If you’re a music theory enthusiast, you might have come across the term “interval vector.” But what exactly does it mean?

In simple terms, an interval vector is a numerical representation of the intervals in a piece of music. It’s a useful tool for analyzing and comparing different pieces of music and identifying patterns.

What are Intervals?

Before we delve into interval vectors, let’s first understand what intervals are. In music theory, an interval refers to the distance between two notes.

It can be measured in half-steps or semitones. For example, the interval between C and E is a major third, which consists of four half-steps.

Calculating Interval Vectors

To calculate an interval vector for a piece of music, we first need to identify all the intervals that occur within it. Let’s take a simple melody as an example:


The intervals between each pair of notes are:

– D-C: 2nd
– E-D: 2nd
– F-E: 2nd
– G-F: 2nd
– A-G: 2nd
– B-A: 2nd
– C-B: 2nd
– C-C: octave

We can represent these intervals as numbers by counting how many times each interval occurs:

– 0 6 1 0 0 0
– (or)
– (0) (6) (1) (0) (0) (0)

In this case, there are no minor seconds or major sevenths, so those slots are left empty.

Interpreting Interval Vectors

Now that we know how to calculate an interval vector, let’s talk about how to interpret it. The numbers in the vector represent the number of occurrences of each interval class within the piece of music.

An interval class is simply a group of intervals that share the same number of half-steps. For example, both a minor second and a major seventh are considered part of the interval class “1,” because they are both one half-step apart.

So, in our example interval vector, we see that there are 6 occurrences of the interval class “2” (major seconds) and 1 occurrence of the interval class “3” (minor thirds).

Uses of Interval Vectors

Interval vectors can be used for a variety of purposes in music analysis. For example:

– Comparing different pieces of music: By calculating interval vectors for multiple pieces, we can compare them and identify patterns or similarities. – Identifying tonal centers: If a piece has a strong tonal center (i.e.

key), its interval vector may reflect this by having more occurrences of certain intervals. – Analyzing melody vs. harmony: We can calculate separate interval vectors for the melody and harmony of a piece to see how they differ.


In conclusion, an interval vector is a numerical representation of the intervals in a piece of music. It can be calculated by identifying all the intervals in a piece and counting how many times each one occurs.

Interval vectors are useful for comparing different pieces, identifying tonal centers, and analyzing melody vs. harmony. By understanding interval vectors, we can gain deeper insights into the structure and patterns within music.