Download (1) Sound and Music

(1) Sound and Music
Music would not exist without sound. Everything musical is made from sound. And yet, the
reverse is not true - there are many sounds which are not musical.
Clearly there is a difference between musical sounds, and non-musical sounds.
We begin, in this first tutorial, by exploring the relationship between sound and music.
This lays the foundation for other tutorials, which introduce the Major scale, as well as all of the
other chords and scales used in music.
By the time you are finished, you will have a solid and practical understanding of how all types
of music work.
You will also be off to a flying start with advanced activities like improvisation and songwriting.
Sound Waves
Sound is the vibration of air particles, which travels to your ears from the vibration of the
object making the sound. These vibrations of sound in the air are called sound waves.
When a door is slammed, the door vibrates, sending sound waves through the air.
When a guitar string is plucked, the string vibrates the soundboard, which sends sound waves
through the air.
What makes one sound different from another? To answer this question, we need to look at
the waveforms of the two different sounds, to see the shape of their vibrations.
Copyright c 1997-2007
(1) Sound and Music
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 1 of 10
The waveform of a door slamming looks something like this:
This waveform is jerky and irregular, resulting in a harsh sound. Notice how it is loud (with big
waves) at the start, but then becomes soft (small waves) as it dies away.
The waveform of a guitar string looks something like this:
This waveform makes the same transition from loud to soft as the first, but otherwise is quite
different.
The guitar string makes a continuous, regular series of repeated cycles, which we hear as a
smooth and constant musical tone.
This regularity of the vibration is the difference between a musical sound and a non-musical
sound.
Musical Sounds
Musical sounds are vibrations which are strongly regular. When you hear a regular vibration,
your ear detects the frequency, and you perceive this as the pitch of a musical tone.
Non-musical sounds are a complex mix of different (and changing) frequencies. Your ear still
follows these vibrations, but there is no strong regularity from which you can pick up a musical
tone.
Copyright c 1997-2007
(1) Sound and Music
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 2 of 10
Many sounds are a mixture of both, such as drums and other percussion instruments. You can
usually decide which of two drums has the higher pitch, even if it might be difficult to decide
exactly what that pitch is.
Most sounds have some regularity in them (even a door slamming) but not enough for your ear
to detect a specific pitch.
Amplitude and Frequency
There are two main properties of a regular vibration - the amplitude and the frequency - which
affect the way it sounds.
Amplitude is the size of the vibration, and this determines how loud the sound is. We have
already seen that larger vibrations make a louder sound.
Amplitude is important when balancing and controlling the loudness of sounds, such as with the
volume control on your CD player. It is also the origin of the word amplifier, a device which
increases the amplitude of a waveform.
Frequency is the speed of the vibration, and this determines the pitch of the sound. It is only
useful or meaningful for musical sounds, where there is a strongly regular waveform.
Frequency is measured as the number of wave cycles that occur in one second. The unit of
frequency measurement is Hertz (Hz for short).
Copyright c 1997-2007
(1) Sound and Music
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 3 of 10
A frequency of 1 Hz means one wave cycle per second. A frequency of 10 Hz means ten wave
cycles per second, where the cycles are much shorter and closer together.
The note A which is above Middle C (more on this later) has a frequency of 440 Hz. It is often
used as a reference frequency for tuning musical instruments.
Musical Instrument Tone
There is a huge variety of musical instruments and sounds, as you would already know from
your experience with music. Even two instruments playing the same note can sound very
different.
This is because a musical instrument produces a sound wave which is a combination of different
but related frequencies (known as harmonics) which all mix together to create the distinctive
tone or voice of the instrument.
The lowest frequency is usually dominant, and you perceive this one as the pitch. The
combination of the other harmonics provides the distinctive shape of the waveform, and
thereby the distinctive tone of the instrument.
The piano and trumpet each contain different combinations of harmonics, and therefore sound
different to the guitar, even when they are all playing a single note of the same pitch.
Copyright c 1997-2007
(1) Sound and Music
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 4 of 10
Frequency and Pitch
Frequency and pitch describe the same thing, but from different viewpoints. While frequency
measures the cycle rate of the physical waveform, pitch is how high or low it sounds when you
hear it.
This is directly related to frequency: the higher the frequency of a waveform, the higher the
pitch of the sound you hear.
Think of the sound of a car or motorcycle engine accelerating. As the engines turns faster (at a
higher frequency) the engine makes a higher-pitched sound.
Human ears can only hear sounds within a certain range of frequencies. As people grow older,
their hearing range reduces. A young person can usually hear sounds in the range of 20 Hz to
20,000 Hz.
Click on the button below to hear a continuous pitch sweep from the lowest to the highest
audible frequencies.
At the lower end of this range are low-pitched sounds like the booming of thunder before a
storm. At the upper end of this range are high-pitched sounds like the piercing whine of a
mosquito.
Between these is the whole spectrum of sound and music!
Doubling Frequency
Something very interesting happens when you double the frequency of a note. The pitch of the
doubled frequency sounds higher, but somehow the same as the original note, while the pitches
of all frequencies in between sound quite different.
Lets use the pitch of frequency 440 Hz as an example. It is the note A, as mentioned earlier.
The pitch of frequency 880 Hz is higher, but sounds like the same note.
It seems strange, but there is a logical reason for this similarity. The sound waves below show
us that two cycles of the 880 Hz frequency fit exactly in the space of a single cycle of the 440
Hz frequency.
Copyright c 1997-2007
(1) Sound and Music
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 5 of 10
If we keep doubling this frequency, we find that all of the resulting pitches sound similar,
except that each one is higher than the last. In fact, they are all the note A, just like the
original, but they are all one octave apart from each other.
Octaves
An octave is the difference in pitch between two notes where one has twice the frequency of
the other. Two notes which are an octave apart always sound similar and have the same note
name, while all of the notes in between sound distinctly different, and have other note names.
This is a very important concept in music. Although notes are arranged, like a piano keyboard,
in a long series from low to high, there is a repeating pattern.
Copyright c 1997-2007
(1) Sound and Music
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 6 of 10
Notes naturally fall into groups of twelve, which are all one octave apart from each other.
These groups repeat going up and down the piano keyboard (and indeed, the musical spectrum
for any instrument).
The Octave of a Note
You might be wondering how to refer to a particular A note, now that we know there are
several of them.
The easy answer is that it often doesn't matter. Since notes an octave apart sound similar, a
tune played one octave up or down will still sound the same as the original, just higher or
lower.
If the exact octave is important, you can relate it to Middle C, which has a frequency of
261.63 Hz. For example, you could refer to 'A above Middle C' as we did earlier.
The 'middle' in Middle C comes from it being the C note in the centre of the piano keyboard. It
is also the note in between the bass and treble staff lines in standard musical notation (more on
this later).
Writing notes on staff lines pinpoints them in a specific octave. Each of the staff lines, and the
spaces in between them, represent a note relative to Middle C.
Another convention, often used with computer music, is to follow the note with an octave
number. For example, Middle C might be labelled C4, while C5 would be the C note one octave
up from it.
These numbers are not standardised, so you will need to make it clear which octave number
you are using for Middle C. Also, within an octave the notes should be arranged from C to B
and not (as you might expect) from A to G.
Copyright c 1997-2007
(1) Sound and Music
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 7 of 10
The Chromatic Scale
There is a magic number in western music, known as the twelfth root of two, and it has a
value of approximately 1.0595. This is the number that, when multiplied by itself twelve times,
gives a result of two.
Why is this important to music?
Remember that with notes one octave apart, the higher note has double the frequency of the
lower note. The range of frequencies in between is divided up into the twelve steps that give
us all of our notes.
The frequency of a note, when multiplied by the twelfth root of two, gives the frequency of the
next note up. The different in pitch between adjacent notes is called a semitone.
After doing this for twelve notes, you end up with twice the frequency, which is the note one
octave up from the starting note. We can do this in both directions (multiplying upwards and
dividing downwards) to calculate the frequency of every musical note.
Copyright c 1997-2007
(1) Sound and Music
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 8 of 10
The set of all musical notes is called the Chromatic Scale, a name which comes from the
Greek word chr獽a, meaning color. In this sense, chromatic scale means 'notes of all colors'.
Colors, in fact, are also made up from different frequencies, those of light waves.
