Music theory part 2

This is the second music theory post and we will discuss intervals and chords. An interval is basically the distance between two notes as measured in semitones (see my first music theory post for a definition of a semitones). If you remember the table of modes from my previous post (shown below), there is roman numeral for each of the scales and that represents the interval from the tonic (the note C) to the starting note in the scale. These roman numerals will also come into play when I talk about chords.

So if we look at the C major scale and the corresponding roman numerals:

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

The interval from C to the other notes are:

C is unison at zero semitones
D is the second at two semitones
E is the third at four semitones
F is the fourth at five semitones
G is the fifth at seven semitones
A is the sixth at nine semitones
B is the seventh at eleven semitones
C is the octave at twelve semitones

If we look at the minor scale and remember from the circle of fifths that A minor contains the same notes as the C major scale, we have the following notes

A B C D E F G A
I II iii IV V vi vii I

A is unison at zero semitones
B is the second at two semitones
C is the minor third at three semitones (designated by lowercase roman numeral)
D is the fourth at five semitones
E is the fifth at seven semitones
F is the minor sixth at eight semitones
G is the minor seventh at ten semitones
A is the octave at twelve semitones

Why do the third, sixth and seventh intervals have a minor in their name? Because they have a different number of semitones in the interval than the third, sixth, and seventh in the major scale and because they are the notes in a minor scale they are defined as minor third, minor sixth, and minor seventh. The second, fourth, and fifth are not minor intervals because they have the same number of semitones as in the major scale. The fourth and fifth are special in that they maintain the same number of semitones whether the scale is major (Ionian and Mixolydian modes) or minor (Aeolian, Dorian, or phrygian). That is why they are called perfect intervals. The other intervals are either major or minor depending on the mode. The table below shows the intervals that are contained in the seven diatonic scales.

In two of the scales (Lydian and Locrian) you see that the fourth is augmented and the fifth is diminished. Augmented means that the interval is one semitone higher ( also called raised a semitone) and diminished means the interval is one semitone lower (also called lowered a semitone).

Chords

Chords are made from at least three notes. The first common chord is the major chord. The major chord contains the root note, the third above the root and the fifth above the root. The root identifies the chord. For example the G major chord (commonly called just a G chord) is made up of the following notes.

G B D
I III V

To get any other major chord you just take the root, the third, and fifth note from the corresponding major scale. The other commonly used chord is the minor chord. This is similar to the major chord except you use the minor third in place of the major third. If we look at the G chord again but make it a G minor (Gm), it contains the following notes

G Bb D
I iii V

Like the major chord, you can form any minor chord by taking the root, the third, and fifth note from the corresponding minor scale. OK that's cool you say but are there other chords? Yes, you can add other notes from the scale to form more chords and here are some of the common ones:

Seventh chord: this contains the root, the third, the fifth and the minor seventh
Minor seventh: this contains the root, the minor third, the fifth, and the minor seventh
Major seventh: this contains the root, the third, the fifth, and the seventh
Diminished chord: this contains the root, the minor third, and a diminished fifth
Augmented chord: this contains the root, the third, and an augmented fifth

The other set of chords that I will discuss are the ninth, eleventh, and thirteenth chords. Hey wait... The intervals only go up to seven, how can you have a ninth chord. Well the scale is cyclical so if you continue counting beyond the octave note you can get a ninth interval and that is the same note as the second interval. So this set of chords take the seventh chords and add a ninth (second), eleventh (fourth), or thirteenth (sixth) note to the chord. Below is a table that shows the construction of these chords

So those are the common chords use see used in songs. The last thing I will discuss is chord progressions. This is the series of chords that are formed by using the notes of a scale but having the root note be each note in the scale. For example in the C major scale, the notes are

C D E F G A B C

What is the C chord that fits in the scale, same with the D chord, and so on. Well the progression of chords is

Major - minor - minor - major - major - minor - minor diminished

For the C major scale that is C - Dm - Em - F - G - Am - Bm(dim)

Using roman designation again the progression is

I ii iii IV V vi vii(dim)

So we have the same relationship between chords and we do with notes. So in the key of C the Em chord is the minor third of the C chord.

So hopefully this will give you enough background on intervals and chords so you can follow along as I discuss the creation of my songs. Enjoy...

