Understanding musical theory

Welcome to kamatsu's article on Understanding Musical Theory.

The purpose of this article is to teach you:

• Basic Musical Notation
• Scales, Modes and Intervals
• Timing and Rhythmic Techniques
• Basic Harmony and Dissonance
• Chord Progressions

Scales, Keys, and Modes

The C Major Scale

Music is made up of notes. Notes are sounds of a particular frequency (measured in hertz). Different frequencies produce different pitches. For the purposes of musical composition, we have culturally assigned particular names to different frequencies as we hear them, usually letters. C, for example, is the note produced when you play the white key before a group of two black keys on a keyboard.

keyboard showing C notes

Note: You will notice that C occurs every 8 notes on the keyboard. Why is this? The notes are separated by a specific distance of frequencies called an octave, and, for those that know the physics, the frequencies are logarithmically compatible, so that playing them together will sound like the one note. This means that for almost all purposes they can be treated as effectively the same note. Try it, if you have access to a keyboard. You will hear that they sound the same, just with different stylised pitch.

On a Musical score (with a treble clef), we see C as one of these two notes (usually):

staff, treble clef, C4 & C5

From this point, one can easily deduce the names of the other white key notes:

keyboard showing all letter notes

If you play the white keys on the keyboard, starting at C (C, D, E, F..) you will hear a distinctive sequence of notes that most people recognize as the major scale (Do, Re, Mi, Fa...). If you have no idea what a major scale sounds like, here's a recording:

( link "Link Here" formerly at http://kamatsu.spheredev.org/majorscale.ogg : OGG of C major scale )

This is a major scale in the key of C. That means, Do, or the tonic, is C. Later on, we'll learn how to change the tonic. Here's what a full C Major scale looks like in Musical Notation (with a treble clef):

staff, treble clef, C major scale labeled

Extra Info: Think of a melody, say, your national anthem. Then, change the note at which you start the melody. Can you still sing/play it? You should quickly realize that it doesn't actually matter what note you start on, or what note Do is, for a melody to be recognizable to the human ear. Most humans think of notes relative to each other, not relative to specific frequencies. So, you could sing the Major scale at any pitch, from A through G#, and it would still be a major scale. But, if you start playing a piano from D, and play all the white notes up to the next D, it doesn't sound like a major scale (it's actually a dorian scale). So, obviously, simply shifting all the notes up a line or space in the Notation isn't going to achieve a D Major scale. How do you achieve this? Well, first, we need to learn about semitones, and then keys.

Clefs

A clef is a sign that is put at the beginning of a line of notation (a staff - plural staves), that determines what each line represents pitch-wise. On a treble clef, the note on the line below the bottom line of the staff (i.e, Do:C in the above diagrams) represents a specific note called Middle C (so called because it is in the middle of a piano keyboard). In the Bass clef, Middle C is on the line above the top line of the staff.

Mnemonics for Treble Clef: Suppose you want to be able to immediately identify a note name from looking at a staff (a useful skill). Having a mnemonic or verse to help you remember what each line and spaces stands for is quite useful. Here's the mnemonics for the treble clef.

• For lines (starting at the bottom and going up) - Every Good Bolshevik Deserves Freedom. Or, less politically, Every Green Bus Drives Fast. Your choice.
• For Spaces (Starting at the bottom space and going up) - F A C E - It spells "FACE", or, alternatively, you can use: Free Alcohol Can Entice. Once again, your choice.

While for the most part in this article we will be using notation in the treble clef, the most common clef, some scores may be written in the bass clef. The Bass Clef is more suited to lower ranges.

staff, bass clef, C major downward scale labeled

Mnemonics for remembering the bass clef:

• Lines (starting at the bottom and going up) can be remembered by "Good Boys Deserve Free Alcohol".
• Spaces can be remembered by "All Cows Eat Grass."

Intervals, Tones, and Semitones

If you examine a keyboard:

keyboard showing 3 octaves, white keys labeled

You will quickly see that there are no black keys between E and F, and B and C. Even more importantly, some of you may be wondering what those black keys actually represent. Between most lettered notes (C, D, E...) there is another note. This note is named relative to the notes it is adjacent to, so the black key between C and D would be called C Sharp (C♯) or D Flat (D♭), depending on your point of reference. The interval between notes is the distance pitch-wise between them. The interval from C to D is called a tone. The distance, therefore, from C to C♯/D♭ is a semitone - half a tone.

Note: The interval between E and F, as well as B and C is not a tone as you would expect but a semitone. That is why there is no black key between these notes. As a corollary of this, E♯ is therefore the same note as F, and B♯ is the same note as C (And C♭ = B, and F♭ = E). If you listen carefully to the major scale recording I played earlier, and you have a good musical ear, you may be able to hear the difference in the interval on these notes. An octave is another type of interval. We will learn more about intervals later in the introduction to harmony.

