Major and minor intervals

An interval measures the distance between two pitches and consists of two parts, a quantity (a number) and a quality (major, “MA” or “M”; minor, “mi” or “m”; perfect, “P”; diminished, “d” or “o”; or augmented, “A” or “+”).

Quantity. To determine the quantity of an interval, simply count the number of lines and spaces between two notes on the staff, including the notes themselves. Some examples of this process are shown in Example 5‑1.

Example 5‑1. Determining quantity of intervals

Quality. Determining the quality of an interval is more complicated than determining the quantity. There are two basic types of classification: major/minor and perfect. Each interval quantity fits into only one classification: for simple intervals (those of an octave or smaller), seconds, thirds, sixths, and sevenths are major/minor, and unisons, fourths, fifths, and octaves are perfect.

Major and minor intervals. We have studied some intervals already—the half step and whole step. Using the major/minor classification system, we call a half step a minor second (mi2) and a whole step a major second (MA2). Thirds may be understood as combinations of seconds. A minor third (mi3) is equivalent to three half steps or MA2+mi2. A major third (MA3) is equivalent to four half steps or two MA2s.

If you think of the lower note of an interval as tonic of a major scale, you can use that scale to identify any major interval. Example 5-2 shows this technique: A is the lowest note of each interval in this case, so we use the A major scale to determine the higher note.

Example 5‑2. Finding major intervals from the major scale

Minor intervals are always a half step smaller than major ones. Example 5‑3 shows how to derive minor intervals from the major ones by reducing their size by one half step. This is done by either raising the lower note or lowering the higher note by one half step.

Example 5‑3. Finding minor intervals from major intervals

Sometimes large intervals can be difficult to identify. If seconds and thirds are easier for you to identify than sixths and sevenths, you may use interval inversion to make the process easier. Interval inversion—creating the inversion of the original interval—works either by displacing the lower note of an interval up an octave or by displacing the higher note down an octave. Once the interval is inverted, the quality inverts (major intervals become minor and vice versa), and so does the quantity (sevenths become seconds and vice versa, and sixths become thirds and vice versa). Example 5‑4 shows how interval inversion works for major and minor intervals.

Example 5‑4. Inversion of major and minor intervals

Perfect intervals

Perfect intervals include unisons, fourths, fifths, and octaves. Like with major intervals, you can identify any perfect interval from a major scale by thinking of the lower note as tonic of the scale. Example 5-5 shows this technique: A is the lowest note of each interval, so we use the A major scale to determine the higher note in each case.

Example 5‑5. Perfect intervals derived from the major scale

Using interval inversion, fourths invert to fifths and vice versa, and unisons invert to octaves and vice versa. Unlike with major and minor intervals, quality does not change when a perfect interval is inverted.

Diminished and augmented intervals

Major, minor, and perfect intervals may be modified in additional ways to create diminished and augmented intervals, which are less common than the other interval qualities.

A diminished interval results when either a minor or perfect interval is made smaller by one half step. This is done either by raising the lower note or lowering the higher note by one half step, as shown in Example 5‑6.

Example 5‑6. Diminished intervals derived from minor and perfect intervals

An augmented interval results when either a major or perfect interval is made larger by one half step. This is done by either lowering the lower note or raising the higher note by one half step, as shown in Example 5‑7.

Example 5‑7. Augmented intervals derived from major and perfect intervals

Using interval inversion, augmented intervals invert to diminished ones and vice versa. Quantities invert in the same way as major, minor, and perfect intervals (seconds become sevenths, thirds become sixths, fourths become fifths, and so forth). No matter what the interval, its own quantity and the quantity of its inversion always add up to nine.

Compound intervals

The previous examples deal with simple intervals, which are intervals that are an octave or smaller. Compound intervals are intervals that are larger than an octave. Convert any simple interval to a compound one by adding seven to its quantity and displacing the higher note by one octave, as shown in Example 5‑8.

Example 5‑8. Simple intervals and their compound counterparts

EXERCISE 5-2: Analysis of Judith Cloud, Six Forays for Flute and Clarinet, mvt. 2

Listen to Judith Cloud’s Six Forays for Flute and Clarinet and provide labels for each harmonic interval formed between the flute and clarinet in the score below. The first measure is done for you.

Worksheet example 5‑1. Judith Cloud, Six Forays for Flute and Clarinet, mvt. 2

Used with permission of the composer © Judith Cloud, all rights reserved

Learn about living American composer Judith Cloud by reading her bio here.

Access a printer-friendly .pdf of the exercise here: Ex5.2 Analysis with Judith Cloud Six Forays mvt 2

Want more practice identifying intervals? Try these drills:

Practice identifying all intervals in various clefs (teoria)

Practice identifying all intervals in various clefs (musictheory.net)

Identifying intervals aurally

Learning how to identify intervals aurally can be a daunting task. If this is a goal you wish to achieve, I offer here some techniques for mastering aural interval identification. A combination of three different techniques—song association, tonal implication, and degree of dissonance—may be used for optimum success.

Song association

Are there particular intervals that you have difficulty identifying? Try associating the interval with a catchy tune that you already know. Figure 5‑1 summarizes some common musical themes with ascending, descending, and harmonic intervals. You can add your own favorite tunes to this chart, as needed.

Tonal implication

Depending on an interval’s context (timbre, register placement, and so forth), using song associations may not always render successful results. However, with a solid knowledge of relative pitch relationships through solfege, you can learn to identify intervals. Figure 5‑2 relates intervals to their most common usages in tonal music.

Figure 5‑2. Tonal implication interval chart

Access a screen-reader friendly .pdf of this figure here: Figure 5-2. Tonal implication interval chart

Degree of dissonance

For millennia, scholars have examined the properties of intervals, often classifying them as dissonant or consonant. Some intervals have been considered dissonant during one era and later considered consonant, and vice versa. Active in the 20th century, composer, theorist, and pedagogue Paul Hindemith created a table (called “Series 2”) that places intervals along a continuum ranging from most consonant to most dissonant. This table is reproduced in Figure 5‑3.

Figure 5‑3. Hindemith’s “Series 2”^[1]

You can listen for an interval’s degree of consonance or dissonance to help you aurally identify it. Pedagogue and scholar Rudy Marcozzi has developed a strategy for interval identification based on binary logic. His flowchart summarizing binary decision-making appears in Figure 5‑4.

Figure 5‑4. Marcozzi’s interval flowchart^[2]