{"id":368,"date":"2020-04-23T01:18:12","date_gmt":"2020-04-23T05:18:12","guid":{"rendered":"http:\/\/dantepfer.com\/blog\/?p=368"},"modified":"2020-04-27T19:37:45","modified_gmt":"2020-04-27T23:37:45","slug":"negative-harmony","status":"publish","type":"post","link":"https:\/\/dantepfer.com\/blog\/?p=368","title":{"rendered":"Negative Harmony: a primer"},"content":{"rendered":"

Ever since Five Pedals Deep<\/em>, my trio record with Thomas Morgan and Ted Poor, came out in 2010, I’ve gotten a steady trickle of emails asking about a particular tune on it called Back Attya<\/em>.
<\/a><\/p>\n

\"\"<\/a><\/p>\n

If you listen to it without knowing what it is, there’s something about the harmonic movement that might feel surprising. You can feel intuitively that it has a really solid structure, but at the same time, the chords don’t seem to move in a way that you would expect. There’s a reason for that: Back Attya<\/em>, as the name cryptically suggests (ATTYA<\/em> being an acronym), is an inversion of All The Things You Are<\/em>, by Jerome Kern.<\/p>\n

\"\"<\/a><\/p>\n

(An inversion, for our purposes here, is a chromatic<\/em> inversion \u2014 a mirror image, with the mirror placed horizontally, where all the intervals are preserved exactly \u2014 not to be confused with a diatonic inversion. So if the original melody moves up by a major third, say, the inverted version moves down<\/em> by a major third. A descending perfect fourth becomes an ascending perfect fourth, and so on. What note do you start on? More on that later.)<\/p>\n

\"inversion\"<\/a>

The bottom staff is a chromatic inversion of the top staff, with middle C as the axis of symmetry<\/p><\/div>\n

The first question I usually get about it is: “my friend told me that this was an inversion of All The Things You Are<\/em>, and I can see how that works with the melody, but what’s going on with the harmony? Why is the first chord B Major?” At this point I tell people to look up saxophonist\/theorist Steve Coleman’s<\/a>\u00a0theory of negative harmony, because my transformation of ATTYA above is basically a textbook application of that concept.<\/p>\n

(I attended a couple of Steve’s workshops at the Jazz Gallery when I first moved to New York in 2006, and I learned a lot from them. Steve is exceptionally generous with sharing his ideas \u2014 where many people would keep them to themselves, he\u00a0wants<\/em> you to know his secrets.)<\/p>\n

More often than not, I then get another email saying the person still couldn’t figure it out. Which I can understand, to a certain extent, because Steve rarely lays anything out in writing in an easily digestible way \u2014 he always goes deep, exploring every possible ramification of a topic. So I thought I’d explain my understanding of his method in as clear a way as possible, since 1) it’s\u00a0a technique that can give gorgeous results and 2) it’s actually an application of very<\/em> old musical ideas to jazz.<\/p>\n

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Here’s how you do it \u2014 from first principles:<\/strong><\/p>\n

1.<\/strong> Find the key of the tune you want to invert. In the case of All The Things You Are<\/em>, it’s Ab Major. The tonic of the song\u00a0is Ab.<\/p>\n

2.<\/strong> Determine the axis you’re going to use for the inversion. This will stay the same for the whole tune, even if the song temporarily modulates to another key. The axis is\u00a0exactly half way between the tonic and the perfect\u00a0fifth above it. In the case of ATTYA<\/em>, half way between Ab and Eb puts the axis halfway between B and C:<\/p>\n

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Finding the axis for ATTYA<\/p><\/div>\n

3.\u00a0<\/strong>Invert the melody around the axis. In the case of ATTYA<\/em>, the axis is between B and C, so B inverts to C, Bb to Db, A to D, etc \u2014 and vice-versa (C becomes B, Db becomes Bb, etc).<\/p>\n

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Inversion map for ATTYA<\/p><\/div>\n

The first melody note of ATTYA<\/em> is Ab, which gives us Eb (or D#). Next one is Db, which gives us Bb (or A#), and so on.<\/p>\n

\"\"<\/a>

Inverting the first 4 bars of the ATTYA melody<\/p><\/div>\n

4.<\/strong>\u00a0Invert the harmony. This is a little more complicated but still pretty straightforward. The first chord of ATTYA<\/em> is F minor \u2014 let’s ignore the 7th for now. F is the root<\/em> of the chord. We invert this root around the axis to get F#, which we call the\u00a0generator<\/em> of the negative chord. Now, we recreate the original chord going down from this generator, rather than up. The notes of Fmin are\u00a0F, Ab and C; moving up<\/strong> from the root, this is\u00a0a minor\u00a0third, then a major\u00a0third.\u00a0To get our inverted chord, we move\u00a0down\u00a0<\/em><\/strong>from the generator with the same sequence of intervals, first a minor third, then a major third. This gives us (reading downwards) F#, D# and B. We call this chord F# negative minor, or F#Nmin.<\/p>\n

