If you’re a musician, you’ve likely come across the term “interval class” in your studies. But what exactly is an interval class and how do you find it? In this article, we’ll explore the concept of interval class in music theory and provide a step-by-step guide on how to calculate it.

## What is an Interval Class?

An interval is the distance between two notes. For example, the distance between C and G is a perfect fifth. Interval class, on the other hand, is a way of grouping intervals that sound similar together.

Interval class takes into account both the size and quality of an interval. The size refers to the number of steps between two notes (e.g., a major third has two whole steps), while the quality refers to whether an interval is major, minor, perfect, augmented (one half step larger than perfect), or diminished (one half step smaller than perfect).

## How to Calculate Interval Class

To calculate interval class, follow these steps:

### Step 1:

Determine the size of your interval by counting the number of half steps between two notes. For example, if you have an interval that goes from C to E, you would count four half steps: C to C#, C# to D, D to D#, and D# to E.

### Step 2:

Determine the quality of your interval by comparing it to a major or perfect interval of the same size. For example, if your interval has a size of 4 (four half steps) like our example above, compare it to a major third (also four half steps).

If your interval is one half step smaller than a major third (e., C-Eb), it’s a minor third. If it’s one half step larger than a major third (e., C-E#), it’s an augmented third. If it’s the same size as a major third (e., C-E), it’s a major third.

### Step 3:

Reduce your interval to its smallest equivalent by inverting it if necessary. Invert the interval by subtracting its size from 12 (the number of half steps in an octave).

For example, if you have a major sixth (nine half steps), subtract nine from 12 to get three. This means that the interval class of a major sixth is the same as the interval class of a minor third.

## Examples

Let’s look at some examples to help solidify these concepts.

• C to G is a perfect fifth. It has a size of seven half steps and is already in its smallest equivalent, so its interval class is 7.
• C to E is a major third.

It has a size of four half steps and is already in its smallest equivalent, so its interval class is 4.

• C to Eb is a minor third. It has a size of three half steps, but we need to invert it to find its smallest equivalent: 12 – 3 = 9. Therefore, the interval class of C to Eb is also 4 (the same as C to E).

## Conclusion

Interval class may seem like an abstract concept, but it’s an important one in music theory. By understanding how to calculate it, you can better analyze and understand the relationships between different intervals and chords in music.

Remember: interval class takes into account both the size and quality of an interval, and you can find its smallest equivalent by inverting it if necessary. With these tools in hand, you’ll be well on your way to mastering this important concept in music theory.