Intervals

An interval in music is the ratio of the frequencies of two pitches.

NOTATION

Most commonly, intervals are denoted as reduced fractions with the colon sign such as $2:1$, $5:4$, $4:7$ etc. However, it is also possible to denote them by their decimal value, obtained after the division of the numbers such as $2$, $1.25$, $0.5$, etc. The latter is actually the only option when the ratio is an irrational number.

Depending on how the sounds are arranged temporally, we distinguish two types of intervals:

• harmonic intervals - we say that the interval between two pitches is harmonic whenever they are playing simultaneously;
• melodic intervals - we say that the interval between two pitches is melodic whenever they are to be played sequentially, one after the other.

Furthermore, we distinguish two types of melodic intervals:

• ascending intervals - an interval is ascending whenever it is a number greater than $1$, i.e. the second pitch has a higher frequency than the first;
• descending intervals - an interval is descending whenever it is a number between $0$ and $1$, i.e. the second pitch has a lower frequency than the first.

There are two fundamental Intervals which are crucial for all of music:

Definition: Unison

A (perfect) unison is the interval between two identical pitches, i.e. the interval with value $1:1$.

Definition: Octave

An (perfect) octave is the interval between two pitches where the frequency of one of the pitches is exactly double the frequency of the other, i.e. the interval with value $2:1$.

Naming

For us humans, working directly with numbers is unintuitive and confusing. This is why we have devised a more comprehensible naming system for Intervals. |