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I have a question on jazz chords, and what notes can be removed from the chord. My understanding is fairly superficial - mostly from what I've read in books. This is what I understand:

In some chords, it is necessary to omit some of the notes in order to reduce dissonance within the chord. For instance, the 11th often clashes with the 3rd in 13th chords, so the 11th is generally omitted.

Further, to make fingering chords more practical (I'm mainly considering guitar here), other notes are often optionally omitted as well. Some examples:

FORMULA                 CHORD NAME            OMITTED   OPTIONAL

1  3 5 ♭7  9  11        Eleventh              3         1 5 9

1  3 5 ♭7  9  11 13     Thirteenth            11        1 5 9

1 ♭3 5 ♭7  9  11 13     Minor Thirteenth      11        1 5 9

1  3 5 ♭7  9 ♯11        Nine Sharp Eleven               1

1  3 5 ♭7 ♭9  11 13     Thirteen Flat Nine    11        1 5

My question now is, how far can we go with removing notes, whilst still retaining the harmony of the original chord?

The chord books I have generally only remove one or two notes from a chord. But I want to know if there are any "rules" around what combinations of notes can or cannot be removed from a chord. What if we take this concept to it's logical extreme:

For example, is this a valid expression of an 11th chord, if I am only left with these intervals?

1  ♭7  11

Probably not, because it looks more like a sus7 chord to me.

What if I then removed the root:

♭7  11

That's definitely going too far now - we don't even have three notes now.

Or is it?

What do others think about this?

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2  
How'd you get the flat and sharp symbols? I've wanted to use them for months! –  Alex Basson Aug 16 '11 at 23:11
    
@Alex You can use something like this for reference if you like, or just copy-paste from a post :) –  Matthew Read Aug 16 '11 at 23:33
    
The sharp and flat symbols are part of unicode: fileformat.info/info/unicode/char/266f/index.htm You can find them in windows "char map" program and then copy them into any text box. Or look at this page: fileformat.info/tip/microsoft/enter_unicode.htm –  asgeo1 Aug 16 '11 at 23:47
    
If you can type Japanese, you can type フラット and シャープ to get the symbols :-) –  snailplane Nov 16 '12 at 19:59

6 Answers 6

up vote 20 down vote accepted

In classical theory, the necessity or lack thereof of a particular chord member is generally determined by the note's tendency to lead to another note. That tendency comes most often from the interval of an augmented fourth or diminished fifth. Enharmonically, those intervals are the same, but in context, they are not, and they resolve differently. In a "dominant seventh" sonority, the third and seventh of the chord form a diminished fifth if the third is below the seventh, or an augmented fourth if the third is above the seventh. In the diminished fifth, the upper note resolves down by step, and the lower note resolves up by step. In the augmented fourth, the upper note resolves up by step, and the lower note resolves down by step. What this means for the dominant seventh is that scale degree seven, the "leading tone," resolves up to tonic, and the chordal seventh, scale degree four, resolves down to scale degree three. Scale degrees one and three strongly imply the tonic chord of the key, so there is a feeling of resolution. In other seventh chords, the seventh still resolves down by step. It is possible in the dominant seventh to omit the root without changing the function of the chord. Often, then, what would have been the lowered ninth is added, providing another diminished fifth or augmented fourth (against the fifth of the chord). If I had a convenient way to draw all this out on a staff right now, I would.

In jazz, we don't always resolve chordal sevenths. However, we still hear the tendencies toward resolution as defining of chordal quality. Further, there are dissonances within chords that we do not necessarily want to sound, as you have pointed out. In those cases, we will keep the note that is more responsible for defining the chord quality (usually). So, in your examples:

