Intervals

Intervals are distances between objects. The table below shows that intervals may be formed by pitches, pitch classes, name classes, or octaves. Furthermore, intervals may be ordered or unordered.

An ordered interval is formed when objects occur successively.
The most familiar example is a melodic interval.
An unordered interval is formed when objects occur simultaneously.
The most familiar example is an harmonic interval.
Objects Ordered Intervals Unordered Intervals
Pitches

Ordered pitch interval
ip<a,b> = b - a

 Unordered pitch interval
ip(a,b) = | b - a |
Pitch Classes

Ordered pc interval
ipc<a,b> = mod12 (b - a)

 Unordered pc interval
ipc(a,b) = lesser of (ipc<a,b>, ipc<b,a>)
Name Classes

Ordered nc interval
inc<a,b> - mod7 (b - a)

Unordered nc interval
inc(a,b) = lesser of (inc<a,b>, inc<b,a>)
Octaves Ordered octave interval
ioct<a,b> = octb - octa
 Unordered octave interval
ioct(a,b) = | octb - octa |

 

Pitch Intervals

To compute an ordered pitch interval, follow the sequence shown by the Flash movie. Click the red arrow to proceed to the next stage.

 

To compute an unordered pitch interval, follow the sequence shown by the Flash movie. Click the red arrow to proceed to the next stage.