Music Theory Fundamentals

Music Theory

The occidental system of music notation has been developed and refined over hundreds of years by composers and music theorists. It allows musicians to write down, on paper or otherwise, instructions for the performance of symphonies, songs or musical phrases. Such instructions can then be read by a performer, enabling them (at least in theory) to reproduce the music exactly as intended by its creator.

Prior to the advent of modern recording technology, such a process of interpretation and performance was required every time one wished to listen to musical compositions. Although notation may be typically associated with "classical" music, every musical work can be scribed in such a form, with varying degrees of success. Contemporary electronic music, for example, often relies heavily upon the sonic qualities of the constructed sound itself. This may be of more importance to the piece than the actual notes that are played, and as such may not be as readily translated into a score of typical notation.

The Elements of Rhythm

The most common rhythmic structure in music is 4/4 time, or common time. This means that every bar contains four beats - an arrangement often referred to nowadays as "four to the floor". A bar can be defined as a rhythmic unit of a piece of music, which is divided into a number of smaller units, into which the notes or musical elements can placed.

A whole note, or semi-breve, fills a whole bar, and is the longest note available in this notation.

A half-note, or minim, is half the length of a semi-breve and therefore its duration is half that of the bar itself. It is represented by an empty circle with a stem (which can either face upward or downward).

Next we have the quarter-note, or crotchet. Two of these equal one minim, and four will equal a whole note. The quarter-note is drawn in the same manner as the minim, but the circle is filled rather than hollow.

The crotchet is an important element, in that the length of a bar is usually determined by how many crotchets will fit into the bar. The examples shown here are set in common time (4/4) and therefore the bar will fit four crotchets. If we employed a bar that fits only three crotchets then this would be 3/4 time (see the section on Time Signatures).

Moving to the next level of brevity, we encounter quavers - these are eighth-notes, each equivalent to two crotchets. Beyond this, we have semi-quavers (sixteenth notes), demi-semi-quavers, and so on as needs be. Quavers and semi-quavers are notated in a similar manner to crotchets, but they have tails (or flags) which vary depending on what value they represent. Groups of such flagged notes may be beamed together, usually in a way that highlights the underlying pulse of the bar. In the example below, the first groups are beamed together to highlight the length of a minim or crotchet. Notating a piece in this manner allows a performer to quickly see the rhythmic pulse of the music, particularly if there are lots of short notes.

Time Signatures

The time signature is a convention for organising the distribution of beats in a bar. The most common of these is 4/4 or common time. The next most common time signature is probably 3/4 time, which is typical of the waltz. The figure before the slash determines the number of values to be found in a bar, and the figure after determines the type of value they are. Therefore, 3/4 time features three quarter-notes (crotchets) in a bar; 5/8 time features five eighth-notes (quavers) per bar.

Emphasis

With a simple marching beat, emphasis may be placed on one of the beats above the others. For example, a drill sergeant may lead his troops thus: "hup, two, three, four, hup, two, three, four" (a simple 4/4 arrangement).

In this example, he is likely to place emphasis on the first beat - often referred to as the downbeat. Thus his march will sound more like this: "HUP, two, three, four, HUP, two, three, four"

The illustration below shows two methods for notating an emphasis. The pointed symbol positioned over the first crotchet is called an accent, and indicates that heavy emphasis should be applied to this note. The short horizontal line over the third note also indicates emphasis, albeit of a lesser magnitude than the first.

Modifying Note Lengths

When dealing with some of the more esoteric time signatures, it may be necessary to employ extra notation to convey accurate timing information. For example, in a 3/4 time bar, one cannot use a semi-breve to denote a value that lasts for exactly the duration of the bar - there is no single note that lasts as long as three crotchets.

To solve this problem, the concept of dotted notes was introduced. By placing a dot to the right of a note�s head, the duration of that note is increased by half. Therefore, a dotted minim will expand from a value of two crotchets to three crotchets - precisely what is required to fill a 3/4 time bar.

Another way of approaching this matter is by using tied notes; by inserting a linking arc between two notes, the first note acquires the additional duration stipulated by the second note. The second note remains silent; its only function here is to increase the length of the first. The illustration below shows these solutions in action; first the use of the tied note, and then the dotted note.

Tempo

Although the time signature reveals much information about the structure of a musical work, it tells us nothing about how fast it should be played. This is essentially what tempo is; how many beats will fall within a set amount of time. As the tempo increases, the relationship between the beats remains the same, but the number of beats falling within a set amount of time will also increase. To put it simply, the time signature defines the rhythm and tempo defines the pace. Generally speaking, beats are regarded as being synonymous with crotchets, and tempo is measure in beats per minute (BPM). Sequencing software will have a readily visible BPM meter with which the tempo can be easily adjusted; more traditionally, a metronome was (and still is) used to accurately set the tempo of a performance.

