Intervals#
An interval in music is the ratio of the frequencies of two [[Sound#Pitch|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 [[Sound|sounds]] are arranged temporally, we distinguish two types of intervals:
- harmonic intervals - we say that the interval between two [[Sound#Pitch|pitches]] is harmonic whenever they are playing simultaneously;
- melodic intervals - we say that the interval between two [[Sound#Pitch|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 [[Sound#Pitch|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 [[Sound#Pitch|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 [[Intervals|interval]] between two identical [[Sound#Pitch|pitches]], i.e. the [[Intervals|interval]] with value \(1:1\).
Definition: Octave
An (perfect) octave is the [[Intervals|interval]] between two [[Sound#Pitch|pitches]] where the frequency of one of the [[Sound#Pitch|pitches]] is exactly double the frequency of the other, i.e. the [[Intervals|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]].
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