Now that we have learnt about semitones, we can develop a chromatic scale. A chromatic scale is a scale that goes up by a semitone each interval. Here's a chromatic scale in musical notation.

staff, treble clef, chromatic scale labeled two ways

Note: The first staff uses sharps to notate the semitones, whereas the second staff uses flats. They produce the same tune.

As with before, you can listen to the chromatic scale produced by the above staves below:

( link "Link Here" formerly at http://kamatsu.spheredev.org/chroma.ogg : OGG of chromatic scale )

Notice how we start and finish the scale on the same two notes (an octave apart) that we see from the Major Scale, however we fit a helluva lot more notes in?

Compositional Tip: Moving chromatically in a piece can add a chaotic, tense element to your sound. Note however that chromatic music is very difficult to write well, so wait until you're fairly experienced.

Extra Info: Notating sharps or flats in this fashion - next to the notes that are modified - is called accidental notation. If you apply an accidental to a note, that accidental will apply for the rest of the bar to all notes on the line or space on which the accidental occurs. A bar is a way of grouping notes according to time, and they are separated by long vertical lines (as we see in the above staves). We will learn more about bars, barlines, as well as the natural symbol after we have covered keys and time signatures.

Key Signatures and Accidentals

If we examine the intervals of a C Major Scale, we can construct the following list of intervals:

• C to D - Tone
• D to E - Tone
• E to F - Semitone
• F to G - Tone
• G to A - Tone
• A to B - Tone
• B to C - Semitone

This should lead the more apt of you to consider applying the same sequence of intervals from a different starting note. By doing this, you can "move" the major scale to any tonic note. For example, suppose we wanted to make our Major scale start on a G, we simply need to keep the interval pattern of tones and semitones the same as in the C Major Scale:

• G to A - Tone
• A to B - Tone
• B to C - Semitone
• C to D - Tone
• D to E - Tone
• E to F♯ - Tone
• F♯ to G - Semitone

Playing or singing this through will result in a similar sounding scale to the C Major one we heard earlier - except it starts on G.

This leads one on to a concept of a key. A Key is defined in musical notation with a Key Signature. They look like a series of accidentals that are placed at the beginning of a bar (or line) rather than at the beginning of a note.

A Key Signature that, for example, has a sharp in the "F" line on the staff (that is, G Major), looks like the following (with a preceding treble clef):

staff, treble clef, G major key signature

This instructs the reader of the music to read all occurrences of "F" in the music as "F♯" instead of just plain old F, until another key signature occurs. The advantage of this is that you can write music in another key (i.e using another scale and another tonic) without cluttering up your music with pesky accidentals.

So, we can now produce a G Major Scale in musical notation with a key signature (as F is replaced with F♯ in all instances), as follows:

staff, treble clef, G major key signature and scale

Note: Notice how the "Do, re, mi…" scale has moved so that "Do" (tonic) is now on G? That is the effect of the key signature.

The Natural Sign

In many situations, it may be appropriate to "Cancel out" one of the note modifiers present in a key signature, and make it change back to the original note - just for one or two notes. This is achieved with another accidental sign (other than sharp(♯) and flat(♭)) that we have not yet learnt.

This sign is called the natural sign. That is because, the natural of the note is the note without a sharp or flat. So, the possible modifications to D are:

• D♯ - D Sharp
• D♭ - D Flat
• D - D Natural

Note that the Natural sign is usually only used as an accidental to show a reversion from the key signature. Here's a C Major scale, written in a G Major key signature, using the natural sign to cancel out the F♯ where it occurs.

staff, treble clef, G major key signature and scale with natural F

A List of Major Key Signatures

Here's a list of common major keys, and their key signatures (i.e what sharps and flats are present).

grand staff, major keys with sharps

grand staff, major keys with flats

Use this as a handy reference when composing.

Extra Info: Note that we have only been dealing with major scales so far. Later on, when we learn about modes, we will also learn about the other common tonality: Minor. Minor keys have the same key signatures as other, equivalent, major keys, except they start on a different note. They tend to sound more mournful and militaristic.

Modes

Now that you have a fair understanding of keys, we can learn a more advanced aspect of musical theory, modes. We have touched on this earlier. When we first developed a Major scale, we observed that the C Major (and, all other major scales) use the following sequence of tones and semitones:

T,T,S,T,T,T,S

(where T=Tone, and S=Semitone)

In addition to being a major scale, this sequence is also called a scale in the ionian mode. All major scales are ionian.

You can achieve a variety of other modes by changing the sequence of tones or semitones. On a clear key signature (that is, no sharps or flats), it is as simple as playing all the white keys, except starting on a note other than C. For example, if you play all the white keys from middle D to another D, that produces a dorian scale.

