Negative Harmony

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What is is negative negative harmony in music? Why is musical musica l harmony so pleasing to the ear? Promoted by The Great Courses Plus

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How does someone som eone learn how to sing harmony? Is jazz a music al genre or a type of harmony? What are some som e song with good harmony? How can I have a have  a better memory for harmony in songs?

2 Answers Curtis Lindsay, pianist, composer. TW '14 - '17.  Answered 6d ago ago

F unctionally, in present thinking, th inking, it amounts to the conversion of a progression by fifths (e.g. VI - II - V - I) i nto an equivalent, equivalent, negative-image progression by fourths ( e.g. b III - bVII IV - I). We can get considerably more fiddly with the idea than this, though. “Negative harmony” has emerged of late as as a hot topi c in jazz theory because of its popularization popula rization by Jacob Collier, Collier, a phenomenally gifted and skilled young musician from London, Londo n, who has referenced discussions with Herbie H ancock on the subject. A very recent shop-talking interview

Why is harmony harmon y important in music?

 wi th Jacob has already already attra attracted cted several hundreds of thousands of 

views—a big deal when we’re talking about music theory!

What is the importance im portance of rhythm and harmony in music? I hate the loud music coming from the Harmony Cafe, a bar in Rhode Island, at night. What should I do aboutt the s itua abou ituation? tion? Who are the models from Fifth Harmony's new music video "Work From Home"? What defines a harmony harmony as complex?

In the key of C, the VI - II - V - I progression moves from the sharp side of the ci rcle of fifths toward the flat side: A - D - G - C, in a chain of d ominant-relation cadences. We can also approach C from the flat side of the circle movi ng sharpward, u sing the same number of steps. In that case we would get Eb - Bb - F - C, which is a chain of plagal cadences. The notion that these two processes are functionally comparable is the essence of negative harmony.

This concept is d erived, Jacob says, from the Theory of Harmony by Swiss composer Ernst Levy (1895 – 1981). Relative to any given key center, an axis of tonality is defined such that the circle of fifths is divided by that axis into mirroring halves. In the key of C, the axis would be drawn between C and G; in A-flat, it would be drawn between A-flat and E-flat. For every pitch on one side of the axis, there exists a corresponding “reflection” or “negative” on the other side. Let’s try a nu mber line-like presentation:

Here we’ve identified the origin as the midpoint of the C-G axis, falling between the pitches E and E-flat. Sorting by absolute value, we see that the reflection of F is D ( 1 and -1), the reflection of F#/Gb is C#/Db (2 and -2), and so on. Referring back to the circle of fifths, you ’ll note that this presentation is the same as if we drew a line from the 12 o’clock to the 6 o’clock of the ci rcle, where 12 o’clock is halfway between C and G and 6 o’clock is halfway between G-flat and D-flat. Levy’s characterization, coming from the standpoint of common practice classical harmony, is that the traditional dominant-chain cadence by fifths is like a tree branching out above ground, while the plagalized chain of cadences by fourths which mirrors that motion—its “negative harmony”—i s like the root system, unseen beneath the surface.  It’s vaguely similar, if in silhouette only, to Harry Partch’s distinction between Otonality and U tonality—wherein minor tonality, which is not native to the natural overtone

series, is

derived by means of inversion of the series downward toward an imaginary fundamental “ undertone.”

Earlier I said that we can get rather more involved in this p rocess of reflection if we like. Well, it i s one thing to contrast a flatward-trending series of chord roots against a sharpwardtrending series of chord roots—but what if we then go on to flip all the individual pitches of  each of these chords across the axis while we’re at it—thinki ng about the whole chord instead of only the root? We already know that from A - D - G we will derive Eb - Bb- F, th e plagalization of that progression, toward the target of C. It turns out that flipping all of the involved pitches within the chords of this dominant seven chain looks like this:

Flipping any major chord will yield a minor chord; flipping any dominant seven will yield a minor six. So, for i nstance, you can get complementary prog ressions like these unlikely mirror-friends:

You might ask why we don’t also flip the tonic chord across the axis—doing so would yield C minor. But the whole point i s to come up with two opposite but equivalent means of approaching the same harmonic goal, so in that framework there is no reason to flip the target chord itself. It’s nothing earth-shattering, this i dea of “negative harmony.” It isn’t the d ark matter or the

harmonic prog ressions, and of di scovering new tools to stash in y our chest, as Jacob says.

One final thought: When we mirror the major scale over this axis, we get the phry gian built on the d ominant degree of the source scale.

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Related Questions Why is musical harmony so pleasing to the ear? Why is harmony important in music? How does someone learn how to sing harmony?

More Answers Below

Is jazz a musical genre or a type of harmony? What are some song with good harmony?

Caleb Creed, studied at Musi c Theory Updated 6d ago

EDIT: Curtis Lindsay has given a far superior answer, don’t waste you’re time here, until you’ve read his. Negative harmony would perhaps be better named symmetrical harmony. Wouldn’t it be nice, in a given key, to have a simple method of substitution, so that given any chord I could spit out a “symmetrical” or “negative” chord, that could be played instead? This is the i dea. You can mirror anything, you just have to choose where the axis is. -5 -4 -3 -2 -1 0 1 2 3 4 5, Negative numbers provi de a symmetry to positive numbers only because they have an axis around 0. The term ‘negative’ provides no insight into the technique outside of  that. So stop thinking about it. Here’s the recipe for producing a negative chord. For the key of C 1. Find Tonic (That’s C) 2. Find Dominant (That’s G) 3. Find the Midpoi nt of those two (That’s E) 4. The result of #3 is your axis of symmetry. (E) 5. The symmetrical counter part 1 half step above E is 1 half step below E. 6. The symmetrical counterpart of F is D 7. The symmetrical counterpart of F# is Db 8. Take any chord in the key (Say G7) 9. Take the notes that that chord is comprised of (GBDF)

11. Name the chord comprised of the counterparts (Either D half dimini shed, or F minor 6th) So negative harmonies are simply th e result of that process

NH(G7) -> Fm6 NH is the function we were looking for in the begi ning. a simp le transformation that will provide us with a harmonic alternative for any chord given. For a little more insight consider the tenencies of motion for each of these chords. DO is stable so is i ts symmetrical counterpart SO. RE wants to move up to MI, RE’S symmetrical counterpart is FA which want’s to move down to MI. LA will go in either direction. Each member of the negative harmony wants to move to the same chord as the posi tive harmony 570 Views · 4 Upvotes

Related Questions How can I have a better memory for harmony in songs? What is the importance of rhythm and harmony in music? I hate the loud music coming from the Harmony Cafe, a bar in Rhode Island, at night. What should I do about the situation? Who are the models from Fifth Harmony's new music video "Work From Home"? What defines a harmony as complex? Why is most rock music negative and depressing? What is harmony? How can one learn to write harmony for brass music? Is arpeggio a harmony or a melody? Is bad music music?

How does unison and harmony differ? What song is used in "Werckmeister Harmonies"? Has rap music had a positive or negative effect on society and how so?  As a musician what should I know about harmony other than music scales? Why are people so impressed by harmony?

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