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intervals (melody)
Interval is the word used to describe the 'distance' of two notes in terms of pitch. As you can imagine, if we take the first note of an octave, there will be twelve intervals that relate to that note (one for each semitone). The intervals have unique names, and each one implies a specific number of semitones of distance from the reference note. Let's see it in an example, starting our octave with a C:

The first column shows the notes and their alterations (using the sharp notation) that are in an octave, the second shows the same thing using the flat symbols, the third shows the distance of each note from the first note in semitones, and the fourth shows the name of that distance, or interval

note note distance interval name
C C 0 unison
C# Db 1 minor second
D D 2 major second
D# Eb 3 minor third
E E 4 major third
F F 5 fourth
F# Gb 6 diminished fifth
G G 7 fifth
G# Ab 8 minor sixth
A A 9 major sixth
A# Bb 10 minor seventh
B B 11 major seventh
C C 12 octave

A sequence of notes at specific intervals is called a scale. The sequence in the above table is called a 'chromatic scale': it is made of twelve notes, and each following note is one semitone above the previous one. Basically a chromatic scale encompass every note in an octave.

Every interval expresses a specific relationship between the frequency of the two notes (remember the Harmonics?): this table shows these relationships in a notation system that is now practically discontinued, the Just System.

note note interval name relation to fundamental
C C unison 1
C# Db minor second 25/24
D D major second 9/8
D# Eb minor third 6/5
E E major third 5/4
F F fourth 4/3
F# Gb diminished fifth 45/32
G G fifth 3/5
G# Ab minor sixth 8/5
A A major sixth 5/3
A# Bb minor seventh 9/5
B B major seventh 15/8
C C octave 2

The system in use in western music now, is called equally tempered, and basically uses this relationship, but the values have been slightly adjusted to make it easier transpose musical pieces from a scale to another. So the intervals will not be exactly the ones shown above.

This is why, the distance between the two notes expressed by one interval will sound exactly the same, no matter what the initial pitch is. In the following examples, the interval is always a major third, but the notes are very different.

Major third 1
Major third 2
Major third 3

Scales are used by musicians to communicate a specific mood: it is amazing how the same notes in different order or relationships can convey different emotions and feelings.

Of course it is difficult to label the different scales with one or more feelings or emotions, being them extremely subjective, but there are some general consideration that we can make:

For example, a major scale is usually described as bright, solid, open. These are the notes that are part of a major scale starting with the note C. The column 'distance' shows the distance of a note from the previous (T=Tone, S=Semitone), and the third column shows the interval between every note and the C note.

note distance interval name
C - unison
D T major second
E T major third
F S fourth
G T fifth
A T major sixth
B T major seventh
C S octave


So the progression of a major scale is the following:


Every set of notes arranged as such, can be called a major scale. So we could start with an F:

note distance interval name
F - unison
G T major second
A T major third
A#/Bb S fourth
C T fifth
D T major sixth
E T major seventh
F S octave


This is a very simple variation: basically, in order to keep the same intervals pattern, we need to use an alteration (the A# or Bb). If we didn't alter that note, the interval would not have been a 'fourth' but a 'diminished fifth', and the scale could have not been considered a major scale. A scale can start with any note, and as long as it keeps that intervals pattern, it can be called 'major'.

Minor scales on the other hand are usually described as dark, solemn, sad: this is how a minor scales develops, let's start with the A note:

note distance interval name
A - unison
B T major second
C S minor third
D T fourth
E T fifth
F S minor sixth
G T minor seventh
A T octave


We can see that the progression is:

Again, it is not important which note we start from, but the interval pattern that we are keeping. Let's compare the interval patterns of a major and of a minor scale:



major minor
unison unison
major second major second
major third minor third
fourth fourth
fifth fifth
major sixth minor sixth
major seventh minor seventh
octave octave
Listen Listen

The interval pattern is very similar, only three intervals change: the third, the sixth and the seventh, which are respectively all major or all minor.

There are other types of scales, but we will not cover them in this course.

The concept of scale leads us directly to the concept of key. Basically, a composer chooses to use a specific scale according to the mood of the piece of music: for the whole piece, the notes that a musician will perform will belong to that specific scale. If someone is playing along a specific scale, the notes that are not part of the scale will sound 'strange' or out of place to our ears: listen to this succession of notes that belong to a C major scale. At some point, a single not that does not belong to that scale will be played. See how easy it is to pick it!

Easy wasn't it? Listen to it again looking the score this time:


Sometimes, however, a few notes that do not belong to the scale can be played, and their being 'out of context' will actually sound fresh and original, and it will add character to the music:

That was better wasn't it? Listen to it again looking the score this time:


So, in order to let the musician and whoever reads the score know what scale is being used, the key is shown at the beginning of the stave. The key is indicated by placing alteration signs on the appropriate lines or spaces. For example, we have seen that the C major scales does not use alterations, so the stave will look like this:


But in case we are using an G major scale, we will need to add a sharp on the second space from the bottom, to indicate that every F written on the stave, has to be intended as an F#


Other scales use the b notation, such as F major:


For the purpose of defining the key, nothing changes whether we use the # or the b notation, technically there are occasions where one is more appropriate than the other, but we will not examine them so closely.

So, this is the set of keys using the sharps, and their different corresponding scales:


And this is the set of keys using the flats, and their different corresponding scales:


You must have noticed that each key indication corresponds to two scales (like C major and A minor) so how can one tell what key is the musical piece? This can be understood by the mood of the song, and by the notes played in the first few bars (classical music pieces enforces strict rules about this).

The linear succession of notes horizontally and its qualities (from left to right) are usually referred to as 'Melody'. In the next chapter we are going to analyse a few things related to the vertical succession and its qualities, which is referred to as 'Harmony'.

There are some tests on this topic in the free tests section.