Because notes repeat in each octave, the term 'chromatic scale' is often used for just the
twelve notes of an octave.
This method of dividing the octave using the twelfth root of two is known as equal
temperament tuning, pioneered several centuries ago in the time of JS Bach. Since then, the
music of the western world has been based on the notes of the Chromatic scale.
Equal temperament tuning was a major breakthrough in the development of music. It replaced
the earlier method of using simple frequency ratios to divide up the octave, which had great
limitations when trying to transpose music from one key to another (more on what this means
later).
Chromatic Scale Notes
The Chromatic scale could start on any note, but would always end up containing the same
notes (because it contains all notes). So in practice, there is only one Chromatic scale.
The table below shows the frequencies of the twelve notes between note A at 440 Hz, and note
A one octave up from it.
Higher pitched notes have larger frequency steps (in Hertz) between them, but each step
makes an equal change to difference in pitch (one semitone) that we perceive.
Copyright c 1997-2007
(1) Sound and Music
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 9 of 10
Even though there are twelve notes in an octave, only the first seven letters of the alphabet are
used to name them (from A to G). We'll look at the reason for this later.
The other five notes of the Chromatic scale are named by placing a sharp (#) symbol after a
note letter to make it one semitone higher, or by placing a flat (b) symbol after a note letter to
make it one semitone lower.
Often there are two name choices for these other five notes. For example, the note Ab in the
table above could also be called G#. Sometimes, as we'll see later, there is a definite rule for
which name is more appropriate.
Chromatic Scale for Piano
The piano keyboard is one of the classic ways of viewing the Chromatic scale.
Notice how the white keys play the simple notes (called natural notes) and the black keys play
the altered notes (which have sharps or flats added). Also, the whole pattern of note names
repeats after every seven white notes.
Chromatic Scale for Guitar
Notice how all the notes of the Chromatic scale can be played on any group of five frets (using
all strings), without needing to move the hand along the fretboard.
Copyright c 1997-2007
(1) Sound and Music
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 10 of 10
(2) The Major Scale
A scale is a collection of notes, selected from the full set of notes in an octave. The choice of
notes in the scale provides the framework on which a piece of music is built.
We have already been introduced to the Chromatic scale. It is very rarely used as the basis
for a piece of music, because it excludes no notes, and so provides no structure.
The importance of the Chromatic scale is that it defines the full set of notes in music, from
which all other scales are built.
There are many different types of scales, and we will look at all of them in detail later. To
begin with, we are going to meet the most important scale in western music, the Major scale.
Scales and Music Structure
A scale type is defined by the particular pattern of semitone intervals between its notes,
which gives it a characteristic sound.
Other scale types have different patterns of intervals, giving each of them a different
characteristic sound.
Most scale types have between five and eight notes in them, with seven notes being the most
common. Some examples are shown below.
Copyright c 1997-2007
(2) The Major Scale
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 1 of 15
The seven-note Major scale is such a dominant force in western music that it provides the
foundation for the naming of notes and chords, even with music using different scale types.
When a scale type is played from a particular starting note (also known as the root or key
note) it becomes a scale. Scales of a certain type may contain 12 different sets of notes,
depending on this starting note.
The scale of a song defines its melodic structure, by identifying which notes can be used in
the melody (or tune) of the song.
The scale also strongly influences the harmonic structure of a song, because these same
notes are generally used for building chords to accompany the melody.
This is not a fixed rule, and many songs use notes outside of their scale, but these are
considered to be exceptions. They are called accidental notes, and in sheet music they are
specially marked to show that they do not belong to the scale.
Intervals of the Major Scale
The Major scale is by far the most common scale in western music. When played in sequence,
the notes of the Major scale make the famous do-re-mi-fa-so-la-ti-do sound.
This characteristic sound of the Major scale is created by the pattern of intervals between its
notes. There are seven notes in the Major scale and seven intervals between them. This
pattern is:
When this pattern is used to extract notes from the Chromatic scale, we arrive at the Major
scale.
Copyright c 1997-2007
(2) The Major Scale
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 2 of 15
Adding the semitone interval sizes together (2+2+1+2+2+2+1) gives a total of 12, the
number of semitones in a octave. This is also true for every other (non-Major) scale type.
The picture below shows how this pattern of intervals appears for the C Major scale on the
piano.
Notice how this interval pattern and starting note perfectly corresponds with the black and
white keys of the piano, so that only white keys are used in the scale.
This is a special property of the C Major scale. Major scales starting on other notes need at
least one black note, and in most cases several.
Notes of the C Major Scale
The Major scale is so fundamental to our system of music, that the names of our notes are
based on it.
It is no coincidence that we use only the first seven letters of the alphabet to name the twelve
notes of chromatic scale. Each of these letters corresponds to one of the seven of the notes of
the Major scale. This is true no matter what the root note of the scale is.
The C Major scale works very neatly in this way. As you can see, its seven notes are:
Copyright c 1997-2007
(2) The Major Scale
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 3 of 15
Songs using these notes are said to be in the Key of C. Given the interval pattern of a scale
type, the root note of a scale is the 'key' that tells you the other notes.
Major scales in other keys are made from different notes, but the same seven note letters are
still used, in a different order, together with sharp (#) and flat (b) symbols to preserve the
Major scale pattern of intervals.
The C Major scale is the only key where all of the notes are natural (without sharps or flats).
We'll see later why this privilege belongs to the key of C.
Staff Line Notation
For centuries, the notes in pieces of music have been described by writing them on staff lines
.
Staff notation is based on staves. A stave is a set of five horizontal lines, where each line
(and each space in between) represents a different note letter. Note symbols are placed
either on or between the lines.
Extra notes can be accommodated outside these five lines, by adding extra leger lines (also
spelled ledger) where needed.
There may be different arrangements of note letters on the staff lines, depending on which
Copyright c 1997-2007
(2) The Major Scale
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 4 of 15
clef symbol appears at the start. There are only two clefs you really need to know.
The most important is the treble clef, which has note letters arranged as shown. It is
sometimes called the G clef, because the inner twirl of the symbol centres on the line for note
G.
The notes of each line, from bottom to top, are E, G, B, D, F. You might find the phrase 'Every
Good Boy Deserves Fruit' helpful for remembering this.
Also common is the bass clef, which has note letters placed as shown below. It is sometimes
called the F clef, because the two dots are centred on the line for note F.
You can use the phrase 'Good Boys Deserve Fruit Always' to remember notes on the lines of
the bass clef.
The treble and bass clef are often used together as a pair, covering a wider range of notes.
They fit together neatly with a single leger line, used for Middle C, in between them.
This is known as a grand stave, and the treble and bass staves are always joined with a
vertical line at the left end, to show that they belong together.
In piano music, the left hand often plays the notes on the bass clef, while the right hand plays
the notes on the treble clef.
Finally let's see how the C Major scale appears on staff lines. Shown below are two octaves of
the C Major scale, centred on Middle C.
Copyright c 1997-2007
(2) The Major Scale
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 5 of 15
Most ChordWizard products contain the View Staff tool, or have a Track
View which can show you how any scale or chord would appear on staff
lines.
C Major Scale for Guitar
Compare this diagram to the Chromatic scale for guitar shown earlier.
Again, notice that all the notes of the C Major scale can be reached on any group of five frets,
and in some fret positions, with only four frets.
Notes of the G Major Scale
Taking a set of notes from one key to another is called transposing. Here we will be
transposing the Major scale, but the term is also used when changing the key of a piece of
music.
Let's start by transposing the Major scale to the key of G, the fifth note of the C Major scale.
You will soon see the reason for this choice.
To find the notes of the G Major scale, we follow the interval pattern of the Major scale (2-2-12-2-2-1), starting with the note G. This gives us the following seven notes:
Copyright c 1997-2007
(2) The Major Scale
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 6 of 15
Here we have an interesting problem, because the last note of the scale has an ambiguous
name. Should it be called F# or Gb? There is a simple rule to answer this question for any
Major scale:
Each of the seven letters of the alphabet must be used exactly once when naming
the notes of a Major scale. Sharps and flats are added to adjust the notes to the
correct pitch for the scale.
Using this rule, we can see that the name of the last note of the G Major scale should be F#,
otherwise there would be two G notes and no F notes.
