No__71___Chord Inversions

[Peter Anderson]

Chord Inversions

In music theory the word INVERSION has several meanings.    There are inverted melodies, inverted intervals and (in counterpoint) inverted voices, but we are probably most familiar with the term inverted chords.

By chord inversion, we mean the playing of the same notes in a particular chord, but varying their order or position relative to each other.

For instance, we often play a C chord   as C  E  G.     This is often referred to as the root position, because the note C, is at the bottom and therefore in what we again refer to as the bass or root position.

What difference does inverting a chord make.     Surely, because we are playing the same notes, albeit at different pitches, they must be the same, mustn't they?
Well that is not strictly true.   Read the following postings to discover the subtle difference.

Peter

[Peter Anderson]

SUMMARY

Under Inversion,

Perfect intervals remain Perfect

Major intervals become Minor intervals     and     vice versa

Augmented intervals become Diminished intervals    and    vice versa

Double Augmented intervals become Double Diminished intervals    and    vice versa

Fourths become Fifths     and    vice versa.


So, for example, a perfect fourth when inverted, becomes a perfect fifth

an augmented fourth becomes a diminished fifth, etc.

Here are a pair of Summary Charts:







A Chord's Inversion describes the relationship of its bass to the other tones in the chord.

For example a C Major triad consists of     C,  E  and  G,      and     its inversion determines which of these tones is the bottom note in the chord.

So this term Inversion is mostly used to refer to the different possibilities of where we position the individual notes that make up that chord.

Peter

[Peter Anderson]

Before we explore this further, we have to define an Interval.

An Interval is the distance between two pitches, either heard together or separately, by which we mean either sounding as a chord or played successively, one after the other.

When played together they are called Harmonic Intervals and when played successively they are called Melodic Intervals.

When these two notes are sounded they either sound pleasant or unpleasant.   In 'Western' music consonant intervals sound agreeable, as opposed to dissonant intervals.

Consonant intervals include Major and Minor Thirds, Major and Minor Sixths and Perfect Fifths.

Are Thirds and Sixths related?      If so, how?

To find out more see the next post.

Peter

[Peter Anderson]

Play a simple Major Third.     Let's choose C as an example, so the major third would be the notes:
C  +  E

Now invert it and play the notes:
E  +  C

What are you playing?       Yes that's right - a Major Sixth

C to E   is a Third and spans 3 diatonic degrees, whereas
E to C    is a Sixth and spans 6 diatonic degrees.

So to appreciate that inversion of a Third produces a Sixth and vice versa, will prove helpful to us.

To put this another way, if you think of intervals as having quality and quantity, the inversion of intervals actually changes both their quality and quantity.

Of course, I should point out that perfect intervals are an exception to this.   (But more about these later on.)

For other inversions of an interval, a Major quality will become a Minor quality and vice versa.

But what about the changing of the quantity?
Let us try to understand the quality and quantity of an interval.

Major Third   
Here the Major refers to the quality of the interval and the enharmonic environment surrounding it.
While the Third refers to its quantity, i.e. the size of the interval.  This is depicted by the number of scale tones covered.

So when we invert an interval (or chord) we invert the quality and the quantity of that interval, as well.    Remember then, that words like Major describe quality and words like Third describe quantity.
Here are some simple examples, that you won't need a keyboard for, but if you prefer  to use yours, then by all means move to your AR.   By playing them you will detect the differences in the sounds you hear.

1       Major Third
Inversion of quality      Major becomes Minor
Inversion of quantity       Third becomes Sixth
Therefore a Major Third, when inverted becomes a Minor Sixth.

2       Minor Third
Inversion of quality      Minor becomes Major
Inversion of quantity       Third becomes Sixth
Therefore a Minor Third, when inverted becomes a Major Sixth.

3       Minor Sixth
Inversion of quality      Minor becomes Major
Inversion of quantity       Sixth becomes Third
Therefore a Minor Sixth, when inverted becomes a Major Third.

4       Major Sixth
Inversion of quality      Major becomes Minor
Inversion of quantity       Sixth becomes Third
Therefore a Major Sixth, when inverted becomes a Minor Third.

We look at the perfect fifth in the next posting.

Peter

[Peter Anderson]

Now what about the Perfect Fifth?     We alluded to this in the previous posting.

