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2/05/2013

Guitar Theory Lesson 3 - The Concept of Key, Scale Harmonization and Finding the Key of a Song

"What would you do if I sang out of tune, 
Would you stand up and walk out on me?
Lend me your ears and I'll sing you a song,
And I'll try not to sing out of key."

                                      The Beatles - With a little help from my friends



THE CONCEPT OF KEY


On Western music, there is a huge variety of scales and chords. They all have their rules, their "formulae" to be musically correct. But there seems to be a mysterious mental streamline that makes us feel some chords don't combine quite well... as if they're not correctly interpreted.

When this happens, you might rush to verify each chord is not breaking the rules of harmony we've been learning. Even when you find out everything is fine, the chord transition still feels awkward... because they are out of key.

Singing or playing out of key might feel like an idiomatic expression. Maybe it is to some extent, but it is also more technical than you might think. There is a concept called key of a song.

Every chord played individually must respect some kind of order - we've learnt that already. But if they are to be laid in sequence, the whole sequence must have a constant streamline. They must have something in common. That something is a scale, that is instinctively perceived by the listener throughout the chords being played.

Remember when I said musicians use scales like paintors use color palettes? It is true. In a certain way, a paintor would better stick to one palette as he works throughout one of his paintings; using other palettes from other brands and other materials could become evident at the end, with texture differences and such. All the colors he uses on each painting are very likely to belong to the same color palette, so he doesn't have to worry about mending the differences and "dissonances". The musician works the same way. All the chords and notes he plays belong to one scale. If he plays outside the scale, he must know what he's doing and be prepared to mend and blend the dissonance.

And now you say "But scales are made of notes, not chords!". True, but what are chords made of? Notes as well! And where do chords take their notes from? From scales! It's all linked!

What this means is all the notes from all the chords must fit on at least one scale.


Let's take a look at the chords of With a little help from my friends:



E                                  F#m

What would you do if I sang out of tune,
                  B                                    E
Would you stand up and walk out on me?
E                                      F#m
Lend me your ears and I'll sing you a song,
            B                             E
And I'll try not to sing out of key.




The sequence of chords here is E major - F# minor - B major - E major, and then repeats itself.
So, let's write down the major scales corresponding to these chords:

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

The major chords are formed with the first, third and fifth degrees of the corresponding major scale, remember?
1 - 3 - 5

The minor chords, on the other hand, move the third degree half a step down...
1 - 3b - 5


So, E major has E, G# and B.
F# has F#, A and C#.
B has B, D# and F#.


E - G# - B          - E major chord
F# - A - C#        - F# minor chord
B - D# - F#        - B major chord

Considering all the chords, the only notes that are used are:
E - F# - G# - A - B - C# - D#

Have you noticed this is exactly the E major scale? The palette used to build this part of the song was the E major scale! As you can see, the chord sequence throughout the whole verse never uses any note outside the E major scale; that's what helps make the sequence sound pleasant and "stable" to the listener.


The chorus and the bridge of this song use a common rock harmony technique that actually breaks this rule; it would be very confusing to explain right now, so we'll just skip it and come back to it later. But don't worry, you will understand it in a bit.



SCALE HARMONIZATION

What we did just now was some kind of "reverse engineering": grabbing the final sequence of chords and trying to find out how it was built (and with what scale). When a song is written, however, the process goes from scales to chords. But how do composers make sure every chord sticks to the scale's notes?

This process is called scale harmonization. In other words, making harmony (several notes played at the same time) with notes from a scale. Chords within a scale are built with the same principle we've reviewed already: grabbing the first, third and fifth degree and putting them together. However, instead of grabbing the major scale of the chord, we keep working inside the song's scale only. It sounds confusing, I know, but I'll give you an example and you will understand it.

Let's see the E major scale again:
E - F# - G# - A - B - C# - D#

Now imagine you want to play an F# chord staying in the scale of E major. You don't know which type of F# chord fits on the scale of E major. Is it F# major? F# minor? F# diminished? F# augmented?

1 - 3 - 5       - major chord formula
1 - 3b - 5     - minor chord formula
1 - 3b - 5b   - diminished chord formula
1 - 3 - 5#     - augmented chord formula

Whatever the chord type is, there is a pattern: it always involves the first, third and fifth degree of a scale, and then adjusting some degree(s) up or down half a step. So what we have to do to build chords inside one and only one scale is forget about the chord types and simply count one - three - five inside that scale. We don't care about the type of chord - we just need it to use the notes inside the scale!

So, we wanted an F# chord inside the E major scale...
E - F# - G# - A - B - C# - D#           - E major scale

Let's count one three five starting from the F# inside the E major scale. One...
E - F# - G# - A - B - C# - D#

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

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


We have an F# chord built with the 1 - 3 - 5 rule AND making sure we only use notes from the E major "palette"!
F# - A - C#        -    F# chord in the scale of E major


What kind of F# chord is this? Let's look at the F# major scale and find out...
F# - G# - A# - B - C# - D# - F    -      F# major scale
F#    -      A     -     C#                   -     F# chord in the scale of E major

It took the first, third and fifth degree of the F# major scale and lowered that third degree (A#) half a step... That's the way you build an F minor chord!
1 - 3b - 5                  -         formula of a minor chord


Now imagine you wanted a B chord staying within the scale of E major. Let's count one three five starting from the B note on the E major scale...

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

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


...five...

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


We have a B chord with the notes B - D# - F#... what type of chord is this? Let's compare it with the B major scale...

B - C# - D# - E - F# - G# - A#         - B major scale
B    -      D#    -    F#                          - B chord inside the E major scale

It's the B major chord, because it took the first, third and fifth degrees of the B major scale!