As you can see, the key of a song determines not just the notes of its scale, but also how they
are named.
G Major Scale on Staff Lines
The notes of the G Major scale appear on staff lines as shown below. We can fit three octaves
of G Major within the paired staff lines.
Every time a note appears on the F lines, the sharp (#) symbol is put before it as an
accidental, to show that it is really F#.
Because F always means F# in the G Major scale, it is inconvenient to do this every time the
note is used. Instead, a sharp can be placed at the start of every staff, to indicate that all F
notes are to be played sharp.
Copyright c 1997-2007
(2) The Major Scale
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 7 of 15
This is known as the key signature of the G Major scale. Only one F line on each clef is
marked in this way, even though the treble clef, for example, also has an F in the space
between the bottom two lines.
The same three octaves of the G Major scale shown above can now shown more simply as
follows.
The note F# would be called an accidental in the C Major scale, but not in this case, because it
rightfully belongs to the G Major scale.
In fact, F natural is now the accidental, because it does not belong. The following shows how
the note sequence E, F, F#, G is written in the key of G.
First the natural symbol is used as an accidental, to override the sharp of the key signature,
and then the F needs to be 'resharpened' afterwards, with a sharp accidental.
Every key has a different key signature, as we will see shortly. The absence of a key
signature always indicates the C Major scale.
All Major scales apart from C Major have at least one sharp or flat (and most of them have
several) but there are no Major keys which have both sharps and flats in their key signature.
Major Scales in All Keys
Now let's look at the notes of the Major scales in all of the 12 possible keys. They have been
arranged in a particular order here, with C Major in the middle, to reveal a very interesting
Copyright c 1997-2007
(2) The Major Scale
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 8 of 15
and important pattern.
The fifth note of each scale is the key of the scale on the row below. Notice the effect that this
has on the number of sharp and flat notes.
Each scale has one more sharp, or one less flat, than the scale on the row above. They are
the same sharp or flat notes each time, except for the one which changes between rows.
Start with the C Major scale in the middle and work downwards and then upwards to confirm
this for yourself.
Major Scale Note Names
Notice how the C# Major scale is almost identical to the C Major scale, except that every note
is sharp.
Copyright c 1997-2007
(2) The Major Scale
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 9 of 15
This seems logical, and yet it contains the notes E# and B#. These don't seem to exist,
because we know that there is only a one semitone interval between the notes E and F, and
between the notes B and C.
In fact, E# is simply another name for F natural, and B# another name for C natural. The
names are written like this because of the golden rule above introduced earlier - each note
letter must be represented once in the scale.
For the C# Major scale, the letters F and C are needed for the notes F# and C#, but the letters
E and B are spare. So E# is used for the third note, B# is used for the seventh note, and
everything fits perfectly.
In a similar way, when necessary, Cb is another name for B natural and Fb is another name for
E natural.
We see something even stranger if look at the notes of the G# Major scale.
The last note in this scale is pronounced F sharp sharp or F double sharp (in sheet music, the
symbol x is used instead of ##). This, as you might guess, is another name for the note G.
Double sharps and flats are perfectly legal, and often necessary to preserve the correct
sequence of note letters in the scale. They do look strange though, and in practice eccentric
keys like this are not often used.
Most ChordWizard products allow you to select how notes are named within
the workspace. There are up to four different methods.
-Strict naming works according to the rules described above.
-Single Symbol naming converts double sharps and flats to the next
natural note up or down, to reduce visual complexity.
-Simplified naming is the same as Single Symbol naming, but it also
simplifies Fb to E, E# to F, Cb to B and B# to C.
-Default naming simply uses your preferred default names for each sharp
or flat note.
Key Signatures for All Keys
We saw earlier the key signature for the G Major scale. This indicates that all F notes are to
played as F#, so we don't have to mark each F# note with an accidental sharp symbol.
In the same way, there are key signatures for all of the Major keys, placed at the beginning of
each staff, and containing a specific pattern of sharps or flats.
Copyright c 1997-2007
(2) The Major Scale
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 10 of 15
These key signatures adjust the notes on the staff lines to suit the Major scale of each key, as
listed in the table of the previous topics.
The key signatures containing sharp notes are:
Notice how the patterns of sharp symbols are very similar between the treble and bass clefs just shifted vertically by one line.
The key signatures containing flat notes are:
Try to remember these key signatures, or at least the more common ones in the first rows.
Knowing the key of a piece of music not only helps you play the right notes, but also gives you
a good idea of what chords are likely to be used with it. We'll see more on this later.
Copyright c 1997-2007
(2) The Major Scale
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 11 of 15
ChordWizard products such as Songtrix offer unlimited flexibility with key
signature changes. Any or every bar can have a new key signature. The
notation in Staff View is updated automatically.
Using Octave Clefs
Earlier we were introduced to the bass clef and the treble clef, which give us a reference
point for which notes are represented by the lines of the stave.
Often, music will stray outside of these lines. We have seen that even the grand stave (bass
clef + treble clef pair) has a range of only about three octaves, whereas the piano, for
example, usually has a range of about ten octaves.
How then are we to write notes which would appear outside the staff lines? One way,
mentioned earlier, is to use leger lines to extend the stave for particular notes.
However, this is only useful up to about three legers, and even then only for temporary
melodic excursions outside the stave. Extended passages written on legers, or large stacks of
legers, are very hard to read.
A better solution is to use octave clefs. These are the same as regular bass or treble clefs,
but they have one or more figure 8 symbols added above or below the clef to indicate that the
notes on the clef are shifted by one or more octaves from what you would normally expect.
Let's see a few examples. The G Major scale written on a treble clef could appear like this:
Suppose we wanted to play the same scale, but an octave higher. Then it would look like this,
much less convenient to write and read:
If we make an octave clef by joining a figure 8 to the top of the treble clef, this indicates the
higher octave instead, allowing us to shift the actual note positions down onto the main stave
lines again.
Copyright c 1997-2007
(2) The Major Scale
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 12 of 15
It works in the opposite direction, too. A figure 8 joined to the bottom of a treble clef
indicates that notes are to be played an octave lower than normal. And for additional octave
shifts, extra figure 8 symbols can be added above or below the clef as required.
The same method can be used to shift the bass clef. If either the bass or treble clef in a grand
stave is shifted using octave clefs, then both must be shifted by the same amount, to keep
them compatible with each other.
ChordWizard products such as Songtrix manage the use of octave clefs
automatically. Depending on the clef type and leger line count you have
chosen for each part, they will adjust the octave of the clef to provide the
optimum display of symbols on the stave.
The Circle of Fifths
The previous topics demonstrated an important relationship between a Major scale, and the
Major scale which starts on its fifth note - it is the same, but one note is sharpened (or one
less note is flattened).
This is a special characteristic of the Major scale. The same thing can be illustrated with the
circle of fifths, where the 12 keys of the Major scale are arranged like a clock, with C Major
at the top.
Copyright c 1997-2007
(2) The Major Scale
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 13 of 15
As you move clockwise around the circle, each key note is the fifth note of the key before it
(giving the circle its name), and each key has one more sharp note, or one less flat note, than
the key before it.
As you see, the keys appear in the same order as they did in the earlier table, and as they did
with the key signatures.
At the bottom of the circle, the anti-clockwise series of keys with flat notes, and the clockwise
series of keys with sharp notes, join at F#=Gb. They give us two alternate ways to look at
this this key.
If we call it F# Major, then it has six sharp notes. If we call it Gb Major, then it has six flat
notes. In either case, the notes in the scales are the same, and only the names are changing
to fit the name of the key note.
If we compare the note names in these two scales, we find they match perfectly as the same
notes:
Notes like this, which are the same but have different names, are called enharmonic notes.
The same situation also exists if we extend the overlap in the circle of fifths on either side.
So, for example:
Copyright c 1997-2007
(2) The Major Scale
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 14 of 15
(3) Chords and Harmony
Music sounds a little empty if notes are only played one at a time. It is the interaction
between different notes played together that gives music its richness and color.
Playing more than one note at the same time is called harmony. The difference in the pitch
between two notes is called their interval, a word we used earlier to describe the separation
of notes in the Major scale.