This is another consonant interval, which in classical music is called the perfect consonance.

It contains two very important scale degree notes.    These are the tonic, or base note, and the dominant or the perfect fifth note.

In our example of the key of C, these notes are
C  (tonic)      +      G    (dominant)

The term perfect fifth describes the relationship in pitch between these two notes.

Now when a perfect fifth is inverted, its quality remains the same, because perfect intervals remain perfect after inversion.
However a perfect fifth when inverted changes its quantity, as a perfect fifth, when inverted becomes a perfect fourth, and vice versa.

It goes without saying, but remember, all this is true for all 12 keys.

In the next posting we explore Triads and how the intervals we have discussed above are the building blocks of Triads.

Peter

[Peter Anderson]

Triads contain, yes you've guessed it, three elements.   That is why they are called triads.   

These three elements are the Root, the Third and the Fifth.

So, knowing that triads contain a third and a fifth, it means that these consonant intervals are the building blocks of all triads.
We use thirds and fifths to build triads and most thirds and fifths are consonant.   We already know that there are major thirds and minor thirds, but there are also diminished and augmented thirds and fifths.   But, these diminished and augmented thirds and fifths are dissonant intervals.

That means that triads can be categorised into consonant and dissonant triads.   This is because Major and Minor Triads are formed from consonant intervals.   Whereas, diminished and augmented triads are formed from dissonant intervals.

The technical term for triads formed from consonant intervals is concord.

Therefore, major and minor triads share this in common - they are concords - because the intervals that make them up are consonant.    i.e. the quality of the third and the fifth.

To restate these qualities again:

we have        Major Third
                     Minor Third
                     Perfect Fifth

which means there are 2 qualities of thirds and one quality of fifths.     So this implies that Major and Minor triads differ in their quality of Thirds, but have a Perfect Fifth in common.

The Major Triad has a Major Third, whereas the Minor Triad has a Minor Third.

This is different for Diminished and Augmented Triads, which we explore later under Dissonant Intervals.

Peter.

[Peter Anderson]

Let us now consider the Perfect Fifth.

You ought to know all the Fifths, in every key, like the back of your hand.

A wonderful aid to this is the Circle of Fifths, which you will find in the Playing Technique section.

To read about that click this link to go directly there:

http://www.ar-group.org/smforum/index.php?topic=954.0

Perfect Fifths are easy to play because of their colour pattern!      Over 83% of them have the same colour pattern.      What do I mean?

If you categorise the perfect fifths by their colour pattern,  (i.e. the colour of their notes, by which I mean White or Black)  you will have 4 different colour patterns.      Colour Patterns are a simple aid to memorising these intervals and we see more of this idea in subsequent postings.

These are
White  -  White
Black  -  Black
White  -  Black
Black  -  White

If you memorise them according to their colour patterns that makes it easier.

So let's list all of them that way.

White  -  White

C      -       G
D      -       A
E       -       B
F       -       C
G      -       D
A      -       E


Black  -  Black

C#    -      G#
F#    -      C#
Eb    -      Bb
Ab    -      Eb


White  -  Black

B      -       F#


Black  -  White

Bb      -      F


Since the White - White, and Black - Black retain their colour when inverted, you can see that just one sixth, or less than 17% change colour, when inverted.

So the B changes from a White - Black pattern, to a Black - White pattern.
Similarly the Bb changes from a Black - White pattern, to a White to Black Pattern.

Notice with the inversion of a Perfect Fifth

The quality remains unchanged.       i.e.  Perfect.

However the quantity changes from Perfect Fifth to Perfect Fourth

In the next posting you can learn more about Thirds.

Peter

[Peter Anderson]

Thirds.

Thirds are the building blocks of harmony, so knowledge of them, both Major and Minor, in all keys, will assist you as you mature in harmony.
Note that every tertian chord, no matter how large it is, is divisible into thirds.

First we consider Major Thirds

So let us use the same colour pattern as we used in the last posting to list our Major Thirds.   
These are
White  -  White
Black  -  Black
White  -  Black
Black  -  White

White  -  White

C   -   E
F   -   A
G   -   B


Black  -  Black

F#    -    A#              (this is the same as       Gb   -    Bb)


White  -  Black

D    -   F#
E    -   G#
A    -   C#
B    -     D#


Black  -  White

Db    -    F
Eb    -    G
Ab   -     C
Bb    -    Eb

Obviously when inverted, White to White, and Black to Black patterns do not change.
However, Black to White, and White to Black patterns will change.


