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Keys and Chords - Foundations for Understanding Music
What follows is initially extremely complex. If you wish to try to understand it, it may help for you to have a teacher to help explain it to you. You can then use what follows for reference and continued study. If you do not have a teacher then I would encourage you to read all of what follows, even if much of it goes over your head. Then re-read the information regularly trying to understand it by using it. Hopefully you will begin to understand a little better each time you try to read it and apply it. Much of what we learn is learnt best as we try to use or apply it. Imagine trying to learn to drive a car without actually driving. We learn as we do. And as you try to apply it, you can keep referring back to these pages and re-read the relevant parts in order to understand them better. It may take some time before it makes complete sense, but once you understand it you will be in a position to really understand how music is formed and understand the foundations of music.
I believe that the most important foundation in learning music is chords. At the Rock & Pop Music School we begin by teaching pupils to become confident in playing their chords (this, of course, is in the case of keyboard and guitar players). In what follows I will outline chord theory. If you can grasp this, I believe you will have the key tools necessary in order to understand music. I may slightly simplify some information in what follows, since it is more important to me to explain things in a way that helps the reader to understand what is written, rather than to explain it in all its technical complexity.
Notes are grouped in octaves. There are 12 different notes in each octave. An octave can begin on any note. Let us for example assume an octave begins on the note C. (Notes are given letter names). Then count up 12 notes and you will reach the end of the octave. At the end of the octave the last note marks the beginning of the next octave. This note is also called C. Why does this note have the same name as the note at the beginning of the previous octave?
I am not a physicist, but I will explain this as best as I understand it (which may not be exact but will hopefully help to explain this situation). If something vibrates (moves quickly from side to side), you may hear a note sound. (Every sound we hear is made up of notes). The faster it goes the note gets higher in pitch. The number of movements per second is known as the 'frequency'. Pressure waves move through the air from the object to our ears, copying the movement. If you pluck the bottom E string on a bass guitar, the pressure movement will be at a frequency of about 73 movements per second (usually referred to as Hertz). This is around the same note as a kick drum creates on a drum kit. If you pluck a higher note, the number of movements per second increases – which is what makes the note higher.
Here’s the important part. If you double the frequency – so for example move from 73 Hertz (around a bottom E on bass guitar) 156 Hertz, the note that is created harmonises very powerfully with the original note – possibly better than it would with any other note. In fact, the new note harmonises so well that it is given the same name as the original note. (Actually the reason is slightly more complex than this but is not necessary at this point). It is also called an E, but it is called ‘E an octave higher’. It therefore marks the beginning of a new octave. There are twelve notes between these two Es (including the bottom E but not the ‘E an octave higher’). There then follows another octave of twelve notes, which is exactly the same as the previous octave but the entire octave is an octave higher: each note from the original octave is now reproduced in the new octave but each note is an octave higher than in the original octave.
Thus
notes fall into clusters of octaves. The notes in each octave are
named letters of the alphabet. Seven letters are used – A to G.
The naming is very arbitrary, since mostly it is every other note that
has a letter name. In between most of these letter named notes there
are other notes. I will write the notes from A to the end of an octave
to demonstrate.
| A | A# | B | C | C# | D | D# | E | F | F# | G | G# |
As
you can see, most of the letter named notes have another note between them
– for example, between A and B there is a note A#, pronounced A sharp.
Sharpening a note means moving up a note, but flattening a note means moving
down a note, so the same note can also be called B flat (written Bb).
So the same notes written above could be written as follows:-
| A | Bb | B | C | Db | D | Eb | E | F | Gb | G | Ab |
Note that there are no notes between B & C and between E & F. I think this is to do with the way the notes are set up on the keyboard – I think it would make just as much sense to name the notes 1 to 12. In fact I wonder if it might have made things easier for non-keyboard instruments to use numbers instead of this rather strange looking letter system. In any case, on the keyboard all the letter names are white keys and all the #s or bs are black keys.
A song
will generally centre around seven different notes from each octave.
If a song uses a certain group of notes then it will mainly stick to just
these notes for the whole song. The most common 2 groups of notes
are known as the major scale and the minor scale. I usually explain
that the major scale sounds happy and the minor scale sounds sad.
The 12 different notes of an octave are more or less equidistant.
If we call the first note of the scale note 1, then the major scale will
use
the following notes in an octave (the first line below shows all 12 notes
for comparative purposes).