Pitch

In physical terms, pitch is related to the frequency of the sound in question - put simply, the higher the frequency, the higher the perceived pitch. But notation is all about notes, not frequencies.

On a piano keyboard, notes are arranged ascending from left to right. The pattern of the keys repeats every twelve notes, which is known as an octave. (So called because there are eight whole notes, or tones in an octave - including the black keys, or semitones, we have twelve keys in total).

The black keys are named according to the white key they are adjacent to. If they are located above the white key, they are sharp (#) and if they are below, then they are flat (b). Such notes are known collectively as accidentals.

If a black key is between two white keys, then it may also be an enharmonic. For example, C# could also be called Db - Db is therefore the enharmonic equivalent of C#.

Staves and Clefs

Notation requires a structure on which notes may be placed; five horizontal lines make up what are known as staves, or the staff. These denote various levels of pitch, ascending from bottom to top.

At the beginning (extreme left) of each staff you will see a Clef. There are two main varieties of Clef, the Bass Clef and the Treble Clef. This informs the reader whether the notation is to be located to the left (bass) side of the keyboard or to the right (treble).

As the rules for notation differ between the bass and treble clefs, it is necessary to know which clef is applied to the staff before one can determine which note is represented on any particular line. A variety of mnemonic devices are in common usage to aid the student in remembering which notes appear on which lines, and in the spaces between them. If these are not useful to you, feel free to make up your own.

For the Treble Clef:

The notes on the lines are (starting from the bottom): Every Good Boy Deserves Fun (EGBDF)

The notes in the spaces are (starting from the bottom): FACE

For the Bass Clef:

The notes on the lines are (starting from the bottom): Good Boys Deserve Fun Always (GBDFA)

The notes in the spaces are (starting from the bottom): All Cows Eat Grass (ACEG)

Ledger Lines

The illustration below shows the middle four octaves of a keyboard. If a note appears outside the range of the standard five lines, then additional ledger lines may be placed in the notation to facilitate readability. If the number of ledger lines grows too cumbersome, an ottava sign (8va) may be used to indicate that the note has been transposed by an octave.

Major and Minor Scales

On a piano keyboard, the variation between two contiguous notes can be either a tone or a semi-tone, depending on which particular notes are being referred to. At any rate, the smallest distance between any two keys is a semi-tone - for example, this is the distance between F and F#, or that between B and C.

The octave is another means of separation, and in effect is a doubling of frequency. Within any octave, we have only twelve distinct notes to work with before coming to the same note again, albeit at a higher pitch.

Despite this seemingly limited range of notes to choose from, most music actually uses even fewer - in most cases, seven. Which seven notes these are determines the key of a piece.

Most people will be familiar with the concept of scales; Do, Re, Mi, Fa, So, La, Ti, Do is the classic example. The original meaning of scale was that it formed a ladder, taking you from one octave to the next, with the last note being a repetition of the first, but an octave higher (doubling the frequency). The particular notes that take you up are the rungs of this notional ladder. Small changes to these rungs can greatly affect the quality and mood of the scale as a whole.

Perhaps the most common scale is the major scale, and the simplest way to generate one is by starting at C on the piano keyboard and playing all the white notes up to the next C an octave higher. This is, of course, the scale of C Major.

If we look at the notation for the scale, the separation of the notes follows a definite structure which is characteristic of a major scale. The mood of such scales is generally interpreted as being positive and uplifting. A major scale may be generated for any note by starting on that note and playing upwards whilst preserving the separations observed here - that is, tone/tone/semitone/tone/tone/tone/semitone.

The separation structure of a minor key is only slightly different, yet it creates an entirely different mood. As you can see, the number of tone/semitone separations within the scale remains constant - they have merely been redistributed.

Key Signatures

As most pieces of music only use seven notes, and these are usually taken from a particular scale, it is sometimes convenient to employ a key signature. For example, if a composer is working in E major, she may be required to include a lot of sharps in the notation (the scale of E major includes four sharps, as shown in the illustration below). This can cause undue clutter and confusion in the score. As a shortcut, the composer may simply use a key signature to tell the performer that all notes on a particular line will be sharps or flats, so she doesn't have to keep marking them in individually - and the performer can take it for granted that these will be black notes. The key signature is a collection of sharps or flats located beside the time signature.

The Circle of Fifths

The circle of fifths is used to determine how many sharps or flats a particular scale has. The circle starts at C in the twelve o'clock position (which has no sharps or flats) and proceeds clockwise around in steps of a fifth. Here, a fifth is the fifth step in a scale, but it actually equals seven semi-tones. Looking at the circle, you can instantly see the number of sharps or flats featured in each of the scales.