So, as we read in the earlier posting, when we invert Major Thirds, the quality changes from Major to Minor, and the quantity changes from a Third to a Sixth.

So a final reminder, when inverted All Major Thirds become Minor Sixths

In the next posting we explore Minor Thirds.

Peter

[Peter Anderson]

Minor Thirds

So here we categorise our Minor Thirds in to the (hopefully) now familiar Colour Pattern.

White  -  White

D    -      F
E    -     G
A    -     C
B    -     D


Black  -  Black

C#    -   E
F#    -   A
G#   -    B


White  -  Black

C   -   Eb
F    -     Ab
G   -     Bb


Black  -  White

Eb   -   Gb
Bb   -   Db


So here again the White - White, and the Black - Black patterns do not change when inverted, but the White to Black, and the Black to White will change.

But as we saw in an earlier posting, their musical quality and quantity changes, when they are inverted.
When we invert Minor Thirds, the quality changes from Minor to Major, and the quantity changes from a Third to a Sixth.

All Minor Thirds when inverted become Major Sixths.

Peter

[Peter Anderson]

You can obtain a Minor Third, by shrinking the interval of a Major Chord by a semi-tone.

Obviously there are two ways to do this.    You can either Lower the 3rd tone, or raise the Root tone by a semi-tone.

Let us use the       C  -  E    major third as an example.

First let us lower the 3rd tone, so the notes change from

C   -     E             to

C   -     Eb            which is a Minor Third interval, but in the same key.


Now if we raise the Lower tone of our example so altering our

C    -    E             to

C#   -      E              we still have a Minor Third interval, but on a different note, so it is in a different key.

Therefore it is more common to lower the Upper note, the Third, by a semi-tone.


Enharmonic Intervals

All the Minor Third Intervals are enharmonically equivalent to Augmented Second Intervals.   This means that the only difference between them is the wording we use to define them.
In practice, the ear cannot distinguish between them when they are played.

C   -   Eb       is a Minor Third.

C   -   D#       is an Augmented Second.

But they look alike on the Keyboard and sound the same.

I suppose you could show off by asking, "What's the difference between a Minor Third and an Augmented Second?"      However I can imagine the response from most people, so don't bother.

In the next posting we cover Major Sixths.

Peter

[Peter Anderson]

Major Sixths

When we play Sixths we are obviously covering larger intervals.

Again let us categorise the Major Sixths by using our colour scheme.

White  -  White

C    -      A
D    -     B
F    -     D
G    -    E


Black  -  Black

Db    -   Bb
Gb    -   Eb


White  -  Black

E    -    C#
A    -    F#
B   -     G#


Black  -  White

Eb   -   C
Ab   -   F
Bb   -   G


When Major Sixths are inverted, although White - White, and Black - Black, do not change, White - Black, changes to Black - White and vice versa.

But as we saw in earlier postings, their musical quality and quantity changes, when they are inverted.

When we invert Major Sixth intervals, the quality changes from Major to Minor, and the quantity changes from a Sixth to a Third.

All Major Thirds when inverted become Minor Sixths.

All Major Sixths intervals, when inverted become Diminished Seventh intervals.

In practice the ear cannot distinguish between a major sixth and a diminished seventh interval.

Note:      All Major Sixths intervals are enharmonically equivalent to Diminished Sevenths intervals.


Technically        C   -   A       and        C    -   Bbb         are two different intervals.
Bbb  is  B flat flat,    or B double flat.

C   -   A      is a Major Sixth
while         C    -   Bbb    (notice the double flat)     is a Diminished Seventh.

This means that the only difference between them is the way we write them, because they sound the same, as they use identical notes.


Peter

[Hugh Wallington]

Peter,

I suppose hearing is a bit like seeing, in that I can close my eyes and visualise a river flowing past.  The brain puts in all the missing detail.  If I hum a tune I know, I can 'hear' all the harmonies that go with it .. and I can sit at a piano (keyboard) and can 'search out' those missing notes that my brain tells me are there.  If I ask Bronwyn what the tune is that I am humming, all she hears is me making an appalling groaning noise, yet I can hear the full orchestra playing.  No wonder she can't identify the song I am trying to put a name to.