This is scale harmonization. It takes a lot of work to do from scratch like we did; this was just to show you the principles of the process. There are shortcuts, because the type of chord only depends on the degree of the note that gives its name to the chord you're trying to build inside the scale. Wow, confusing again.

I     II     III    IV   V   VI    VII
E - F# - G# - A - B - C# - D#

We built an F# chord inside the E major scale. F# is the second degree of this scale, and the chord was a minor chord. The truth is, with any major scale you're working on, harmonizing the second degree of the scale (i.e. building a chord from it) always results on a minor chord. You can try it with other major scales and check it out for yourself if you want ;).

Then we built a B chord within E major scale (i.e. we built a chord from the fifth degree of the scale). We ended up with a major chord. This happens with any other scale as well - harmonizing the fifth degree gives us a major chord.

The pattern for chord types when harmonizing a major scale is always the same. And it looks like this:

I                    II                III             IV               V               VI                VII
major           minor          minor         major          major         minor            diminished


This is a really good shortcut whenever you're working with scales, whether you're harmonizing one or trying to find out the "parent" scale of a sequence of chords.

When you're harmonizing a scale, all you have to do is pick a note from the scale and play the appropriate chord type of that note, according to the note degree on the scale.

When you're trying to find the key of a song (i.e. the scale it was based upon), you do some reverse engineering - you try to think of a scale that has the notes of all the chord's names and the appropriate chord types. This one's a bit more tricky. But with a bit of practice and some additional shortcuts, it becomes relatively easy.


FINDING THE KEY OF A SONG

The only major chords of the major scale are degrees I, IV and V. So, whenever you have an isolated major type, you can fit it on three different scales. Any major chord is the degree I of one scale, the degree IV of another scale and the degree V of yet another scale.

For example, consider the B major chord. As we have seen, B major was the fifth degree of E major scale...

I    II    III   IV   V   VI   VII
E  F#   G#  A    B    C#   D#     -    E major scale

But there must be another scale where B major chord is the forth degree...
I    II    III   IV   V   VI   VII
?    ?    ?     B    ?     ?      ?

If you have a chart of the major scales, it becomes easier to find out that F major scale is the scale with Bb on its forth degree. But what we're looking for is a scale with B, not Bb on IV. All we have to do is raise the whole scale half a step, along with IV. So we get F#, which looks like this...

I       II     III   IV  V     VI    VII    
F#   G#   A#   B   C#   D#   F         - F# major scale

Finally, B major chord as the first degree only happens on the B major scale, obviously.
I       II     III    IV    V     VI    VII
B     C      D    E      F#    G#   A     - B major scale

The same goes with minor chords. On a scale, a the only degrees that harmonize to a minor chord are II, III and VI. So, whenever a minor chord is played, it will be the VI degree of one scale, the III degree of another scale and the II degree of yet another scale.

So, when a B major chord is played, you will stay in key whether you play the E major scale, the F # major scale, or the B major scale. Each scale will sound different, but never awkward over the B major chord. This is a great way to change the "flavour" of what you're playing, and boost your creativity with a technique the guitar masters themselves use. But whenever the chord changes, you'll be lost, and need to figure out the possible scales for the new chord all over again. The ideal would be to find a scale that goes with all the chords that are being played...

Many sites teach you to do this exercise with every chord and cross-match the possible scales for every chord, trying to find one common scale to all the chords. This is certainly one way to do it, and it helps understand the way this all works. But eventually it is very tiring and time-consuming, especially for the musician that wants to be told a sequence of chords and be able to quickly find the scale to improvise and impress everyone else. There are mental shortcuts that help you a lot finding out a scale for all the chords.

1 - look at the major chords and try to find two major chords one full step apart from each other. 
        Example, F major and G major, E major and F# major, Bb major and C major...

     The only way they will fit on a common major scale is putting them as the IV and V degrees of a scale,                           respectively.
        Example: F and G only have in common the C major scale; E and F# only fit together in B major scale;    Bb and C only fit on F major scale.


2 - look at the minor chords and try to find two minor chords one full step apart from each other.

     The only way they will fit on a common major scale is putting them as the II and III degrees of a scale,                           respectively.

3 - look for a diminished chord. 
     A diminished chord can only be VII degree of a scale.


You can now go look for sites with the chords of your favorite songs and find their keys! That is a great way to practice the concepts you learnt today ;)

And finally...

THE TRICK OF THE MASTERS

Remember when I said the chorus and bridge of With a little help from my friends break the rules? They do, in a way that is very common on the rock genre. What they do is use the VII degree of the E major scale, lower it half a step and transform it on a major scale. Many other songs do this; it's a way to break the rules that still sounds pleasant. After all, the true art of music is knowing when and how to break the rules on a creative and pleasant way.
I     II     III    IV   V   VI   VII
E - F# - G# - A - B - C# - D#           - E major scale

Without breaking the rules, only D# diminished chord could be played. But lowering it half a step to D and transforming it on a major chord brings us a D major chord...

Chorus:
               D                   A                 E
Oh, I get by with a little help from my friends
               D                      A                 E
Hm, I get high with a little help from my friends
                      D                    A                  E
Uh, I'm gonna try with a little help from my friends



So we have the modified VII degree (D major), the IV degree (A major) and the I degree (E major).

Bridge:
            C#m       F#m
Do you need anybody?
  E              D          A
I need somebody to love
            C#m    F#m
Could it be anybody?
      E            D              A
It's got to be someone I trust


C# minor is the VI degree of E major scale; F# minor is the II degree; E, D and A were already present on the chorus. It's always the scale of E major!

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