The richness and variety of harmony multiplies with each extra note. Two-note harmonies
have one interval. Three-note harmonies have three intervals, between each note and each
other. Four-notes harmonies have six intervals, and so on.
With some intervals, notes blend naturally together to create a pleasing or consonant sound.
Other intervals create a more jarring or dissonant sound. Both consonant and dissonant
intervals are used in music, ideally in a balanced way.
Too much consonance in music makes it easy to listen to, but a little bland. Dissonance adds
a powerful tension, but too much can make music hard to connect with.
Harmonies with three or more notes are called chords and they provide the harmonic
structure or background mood of a piece of music. Intervals are the building blocks of
chords.
Most ChordWizard products contain a collection of standard chord types,
including those in this topic, and provide powerful tools for working with
chords of all types.
These include tools for exploring how chords are played on your
instrument, identifying the names of chords you have discovered, and
printing chord book reports.
Copyright c 1997-2007
(3) Chords and Harmony
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 1 of 15
Interval Sizes
There are many different interval sizes, each with a different sound. Interval names are based
on the notes in the Major scale.
Shown below are the interval sizes up to an octave (measured in semitones) with a brief
description of their sound.
Unison intervals are two identical notes played together. They are always strongly consonant,
and difficult to tell apart.
Minor second intervals are strongly dissonant, with a warbling sound in the background, as if
the two notes are fighting with each other.
Second intervals are less dissonant, but the notes still do not sit completely at ease with each
other.
Minor third intervals are strongly consonant, with a melancholy flavour to the sound. They
form the basis of minor chords and scales.
Major third intervals are strongly consonant, making a stable and pleasing sound. They form
the basis of major chords and scales.
Perfect fourth intervals are mildly dissonant, with a stretched feeling as if they would rather
return to a major third.
Tritone intervals are dissonant, and are often found in chords of four notes or more, where
they add a particular harmonic spice.
Copyright c 1997-2007
(3) Chords and Harmony
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 2 of 15
Perfect fifth intervals are strongly consonant, and are found in both minor and major chords.
They add solidness, but not much character to the harmony.
Minor sixth intervals are mildly dissonant.
Major sixth intervals are consonant.
Minor seventh intervals are mildly dissonant.
Major seventh intervals are dissonant.
Octave intervals are strongly consonant, like unison, because notes an octave apart sound
similar to each other, just higher or lower.
Interval Names
Interval names are based on the notes of the Major scale, where the lower note of the interval
takes the place of the root note (starting note) of the Major scale.
For example, the upper note in an interval of two semitones corresponds to the second note of
the Major scale. This interval is called a second or more precisely, a major second.
The upper note in an interval of four semitones corresponds to the third note of the Major
scale, so this interval is called a third, or major third.
Copyright c 1997-2007
(3) Chords and Harmony
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 3 of 15
The use of the word major is important, because there are also minor second (one
semitone) and minor third (three semitones) intervals.
These intervals have no corresponding note in the Major scale, so the modifier minor is used
to reduce the size of the next larger interval by one semitone.
The term diminished also means to reduce by a semitone, and augmented means to
increase by a semitone. The term perfect explicitly indicates an interval which has not been
modified, and is usually only applied to the fourth or fifth.
The tritone interval has a size of six semitones, or three tones. It sits on the halfway mark in
the octave, so it has the special property of still being a tritone when turned 'upside down'
(raising the lower note, or lowering the upper note, by an octave).
Intervals with no exact note in the Major scale can often have alternate names, depending on
whether you choose to augment the interval below or diminish the interval above. For
example, the tritone interval can also be called an augmented fourth or a diminished fifth.
Above the first octave, interval names are formed by continuing the count of the Major scale
notes into an extra octave.
Copyright c 1997-2007
(3) Chords and Harmony
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 4 of 15
These extended intervals are essentially repeats of the first octave intervals, but with a
slightly different effect because of the extra octave of separation.
The octave interval itself is an eighth, a name which is rarely used in practice, but reveals the
origin of the word 'octave'.
The major ninth falls on the same note as the major second, the major tenth on the same
as the major third, while the other intervals pair up as the fourth/eleventh, fifth/twelfth and
sixth/thirteenth.
Intervals of up to the major thirteenth are commonly used in the construction of chords.
Intervals and Degrees
Every musical chord is made up of a set of notes played together, based on a pattern of
intervals from the root note of the chord. We will see how this works in the next topic.
The intervals in a chord are referred to with the special term degrees. Degrees names are
very similar to interval names, but use a more convenient shorthand notation.
Listed below are the symbols and names of the degrees, and their equivalent interval names
and sizes (in semitones).
Copyright c 1997-2007
(3) Chords and Harmony
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 5 of 15
Building Chords
Chords are built from the combination of intervals formed by playing three or more different
notes together.
There are many different chord types, and each one is defined by its unique formula or
spelling, a combination of intervals (degrees) measured from the starting note (known as the
root note or tonic note).
Let's take an example. A very common chord type is the major chord (maj for short) which
has the formula shown below.
As you see, it contains the degrees 1, 3 and 5. In other words, these are the first, third and
fifth notes of the Major scale with the same starting note.
Copyright c 1997-2007
(3) Chords and Harmony
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 6 of 15
When we assign a root note to a chord type, these degrees allow us to work out what the
other notes are, and the chord type becomes a chord.
Let's see how this works for the Cmaj chord. The C root note tells us that we will be using the
notes of the C Major scale. The maj chord type tells us to take the first, third and fifth notes
from this scale.
We have now worked out that the Cmaj chord contains the notes C, E and G. Here's how it
appears on the piano.
The maj chord and the Major scale are strongly related to each other, and both are
fundamental elements of music. Notice the difference in notation between the chord (Cmaj)
and scale (C Major).
Degrees and Notes
It is important to be comfortable with the difference between the degrees and notes of a
chord.
Copyright c 1997-2007
(3) Chords and Harmony
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 7 of 15
Degrees indicate how the intervals of a chord type contribute to its overall sound, regardless
of the root note. They do not correspond directly to notes until a root note is chosen, and the
chord type becomes a chord.
The degrees could correspond to twelve different sets of notes, depending on the root note.
We created the Cmaj chord in the previous topic, but we can also build a major chord on any
other root note.
Some ChordWizard products use overlay labels to show where the notes
and degrees of a particular chord or scale occur on an instrument. You can
select whether these labels should display note names or the equivalent
degree names.
The table below shows how degrees become notes for all possible major chords. You might
find it interesting to compare these with the table of all Major scales shown earlier.
You can see that a note can have differently names in different chords. Bmaj contains the
note D#, taken from the B Major scale, while the same note is called Eb when it appears in
Abmaj, taken from the Ab Major scale.
As with the Major scale, the name of the root note also affects the names of the other notes,
even when the chord is otherwise exactly the same.
Copyright c 1997-2007
(3) Chords and Harmony
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 8 of 15
(4) Scales and Melody
The Major scale is overwhelmingly dominant in western music, and everything in these
tutorials so far has been based on it.
However, there are many other scale types which also play a significant role in western music,
and several others besides that originate from the music of other cultures. Some of these are
shown below.
Scale types other than the Major scale lend a completely different flavour to a melody,
because of the different set of notes and intervals they provide.
While music can be written directly in one of these scales, they are also often used as the
framework for improvisation, the playing of a spontaneous melody line over a backing chord
progression.
Most ChordWizard products contain a collection of standard scale types,
including those in this topic, and provide powerful tools for working with
scales of all types.
These include tools for exploring how scales are played on your
instrument, conducting interactive scale practice sessions, and printing
scale reports.
Major Scale Revisited
Recall that the series of semitone intervals that defines the Major scale is 2-2-1-2-2-2-1.
This is illustrated graphically below, together with an example of the notes in the C Major
scale. All of the other scale types introduced in this tutorial will be shown in the same format,
to make comparison easier.
Copyright c 1997-2007
(4) Scales and Melody
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 1 of 16
The numbers 1 to 7 in the box above are the degrees of the Major scale which, as with
chords, are a shorthand way of expressing the intervals relative to the root note.
The small 1 at the end of the list of degrees indicates the root note at the end of the scale, one
octave up. By convention, scales usually end with a repeat of the starting note, although it is
not necessary for defining the scale.
