.  You could also think of a scale's tritone as it's center and find the distance the from the tritone.

C's tritone would be F# 

If I wanted to mirror F it would 1 semitone below F#.  So add 1 semitone to F# - G

If I wanted to mirror E that's 2 semitones below F#. Add two semitones G#

On 4/14/2021 at 7:17 AM, marsbars said:

Interesting.  You could also think of a scale's tritone as it's center and find the distance the from the tritone.

C's tritone would be F# 

If I wanted to mirror F it would 1 semitone below F#.  So add 1 semitone to F# - G

If I wanted to mirror E that's 2 semitones below F#. Add two semitones G#

 

 

Yeah, I guess you could. What I described in this post is usually referred to as "negative harmony." By inverting the notes over the axis between the root and the fifth, you are utilizing the polarity between the circle of fifths, and the circle of fourths (is that a thing?) Generally, going clockwise across the circle of fifths sounds "bright." Going counterclockwise sounds "dark." The bVII-iv-i is the "negative" version of the ii-V-I, because it approaches the key center from the opposite side of the circle of fifths.

Sounds like something film composers might do. 

Like off the soundtrack of field of dreams or something.

If you try I- IV V it sounds rather hilarious like you turned elmo inside out or something. 

5 hours ago, marsbars said:

Sounds like something film composers might do. 

Like off the soundtrack of field of dreams or something.

If you try I- IV V it sounds rather hilarious like you turned elmo inside out or something. 

 

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Your inverted I-IV-V was a i-iv-v, when it should have been a i-v-iv.

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