Music Theory for Guitar

Building Chords

Chart of Chord Formulas

     Music theory can be thought of the study of what notes sound good together. Whether that group is a chord or a scale, the different varieties each have their own color or flavor. For example, minor scales tend to sound somber, whereas major scales are brighter or more cheerful. So in the study of music theory it's good to familiarize yourself with the particular quality of sound that each chord or scale conveys.

     If you take all the notes on the guitar's fretboard together, you end up with what is called the chromatic scale. Turn a three year old loose on your guitar, and you'll get a feel for the chromatic scale. The chromatic scale instills a lack of sense of musical direction or key. In a word, it's musically chaotic. However in some compositions, that may be considered beneficial. Anyway, the notes of the chromatic scale are A, A#/Bb, B, C, C#/Db, D, D#/Eb, E, F, F#/Gb, G, G#/Ab. Notice that some notes can have two different names. For example, A# (A sharp) and Bb (B flat) both refer to the same tone or note. The interval between each successive note of the chromatic scale is known as a half step or half tone. In the language of intervals, a half step is also called a minor 2nd. The subject of intervals will be dealt with later. In the meantime, here's the chromatic scale illustrated as a series of half tones:

     Although the chromatic scale is occasionally used in short durations within music, most songs are written with scales that are a subset of the chromatic scale. The most important of these is the major scale, if for no other reason than that all the formulas in music theory are based on the major scale. What characterizes the major scale is its pattern of whole and half steps, where a whole step is equal to two half steps. The pattern is: whole, whole, half, whole, whole, whole, half. So say that we want to know the scale of B major. Referring to the chromatic scale, we start with B and jump to the right one whole step (two halfs) and find C#/Db. Then we jump another whole step and find D#/Eb. We continue this until we get back to B:

     Using this method we can build any major scale. For example here's the key of C:

     The key of C major is the simplest, since it doesn't have any sharps or flats. For this reason music for beginners is usually written in the key of C.

     Another important scale is the minor scale. It has the following pattern: whole, half, whole, whole, half, whole, whole. We can use this pattern and build minor scales in the same way as we did the major scales. Here's the scale of C minor:

     There is also a minor scale that doesn't have any sharps or flats. It's the scale of A minor:

     At this point you might be wondering why C major and A minor are two different scales when they have exactly the same notes. The difference is how music is written for these two scales. The first note of any scale is called the tonic. The tonic for C major is the note C, and the tonic for A minor is the note A. The tonic provides direction for music, because there is an expectation with a piece of music to end with the tonic or with the root chord (which in the key of C would be the chord C major; in A minor the root chord is A minor). In the key of C, a common choice for chords are C, F, and G, and any chord progression with these three chords creates the expectation that the progression will finally end with the chord C. If you try to end it with F or G, you're left with a sense of incompleteness. The corresponding chords in A minor are Am, Dm, and Em. When you compare the sound of a progression with these chords with the chords C, F, and G, there is a totally different feel to the music even though none of the chords in either scale contain notes with a sharp or flat.

     This leads to the subject of scale and chord formulas. As was stated before, these are all based on the major scale. The notes of the major scale are numbered 1 to 7 starting with the tonic. The number 8 is used to refer to the octave, which is the same note as the tonic but 12 half-steps higher. There are also other numbers in chord formulas such as 9, 11 and 13, but since the numbering can start over after 7, 8 is the same note as 1, 9 is the same as 2, 11 is the same as 4 and 13 is the same as 6. We'll concern ourselves with such chords later. First, here's the numbering scheme for the major scale:

     This is the same for all major scales no matter what key it is in. When it is applied to the scale of C major, we can see that the numbers refer to the following notes:

     Notice that between some numbers there are whole steps. This allows for values between some numbers. For example, between 4 and 5 there is the value of either #4 or b5 (sharp 4 or flat 5). That means a half step above 4 or a half step below 5. Since we allow for intermediate values, we can assign values to the entire chromatic scale:

     Notice that there are no intermediate values between 3 and 4 and between 7 and 1 (or 8). This is because the numbering is relative to the major scale, and in the major scale there is only a half step between 3 and 4 and between 7 and 1. Now that we have the chromatic scale mapped out we can figure out what the formula is for the minor scale in the same way that we found the notes for the minor scale. Remember the pattern for minor scale: whole, half, whole, whole, half, whole, whole. So starting with 1 and moving to the right one whole step on the chromatic scale, we find the second value 2. Then at one half step we find b3. I could have said #2, but the formulas are traditionally enumerated trying to avoid (when possible) the same number twice. Since we already have a 2, we avoid #2 and designate it b3 instead. Continuing in this manner we can find the formula for the entire minor scale:

     There are a lot more scales than just the major and minor. Their importance is primarily a matter of composing music, and we'll take a look at some of those later. When it comes to the way sheet music is written, all the other scales are considered as variations of the major and minor scales. The reason I say that is because the key of a piece of music is designated by what is known as a key signature, and the key signatures are named as either a major or minor scale. In other words, there is no key signature for the hungarian minor in D, for example.

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Building Chords

     Building chords uses the same tools as building scales. In fact it's done in exactly the same way. The most important thing to remember about building chords is that the name of the chord indicates which major scale its formula is relative to. For example, C, F and G are common chords of the scale C, and all their notes are in the scale C. But what's important to remember is that even though they're common chords in the key of C, F must be built from the scale of F, and G must be built from the scale of G. Here's the three steps:

     1. Find the notes of major scale in question. Remember this is done with the major scale pattern: W, W, H, W, W, W, H, with reference to the chromatic scale:

     2. Number the major scale with the numbers 1 to 7.

     3. Build the chord with its particular formula. Major chords have the formula 1-3-5 and minor chords have the formula 1-b3-5.

     As you can see b3 means a half step below the 3rd note of the major scale, and you will also see things like #5, which means a half step above the 5th note of the major scale. One thing to watch out for is that a half step below a note doesn't necessarily mean a note designated with a flat. Consider the following scale, for example:

     Be careful, for instance, if you were to build the chord Abm (A flat minor), because it would not be: Ab, Cb, Eb, because a half step below C isn't Cb but B. Take a look at the chromatic scale. Rather Abm is Ab, B, Eb. Another example would be an augmented chord in this scale. Augmented chords have the formula 1-3-#5, so watch out building the chord Ab+ (A flat augmented), because it would not be: Ab, C, E#. Even though #5 might seem to suggest a sharp note, it actually only means a half step above the 5th of the scale, and a half step above Eb is E, so Ab+ is: Ab, C, E.

     To make this subject complete, chords containing formula values above the octave need to be considered. There's really nothing difficult about that if you remember that the counting starts over after 7. As stated before, 8 is the same as 1; 9 is the same as 2; 11 is the same as 4; and 13 is the same as 6. Since we just laid out the scale of Ab, let's consider an example in that scale, and we'll take a look at the "add 9" chord which is nothing more than a major chord with a 9 tacked on, so as you probably have guessed, its formula is 1-3-5-9. However since 9 is the same as 2, we could rewrite it as 1-3-5-2, keeping with the traditional ordering of the formula. So referring to the scale of Ab, this chord is easy to build:

     So that's all there is to building chords. All you need now is some more formulas.

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Chord Formulas

     Much more to come!