-Ron-

[Edit 7/17/11]
I forgot to add that all figures in this post were provided by Wikipedia

Music theory part 1

OK this is the first music theory post. I will try to keep to the important parts that pertain to my discussions on songwriting. The main points I will discuss are scales, intervals, and chords. This post will discuss scales. He we go...

The basic tonal building block in Western music is the note. There are 12 note names and these note names repeat over and over again and each of these cycles is called an octave. This series of twelve notes is called a chromatic scale. If you look at a piano each key is a note. The note names are:

A A# B C C# D D# E F F# G G#
Bb Db Eb Gb Ab

So what are are those '#' and 'b' symbols. They are called sharps and flats and they increase or decrease a note by a semi-tone or half step (this will be discussed later in the interval section). The sharps and flats correspond to the black keys on a piano. I guess you are asking at this point why have letter names in combination with sharps and flats instead of just using only letter names and why have both sharps and flats when they look redundant? Well this has to do with the construction of scales.

Ok, what is a scale? A scale is a subset of notes that when played impart a particular sound to the music. Scales in traditional Western music generally consist of seven notes and repeat at the octave. Notes in the commonly used scales are separated by whole and half step intervals of tones and semitones. These seven note scales are called diatonic scales.

Ok but why are there sharps and flats. That's because the way diatonic scales are constructed, they contain every letter and each letter is represented only once in the scale (ie, a scale cannot contain an A and an A#). Why you ask.... because it is a convenient way to define diatonic scales. Seven notes in the scale and seven letters representing the notes, isn't that a coincidence. If a scale has an A and an A# then the A# is actually a Bb.

So how do you determine what notes are in a scale. Well it starts with the C note. If you start at C and progress through the letters with no sharps and flats, you have what's called the Major scale. The C Major scale contains the notes C-D-E-F-G-A-B and if you look at the list of notes you see that this scale by starting at a note and use the following progression

w-w-h-w-w-w-h

Where 'h' is a half step and 'w' is a whole step (two half steps)

You can now form a major scale in any key using this progression. Wait, hold on a minute... what is a key? Its just the note you started the progression on (and is also called the root note). So a specific scale is identified by the key and the type of scale (for example the major scale that is in the key of C is called the C Major scale or in the key of C Major). If no scale type is given, it is assumed to be the major scale (e.g., in the key of C really means in the key of C Major).

Now let's try this in the key of A

A B C# D E F# G# A
w w h w w w h

Now let's try this in the key of F (using sharps)

F G A A# C D E F
w w h w w w h

Since this scale has two A notes (A and A#) so we replace the A# with Bb. That is why we have both sharps and flats. Also another rule for thumb for the diatonic scales is that the notes in the scale can contain sharps or flats but not both.

So what are the different diatonic scales? Well they are defined by starting on a different note and progressing through the letters with no sharps or flats. The different scales formed using this method are called modes. Here are the seven scales (modes) that are possible.

In this table s is a half step T is a whole step and the white note is the start of the scale. The two most import scales are the Ionian scale which is also called the Major scale and the Aeolian scale which is also called the minor scale. You can use interval sequence from the table to form any scale in any key.

There is one other concept that is important to musical scales and that is the circle of fifths. The Circle of Fifths chart used in music theory shows the relationships among the twelve tones of the Chromatic Scale, their corresponding number of sharps or flats in the key, and the associated Major and Minor keys.

At the top of the Circle Of Fifths diagram, the key of C has no sharps or flats. Starting from there and going clockwise by ascending fifths (an interval that spans five notes in a diatonic scale), the key of G has one sharp, the key of D has 2 sharps, and so on. Going counterclockwise from the top by descending fourths (an interval that spans four notes in a diatonic scale), the key of F has one flat, the key of B♭ has 2 flats, and so on. The circle is commonly used to represent the relationship between diatonic scales. Adjacent keys on the circle of fifths represent Diatonic Scales that are a perfect fifth apart and share six of their seven notes. Furthermore, the notes not held in common differ by only a semitone. Thus moving to a new scale by a perfect fifth can be accomplished in a very musical fashion.

I hope that gives you a good introduction to the concept of scales. The next music theory post will describe the basics of intervals and chords. Until then enjoy...