The dominance of the Major scale means that its degrees are a convenient benchmark for
describing the intervals in all of the other scale types.
As you will see, the degrees of the other scale types have sharps and flats added to indicate
how their intervals compare to the Major scale. For the degrees of the Major scale itself, of
course, no sharps or flats are used.
Staff notation and the key signatures we have looked at previously are also firmly based on
the Major scale.
When music using other scale types is written in staff notation, it often contains many
accidental notes, because they do not align completely with the notes of the Major scale. You
will see examples of this as we proceed.
Natural Minor Scale
While the Major scale is considered the foundation of western music theory, the next most
important is probably the Natural Minor scale, also known as the Pure Minor or Aeolian
scale.
The terms major and minor are essential concepts in music, and as with chords, they arise
from the third degree of the scale.
All major scales and chords include a major third degree (four semitones), giving them a
strong, assertive feel. All minor scales and chords include a minor third degree (three
semitones) instead, giving them a gentle, melancholy feel.
Copyright c 1997-2007
(4) Scales and Melody
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 2 of 16
When the Major scale was introduced earlier, you may have wondered why the key of C has
the special privilege, compared to the other keys, of containing only natural notes. Why not
for example, the key of A, which is our first alphabetical letter?
Also, why do single semitone intervals occur only between B/C and E/F, while there are two
semitones between all the other natural notes?
It seems that centuries ago, when letters were first given to notes, the Natural Minor scale
was considered the most important. Note letters were therefore allocated to suit the intervals
of the Natural Minor scale.
As you can see above, this means that the A Natural Minor scale contains all natural notes, the
same as the C Major scale. The Natural Minor scales with other root notes all have at least
one sharp or flat note.
This makes a lot more sense. It also offers insight why it has the name of 'Natural' minor,
compared to the other minor scales, which have different names, and different patterns of
intervals.
Major and Minor Keys
As we noticed in the previous topic, the A Natural Minor scale contains the same notes as the
C Major scale, with just a different starting note. This is a very important property of the
Natural Minor scale.
Every Major scale has a relative Natural Minor scale, starting on its sixth note, which contains
the same notes. This means that music in a Natural Minor scale can be written on staff lines
in the key signature of its relative Major scale without any accidentals.
Some examples of equivalent Major and Natural Minor keys are shown below. You can assume
that when a minor key is referred to, it is the Natural Minor scale, unless one of the other
minor scales is specifically mentioned.
Copyright c 1997-2007
(4) Scales and Melody
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 3 of 16
So how do you know when music is in a major key, or the related minor key? The starting or
ending chords in the song often give the best clues.
Music in a major key has the characteristic major sound, and tends to use more of the related
major chords of the scale (such as Cmaj, Fmaj and Gmaj in the C Major scale).
Music in the related minor key has the characteristic minor sound, and tends to use more of
the related minor chords of the scale (such as Am, Dm and Em in the A Natural Minor scale).
Harmonic Minor Scale
We are now really starting to look at other types of scales. As mentioned earlier, everything
up to this point has been very much based on the Major scale.
Even the Natural Minor scale is basically equivalent to the Major scale. Because it contains the
same pattern of intervals, but starting on a different note, it is known as a mode (the Aeolian
mode, to be precise) of the Major scale. More on this later.
By contrast, the Harmonic Minor scale contains a distinctly different pattern of intervals.
At first glance, it looks quite similar to the Natural Minor scale, except with the last note
raised by a semitone (making a natural seventh degree instead of a flat seventh).
However, this one change makes a big difference to melodies and harmonies formed from the
notes of the scale. Here again is the chord sequence in A Natural Minor from the previous
topic.
Copyright c 1997-2007
(4) Scales and Melody
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 4 of 16
(5) Meter and Rhythm
We have now explored the basis of harmony and melody in music, but there is a third
essential element - rhythm - that we have not yet covered.
Music is an art form that is instrinsically based on the passing of time, unlike static arts such
as painting or sculpture, which exist in their entirety at every instant.
Perhaps this one of the reasons why music appeals so broadly to so many people. It is
dynamic, and like our own lives, it is constantly changing and unfolding, creating a story as it
develops.
Music shares this characteristic with other art forms such as film or drama. But it stands alone
in the extent to which it is governed by precise lengths of time, and the sophistication with
which these must be expressed to truly capture a piece of music.
So far, when displaying staff notation, we have largely ignored the issue of timing. For
example, we would present the melody of Twinkle Twinkle Little Star like this:
In fact, this is only a shorthand sketch of the melody, because it includes no timing
information. To describe it completely and accurately, it would have to be notated more like
this:
This tutorial explains the concepts of musical rhythm and timing, and the staff notation
symbols that are used to represent them.
ChordWizard products such as Songtrix prepare the staff notation of a
piece of music for you automatically.
As you edit or record the musical events that make up your song,
Songtrix updates the layout of Staff View so you can see immediately the
effect of any changes.
You can also use a Staff Sheet report to print your staff layout.
Copyright c 1997-2007
(5) Meter and Rhythm
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 1 of 23
Note Lengths
It is obvious that in music, notes of many different lengths are played. Consider the passage
below, composed by Rimsky-Korsakov. The melodic notes are very short and fast, while the
harmonic (chord) notes are longer and fewer.
What may not be so obvious is how dramatically the lengths of the notes can affect the
melody of a piece of music. Shown below are three variations on a melody. The original is
easily recognized as Mary Had A Little Lamb. The other two contain the same notes, in the
same sequence, but with different lengths.
You will agree the variations sound very different from the original melody, as if they belong
to a different song. And yet they look the same if they are notated without indicating their
note lengths.
Clearly, the shorthand notation we have used so far in these tutorials is not adequate for
accurately describing a piece of music. Staff notation has a range of symbols for showing note
length, using a combination of hollow and solid noteheads, stems, and flags.
In fact, the simple black notehead is not a proper staff notation symbol at all. This makes it
perfect to indicate where no attempt at showing note lengths has been made.
We will still use it where timing is not important, such as discussing the notes of a single
chord. But from now on, we will be notating most of our musical examples fully, using the
correct staff symbols to show the lengths of the notes.
Copyright c 1997-2007
(5) Meter and Rhythm
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 2 of 23
Note Symbols
Note symbols in staff notation are a series, where each symbol represents half the length of
time of the previous one. There are two naming schemes for note symbols.
The American scheme is based on the fractional nature of the symbol series, using names
such as whole-note, half-note, quarter-note, and so on. These names are practical, if a little
dull.
The British scheme uses traditional names taken from Italian and other languages, such as
semibreve, minim, crotchet, and so on. These names are romantic, if a little idiosyncratic.
You can use either scheme, as they both refer to exactly the same note symbols. You should
probably learn both. However, the American scheme is more helpful for understanding meter
and time signatures, and so this is the scheme we will use in these tutorials.
Let's start with the longest note symbol, the whole-note or semibreve. It appears as a
single hollow notehead.
You might reasonably wonder why, if this is a whole-note, it is also called SEMI-breve. In
fact, there is a symbol called breve, which is twice as long, but we can safely ignore it. It is
of historical interest only and is rarely seen, being incompatible with all commonly used time
signatures. More on this later.
Next is the half-note or minim. It is half the length of a whole-note, and appears as a hollow
notehead with a stem.
The stem can be oriented either upwards or downwards, and both are shown here. When
pointing up, the stem is attached to the right of the notehead, like a letter 'd'. When pointing
down, it is attached to the left, like a letter 'p'.
For notes on the lower half of the stave, the stem would usually point up, and for notes on the
upper half, it would point down. For notes around the middle of the stave (such as A, B or C
with the treble clef), either can be used, whichever works best with the orientation of the
surrounding notes.
Copyright c 1997-2007
(5) Meter and Rhythm
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 3 of 23
Then we have the quarter-note or crotchet. It is half the length of a half-note, and appears
as a solid notehead with a stem. The stem orientation of the quarter-note (and all the other
symbols we will see here) follows the same guidelines as for the half-note.
The quarter-note has a few special claims to fame. Firstly, it is the basis of most common
time signatures used in music, such as 3/4 and 4/4. We will look at how these work soon.
Secondly, it is used for measuring tempo, the overall rate of movement of a piece of music.
A typical tempo might be expressed as '120 quarter-notes per minute' or 120 qpm. This is
often the same as 'beats per minute' (but not always, as we will see).
