Primary Music Theory
  Inversion of triads
 

 
A triad consists of three notes and has three inverted positions. To understand the essence of the inversion, let's examine it on the piano. C Major triad consists of notes: C - the first degree, E - the third degree, G - the fifth degree. Let's play these notes simultaneously; such position of notes within a triad is called "the root position" or just a triad. Now we shift C by an octave higher, so E is the lowest. This shape is called the sixth chord (because of the interval of a minor sixth between the last sounds) or the first inversion. If we shift E by an octave higher, we will get the last inversion of a given triad. G is the lowest note now. This inversion is called the six-four chord (because of a fourth between the first and the second sounds and the interval of a major six between the first and the third sounds) or the second inversion. The next transfer of a G note on an octave above will lead us to the initial position C, E, G, that is to the root position but one octave higher.
Now let's view triad's shapes on the guitar neck. A guitar has six strings, and every inversion can be disposed twice, as it is shown on the picture below. We get three figures, and each of them begins on the sixth string and ends on the first. The first figure, which begins from the first degree, a C note (on the sixth string, the eighth fret), is the exact copy of inversions viewed above on the piano.
Look attentively at the picture; notice that we can play inversions when we move the left hand to the next shape and when we down the left hand on a string below.


It is very important to remember that all keys have the same arrangement. So having learned exercises for example in the C Major key, we can use these applications in any other key. Let's examine every inverted position of the C Major triad separately. Many-colored circles show degrees of the mode, one-colored -fingerings.

Examining the picture "Inversion of triads in the key of C Major" we can notice that any passage of three notes in the inverted positions is a triad in its root position or a sixth chord, or a six-four chord.
As it was mentioned above, the inversion of a chord do not change its harmonic function, the essence of a chord remains the same. This is the reason for a wide usage of a per bar chord notation in contemporary music, where chord inversions are not marked. For example: |G |Am |D7 |G ||, you can use any inversions of these chords, and this won't change the "harmony" of the given passage, because harmonic functions of chords depends on mode degrees from which the chord is built, while inversions are only an octave variations of chord degrees. Let's divide received three inverted figures into all possible triadic fragments. We can see four levels of inversions located across the neck. The first level begins from the third string, the second - from the fourth string, the third level - from the fifth string, and the fourth - from the sixth string. The third and the fourth levels have the same fingerings, because they are located on strings tuned in straight fourth.
Next pictures show the discussed levels in the key of G Major.


As it was mentioned above, all received triads on all levels are the same triad in its various inversions. It appears from this that, while building compound chords, for example G/A (a G Major triad with A in the bass) or G/F (a G Major triad with F in the bass) so on, any G triad from the viewed above will fit; it may be any inversion, built from any level. The only condition is that, we have to find the shape, where we can take a triad and a bass with one hand. It isn't difficult to find a handy combination, because triads and their inversions cover almost all the guitar neck, by the considered rule.
Further, for mastering the material, exercises, based on diatonic sequences of triads with the tonic bass, are suggested. On any level we can play diatonic sequence from any inversion. So as the third and the fourth levels have the same fingerings, we can take only first three levels for exercises. There are three levels with three inversions on each level. Altogether we have nine different sequences.
Below you can find all diatonic sequences based on the first level, that is a diatonic sequence of a triad in its root position, a diatonic sequence of the sixth chord and the diatonic sequence of the six-four chord. The second and the third levels are presented as the diatonic sequence of the six-four chord. Altogether there are five exercises. Let's remember, that a diatonic sequence is a sequence of triads built on the major or minor mode degrees. This is a diatonic sequence in the Major -  |I |IIm |IIIm |IV |V |VIm |VIIm-5||, a diatonic sequence in the Minor - |Im | IIm-5|III  |IVm |Vm |VI |VII ||. To play this sequence, we need to know only three different fingerings. These are fingerings for major, minor and half-diminished triads. Incidentally, here are presented some basic variants of the right hand arpeggiato. Initial positions are contoured in green dotted line. Exercises begin with those positions.
Basic thirteenth diatonic chords with the bass
on the low-E string (the first superposition)

Basic thirteenth diatonic chords with the bass
  on the A string (the second superposition)

The below fingerings for the thirteenth chords are standard for all keys. Having learned these in the G Major key, you can use them from any other note, in any key.
The below fingerings for thirteenth chords are the second level of standard fingerings of "thirteenth chords". Thirteenth chords which are built on the first degree of a Major key and on the first degree of a Minor key are "standard". All other diatonic thirteenth chords can be built by altering corresponding degrees of "standard" fingerings.

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Major thirteenth chord
Minor thirteenth chord with the risen thirteenth degree
Minor thirteenth chord with the lowered ninth degree
Major eleventh chord with the risen eleventh degree
Major minor thirteenth chord (dominant thirteenth chord)
Minor thirteenth chord
  Half-diminished seventh chord
   Diatonic thirteenth chord sequence in the first superposition
  Major thirteenth chord
Minor thirteenth chord with the risen thirteenth degree
Minor eleventh chord with the lowered ninth degree
Major eleventh chord with risen eleventh degree
Major minor thirteenth chord (dominant thirteenth chord)
Minor thirteenth chord
   Half-diminished seventh chord
   Diatonic thirteenth chord sequence in the second superposition
Diatonic progression of a triad in its root position.(in the key of D Major)
Diatonic progression of a sixth chord (in the key of A Major)
Diatonic progression of a six-four chord (in the key of E Major)
Diatonic progression of a six-four chord (in the key of A Major)
Diatonic progression of a six-four chord (in the key of E Major)
Two-octave triad arpeggio in the root position
Two-octave sixth chord arpeggio
Two-octave sixth-four chord arpeggio
    © musicsch.com 2010-2012 GennadiyKlyuevskiy
Picture shows actions of a right-hand man
Picture shows actions of a right-hand man
Picture shows actions of a right-hand man
  Picture shows actions of a right-hand man
Picture shows actions of a right-hand man
 
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Inversion of triads in the key of C Major