Intervals

Topics covered on this page: Harmonic and melodic intervals – Numerical classifications of internals – Compound intervals – Classification of intervals by quality – Inversion of intervals – Enharmonic intervals

There are commonly two types of musical intervals known as harmonic and melodic.

Harmonic intervals are when two or more tones are played together. Melodic intervals are played in succession or one at a time.

Harmonic interval:
1a

Melodic interval:
1b

 

When examining these intervals, we are interested in the difference in pitch between the two.

Intervals that have little difference in pitch are said to be close together, or a small interval. Intervals that have a large difference in pitch are said to be far apart or a large interval.

A small interval:
2a

A large interval:
2b
Intervals are commonly assigned numbers from 1 to 8 to represent their scale degrees of basic notes.

C major scale and interval numbers:
3

 

There are more sophisticated methods for interval analysis, one being the frequency of one interval to another creating a ratio, for example. This method is used in acoustics -the scientific study of sound. For our purposes and most all practical applications in academic study of music the number method is used.

To say again, the numerical classification of intervals is most common and very simple to derive. Call the first interval 1 and then count the staff lines (or basic notes) to the other interval. For example if we call C a “1” and D a “2”, the interval between them is 2, or a 2nd. Calling C a “1” and G a “5” creates an interval of 5, or a 5th.

A melodic interval of a 2nd:
4a

A melodic interval of a 5th:
4b

A harmonic interval of a 2nd (notice because the interval is so close together, the D note is offset to the right side for clarity):
4c

A harmonic interval of a 5th:
4d

Take a look at the following, noting that 1 and 8 have names based on Latin numeration:

1 unison -or prime
2 second or 2nd
3 third or 3rd
4 fourth or 4th
5 fifth or 5th
6 sixth or 6th
7 seventh or 7th
8 octave or 8th (remember that an octave is an interval covering 1 to 8, or 8 lines and spaces on a staff

In your more intermediate musical studies you will encounter intervals greater than an octave. These intervals are referred to as compound intervals. Intervals within an octave are called simple intervals

Common compound intervals are: 9th, 10th, 11th, 13th. These are simple to understand because compound intervals minus 7 (the lower portion of the simple interval) equals a simple interval. Said another way, if we are looking at a 13th then subtract 7 (the numeric span of simple intervals) from it we are left with an interval of a 6th.

Similarly, a 9th is really a 2nd (9 – 7 = 2), a 10th is a 3rd (10 – 7 = 3), and an 11th is a 4th (11 – 7 = 4).

A harmonic interval of a 9th:     5a

A harmonic interval of a 10th:     5b

 

A harmonic interval of a 11th:     5b

 

A harmonic interval of a 13th:     5c

If trying to determine an interval from one note to another below, just count the number of lines and spaces.

For example, here is an interval of a 6th and the lines and spaces numbered:
7

 

Accidentals do not change the basic interval quality of the pitches. They do obviously change the pitch, but the interval classification remains the same. An interval from 1 to 5 is the same for 1 to #5. The number remains the same. In the example below, all examples are 5th.
8a

Expanding on the basic interval concept, we will now divide intervals into two sections:

SECTION A
1 or unison
4th
5th
8 or octave

SECTION B
2nd
3rd
6th
7th

Each section uses terms and respective abbreviations to describe their interval accidentals.
Below are the terms and abbreviations to describe interval qualities:

Perfect     P
Augmented     A
Diminished     d
Major     M
Minor     m
* An exception is a unison cannot be diminished.

A perfect unison is where two pitches have the same pitch and notation:
11a

An augmented unison is where one pitch is one half step higher or lower than the other:
11b11c

Note: in the last example the first note is lowered with a flat and the second note must have a natural to avoid having the same pitch.

Augmented means that the interval is one half step larger than a perfect interval. When looking at a perfect unison, there is no difference in the two tones. When looking at an augmented unison, there is one half step difference between the two.

Unison:
12a
Augmented unison:
12b

Diminished means that the interval is one half step smaller than a perfect interval.

Perfect 5th:
12c

Diminished 5th:
12d

Note: Since the frequency of two tones cannot be less than zero (perfect unison), the diminished unison is impossible.

The other intervals in Section A may be diminished as well as perfect or augmented.
SECTION A
1 or unison
4th
5th
8 or octave

***A perfect octave is the same as a perfect unison except that one note is displaced by the interval of an octave. Octaves may be perfect, augmented, or diminished.***

A perfect interval made a half step smaller is called a diminished interval. A perfect interval made a half step larger is called an augmented interval. The numerical interval remains the same however. For example, 1 to P4 or 1 to d4 (1 and 4 remain the same).

A perfect 4th:
13a

An augmented 4th:
13b

Our next topic is interval inversion where the lower interval is raised an octave higher (lower then becomes the higher), or the higher interval is lowered an octave (higher becomes the lower). Interval inversion is key to understanding and analyzing harmony and counterpoint.

Looking at the example below, the interval is inverted by raising the lower note C up an octave -also known as an octave inversion. A line is drawn between the inverted octave notes.

15a

A 4th inverts to a 5th:
15b

A 5th inverts to a 4th:
15c

A helpful way of remembering interval inversion is that the sum of the interval and its inversion adds up to 9.

For example, let’s say we have two notes: a C and an E. We know this is a major 3rd interval. We could then subtract 3 from 9 to find what the inversion would be. It would be a 6th.
We can apply the same rules to inverting the 6th: subtract 6 from 9 to find the inversion. A 6th inverted creates a 3rd.

A 3rd inverted to a 6th:
16a

A 6th inverted to a 3rd:
16b

 

Interval inversion changes the numerical classification and sometimes changes the quality. See the chart below:
17a* One exception is that perfect intervals remain perfect when inverted. An augmented octave cannot be inverted at the octave

A unison inverted to an octave:
17b

A perfect 4th inverted to a perfect 5th:
17c

A perfect 5th inverted to a perfect 4th:
17d

An octave inverted to a unison:
17e

Both sections of intervals share the possibility of being augmented or diminished. Review the sections below:

SECTION A
1 or unison
4th
5th
8 or octave

SECTION B
2nd
3rd
6th
7th

Let’s take a look now at the example below for examining how section B intervals behave when inverted:
18a

 

By using half step adjustments, a major 2nd can become a minor 2nd and vice versa. A major 2nd with a lowered half step becomes a minor 2nd. A minor 2nd with a raised half step becomes a major 2nd.

Next section is Basic Scales