Finally in computer music (particularly with MIDI, the Musical Instrument Digital Interface) the
quarter-note is used to specify the timing precision of musical events in a piece of music, for
example '144 ticks per quarter-note', or 144 tpq.
The eighth-note or quaver is half the length of a quarter-note, and appears the same except
for the addition of the flag attached to the end of the stem. Notice how the flag always
appears to the right of the stem, even when the stem is oriented downwards.
The eighth-note is also used as the basis of several common time signatures, such as 6/8 and
12/8.
The flags of eighth-notes, and also the rest of the symbols shown below, can be replaced with
horizontal joining beams to improve readability, in cases where several of these symbols
appear next to each other. More on this later.
The sixteenth-note or semiquaver is half the length of an eighth-note, and appears the
same except that it has two flags attached to the stem instead of just a single flag. Usually
the stem needs to be a drawn a little longer to provide the space for the extra flag.
Copyright c 1997-2007
(5) Meter and Rhythm
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 4 of 23
Similarly, the thirty-second-note and the sixty-fourth-note have their lengths halved each
time by the addition of an extra flag to the stem.
Theoretically, this process can continue on for smaller and smaller time lengths, but the
symbols become too hard to distinguish, and the sounds become too short to hear (also the
British names are becoming something of a mouthful!). In most scores, you will rarely
encounter anything shorter than a sixteenth-note.
ChordWizard products such as Songtrix offer a resolution option in Staff
View and when printing. You can use this to specify the smallest time
divisions that you want individally notated, for example quarter-note,
eighth-note, etc.
Using this feature you can control whether to view a piece of music with full
notation accuracy or whether you prefer to see a simplified view of it.
Now that we have been introduced to all the note symbols, let's use them by revisiting the
melody fragments of the previous topic, based on Mary Had A Little Lamb.
Copyright c 1997-2007
(5) Meter and Rhythm
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 5 of 23
The difference between these variations is now visible as well as audible, so our new notation
is doing a much better job of describing the exact melodies.
If you add up the note lengths, you will find the total length of each variation is eight quarternotes (or two whole-notes). You would rarely see a musical passage this long as a continuous
stream. Almost always, music is divided into smaller chunks called bars or measures.
Understanding Meter
One of the most important features of music is repetition, and it occurs at many levels. If
used well, repetition provides the familiarity and regularity needed for a piece of music to
have cohesion and momentum. Or to put it another way, for the music to hang together and
swing.
Most contemporary songs are built from repeating sections like the Verse/Chorus structure,
where the same melody is reused with different - or even the same - lyrics.
Even within a verse or chorus, a musical phrase can be repeated several times. Consider how
the first four notes are repeated in the traditional song When The Saints Go Marching In.
But the most fundamental level of repetition in music is the meter, or underlying rhythm.
You may be familiar with the 'one - two - three - one - two - three' feel of a waltz, or the 'left right - left - right' feel of a march. These are both examples of meter.
Meter is the driving force that repeats over and over as the music progresses, keeping time.
Drums will often mark out the meter when they are played. But meter always exists in music,
with or without percussion.
Meter can be counted out with a device you have probably already heard of - the metronome
(notice the similarity of the words). It plays a click sound on each beat of the meter, usually
with an accented click on the first beat of each repetition. Here is the sound of a metronome
playing a four-beat rhythm.
You may not have noticed before, but When The Saints is based on a four-beat rhythm. Let's
hear it again, this time with the metronome marking out the meter.
Meter also occurs as rhythms of other beat counts. Another common meter is based on a
Copyright c 1997-2007
(5) Meter and Rhythm
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 6 of 23
three-beat rhythm. Compare the feel of the meter below with the four-beat rhythm you have
already heard.
A good example is the Blue Danube, a waltz by Johann Strauss. Here is the main theme of
that piece, with the metronome marking out the meter. In general, all waltzes are based on a
three-beat meter.
Bar/Measure Divisions
As mentioned earlier, staff notation is not written as one long stream of musical note symbols.
Instead, it is divided into chunks called bars or measures.
Both terms mean the same thing. In American music 'measure' is more commonly used, while
'bar' is preferred in other English speaking countries. Generally, musicians should be
acquainted with both terms. For these tutorials, we will use 'bar'.
ChordWizard products such as Songtrix can use either the term bar or
measure. Once you have selected your preference, the entire workspace is
updated to use your preferred term.
Dividing music into bars provides regular reference points for identifying locations within a
piece of music. It also makes written music easier to follow, since each bar of staff symbols
can be read and played as a batch, helping musicians to avoid becoming lost or out of time.
The most obvious place to put the bar divisions in written music is on each repetition of the
meter, and this is exactly what happens.
Let's revist the theme of the Blue Danube from the previous topic, and see how it would be
divided into bars when written on staff lines. You may notice three notation marks used here
that have not yet been explained.
Copyright c 1997-2007
(5) Meter and Rhythm
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 7 of 23
The 3/4 symbol appearing after the first treble clef is the time signature. It tells us that the
meter of the music has a three-beat rhythm, where the length of each beat is written as a
quarter-note. If we add up the lengths of the notes in each bar, we will get a total value of
three quarter-notes. You can check this.
A dot has been placed after each of the notes which have a length of three beats. Recall that
we have a symbol for a whole-note (four beats) and a half-note (two beats), but not a threequarter-note. Placing a dot after any note symbol extends it by an extra half of its length, so
in this case, a half-note with a dot becomes the three-quarter-note that we need.
Finally, there are some long notes in this piece which should last for six beats. However these
are split by our three-beat meter, forcing us to put a three-quarter-note in each of two bars.
So we need to use a curved line called a tie to rejoin the two parts and make clear that they
are really a single long note.
Music for more than one instrument can be notated by using additional staves running in
parallel to the first one. In these cases, the bar lines join the staves together on each row to
keep the timing coordinated and make the whole arrangement clearer.
Let's add a simple accompaniment to the passage from When The Saints Go Marching In (that
we first saw in the previous topic).
As you might expect, this piece begins with a 4/4 time signature, telling us that each bar
contains four beats, where a beat is a quarter-note in length. Both parts need their own time
signature, but only at the start, not on each line as with the clef.
Copyright c 1997-2007
(5) Meter and Rhythm
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 8 of 23
Notice how the notes of each part are horizontally aligned with each other. In other words,
notes from each part that are played at the same time appear directly above or below on the
other stave. It is very important to keep the timing coordinated like this in multipart scores.
There are also a couple of new symbols appearing here. In the melody part there are
squiggles in the first, third and fifth bar, and in the accompaniment part there is a rectangular
block in the first bar. Perhaps you can already guess what they are for?
They are called rests and they indicate when no notes are played. Remember that the length
of all symbols in a bar must add up to the total value (in this case four quarter-notes) so rests
are needed to fill the gaps and keep the timing accurate, especially in multipart scores.
As with note symbols, there are many different lengths of rests. Let's have a look at them.
Rest Symbols
In music, the spaces between notes are often as important as the notes themselves.
If this sounds strange to you, imagine listening to someone giving a speech who never paused
for a breath! It would soon sound painfully monotonous, and your ear would crave for a break
to give relief to the unending stream of words.
Likewise with music it is important to provide spaces, allowing the listener to absorb each
musical phrase before the next one starts. This goes a long way towards creating satisfying
music, with good dynamic balance between musical activity and rest.
Even within a phrase, rests can be used with great effect to add strength to the rhythm of the
melody.
Compare the two bass lines below. One uses full length notes, while the other uses shorter
notes with rests in between. You can hear that the second version sounds much more punchy,
because the discontinuities at the end of each note also contribute to the rhythm, making it
richer and tighter.
As with note symbols, there is a series of symbols used for rests, each one half the length of
its neighbour. In fact, there is an equivalent length rest for every note symbol that we
covered earlier.
Copyright c 1997-2007
(5) Meter and Rhythm
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 9 of 23
Normally rest symbols are placed in the same way as note symbols, evenly spaced across the
bar from left to right. The whole-rest is something of an exception, because it generally
occupies the whole bar, and so it is placed in the centre.
