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How to find chords and scales using simple formulas.
The only musical knowledge you need is the ability to read the melody line and
how
to find
the
notes
on a keyboard.
If you can do that playing keyboard is easy. If you
can't do that please visit your local library and borrow a book for beginning piano.
Did you know that a keyboard can be played using mathematical formulas?
Well, it can but some
people find it difficult to get to grips with maths. However, with this system you only need to be
able to count up
to nine. Now, there are seven
very simple formulas to help us find
all the scales
and most of the important chords. Here they are:
2212221: Major Scales.
2122122: Minor scales.
4 + 3: Major chords. = Triad ( 3-note chord).
4 + 3 + 3: Major 7th. Chords (4-note chord).
4 + 6: = Major 7th. Chords = (3-note chord).*
*This is easier to play but I recommend you go for the full, 4-note 7th. chord using inversions.
3 + 4. Minor chords. = Triad (3-note chord).
3+4+3. Minor 7th. chords. (4 note chord).
3+3: = Diminished chord.
4+4: = Augmented chords.
And that's all there is to it. Who needs chord charts? Just remember the 7 formulas
above and you will be
able
to find all the scales and all the most widely used chords on a keyboard.
And the great thing about
this system is that you don't actually have to remember
loads
of scales and chords because, with these formulas, you already know them all!
Here is how it works:
Finding the scales.
Let's start where everybody starts from - Middle C.
Every note which we start with, for our formula, is always the 'Root Note', also called
the 'Home note', and is zero-rated. In other words it is never counted. See below:
C scale. C is zero rated because it is the Home/Root note.
C D E F G A B C
0 2 2 1 2 2 2 1
If you start at C and count every note from there - including the black notes - using the above formula you will play the C scale. C is the home note. Now count 2 and we hit the D. Now count 2 again and we hit the E, now count 1 and we hit F, and so on. No matter which note you start on - as the home note - you will always end up playing the correct scale. Try it out for yourself right now. Easy, isn't it. In about two minutes you have learned how to play every scale there is. Great! Look at the scale of Bb below:
| Bb |
C |
D |
Eb |
F |
G |
A |
Bb |
The Bb scale using the formula underneath it. |
0 |
2 |
2 |
1 |
2 |
2 |
2 |
1 |
It works every time and takes a minute or so to remember. Try finding any scale picking any note
to start with. |
Minor scales: Use the above rules and the following formula to find all the minor scales: 02122122.
Now for the best part!
How to play all the most important chords without having to remember how
to play them all.
And remember, count all the notes including the black ones but
not the home note.
Major chords.
Let's start with C again: Formula: 4 + 3
C is Home note. Count 4 which takes us to the E, then count 3 which takes
us to the G.
So C + E + G is the C chord.
Now try Eb.
Eb is the Home note. Count 4 which takes us to the G. Now 3 which
takes us
to the Bb.
So - Eb + G + Bb - is the Eb chord. And there you have it.
Major 7th.
Formula: 4 + 3 + 3. (4-note 7th. chord). (Major chord formula + 3).
C7: Home note C + 4 is E + 3 is G + 3 is is Bb. ( C + E + + G + Bb ) 4-note chord.
D7: Home note D + 4 is F# + 3 is A + 3 is C ( D + F# + A + C ) 4-note chord.
So, with the Major and Minor chords just add 3 to the count to get a 7th. chord.
Minor chords.
Formula: 3 + 4.
Let's start with F# minor.
F# is Home note: Plus 3 is A + 4 is C#. ( F# + A + C# )
Ab minor.
Ab is Home note: Plus 3 is B + 4 is Eb. ( Ab + B + Eb )
N.B: Major and minor chords are usually always triads - 3-note chords. Seventh chords should always
be 4-note chords to give them depth.
To change a major chord into a minor just lower the second note - within the formula - one half step.
( semitone).
C major = C + E + F. The second note is E so lower it a half step to Eb. C minor = C+Eb+F.
G major: G + B + D. The second note is B so one half step back takes it to Bb. G minor = G+Bb+D.
Minor 7th.
Formula: 3+4+3. ( Minor formula + 3).
D minor 7th.
D is the home note: Plus 3 is F + 4 is A +3 is C. ( D + F + A +C). (The inversion of CDFA may be easier for you to play).
Most songs can be
played using only the major, minor and seventh chords.
Diminished Chords. (o = dim).
Formula: 3+3. (usually written o, or dim )
Gdim: G is the Root note + 3 = Bb + Db. (G + Bb + Db).
Augmented chords. (aug) (usually written +, or aug)
Formula: 4 + 4.
B+: B is the Root note + 4 = Eb + 4 = G. (B + Eb + G).
There are, of course, inversions to all the chords which you can easily work out for yourself. Any combinations of each chord will work on a keyboard. You simply choose the one which works best for
you, or is easier for you to play. Sometimes you will not be able to play a particular inversion as it might
go beyond the 'Split' point on your keyboard. For example, I cannot play Bb7 on my keyboard in the first mode as it goes past my split point which is the F below Middle C. So I play the inversion: F, Ab, Bb, D.
We are discussing here only the most widely used chords. The more experienced you become with your playing the less you'll need the formulas. But heh, if they help you remember your chords use them all the time.
To check your chords and inversions download a free Chord finder software package. Try Will Dallimore's free keyboard chord chart here. Download
As an exercise why not try to work out the formulas for 6th. and 9th. chords. You will not be called upon
in your early playing days, as a beginner, to play 6th. and 9th. chords on a keyboard, guitar players are more likely to use these.
Have you noticed that the Major, Minor, 7th, Augmented and Diminuished chords all have a formula containing combinations of only two numbers? 3 and 4.
There is a Chord Chart with over 100 popular chords for you to download and print in PDF format.
View it Here. Use right click and 'Save Target' to copy it to your desktop. Plus a formula reminder for you to print and keep by your keyboard Download.
Here is a very popular song from the 60s with easy chords: Mack the knife ( from the Threepenny opera) again in PDF format. It also comes with a MIDI file for you to listen to and download.
Sheet Music | Midi.
You will need Adobe Acrobat to view the PDF. Download it free below.
Adobe
Study all the above information and remember it. It's not really difficult. Once you have these formulas committed to memory you will never have problems in remembering all the most widely used chords.
As you can now see it is possible to play keyboard using mathematics.
Remember this!
There are thee major chords in each scale based on the 1st. 4th. and 5th. notes in that scale. If you
played only the three major chords in each song you play you'll play to an acceptable level,
but your playing would sound a lot better if you also played minor and seventh chords.
Also, you should experiment by inverting the chords to see if you get a more pleasurable sound. Major chords always sound better when inverted and not in the root position.
When counting the notes in a scale, for the 1st. 4th. and 5th. notes, the home note is counted as 1.
So in the scale of C, the first chord (Note 1) would be C major, the second chord (Note 4) would be F major and the third chord (Note 5) would be G major.
As a beginner I used to work out the Key (scale) I would be playing in (2212221) write it at the top of
the page, then I would write the Formula along side it. So the top of my page would look like this:
Scale = G. (G A B C D E F# G). Formula 4 + 3. Main chords = G, B, C. If I missed a chord I would simply play one of the three main chords for that scale and usually got away with it, but not always. NB. You should always play a chord which has the melody note in it.
There's only one thing left for you to do now - Practice!
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