Friday, September 21, 2012

Life Beyond the Triad

Chords Extensions


Eventually most arrangers and composer seek fresh harmonies and unexpected harmonic movements.  To do that requires venturing into the province of the jazz-cats:  the 9th, 11th and 13th chords.   This province is not terra-incognito and there be no dragons.  It is all quite logical and the essential rules are clear and simple.

Tones added to the basic triads (major, minor, diminished, augmented), 6th and 7th chord are called “chord extensions”.  These additional tones form 9th, 11th and 13th chords.  Each of these chords can be major, minor, augmented, suspended, use the flatted 5th, introduce a 6th, and more. 

All Chords are Just Stacks of 3rds


By convention, chords are constructed as stacks of 3rds. Each set of bracketted numbers is an interval of a 3rd. 

Basic Triad 1 - 3 - 5
[1 to 3] plus [3 to 5]

7th or MAJ 7th chord 1 - 3 - 5 - 7 
[1 to 3] plus [3 to 5] plus [5 to 7]

9th chord 1 - 3 - 5 - 7 - 9
[1 to 3] plus [3 to 5] plus [5 to 7] plus [7 to 9]

11th chord 1 - 3 - 5 - 7 - 9 - 11
[1 to 3] plus [3 to 5] plus [5 to 7] plus [7 to 9] plus [9 to 11]

13th chord 1 - 3 - 5 - 7 - 9 - 11 - 13
[1 to 3] plus [3 to 5] plus [5 to 7] plus [7 to 9] plus [9 to 11] plus [11 to 13]

This stacking of 3rds is the reason a 9th chord is NOT called a 2nd chord.  The interval of a 9th is just the interval of a 2nd played an octave higher.  However, the convention of stacking 3rds requires the chord to be called a 9th.  Remember the 9th is a 3rd above the 7th just as the 7th is a 3rd above the 5th.

Okay, one exception.  That pesky 6th chord:   1 - 3 - 5 - 6.  A D6 chord is spelled D - F# - A - B.  But,  voice the chord using the 6th tone as the root.  Now, stacking 3rds, the chord becomes B - D - F# - A.  That chord is a Bm7.  Think of any 6th chord as a 1st inversion voicing of the relative minor 7th chord. That is D6 is the same as a first inversion of a Bm7 chord.  Just as a G6 is a first inversion of Em7.   And, A6 is the first inversion of an F#m7 chord.  So, how do you know what to call the chord?  Context will decide.  What the chord is called does not change the way a listener perceives the music.

Musicologists are still uncertain about how to correctly describe the keys and name the chords Wagner used in some of his music.  Don't let ambiguity in naming complex chords put you off.  Learn the sound they make and experiment with them in your music.  The result you achieve might correctly have more than one name. 

Options - Uncontrolled Growth!

All this means that very quickly the arranger’s little pallet of three chords for each melody tone explodes into a mind-numbing catalog of possibilities.  A basic triad uses three tones out of the seven available on the diatonic scale.  Ignoring chord inversions, using only triads, there are thirty-five available choices on the diatonic scale.  That’s manageable. 

However, chord extensions expand the numbers greatly.  For example, let’s say we limit an arrangement to triads, 7ths and 9th chords.  Now the available chord choices number at least seventy.  Open up 11th and 13th chords and the number of available chord options soar.  Include augmented, diminished and suspended chords or chord alterations like the flatted 5th as options and the available chord possibilities seem to fill an encyclopedia.  Seems like the sort of database waiting for a smart-phone app!

Two practical points need to be made about 9th, 11th, and 13th chords.  If these chords are played in full, the dissonance can be overwhelming.  Often players drop some of the tones.  The 3rds and 5ths are often dropped in 11th and 13th chords.  A “full” 13th chord uses all of the diatonic scale.  Think about putting your forearm on the white keys of a piano to cover one octave in the key of C.  That’s the sound of a closely voiced 13th chord.  The sound is absurd! In any event, a hammer dulcimer player has only two hammers.  Physical limitations will restrict how many tones can be played at any point in the music.  Perhaps five.  But more than likely three or four.  Choose the chord members carefully to create the color you want to achieve.

The second point is that for clarity, the extensions are generally played in the higher registers.  When the extensions are voiced low in the chord, the effect is often muddy.  So, as a guideline, voice the color high.  Voice the root and basic triad low.  Plenty of exceptions to this guideline exist.  However, this voicing distinction is a good starting point to help you choose the chord members that will finally create the harmony. 

Getting Rid of Harmonic Clutter


Very often, these chord extensions will use the basic triad and add the interval that names the chord.  For example, a D9 chord is spelled:  D – F# - A – C – E.  But a Dadd9 chord is spelled D – F# - A – E.  The Dadd9 is often a better choice.  This chord choice gives harmonic color without generating harmonic clutter and a muddy sound.  The practice of dropping out some tones is especially important when playing solo as many hammer dulcimer players do.  In large ensembles, individual chord tones can be played by different voices.  Trumpet, sax, and bass can each play one of the important chord tones while the piano and guitar fill in the missing tones.  The different voices make the chord sound bigger and clearer and often reduce the feeling of harmonic clutter.

Chord extensions make it possible, perhaps likely, to construct chords that, in practice, are never used.  This is an arena in which aesthetic judgment has to rule.  That judgment comes through critical listening and thoughtful experimentation. 

The table below shows most of the options an arranger has when using a 9th chord built upon a G Triad.


9th Chord Options on a G Chord
Name
Symbol
Spelling
Example using a G Chord
Major 9th
Gmaj9  or  G9
1-3-5-b7-9
G-B-D-F-A
Dominant 9th
G9
1-3-5-7-9
G-B-D-F#-A
Minor 9th
Gm9 or G9
1-b3-5-b7-9
G-Bb-D-F-A
Augmented 9th
G+9 or Gaug9
1-3-#5-b7-9
G-B-D#-F-A
Augmented major 9th
Gmaj9+
1-3-#5-7-9
G-B-D#-F#-A
Suspended 9th
Gsus9
1-4-5-b7-9
G-C-D-F-A
Diminished 9th
Gdim9
1-b3-b5-b7-9
G-Bb-Db-F-A
9th , flat 5
G9 b5
1-3-b5-b7-9
G-B-Db-F-A
Six nine
G 6/9
1-3-5-6-9
G-B-D-E-A
7th flat 9
G7b9
1-3-5-b7-b9
G-B-D-F-Ab
7th sharp 9
G7#9
1-3-5-b7-#9
G-B-D-F-A#
7th, flat five, sharp 9
G7b5#9
1-3-b5-b7-#9
G-B-Db-F-A#
Minor, major9th
G(maj9) or GmM9
1-b3-5-7-9
G-Bb-D-F#-A


A great exercise is to reproduce this table for the 11th and 13th chords.  Most importantly, place these chords on the dulcimer to hear their sound.  You’ll quickly find the ones that are useful and the ones that are lost either to harmonic clutter or the physical limitations of two hammers.