The whole-rest also has the special feature of some flexibility in its length. While it has a
theoretical length of four quarter-notes, it is common to use it for a full bar of rest in any
meter. So for music in 3/4 time (such as the Blue Danube earlier) the whole-rest would have
a length of only three quarter-notes.
The half-rest looks similar to the whole-rest, but you will see that it sits above the third staff
line, rather than hanging from the fourth line (staff lines are numbered starting from the
bottom).
Both it and the quarter-rest can be mixed in with note or other rest symbols wherever they
are needed. Two or more rest symbols together simply extends the size of the rest to their
total length.
The eighth-rest, sixteenth-rest, thirty-second-rest and sixty-fourth-rest use the same
basic figure, but each has an extra hook. Notice how this closely parallels the way their
equivalent note symbols are constructed, with each having an extra flag.
Now let's see how the two versions of our bass line would look when written in staff notation
both with and without rests.
Copyright c 1997-2007
(5) Meter and Rhythm
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 10 of 23
ChordWizard products such as Songtrix include rests automatically when
they prepare the staff notation of a piece of music for you.
As you edit or record the musical events that make up your song,
Songtrix updates the layout of Staff View to include rest symbols wherever
there are gaps between your events.
Note Flags and Beams
The convention of adding flags to note symbols of less than a quarter note to halve their
length is easy to understand, but it can have the effect of making them hard to read,
especially when several of them are clustered together.
For example, the rhythm below has so many flags that it takes long and careful examination
to get a sense of the pattern.
Flagged notes on their own must always use flags, but where more than one appears next to
each other, readability can be improved by replacing the flags with beams that join the notes
together into a grouping.
Single flags are replaced with single beams, double flags are replaced with double beams and
so on, as illustrated below.
Copyright c 1997-2007
(5) Meter and Rhythm
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 11 of 23
Notes of different lengths can also be joined in this way, as long as they are all less than a
quarter-note (in other words, they all have flags). Each grouping must finish wherever there
is a note without a flag, and usually wherever there is a rest. Let's look at some examples.
Here we have two groupings, which have been broken by the presence of an (unflagged)
quarter-note between them. Notice how the slant of the beams reflects the vertical distance
between the notes. This reinforces the shape of the melody, so it's easier and more
comfortable to read.
Here the groupings have been forced to break (twice) by the change in orientation of the note
stems. Notice how the eighth- and sixteenth-notes share a grouping with combined
single/double beams.
Here there is also a grouping with combined single/double beams, but the double beams are
limited to a single note each. The short secondary beam normally aligns with the notehead,
but with the first note in the grouping, this is not possible, so it appears to the right.
So now let's return to the original rhythm at the start of this topic, and rewrite it using beams.
Copyright c 1997-2007
(5) Meter and Rhythm
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 12 of 23
It looks better, although with so many notes, the grouping itself is looking quite unwieldy. We
can improve it further by voluntarily breaking this large grouping into smaller groupings.
Groupings should be broken at whichever point gives the clearest indication of timing within
the bar. Depending on the meter and the lengths of the beamed notes, this will typically be
on half-note or quarter-note boundaries.
For our example, we could break at the halfway point in the bar, or at every quarter-note.
Either way, we get a much more readable notation of the rhythm.
ChordWizard products such as Songtrix offer three modes of Flag
Beaming when they prepare staff notation for you.
- You can prevent beaming, in which case all notes are drawn with flags as
required.
- You can beam within Whole Bars in which case a single grouping is
attempted if possible.
- You can beam to Sub Bars in which large groupings are broken up at
regular boundaries within the bar (depending on the meter).
Note Length Modifiers
We have a series of note symbols available to us, which can cover the range from very short
notes to very long. However, each symbol is half or twice the length of its neighbour, and
these are large differences.
Often we need to notate lengths in between the available symbols. For example, consider the
folk song Kum Ba Yah, notated below.
Copyright c 1997-2007
(5) Meter and Rhythm
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 13 of 23
You can see that we need to show, in several places, notes of one and a half quarter-notes in
length. But no such symbol exists, so we must tie together a quarter-note and an eighth-note
to achieve the correct length.
This is perfectly acceptable notation, but we can also write it in another, simpler way. The
length of any note symbol can be extended by an extra half when followed with an
augmentation dot.
The table below shows the equivalent length of the augmented symbols. You will rarely see a
dotted whole-note, as it is longer than the bar size of most commonly used meters.
You might recall we saw an example of augmentation dots in an earlier topic, with the Blue
Danube. Now let's see how much neater Kum Ba Yah looks when notated in this way.
Copyright c 1997-2007
(5) Meter and Rhythm
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 14 of 23
ChordWizard products such as Songtrix offer the optional use of
augmentation dots when they prepare staff notation for you.
If enabled, augmentation dots will be used wherever possible, otherwise
separate note symbols, joined with a tie, will be used for notes of nonstandard length.
Another type of modifier is needed when we try to notate triplets, a very common rhythm in
music. Listen carefully to the passage below (in 4/4 meter) and you will hear that three equal
notes are being played in the space of one beat.
This simply can't be notated with the symbols we have learned so far. We need a symbol
length which is one third (33.3%) of a quarter-note. An eighth-note is one half (50%) of a
quarter-note, a dotted sixteenth-note is three eighths (37.5%) of a quarter-note, and nothing
else comes close.
The solution lies in adding a '3' (or triplet) sign to a symbol. This has the effect of fitting
three of the symbols into the space of two. In other words, it makes a symbol 2/3 of the
length it would normally be.
Notice how the triplet sign is applied to single notes, beamed groupings and rests.
Using this extra triplet modifier, we can notate the passage above as follows:
One final word on note lengths before we move on. As we have seen, staff notation is very
much based on the idea of splitting time into exact fractional parts, which form the boundaries
of where notes and rests begin and end.
However in practice, performed music never starts or ends on the precise fractional
boundaries that the notation indicates. We are human musicians, not robots, and there is
always variation in the precise timing of the notes we play.
Copyright c 1997-2007
(5) Meter and Rhythm
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 15 of 23
This is a good thing. The variations in timing (and loudness) of notes in performed music is
what allows musicians to layer their own expression on top of the notated melody. The
listener's ear can still pick up the basic rhythm, but the variations (if not too large) add a
pleasing 'fuzziness' to the timing of the music that actually enhances it.
This is quite noticeable with computer music where notes have been entered on these exact
boundaries via editing, rather than playing. Although the music is then perfectly accurate to
the notation, it can actually sound quite rigid, mechanical and expressionless.
To overcome this, most music software has a humanize or randomize function which
specifically adds a little bit of randomness to the positions and lengths of the notes, making it
more 'realistic' and satisfying to listen to.
ChordWizard products such as Songtrix offer a Humanize function, which
can add a controllable level of randomness to either the positions or
lengths of notes, or both.
Time Signatures
Meter and time signatures refer to the same concept, but they are used slightly differently.
Meter is the property of music that it is based on an underlying, repeating beat rhythm,
whereas time signatures are the symbols we use to identify and describe the meter in a
piece of music.
There are many different time signatures used in music. So far we have encountered two of
the most common, 4/4 and 3/4. In this topic, we will take a closer look at how they are
constructed, and explore the range of time signatures you are most likely to see in music.
Time signatures consist of two numbers, resembling a fraction (which it is really, as we will
see). Strictly speaking, the numbers should be placed one on top of the other, as they appear
on staff lines. But when used in text, the closest approximation is to separate the numbers
with a slash (as in 4/4).
The upper number is the count of beats in the meter. The lower number is the symbol length
used to represent each beat. Together they tell us the total length of all symbols (notes and
rests) in a bar.
The 4/4 time signature indicates a quadruple (four-beat) meter, where each beat is a
quarter-note long. The total length of each bar will therefore be four quarter-notes, or 4/4 of a
whole-note. This is the most widely used time signature and you will often see it notated
simply as a 'C' for common time.
Copyright c 1997-2007
(5) Meter and Rhythm
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 16 of 23
A 3/4 time signature indicates a triple (three-beat) meter, where each beat is a quarter-note
long. The total length of each bar will therefore be three quarter-notes, or 3/4 of a wholenote. Are you starting to see how the time signature can be viewed as a fraction?
There are also duple (two-beat) meters. Compare the metronome beats of the three time
signatures below.