As with the major scale, all modal configurations can be changed by introducing a key signature. For example, if you introduce a key signature with one sharp (G Major), then the dorian mode can be achieved by playing from A to A, with an F♯.

I will now go through each mode, explain it's tonal configuration, and some possible compositional uses of each mode. I will also provide a MIDI file of the same tune being played in different modes.

Ionian Mode

T,T,S,T,T,T,S

Played from: C to C

This is a mode that generally sounds uplifting, joyous. A major scale is ionian. This is the most common mode.

Tune: http://kamatsu.spheredev.org/ionian.mid

Dorian Mode

T,S,T,T,T,S,T

Played from: D to D

This mode was often used in medieval times. It sounds like a minor scale at first, but later becomes more melodically major. If writing something for a medieval feel, Dorian mode is often the way to go.

Tune: http://kamatsu.spheredev.org/dorian.mid

Phrygian Mode

S,T,T,T,S,T,T

Played from: E to E

This mode was also often used in medieval times. With the initial semitone it can be somewhat jarring, but can be pulled off well in a good composition.

Tune: http://kamatsu.spheredev.org/phrygian.mid

Lydian Mode

T,T,T,S,T,T,S

Played from: F to F

This mode is somewhat similar to a major scale, except the semitone has been moved by one place.

Tune: http://kamatsu.spheredev.org/lydian.mid

Mixolydian Mode

T,T,S,T,T,S,T

Played from: G to G

This sounds almost like a major scale, once again, except the final few intervals have been altered.

Tune: http://kamatsu.spheredev.org/mixolydian.mid

Aeolian Mode

T,S,T,T,S,T,T

Played from: A to A

This is a sad, mournful mode. It also constitutes a natural minor scale. When one refers to "A Minor", the key signature is therefore the same as C Major (no sharps or flats), but the piece is in a different mode.

More info: There is also melodic minor, which has a raised ficta note on the seventh note in the scale. We will learn more about ficta in the next section.

Note that now that we know the natural minor equivalent of C, we can derive an updated Key signature chart, to show a specific key signature, its major key, and its minor key. One key signature can therefore mean many things!

grand staff, major keys with sharps

grand staff, minor keys with sharps

grand staff, major keys with flats

grand staff, minor keys with flats

Tune: http://kamatsu.spheredev.org/aeolian.mid

Locrian Mode

S,T,T,S,T,T,T

Played from: B to B

This is a dissonant, tense mode. It is rarely used for the entirety of a composition.

Tune: http://kamatsu.spheredev.org/locrian.mid

Ficta and melodic minor

Musica Ficta is a historic practice that dates back to medieval and renaissance performances, as a technique to make harmonies sound more melodic.

It was also used to avoid difficult or jarring intervals such as the tritone, which were not considered stylistically appropriate at the time (in fact, the tritone was called the "diabolus in musica" or devil in music).

There are several common ways in which Ficta is used. Often F major parts will be harmonized with C Major parts. These keys are the same, except for the B♭. Often, therefore, B♭ is notated with an accidental in a C Major part, to preserve harmony. You will also note that this makes the scale sound more melodic.

Another such application of ficta is to the melodic minor scale. This raises the seventh note in the aeolian, or natural minor scale, a ficta semitone higher.

So, an for the A natural minor scale:

A B C D E F G A

A melodic scale would be:

A B C D E F G♯ A

The melodic minor scale sounds more mysterious and can be used to very good effect.

Timing and Rhythmic Techniques

Beats and Bars

Introduction

If you listen to your favorite song, regardless of genre, you will almost undoubtedly hear a regular pulse, or beat, from which every note derives its length. Some might be half of one of these beats, some might be one, two, three or even four. If you listen carefully, some songs may sound like they are grouped into a certain amount of beats (it may be 2, 3, 4, or possibly 5). In music, we have a variety of ways to represent this.

Note Values and Time Signatures

Each note can be assigned a different note value. A note value is the amount of beats for which a note is held.

Notes are grouped into bars, one of which represents one logical grouping of beats as per the time signature.

This seems like alot of terminology to swallow, so I'll start from the top:

When you found yourself counting "1,2,3,4,1,2,3,4", while listening to your favorite piece of music, you were counting out individual beats per bar. In this case, there are 4 beats to the bar. If you found yourself counting "1,2,3,1,2,3" (like a Waltz) then there were 3 beats to the bar.

There are a variety of time signatures in music, and these specify how many beats there are per bar, and how we will represent them on the page.

Some Examples of Time Signatures

treble staff, three-four time signature

In this example, there are three quarter notes to the bar.

treble staff, four-four time signature

In this example, there are four quarter notes to the bar.