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | ||||||||
| 1 | 3 | 5 | 6 | 8 | 10 | 12 |
Note that 5 & 6 are next to each other and that 12 and 1 (the beginning of the next octave) will also be next to each other.
Scales usually have eight notes in them (as in the major scale) hence the term octave. There are actually only seven different notes, when one refers to an octave it means including note 1 at the beginning of the octave and note 1 again at the end of the octave an octave higher than the original note 1.
Many
of the most common scales are exactly the same as the major scale, but
simply start in a different place, continuing until the same note an octave
higher is reached. For example, the other most common scale is the
minor scale – which I usually describe as sounding sad. Looking at
the diagram above, this scale begins on note 10 and continues to note 12,
then continues again onto note 1 (in the next octave), followed
by 3, 5, 6, 8, and then ending on 10 again. So, it would look as
follows (as seen on the second line again – all the notes are included
on the first line for comparative purposes).
| 10 | 11 | 12 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | ||||||||
| 10 | 12 | 1 | 3 | 5 | 6 | 8 |
and the next note would be 10 again in order to complete the octave. The scale could then continue for more octaves above the present one – using the same numbers.
These two groups of notes (major and minor scales) are of course exactly the same. The only difference is where the octave begins. In the major scale the octave began on note 1: in the minor scale the scale began on note 10.
Until I have explained how chords are formed this explanation of the difference between the major and the minor scale will be slightly insufficient. But I will come back to it in a moment.
From now on I will number the notes of the scale 1 to 8, since there are 8 notes in each scale. It would possibly make more sense to use letters in order to refer to the 8 notes of a scale, always beginning with ‘A’ since we have used numbers to refer to all the notes (rather than just the notes in a scale). Unfortunately conventional music has used what seems to me a somewhat strange letter system to refer to all the notes – strange since not all the notes are given a successive letter name – the sequence is A, A sharp, B, C, C sharp, D, D sharp etc. It actually makes perfect sense for the piano since the ‘sharp’ keys are all a different colour on a piano, but this seems to me to be irrelevant on other instruments.
So whichever key we are in, (i.e. whichever scale we are using) we will now call the first note of the scale note 1, the second note, note 2, and so on through to note 7. The next note is note 1 again, but we can also call it note 8 in order to differentiate it from the bottom note of the scale. In other words, note 1 and not 8 are the same but note 8 is an octave higher than note 1. Written under the corresponding notes in number form as above, the Major scale now looks like this.
Major scale
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Notice that notes 2 and 3 in the scale are next to each other, as are notes 7 and 8. The rest of the notes in the scale are 2 notes apart. In music 2 notes apart is called a tone and one note apart is called a semi-tone.
The minor scale will look as follows. Remember that the above scale’s sister minor key (relative minor) will begin on note 10 – which we are now calling note 6 of the scale.
Minor Scale
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Note that now notes 2 and 3 are next to each other and notes 5 and 6 are next to each other – but if you look at the top line you will see that the same notes are being played as in the major scale – it is simply the starting and finishing points that have changed: now the scale starts and finishes on note 10. Looking at the second line of each scale as written above, in essence the real difference between the two scales is where the notes are next to each other. In the major scale notes 3 & 4 and notes 7 & 8(1) (line 2) are next to each other. In the minor scales notes 2 & 3 and notes 5 & 6 (line 2 again) are next to each other.
Chords
Now a chord is made as follows. A chord is a collection of notes and a basic chord usually consists of 3 different notes. To form a basic triad (a 3 note chord) in our scale (numbered 1 to 8 – line 2 above) you can build a chord from any note of the scale. For example let us take note 2. To build a basic triad you simply play every other note for three notes. So from note 2 you would play notes 2, 4, & 6 together. Below I have shown the notes of this chord using blue to highlight them.
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We shall call this chord, chord 2 since it begins on note 2. Similarly, chord 3 would consist of notes 3, 5 & 7 and would look as follows: -
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Chord 1 would consist of notes 1, 3 & 5 and would look as follows: -
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Major & Minor chords
I always say that a major chord sounds happy and a minor chord sounds sad. In the major key there are basically 6 chords available. Chords 1, 4 & 5 are major and chords 6, 2 & 3 are minor. The reason for this is as follows. If you look at chord 1 above (last diagram) you will see that the first and second notes of the chord are four notes apart (counting all the notes from the top line). However the second and third notes of the chord are 3 notes apart. However if you look at chord 2 or chord 3 (the first two of the above examples) you will see that the first 2 notes of the chords are three notes apart where as the second 2 notes of the chords are four notes apart. This is the difference between major and minor chords. However what is most important to understand is that major and minor chords sound different.
