Greg's Music Theory Page

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One thing that needs to be understood about music, is that it is contextual. Rhythm, tempo, mood, tone and types of instruments, style of composition, degree of musicianship, dynamics and keys are all contexts which effect how a note/chord effects the overall song, In regards to keys, a G major chord, in the key of G major will sound "at rest", while in the key of C major, the same chord will sound "climactic". The same G major chord, in the key of F major may sound "majestic" while in the key of Db, it may sound "out of place" or "weird". The following text on the number system, will open up the understanding of how chords function within the context of different keys.

We can derive chords from keys by skipping notes of the corresponding scale. This is called "harmonizing a scale."

If we are in the key of Eb:

Eb F G Ab Bb C D

Here is the complete list of 3 note chords, called chord triads, derived from this scale.

  • Eb G Bb - Eb major
  • F Ab C - F minor
  • G Bb D - G minor
  • Ab C Eb - Ab major
  • Bb D F - Bb major
  • C Eb G - C minor
  • D F Ab - D diminished

Notice that the above chords were built starting upon each note of the Eb major scale. Each chord consists of notes of the Eb major scale derived from skipping scale letters. For instance to find the other two notes within the Eb chord, we skipped the F, in the scale, and gave the chord a G, skipped the Ab and gave it a Bb. We could make this a 4 note chord in the key of Eb by going further, skipping the C and giving it a D, thus yielding an Eb major 7, but for now, we'll stick with chord triads.

* If your understanding of chords is lacking, jump to the Chords section.

Before proceeding any further, let's become acquainted with a couple of terms.

The first note of a chord (G is the root of the G major chord, A is the root of the A minor 7 flat 5 chord, etc.)
The first note of a scale (G is the tonic of the G major scale.)

Returning now to the list of chords, if we were to number these chords, assigning a number for each root, starting our count from the tonic (Eb) and counting up, we'd get the following:

  • Eb G Bb - Eb major - I CHORD
  • F Ab C - F minor - ii CHORD
  • G Bb D - G minor - iii CHORD
  • Ab C Eb - Ab major - IV CHORD
  • Bb D F - Bb - V CHORD
  • C Eb G - C minor - vi CHORD
  • D F Ab - D diminished - vii CHORD

* Capital roman numerals signify major chords, while lower case signify minor and diminished

Notice the pattern. The I, IV and V chords are major. The ii, iii and vi chords are minor and vii is diminished.

This pattern holds true for all major keys.

For minor keys, the pattern is in the same order except starting from the tonic of the minor key, yielding the following pattern:

  • C Eb G - C minor - i CHORD
  • D F Ab - D diminished - ii CHORD
  • Eb G Bb - Eb major - III CHORD
  • F Ab C - F minor - iv CHORD
  • G Bb D - G minor - v CHORD
  • Ab C Eb - Ab major - VI CHORD
  • Bb D F - Bb major - VII CHORD

* The above is for C natural minor, which is the relative minor of Eb. You could also find the numeric pattern for harmonic and melodic minors. See the chords section for more info about relative minors. See the scales section for more info about the harmonic and melodic minors.

Normally, I don't think of minor keys in terms of the above system. Instead, I think of them in terms of their relative major. So if I'm in the key of A minor, I think of the A minor as a vi chord instead of as a i chord. This allows me to think in terms of on numbering system instead of two. So from this point on, I'll speak of the number system exclusively in terms of the major system.

One special note about the vii diminished chord. Diminished chords function best as passing chords. The number system illustrates the function of non-passing chords. Therefore you'll find that you NEVER play the vii diminished chord. Instead, you'll substitute all vii's with V/vii. An example is if you're in the key of C major, instead of playing B diminished, you'll play G/B.

O.k., now that I know the number system, how do I use it?

Well, the first thing that you need to do is figure out what key the song or chord progression is in. There are many ways of doing this. If you have the music, in front of you, you can simply look at the key signature, which will show how many sharps or flats are in the key, then using the circle of fifths, figure out the key. But without the score, if you have either a chord sheet, or you can play by ear well, you can use knowledge of the circle of fifths, and/or the number system to aid you. Examine the notes of the song. Does it have any sharps or flats (accidentals)? Which notes are sharped/flatted?

Using the number system, you can figure out the key of a song/progression by examining the chord progressions of a song or passage. One easy indicator is that if you see a diminished chord, diminished chords are always vii chords within major keys, and ii chords in minor keys. Another indicator would be if you see 2 major chords within one whole step of one another. The only place 2 major chords can be in this position (say F major and G major) and be in the same key, is if these chords are functioning as the IV and V chords of a major key, (or VI and VII for a minor key) respectively. The same holds true for 2 minor chords within a whole step of one another. The minor chords would function as the ii and iii of a major key (iv and v of a minor key).

An example of this would be if I saw a chord progression that consisted of an A major and a B major chord. I could immediately conclude that these chords are functioning as the IV and V chords of the key (assuming that the key is a major key). Counting back 4 notes from the A, (or 5 from B) I could deduce that this progression is in the key of E major.