So maybe with an 'interval' formed by just two notes, the brain needs a few more notes before deciding whether C- A is C6, Cdim, or Am.  If I added an E it could be C6 or Am .. but not Cdim.  If instead, I added an Eb it could no longer be Am, but could be Cm or Cdim.  By adding a Gb as well, the brain at last can discard the Cm and latch onto the Cdim.  Maybe we need to play 4 note chords rather than 3 note chords for the brain to be certain as to what we are playing.

Hugh

[Peter Anderson]

Minor Sixth intervals are a shadow of the Major intervals, which we looked at in the 3rd posting, above.

So let us categorise these by that aid to memory, the colour patterns for all the minor sixth intervals.

White  -  White

E    -      C
A    -     F
B    -     G


Black  -  Black

Bb    -   Gb


White  -  Black

C    -    Ab
D    -    Bb
F    -     Db
G    -    Eb


Black  -  White

C#   -   A
D#   -   B
F#   -   D


Again, when minor sixths are inverted, the Black - White change to White - Black and vice versa.
Obviously, White - White, and Black - Black do not change.

More importantly Quality and Quantity of minor sixths intervals change when they are inverted.

The quality changes from Minor to Major, and the quantity changes as a Sixth becomes a Third.

To summarise, all Minor Sixths, when inverted become Major Thirds.

You can find the notes for a Minor Sixth, by shrinking the interval of a Major Sixth, by a semi-tone.
To do this we can either raise the bottom note, or lower the upper note, by a semi-tone.

Although both methods will produce a Minor Sixth, it is more common to lower the upper note, because this keeps the minor sixth in the same key.      Raising the bottom note by a semi-tone changes the key.


Note:      All Minor Sixth intervals are enharmonically equivalent to Augmented Fifths intervals.


Technically        C   -   Ab       and        C    -   G#         are two different intervals.

C   -   Ab      is a Minor Sixth
while         C    -   G#        is an Augmented Fifth.

This means that the only difference between them is the way we write them, because they sound the same as they use identical notes.

Peter

[Peter Anderson]

Now let us look at what we mean by Chord Inversion.

Like Intervals, triads can be inverted by moving the lowest note up an octave.

The lowest note, which is the bass note, determines the name of the inversion.

When the lowest note is the root of the chord, the triad is in Root Position.


Let us take C Major as an example - i.e.    the three notes     C   E   &   G


And in the root position we would play       C    E    &   G    in that order.



Let us invert it.

We do this by moving the lowest note up an octave and so  ......

we play                 E    G    &          C  (an octave higher)

This is called the first inversion.     The Third becomes the bass or the lowest note.




Now let us invert it again so we play.........

G    C    &    E     again in that order.

This is called the second inversion.    This time the Fifth becomes the bass or the lowest note.



Notice that if we invert it for a third time, the triad reverts to its original root chord, albeit an octave higher.

Peter

[Peter Anderson]

Here is an additional thought that you may find helpful.

On the Yamaha AR whichever inversion you use the instrument recognises it as the basic chord.    If you experiment with all the inversions of the Chord of C, you will notice in the Voice Display screen, the Chord will always be shown as C.  This is true no matter how far apart the notes that make it up are from each other (you will have to use two hands to fully demonstrate this).

Therefore, if you select Auto Bass Chord, then Fingered Chord, it will always play the Home Bass note.     For any inversion of the C Chord this will be, of course, C.

If the music designates    C/E you cannot play that using A.B.C.   It will actually play a C bass note with the C Chord.   But since you have a pedal board, you can physically play the variation of a C Chord with an E Bass.

Now here is the point, that I want to make.
If you are playing a keyboard, that doesn't have a set of pedals, then by inverting the chord you will 'play' the correct bass note, that is stipulated.
So for an C/E use the first inversion of C, and for C/G use the second inversion.
This is true for pianists as well.    Emphasising the bass note when using inversion on a keyboard or piano means that you can sound the correct bass note for that particular chord.

Equally if you use a particular inversion regularly, to make it easier for yourself (saving a lot of awkward finger adjustment) it will actually sometimes  'play' the wrong bass note, either with A.B.C. or simply because the lowest note will be sounding as the bass.

Peter

See comment from me with an MP3 DEMO, on Page 2 .. Hugh