Interval Set Calculator Music Theory

What is an Interval Set?

An interval set is a collection of intervals between notes in a musical passage or chord. In music theory, interval sets are fundamental to understanding harmony, voice leading, and chord construction. They help identify chord qualities, inversions, and harmonic functions.

Interval Set Notation

Interval sets are typically written using numbers that represent the intervals between notes. The numbers are ordered from smallest to largest, and the first note is considered the root (1). For example:

• 1-3-5 represents a major triad
• 1-3-5-7 represents a dominant seventh chord
• 1-3-6 represents a minor triad with a major sixth

Interval Set Classes

Interval sets can be classified based on their harmonic properties. Common interval set classes include:

• Triads (3-note sets)
• Tetrads (4-note sets)
• Pentads (5-note sets)
• Hexads (6-note sets)

How to Use This Calculator

Using the interval set calculator is straightforward. Follow these steps:

1. Enter the intervals of your chord or passage in the input field, separated by hyphens (e.g., 1-3-5 for a major triad).
2. Click the "Calculate" button to analyze the interval set.
3. Review the results, which include the interval set class, chord quality, and harmonic function.

Example Calculation

Let's analyze the interval set 1-3-5-7:

1. The intervals are already in order: 1, 3, 5, 7.
2. The differences between intervals are: 2, 2, 2.
3. This is a dominant seventh chord (1-3-5-7).
4. The harmonic function is typically dominant.

Common Interval Sets

Here are some common interval sets and their musical significance:

These interval sets form the foundation of Western harmony and are essential for understanding chord progressions and voice leading.

Analyzing Interval Sets

Analyzing interval sets involves several steps to understand their harmonic properties:

1. Sort the intervals in ascending order.
2. Calculate the differences between consecutive intervals.
3. Identify the interval set class based on the differences.
4. Determine the chord quality and harmonic function.

Interval Set Differences

The differences between intervals help identify the interval set class. For example:

• 1-3-5 has differences of 2, 2 (major triad).
• 1-3-6 has differences of 2, 3 (minor triad with major sixth).
• 1-3-5-7 has differences of 2, 2, 2 (dominant seventh).

Chord Quality and Function

Once the interval set class is identified, you can determine the chord quality and harmonic function. For example:

• A major triad (1-3-5) has a major quality and tonic function.
• A dominant seventh chord (1-3-5-7) has a major quality with a minor seventh and dominant function.
• A diminished seventh chord (1-2-4-5) has a diminished quality and diminished function.