Interval (music)

In music theory, an interval is the difference in pitch between two sounds.

This concept is fundamental to how we understand melody and harmony. When notes are played one after another, the interval is called melodic, or horizontal. This creates a linear sequence of tones. When notes sound at the same time, the interval is called harmonic, or vertical. These simultaneous notes form chords. Understanding intervals allows musicians to navigate the relationships between different pitches.

Physically, an interval is the ratio between two sonic frequencies. If you compare the frequency of one note to another, you find a mathematical relationship. For example, any two notes separated by an octave have a frequency ratio of 2:1. This means the higher note vibrates twice as fast as the lower one. Because the human ear perceives pitch as a linear increase, but frequency actually increases exponentially, musicians use different measurement systems. One common unit is the cent. The cent is a logarithmic unit used to compare interval sizes more easily.

There are two primary ways to represent the size of an interval. The first method uses frequency ratios. In a tuning system known as just intonation, intervals are expressed by small-integer ratios. These are called just intervals or pure intervals. Examples include a perfect fifth at a 3:2 ratio or a perfect fourth at 4:3. However, most modern instruments use 12-tone equal temperament (12-TET). In this system, the ratios are not simple integers. For instance, an equal-tempered fifth has a ratio of approximately 1.498:1, which is very close to the pure 3:2 ratio.

The second method uses cents to provide a standard scale for comparison. In 12-TET, the distance between an octave's lowest and highest frequency is divided into 1200 equal parts. Each part is one cent. In this specific tuning system, every semitone is exactly 100 cents wide. This allows musicians to precisely measure the distance between any two notes.

Western music theory uses a specific naming scheme for intervals. Each name combines a number and a quality. The number, or diatonic number, indicates how many letter names or staff positions the interval encompasses. For example, the interval from B to D is a third because it includes B, C, and D. This is an inclusive count, meaning you start counting at one with the first note.

If you add accidentals to the notes, the interval number remains the same. This is why the system is often called diatonic numbering.

The quality of an interval is defined by terms like perfect, major, minor, augmented, or diminished. These modifiers describe the specific character of the interval. Perfect intervals, such as the unison (P1), fourth (P4), fifth (P5), and octave (P8), are traditionally viewed as highly consonant.

Other intervals are categorized differently. Major and minor intervals are often called imperfect consonances. If an interval is widened, it becomes augmented. If it is narrowed, it becomes diminished.

Intervals can also be categorized by their size relative to an octave. A simple interval stays within a single octave. When an interval spans more than an octave, it is called a compound interval. The quality of a compound interval is determined by the simple interval it is based on. Additionally, musicians work with intervals smaller than a semitone. These are known as microtones. Some of the smallest microtones are called commas, which describe tiny discrepancies found in certain tuning systems.

Finally, intervals serve as the building blocks for complex musical structures. When you join two intervals together, they form a new, larger interval. Interestingly, the number of the resulting interval is always one less than the sum of the two original numbers. For example, joining two thirds results in a fifth rather than a sixth.

This mathematical logic allows musicians to stack intervals to create scales, chords, and sophisticated harmonies that define different musical styles.