Intervals

Intervals can be calculated between any two notes; if they are played together the interval is described as a harmonic interval and if they are played consecutively it is described as a melodic interval. It must be remembered that intervals are always calculated from the lowest note to the highest note. This applies even if the higher note is played before the lower note.

If you count up one note from the root of any scale, for example from C to D in C major, the interval is some kind of 2nd (always count the first note as one), likewise if you count up two notes, from C to E in C major, the interval is some kind of 3rd. This can be done for all notes of the scale resulting in the following intervals.

PLain intervals

These intervals tell us the number from the root note to the respective steps of the scale but they don’t tell us the quality. The full names of the intervals are as follows

Intervals

These same intervals are found in all major keys. In other words, if you treat the lower note of your interval as the root of a major scale and both notes are found in that major scale, then the interval will be one of the intervals listed above. For example, if we wanted to find out what this interval is

P5

we know it is some kind of 5th, and because both notes are found in the key of C major we also know it is a Perfect 5th.

Likewise, the following interval is some kind of 3rd

M3

because both notes are found in the key of C major we know it is a major 3rd.

How about this interval?

min3

We know it is some kind of 3rd but the B flat is clearly not part of G major. Before we find the quality of this interval perhaps we should look at  the following rules:

  • If the upper note of a major interval is raised a semitone (one fret on the guitar) it becomes augmented
  • If the upper note of a major interval is lowered a semitone it becomes minor

In our example, if the note was a B natural (part of a G major scale) the interval would be a major 3rd. Since the note is B flat we have lowered the major 3rd by a semitone so our interval is now a minor 3rd.

How about the following?

D5

If the notes were G – D natural (both notes part of G major) the interval would be a perfect 5th. Let us consider the rules for perfect intervals:

  • If the upper note of a perfect interval is raised a semitone it becomes augmented
  • If the upper note of a perfect interval is lowered a semitone it becomes diminished

Our D has been lowered a semitone so the interval is a diminished 5th.

Looking at our minor 3rd example again

min3

if we raise the minor 3rd we get a major 3rd, G – B natural, but if we lower a minor 3rd a semitone we get a diminished 3rd.

The preceding rules may be summarised as follows:

  • When the upper note of a major interval is raised a semitone it becomes an augmented interval
  • When the upper note of a major interval is lowered a semitone it becomes a minor interval
  • When the upper note of a minor interval is raised a semitone it becomes a major interval
  • When the upper note of a minor interval is lowered a semitone it becomes a diminished interval
  • When the upper note of a perfect interval is raised a semitone it becomes an augmented interval
  • When the upper note of a perfect interval is lowered a semitone it becomes a diminished interval

 

Intervals can also be made larger or smaller by lowering or raising the bottom note by a semitone. With our major 3rd example

M3

if we lower the C by a semitone we get the following interval

P4

Clearly the interval is now some kind of 4th, and because we know that E is found in the key of B major, the interval is a perfect 4th.

Likewise if we raise the C of our original example a semitone to C sharp

MInor3

we now create a minor 3rd.

The preceding rules may be summarised as follows:

  • If you raise the lower note of a perfect or minor interval by a semitone it becomes a diminished interval
  • If you raise the lower note of a major interval by a semitone it becomes a minor interval
  • If you lower the lower note of a perfect or major interval by a semitone it becomes an augmented interval
  • If you lower the lower note of a minor interval by a semitone it becomes a major interval

 

Enharmonic Equivalents

Sometimes the same note may be spelt differently, for example D sharp and E flat have the same sound, these notes are enharmonic equivalents.

When finding intervals from a score it is important to consider how they are spelled, for example, in the following examples even though the intervals sound identical they are written differently

Enharmonic Eq

In the example on the left we know that some kind of G to some kind of D is a 5th so the interval is a diminished 5th. In the example on the right we know that some kind of G to some kind of a C is a 4th so the interval is an augmented 4th; different spellings but the same sound.

 

As with everything, the more you practice identifying these intervals the easier it will become. Also, don’t forget to learn the sounds of these intervals both harmonically and melodically.