There is sometimes flexibility in selecting a meter for a piece of music. For example, most
music in 4/4 could also be written in 2/4 (and vice-versa) by substituting two bars of 2/4 for a
single bar of 4/4. It really depends on how strong the emphasis seems to be on the third beat
as to which you choose.
Meter can sometimes change within a piece of music. In this case, the new time signature
must be shown at the start of each bar where a change occurs.
ChordWizard products such as Songtrix offer unlimited flexibility with time
signature changes. Any or every bar can have a new time signature. The
notation in Staff View is updated automatically.
Four is not the only number which can appear on the bottom of a time signature. Instead of
quarter-notes, time signatures can also use beats of eighth-notes (quite common) and halfnotes (quite rare).
Compare the difference in speed. Half-note meters are half as fast and eighth-note meters are
twice as fast as quarter-note meters.
Copyright c 1997-2007
(5) Meter and Rhythm
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 17 of 23
Other beat lengths, such as whole-notes, sixteenth-notes, thirty-second-notes, and so on, are
also theoretically possible, but are not particularly useful and are generally unheard of.
All of the time signatures that we have seen so far are known as simple meter, based on
duple, triple or quadruple beats.
Time signatures with larger beat numbers are possible, and these are known as composite
meter as the larger beat count is usually broken down into a combination of duples, triples or
quadruples.
A composite time signature itself does not specifically indicate how the beat count should be
split, but there are conventions for how various meters are usually constructed.
For example, 5/4 meter most often has a 'one - two - three - one - two' feel, in effect acting as
alternating bars of 3/4 + 2/4. You should be able to hear this effect in the sample below, both
with and without the metronome.
This does not have to be the case though, as depending on the music, 5/4 meter could also
have a 2/4 + 3/4 tendency. For higher beat counts, various breakdowns are possible.
Consider these examples, where the metronome uses a sub-accent to show where the breaks
are made.
Copyright c 1997-2007
(5) Meter and Rhythm
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 18 of 23
There is a special class of composite meter where the number of beats is a multiple of three
(6, 9, 12, etc). This is called compound meter and it has a very strong triplet feel, since the
beats are almost always split into subsets of three.
A few common examples are shown below. Although the large number of beat counts in each
bar may look strange, these meters turn out to be very useful, as we will see shortly.
ChordWizard products such as Songtrix offer a wide range of half-note,
quarter-note, and eighth-note time signatures for you to use in your
songs, including all common meters in all musical styles.
Musical Tempo
The notation symbols that we have learned in this tutorial are good for describing how all of
the notes in a piece of music fit together, so that it can be reproduced accurately.
However, we still have no way of indicating how fast the piece of music as a whole should be
played. For this, we need the concept of musical tempo (which is the Italian word for 'time').
Tempo is usually measured in quarter-notes per minute (or qpm), and indicated in staff
notation with a quarter-note symbol and equals sign as shown below in the traditional song
Hatikvoh.
Up to now, all of our other sample pieces have also been played at a tempo of 120 qpm,
though this has not been indicated. In the absence of any specific markings, 120 qpm is
usually a reasonable 'normal' tempo to assume.
Tempo has a strong impact on the mood of music. With our tempo measurement, we can
specify the prcecise speed of a piece of music so that we get exactly the feel we are looking
for. Compare the sound of Hatikvoh played at a range of tempos. It varies from painfully
solemn at slow tempos to slightly manic at high tempos.
Copyright c 1997-2007
(5) Meter and Rhythm
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 19 of 23
There are Italian terms which can be used to indicate tempo, which appear mostly in classical
music. While each covers an approximate tempo range, they are mainly intended to convey a
general 'feel', and are less precise than a simple tempo measurement.
There are so many of them, they can be hard to remember, but here are a few of the more
common terms, to give you the idea:
Adagio - slowly (60-80 qpm)
Andante - walking (80-100 qpm)
Moderato - moderate (100-120 qpm)
Allegro - lively (120-160 qpm)
Presto - quickly (160-200 qpm)
Tempo can change during a piece of music. Classical music routinely uses tempo changes
during a piece of music to add expression and drama.
Contemporary music tends to be based on a more steady meter, but it is quite common to use
a gradual slowdown in the last few bars of a song (called rallentando) to produce a more
satisfying ending.
Less common is the opposite effect - accelerando - where the tempo gradually increases.
You will sometimes hear this in dance or folk songs - such as Zorba The Greek - as they build
to a climax.
You may sometimes see tempo being referred to in beats per minute (or bpm). Be careful
not to get this confused with quarter-notes per minute, as they are sometimes the same but
sometimes not, depending on the meter.
They are the same with time signatures such as 3/4 and 4/4, which have beats of a quarternote in length. However, time signatures based on eighth-notes have a beat length only half
the size, which should normally play twice as fast.
This particularly causes problems if the time signature changes during a piece of music, say
Copyright c 1997-2007
(5) Meter and Rhythm
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 20 of 23
from 4/4 to 6/8. Which beats would a bpm figure refer to - the quarter- or eighth-notes? It
can be unclear, and to avoid this ambiguity it is recommended to use quarter-notes per
minute measurements.
Tempos commonly range from 60 to 200 qpm, where 120 qpm tends to be the 'medium'.
Using a tempo at either end of this range (or outside it) can impact on your choice of time
signature. For example, notating in 4/4 at 120 qpm is equivalent to notating in 4/8 (or even
2/4) at 60 qpm.
ChordWizard products such as Songtrix offer great flexibility with tempo
changes. Any or every bar can have either an immediate or a gradient
tempo change, and changes can be spread easily across several bars. The
notation in Staff View is updated automatically.
Straight and Swing Timing
Two terms you may sometimes comes across, particularly in rock, blues or jazz are straight
timing and swing timing. Most music can be played either way, and will sound like the
same piece, but with a very different feel.
Straight timing is where the beat is split into equal subdivisions (a ratio of 1:1) for playing
notes. Swing timing is where the beat is split into two-third plus one-third subdivisions (a
ratio of 2:1).
The difference can be well demonstrated with a rock'n'roll style rhythm that would typically be
played on the lower two strings of a guitar.
Both alternatives sound very similar to each other, and yet distinctly different. The straight
version has more of a driving regular rhythm, while the swing version, even at the same
tempo, has a more laid back, cruisy feel.
Copyright c 1997-2007
(5) Meter and Rhythm
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 21 of 23
The straight version can be notated relatively easily in simple eighth-notes as follows:
The swing version, on the other hand, presents problems. You will sometimes see this type of
rhythm notated using dotted eighth-notes and sixteenth-notes, as shown below.
This seems convenient, but it is incorrect, and should be avoided. Listen carefully to how this
notation actually sounds and you will hear it is not the same as swing timing.
It sounds jerky and stilted, not at all the smooth rolling rhythm that we should get with swing
timing. Remember that we need a 2:1 ratio of beat subdivisions, whereas this notation has a
3:1 ratio (dotted eighth-note = 1/8 + 1/16 = 3/16, sixteenth-note = 1/16).
To write swing notation correctly, we need to use (as you might have guessed) triplet signs.
The following passage is now faithful to the true timing ratios in swing.
It looks untidy, though. Every note length needs to be adjusted with triplet signs, which will
be scattered throughout our notation, making it tedious to write and messy to read.
There is a better solution which gives the correct timing, while also being simpler to notate.
All that is required is that we change time signatures.
Remember the compound time signatures (6/8, 9/8 and 12/8) we looked at a couple of topics
ago? This is exactly what they are designed for - to simplify notation when the main beat has
been split into triplets. The following conversions are typical:
Copyright c 1997-2007
(5) Meter and Rhythm
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 22 of 23
Our swing rhythm notation can be converted as follows:
Notice that the tempo has also been adjusted as a direct result of the meter change. Since we
are now fitting a quarter- plus an eighth-note into the space of what used to be a quarternote, the length has been increased by 50%. So the tempo also needs to increase by 50% to
180 qpm, to retain the same overall speed of play.
ChordWizard products such as Songtrix offer a powerful and convenient
function which allows you to convert the meter of a song in this way. The
notation in Staff View is updated automatically.
Copyright c 1997-2007
(5) Meter and Rhythm
ChordWizard Software Pty Ltd
http://www.chordwizard.com
Page 23 of 23