In order to write out chord 5 we will need to write out the notes of more than one octave of the major scale. Below I have written 2 octaves of the major scale and omitted line 1 from the diagram in order to save space.
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Major and minor keys
The following is a slightly confusing convention I follow. However I have found it to be very important. If a song settles on chord 1, I would say it is a major song. It will usually begin on chord 1, the chorus will usually also begin on chord 1 and the song will probably end on chord on. The song will feel settled and finished if it ends on chord 1. However, if the song settles on chord 6 I would say it is a minor song: remember the minor scale is the same as the major scale except that it settles on a different note (this note was note 10 on line one of the above diagrams but is note 6 on the second line of the diagrams of the major scale) – now I will clarify that it is actually when it settles on chord 6 that the key will sound minor (and usually sad). In this case the song will usually begin on chord 6 the chorus will usually begin on chord 6 and the song will usually end on chord 6. The point is that when referring to the minor key I use the number system of the major key but simply say that the song settles on chord 6 rather than chord 1. This is unconventional.
The following paragraph is primarily written for experienced musicians who are reading this. I need to explain why I follow the above procedure. The problem is that a song can begin settling on chord 1 and then the chorus may settle on chord six. If the song ended with a chorus it may sound more settled on chord 6, or if it ended with a verse it may sound more settled if it ended on chord 1. Avril Lavigne’s song Complicated does this. Songs can move from one to the other with ease. It seemed to me better for analytical purposes to represent the songs using one key rather than two and so in terms of using numbers to talk about chords I always talk as though the song were in the major key. This means that if the song settles on chord 6 I refer to it as settling on chord 6 rather than referring to this chord as chord 1. (Another more important reason is that for comparative purposes, sequence 6415 and 1564 are the same 2 cadences but in reverse order. It is easier to analyse this if there is a common way of representing the chords rather than in the first example using a different system because it is considered to be minor. For comparative purposes the procedure seems to me to be important.)
© 2006 Phil Warren
In order to play songs in the correct key you will need to be able to translate chord numbers into notes on your instrument. Perhaps unfortunately we have to use the conventional system of note names, which is somewhat confusing for the non-keyboard player. Nevertheless what follows should explain this system.
You need to write out the eight-note scale in order to know what notes each of the numbers refer to when playing in the current key. In order to do this you must know what note 1 is. This note will also be the name of the key (assuming it is major). So if note one is G, then the key of the song is G major. Don’t forget that if the song is minor the root note is then note 6 and the key is based around note 6 (in our system of study – conventional systems always call the root note, note 1). In the case of a minor key, if note 6 is F, then the key is F minor (see ‘Keys and Chords – Foundations for Understanding Music’).
Each of the seven different notes of the key will have a successive letter of the alphabet. So if the root note is F, the notes of the scale will be F, G, A, B, C, D & E. However, for each key some of the letters will be sharps or flats which are the notes in between these lettered notes (other than C major and A minor which have no sharps or flats). For example, the note in between F and G is F sharp, which is written as F#. However the same note can also be called G flat which cannot be written in standard computer symbols found on the keyboard – but it looks a little like a ‘b’ symbol so I will write Gb to denote G flat. Sharp means one note up, therefore F sharp is one note up from F (the note in between F and G). Flat means one note down so G flat means one note down from G (also the note between F and G). However, E and F have no note between them and B and C have no note between them.
The last thing you needs to do, therefore, after listing the seven notes of the key, is make some of those notes into sharp or flat notes. So, let us use the example of the key of D major. First write out the successive alphabet letter names as follows:
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Now D major has 2 sharps, which are F# and C# so F and C need to be sharpened. Therefore we will add them to the diagram as follows.
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This is now all the notes in the key of D major.
The
following will tell you how many sharps or flats each key contains.