  • Eleventh: The third is omitted because of the dissonance with the eleventh. The eleventh is more defining of the chord quality because, without it, you would no longer have an eleventh chord. Further, the eleventh, being a chord member outside the triad of root-third-fifth, has a tendency to resolve down by step. It is resolving "against" the seventh of the chord (even though the interval between the two is a perfect fifth, not a diminished fifth). Because of that, the seventh also should stay. The remaining notes are less important, but to establish the chord quality, it is probably best if the root stays somewhere in the chord if possible.
  • Thirteenth: Unlike in the eleventh chord, the eleventh no longer defines the chord, and it is a weak tendency tone, so it can (and usually should) be omitted in favor of the third. Typically, as in classical theory, when we can keep the third and seventh of a dominant-seventh sonority, we should. The thirteenth is defining, so it should be present. There are no other strong tendency tones, and you already have three notes of the chord (third, seventh, and thirteenth), so feel free to leave everything else out if it sounds fine in context. If you want to include those other tones, that's also fine.
  • Minor Thirteenth: With the flattened third, the diminished fifth between third and seventh is no longer present. This feature completely eliminates the tendency of the third to go upward, and the seventh is now a much weaker tendency tone. On the other hand, the third is the only feature making the chord "minor." So, the third should still be present unless context makes it clear that the chord is minor. The seventh is probably more optional than in the Thirteenth chord, since its tendency is weaker and it does not define the chord when the third is present. The thirteenth must obviously remain, as it defines the chord. The eleventh goes away due to dissonance with the third, though the dissonance is weaker than before and can probably be tolerated. The root is good for defining the minor quality of the chord in some contexts. Other notes can be omitted.
  • Nine Sharp Eleven: The eleventh is not a strong dissonance against the third here. The eleventh defines the chord, so it must stay. Since the third is not a problem and combines with the seventh to create a diminished fifth, both the third and seventh should stay if possible. I believe the fifth really should be omitted due to its dissonance with the eleventh. The other notes seem optional.
  • Thirteen Flat Nine: The flat nine is now defining, so it needs to be present. The thirteenth is likewise defining and needs to be present. The root is a dissonance against the flat nine and is certainly (at least) optional. The eleventh is a dissonance against the third and should be omitted. The root and fifth are not completely necessary.

Note that your assertion of two notes being insufficient to represent a chord is inaccurate. Two-voice baroque counterpoint has clear harmonic progression throughout. The same rules apply when the chords are simpler than those you list. For example, in a major or minor triad, the fifth is not necessary. In a dominant seventh sonority, the third and seventh are necessary (as the tendency tones), while the root and fifth can be omitted.

Of course, if you are playing in an ensemble, other instruments may have chord members that you do not, then, need to double. Finally, if you are performing with a soloist, it is best to avoid using the chord tones that the soloist is using. It will be nearly impossible to do so in an improvised solo setting, but if you are accompanying a known melody line, this principle can guide your voicing choices.

I am not a guitarist, but I hope this perspective generally has been helpful. As on all instruments, technical convenience (or necessity) may guide your choices quite often as well. Don't feel the need to include too many notes, though; sometimes doing so just makes the texture "muddy." Let your ears be your guide.

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Very nice. +1 especially for the concept of "tendency" and its implications for functional harmony. –  Alex Basson Aug 17 '11 at 11:39
    
Wrt 11, both the Dorian and Aeolian modes may retain the third and natural eleventh together, and yield consonant min11 chords. (The iimin11 begins my favorite tritone sub on guitar.) –  Kirk A Apr 24 at 13:17

It depends. It always depends. But the bassist is playing the root and fifth, so I've heard that dropping them in favor of the third and seventh (and ninth, and six, or whatver) is something I've heard suggested.

This analysis of Freddie Green's style shows that he's hitting two notes, and one is muted to be mostly there, but that's in the Count Basie orchestra, where there's many horns and piano to provide the harmony, so the guitar's mostly rhythm.

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General remark: on 7th chords, the 11 is 99% of the time sharp. Otherwise you'll get a minor nineth (aka b9) interval between the 3rd and the 11th.

If you keep the 11th and omit the 3rd, you'll get what is generally refered to as a "sus4" chord, the the 4th/11th tends to resolve to the third, which gives a standard V7 chord, resolving on I Maj7.

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The ii (Dorian) and vi (Aeolian) modes both have natural elevenths which are not dissonant. The IV (Lydian) mode also sounds fine due to the #11 as you describe. –  Kirk A Apr 24 at 12:51

From what I've learned, simply, you only need the 3rd, and all of the extensions above it in a jazz band. Someone in the band will be playing the root, so you don't necessarily have to play it, the 3rd gives the chord some flavor.. it tells if its a major, minor, etc. All of the extensions past the 5th of the chord define it further past what the bands doing, so you'll want to play those also.