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Fmin \u2014> F#Nmin<\/p><\/div>\n

Now what shall we call this chord so that people who don’t know about negative harmony can read it? How do we name it in the positive world? This is really the key of Steve’s approach: the root of the negative chord is always a perfect fifth below\u00a0the generator<\/strong>. This bears repeating: the root of the negative chord is always<\/span> a perfect fifth below\u00a0the generator.\u00a0<\/strong>So the root (in the positive world) of F#Nmin is a perfect fifth below F#, which is B. Looking all the notes together (the root B, plus the notes we inverted \u2014 B, D# and F#), we see that we can simply call this B Major. This seems trivial in this case, but in other situations it’s not, as we’ll see.<\/p>\n

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Let’s look at the second chord of ATTYA<\/em>, Bbmin7.\u00a0Inverting around the B\/C axis, as before, we get:<\/p>\n

\"\"<\/a>

Bbmin7 \u2014> C#Nmin7<\/p><\/div>\n

We’d be tempted to call this chord D#min7, but that would be wrong. Remember: the root in the positive world is always a perfect<\/strong> 5th below the generator. So the root of this chord is a perfect fifth below C#, i.e. F#. We call this chord F#6.<\/p>\n

\"\"<\/a><\/p>\n

We’re almost there. Things get a little more complicated with chords that don’t already have a perfect fifth in them. The last chord of the bridge of ATTYA<\/em>, C augmented, is a good example. Inverting around the B\/C axis, the notes C, E, G# become B, G, D#. The root of this chord is a perfect fifth below B, so it’s E, even though that note isn’t present in the inverted notes. Looking at the combined notes, B, G, D# with an E root, we see that it’s an Emin(maj7) chord.<\/p>\n

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5.<\/strong>\u00a0That’s it. Now play through the gorgeous results. As long as you’ve picked a tune with strong structure to start with, the negative version should have equally strong structure, but will often be unrecognizable. It’s amazing how much this straightforward, linear transformation completely changes the affect of a tune.<\/p>\n\n\n

<\/div>\n\n\n\n
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Here’s how you do it \u2014 the fast and easy way:<\/strong><\/p>\n\n\n\n

If you play around with what I explained above for a while \u2014 and you should definitely do it this way for a few tunes, if you really want to understand how this works \u2014 you’ll soon discover that producing negative harmony this way is the long way around. There are shortcuts you can take. Here’s the fast way:<\/p>\n\n\n\n

1.<\/strong> Find the axis of symmetry, which is always exactly halfway between the tonic of the song and the perfect fifth above that.<\/p>\n\n\n\n

\"\"<\/figure><\/div>\n\n\n\n

Here’s another way of looking at it using the circle of fifths, for the less piano-oriented. This is how my friend Ben Wendel likes to picture it:<\/p>\n\n\n\n

\"\"<\/figure><\/div>\n\n\n\n

2.<\/strong> Invert the melody around this axis, preserving all the intervals exactly (i.e. perform a chromatic inversion<\/em>, not a diatonic one).<\/p>\n\n\n\n

\"\"<\/figure><\/div>\n\n\n\n

3. <\/strong>Find the chord roots for the inversion: invert the chord roots of the original song the same way as the melody, then transpose them all a perfect fifth down.<\/p>\n\n\n\n

\"\"<\/figure><\/div>\n\n\n\n

4. <\/strong>Notice that chord types always invert to the same chord type. <\/p>\n\n\n\n

\n

minor \u21c4 Major
min7 \u21c4 Maj6
Maj7 \u21c4 min(b6)
7 \u21c4 min6<\/strong><\/p>\n<\/div><\/div>\n\n\n\n

5. <\/strong>Fill in the blanks<\/p>\n\n\n\n

\"\"<\/figure><\/div>\n\n\n\n

6. <\/strong>Enjoy!<\/p>\n\n\n\n

<\/div>\n","protected":false},"excerpt":{"rendered":"

Ever since Five Pedals Deep, my trio record with Thomas Morgan and Ted Poor, came out in 2010, I’ve gotten a steady trickle of emails asking about a particular tune on it called Back Attya. If you listen to it … Continue reading →<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"class_list":["post-368","post","type-post","status-publish","format-standard","hentry","category-music-2"],"_links":{"self":[{"href":"https:\/\/dantepfer.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/368","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/dantepfer.com\/blog\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/dantepfer.com\/blog\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/dantepfer.com\/blog\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/dantepfer.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=368"}],"version-history":[{"count":71,"href":"https:\/\/dantepfer.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/368\/revisions"}],"predecessor-version":[{"id":995,"href":"https:\/\/dantepfer.com\/blog\/index.php?rest_route=\/wp\/v2\/posts\/368\/revisions\/995"}],"wp:attachment":[{"href":"https:\/\/dantepfer.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=368"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/dantepfer.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=368"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/dantepfer.com\/blog\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=368"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}