| Key |
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| C major (A minor) |
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| G major (E minor) |
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F# | |||||||
| D major (B minor) |
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F# | C# | ||||||
| C# major (A# minor) |
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F# | G# | C# | |||||
| E major (C# minor) |
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F# | G# | C# | D# | ||||
| B major (G# minor) |
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F# | G# | A# | C# | D# | |||
| F# major (D# minor) |
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F# | G# | A# | C# | D# | E# | ||
| C# major (A# minor) |
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F# | G# | A# | B# | C# | D# | E# | |
| F major (D minor) |
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Bb | |||||||
| Bb major (G minor) |
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Bb | Eb | ||||||
| Eb major (C minor) |
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Bb | Ab | Eb | |||||
| Ab major (F minor) |
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Bb | Ab | Eb | Db | ||||
| Db major (Bb minor) |
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Bb | Ab | Gb | Eb | Db | |||
| Gb major (Eb minor) |
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Bb | Ab | Gb | Fb | Eb | Db | ||
| Cb major (Ab minor) |
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Bb | Ab | Gb | Fb | Eb | Db | Cb |
After each of the major keys I have written the relative minor key in brackets, which is always centred around note 6 of the major scale. Remember that each relative minor has exactly the same notes as it’s relative major. In fact it is the same key – the only difference is that the major settles on chord 1 and the minor settles on chord 6.
You may well need to memorise the notes in most of these keys if you are going to work in the conventional note system. Here are some tips for memorising the above. Each of the successive major keys in list one begins on the 5th in the previous scale. In other words, count four up from each note on the list to find the next note on the list. As you can see, with each key in the list all the #s from the previous key in the list are included in the new key, with the addition of 1 new #. You will also see that as you move down the list, a # is added to the left side for the second key, then to the right side, then to the left, then to the right and so on until all the notes are sharpened (in C# major). You may be wondering why E and B are sharpened if the note above E is F and the note above B is C. Basically E# is really F and B# is really C, but calling them E# and B# in the last 2 keys in the # list is a convention followed in order to ensure that the letters F and C do not appear twice in the scale. Otherwise C# major would be written as follows: C#, D#, F, F#, G#, A#, C, C#. As you can see some letters have been used twice, so the use of E# and B# is to avoid using an F note and a C note twice. (This also has more important implications when being written out in conventional stave notation system, but is not important for our purposes).
In the second list, every new key adds a new ‘b’ (flat). The new b is also the starting note for the next key on the list. So for example, Bb major has one more flat than the previous scale on the list – it has the addition of an Eb. The next note on the list is therefore Eb. One other thing I find helps remember the flat keys is that the first four flats on the list that are added successively to the keys are Bb, Eb, Ab, Db, which spell out BEAD. It may look like a difficult task to memorise all of the above. But some keys are used more than others. I would encourage you to memorise the keys C to B in the sharp keys and F in the flat keys. If you remember the BEAD pneumonic it should also be quite easy to memorise the specifics of the first four flat keys.
Using the above information, if you know the key and you have the numbers of the chords of a song – simply write out the key and then you will be able to see the names of all the chords corresponding to the numbers of the chords used for that song. Don’t forget that if a song is in a minor key it will begin on note 6 of it’s relative major key (see table above). So for example, if the key is A minor, look at the above diagram to find its relative major. In this case its relative major is C major. Then use the C major scale to find out the letters that the numbers will refer to. Below I have written out all of the keys, which should aid you in playing songs written out in number form. If you are playing a song written in number form and you want to know the notes that correspond to each number you may want to cut and paste the relevant key onto another page so that you are able to see it clearly.
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It may also be good to see what one of these scales looks like with all the notes in between so you can see it in context. Here is a major scale (key) in number form (as seen on previous page).
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A C major scale would look as follows. The second line is the C major scale – the first line contains all the notes in conventional note form.
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I have
chosen the key of C major for this diagram deliberately. The key
of C major has no #s or bs (the bottom line). It seems to me that
this letter system was probably set up with piano in mind. Notice
that this key looks like the piano keyboard. On the piano all the
white notes are the notes that fit this key and all the black notes are
the notes that do not fit this key. The white notes have each been
given a letter name of the alphabet (the notes that fit the key) and all
the notes that do not fit the key have been made into black notes (and
are # or b notes). The white notes are also equidistant on the keyboard
whereas the black notes have been slotted in between the white notes as
they fit (in a not-equidistant manner). The white notes therefore
form a major scale if you begin on C. Of coarse the relative minor
to C major is A minor and this uses all the same notes. Since A is
the first letter of the alphabet then this was perhaps the first key that
was in mind when the keyboard was first created. On other instruments,
this notation system is of little value since all notes are linear in location
whereas the piano has two types of notes – black and white, which are positioned
slightly differently. I think it would make more sense to teach other
instruments naming all the notes using numbers rather than using the keyboard
based # and b system – but it seems that the piano system has gained control
and teaching another system would mean that pupils would not be able to
relate their system to a standard # & b system – so alas we are stuck
with what I feel remains a confusing and overly complex system for non-keyboard
players.
© 2006 Phil Warren