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What I am going to write below is just simple jazz harmony fundamentals, and should naturally be considered as school stuff !

You have to understand the role of each voice in a chord, to define what should be played, and what can be omitted.

Mandatory voices

  • The root note defines the root of the chord, and must be played globally. I mean, if you have a bassist, don't play it, if no one plays root notes in the band (e.g. in a duet), play it !
  • The 3rd defines your mode, between Major or minor. So it is also a mandatory note.
  • The 7th, combined with the third, defines the function of your chord. 3rd minor + 7th minor makes a IIm7. 3rd Major + 7th minor (called dominant in this case) makes a V7. 3rd Major + 7th Major makes a IMaj7. 3rd minor + 7th Major makes a ImMaj7.

This is working for basic II, V and I chords, not including altered chords, neither half-diminished chords, nor suspended chords.

Optional voices

  • 5th is most the time omitted. In signal theory, the fifth is the second harmonic, and playing the root note will have this harmonic at 5th level sound, so there is no need to play it.
  • 5th has to be played when it is altered, like in a IIm7b5 chord, a V7#11 chord, or a V7b13 chord.
  • 9th adds depth when added to a II, a V or a I, but does not change its function.
  • It is the same for the 13th in an unaltered V7 chord.
  • 11th, in a IIm7 chord, also adds a color, without changing the function or altering the chord. But this color is less "transparent" than a 9th.
  • Playing the 11th in a V7 chord gives you a V7sus4 chord, but in this case you have to omit the 3rd, because the 11th, called in this case a 4th, replaces the 3rd, in a harmony resolving delay figure.
  • Same remark for the 6th in a IIm7 chord.

Altering voices

This section mainly applies to V7 chords. 5th and 9th can be altered, without changing the function (a V7 remains a V7) but giving deep chord coloring

  • You can lower or raise the 5th, and should play it in this case.
  • You can lower or raise the 9th, and should also play it in this case.
  • You can make all combinations of the 2 previous cases (2x2=4 cases with an altered 5th AND an altered 9th, and 4 other cases when altering one of them and not playing the other).
  • You can lover the 5th in a IIm7 chord, which gives you a IIm7b5 chord. In this figure, you will probably have to play an altered V7 chord, then a minor I chord.
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@Andrew : your post was absolutely brilliant, and "music driven" compared to mine ! Just one remark, as a guitarist and pianist, playing both 3rd and 11th in IIm11 chords is not dissonant, provided the 11th is abobe the 3rd ! –  kall2sollies Nov 16 '12 at 17:03

Notes can be optional for a number of reasons, such as the following:

  1. omitting dissonant voices,
  2. limitations of the instrument (e.g., guitar),
  3. playing "shell" chords in a band context.

Dissonance. While dissonance has been discussed within other answers, those answers did not cite the "rules" for recognizing such chords. For details, reference Berklee Harmony. Chord voices may be divided into “tones" (1,3,5,7) and “tensions” (9,11,13). Generally speaking, dissonant “avoid notes” may be defined as those tensions which create a minor ninth interval (or less) above a chord tone. Dominant chords, however, allow an exception for the ♭9 and ♭13 tensions. Other "avoid notes" also include those tensions which create a tritone interval — the signature dominant sound — within a non-dominant chord. Lastly, in a dominant chord, the ♭13 and the natural 5 should be mutually exclusive. I have illustrated the avoid notes for the C major scale in this table.

Limitations. For example, guitarists don't have the voicing freedom of pianists. When I simplify a chord with omissions, the unaltered fifth is the first to go, since it is implied in the overtones of the root. I typically retain the root, third, seventh, and the highest tension; any additional voices depends upon fretboard fingering.

Band. In a context of other musicians — especially when accompanied by a bassist — it may not be necessary to play the root. In fact, "shell" chords containing just the third and the seventh voices can communicate the essentials without interfering with your band-mates.

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