Sometimes a chord progression can be ambiguous enough to imply more than one key. For instance the following chords, Ab major and Db major could be either in the keys of Ab (F minor) or Db (Bb minor). In the key of Ab, the Ab=I and Db=IV. In the key of Db, Ab=V and Db=I. In a case like this, the broader context of the progression needs to be analyzed to better ascertain which key the song may be in, taking into account which chord (Ab or Db) seems to be the chord which sounds "most at rest" (resolved). The chord in which all of the music seems to center around, is most likely the key. Therefore, one easy indicator to find a key of a song is to simply look for the beginning and ending chords of a song. One of these chords is usually the key of the song, especially when these 2 chords are the same. The musician, soloing over the above chord progression could play either an Ab major scale or Db major scale. See the modes subsection of the scales section for more information.

One thing to keep in mind with the number system is that the musician should not become restricted to it. The number system is just a pattern that chords follow when they are derived from a scale. If this pattern is deviated from, the chords are said to have "modulated" or changed key. Modulations can be permanent or temporary. Sometimes a modulation is just one chord, and sometimes the whole song changes to a new key.

In using the number system. The first thing that I'd advise the musician to do, is THINK IN TERMS OF NUMBERS. To do this, take a song that you already know and find the numbers associated with the chord progressions. Play the song and THINK IN TERMS OF THE ASSOCIATED NUMBERS, in addition to the chords. This will slow you down at first, but in the long-run, this will enable the musician to start to think in terms of numbers. This mindset will provide the unique advantage of giving the musician "musical eyes" to see patterns that he/she wouldn't have otherwise seen.

One easy example of this, is that one will discover when thinking of chords in terms of the number system that the I, IV, V, progression is a very common progression. Within this progression, the V chord gives the greatest amount of dissonance and can be resolved by the C major which sounds "at rest".

Another common chord progression easily seen, when thinking in terms of the number system is the ii, IV, V progression.

Another example; By thinking in terms of the number system, I have discovered that whenever a chord progression (in a major key) goes from the I chord to the IV chord, I can insert a major chord which is one whole step below the I, (I call this a flatted VI chord) between the I and IV chords.

Try it out! If you have a chord progression within the key of G major, and it contains the chords G major and C major, add an F major between the G maj and C maj to yield the following progression; G maj, F maj, C maj.

The reason this works is because this chord progression is creating a temporary modulation (temporary key change). The song was in the key of G major, but the F major chord, temporarily placed the song in the key of C major. This is why placing the F major chord after the G major chord, resolves so easily to the C major chord. The F major chord functions as the IV chord (in the temporary key of C major).

This is just one of many examples of personal rules that I have found and formulated using the number system.

The number system can help with trying to figure out how certain chords can be used within keys. For instance, I've discovered how to use certain chords that I would have otherwise, never been able to figure out how to use within a musical context. One such chord is the dominant seventh sharp 5 sharp 9. I've discovered that this chord functions well as a VI, I and III and V chord. Using it as the VI chord within the key of C major, the A 7#5#9 chord wants to resolve to the ii chord (D minor). A simpler example is a dominant 7 chord. Whenever I see one, I always associate it with the V chord (just as we always associate the diminished chord with the vii chord).

The final benefit of using the number system is the fact that it enables a musician to play within any key, because, although the notes change, relative to the key, the numbers stay the same. Take the following chords for the first few bars of "Amazing Grace":

In the key of G major;

G major G major, C major, G major, G major, A major, D major

In the key of A major;

A major A major, D major, A major, A major, B major, E major

Using the number system, the song is:

I, I, IV, I, I, II, V

for any key

The chords change, but the numbers stay the same. It is for this reason that many Nashville session players use the numbering system in studio work, thus the alternative name "The Nashville Numbering System".

Also, notice that Amazing Grace contains a II major chord instead of a ii minor. This is another example of a temporary modulation.

Chord Harmonization Chart

The following chart demonstrates how you can harmonize chord triads built upon each scale degree. It specifically shows chord triads with roots derived from each scale degree of the major scale. This chart reveals two numbering systems. The Nashville Numbering system, and the basic chord numbering system (for chord triads, that numbering system is simply 1 3 5).

In other words, the Nashville Numbering system demonstrates to us that there is a pattern for every major key where I, IV and V are major chords, ii, iii and vi are minor and vii is dimished. But every one of those chords, no matter what their function is within the key (I or ii or IV, etc...) has three notes in it's voicing. Those notes are numbered relative to the root of the chord. The numbering is 1, 3 and 5). For example, F major is the IV chord within the key of C major, and it contains three notes (1, 3 and 5).

	            Chord Tones

Scale Tones	1	3	5	Chord Types

1	        C	E	G	Major

2	        D	F	A	Minor

3	        E	G	B	Minor

4	        F	A	C	Major

5	        G	B	D	Major

6	        A	C	E	Minor

7	        B	D	F	Diminished

Here's the same chart for 4 note chords:

			Chord Tones

Scale Tones	1	3	5	7	Chord Types

1		C	E	G	B	Major 7

2		D	F	A	C	Minor 7

3		E	G	B	D	Minor 7

4		F	A	C	E	Major 7

5		G	B	D	F	Dominant 7

6		A	C	E	G	Minor 7

7		B	D	F	A	Half-Diminished 7