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I. Fundamentals
Intervals

### Core Idea

Two pitches form an interval, which is usually defined as the distance between two notes. Melodic intervals are played or sung separately, while harmonic intervals are played or sung together.

### Explanation

Two pitches form an interval, which is usually defined as the distance between two notes.

Melodic intervals are played or sung separately, while harmonic intervals are played or sung together.

Every interval has a size and a quality. An interval's size is the distance between two notes on a staff—i.e., it is a measurement of the number of lines and spaces between two notes.

Size is considered generic. In other words, it doesn't matter what accidentals you apply to the notes, the size is always the same.

A quality makes an interval specific when used in combination with a size. Unisons, fourths, fifths, and octaves form perfect intervals, while seconds, thirds, sixths, and sevenths form major and minor intervals.

Any interval can be augmented or diminished. Augmented intervals are one half step larger than a perfect or major interval. Diminished intervals are one half step smaller than a perfect or minor interval.

Intervals between a unison and an octave are called simple intervals. Any interval larger than an octave is a compound interval.

Intervallic inversion occurs when two notes are "flipped." When you need to identify an interval where the lower note is the tonic of a difficult or imaginary major key, inverting the interval can help.

Consonant intervals are intervals that are considered more stable, as if they do not need to resolve, while dissonant intervals are considered less stable, as if they do need to resolve.

Two pitches form an interval, which is usually defined as the distance between two notes. But what does an interval measure? Physical distance on the staff? Difference in wavelength between pitches? Something else? Music theorists have had contradictory ideas on the definition of "interval," and these definitions have varied greatly with milieu. This chapter will focus on intervals as a measure of two things: written distance between two notes on a staff, and an aural "distance" (or space) between two sounding pitches. It will be important to keep in mind at all times that intervals are both written and aural, so that you are thinking of them musically (and not simply as an abstract concept that you are writing and reading).

Size

Intervals can be melodic (played or sung separately) or harmonic (played or sung together). In Example 1, the notes in the first measure sound together (harmonically), while in the second measure, they sound separately (melodically).

Example 1. A harmonic and a melodic interval.

Every interval has a size and a quality. A size is the distance between two notes on a staff—i.e., it is a measurement of the number of lines and spaces between two notes. Sizes are written with Arabic numbers (2, 3, 4, etc.); however, they are spoken with ordinal numbers (second, third, fourth, fifth, sixth, seventh, etc.). Always begin with "one" when counting size. Example 2 shows the eight sizes within a C major scale. As you can see, the sizes are labeled with ordinal numbers, with two exceptions: the interval between two notes on the same line or space is called a “unison,” not a “first,” and notes eight lines and spaces apart are said to be an “octave,” not an “eighth.”

Example 2. Sizes of intervals.

Size is considered generic. In other words, it doesn't matter what accidentals you apply to the notes—the size is always the same. Example 3 demonstrates this: despite the different accidentals, each of these intervals is a third (or “generic third”) because there are three lines/spaces between the two notes.

Example 3. Accidentals do not affect an interval's generic size.

Perfect, Major, and Minor Qualities

A quality makes an interval specific when used in combination with a size. Quality more precisely measures written distance between notes, and—in combination with an interval's size—it describes the aural sound of an interval.

There are five possible interval qualities:

Augmented (designated as A or +)

Major (ma)

Perfect (P)

Minor (mi)

Diminished (d or o)

The quality comes before the size when saying or writing an interval. For example, an interval could be described as a "perfect fourth" (abbreviated P4), a "minor third" (abbreviated mi3), or an "augmented second" (abbreviated +2 or A2).

For now, we will only discuss three qualities: perfect, major, and minor. Different theorists (in different locations and time periods) have applied these qualities to different sizes of intervals, depending on milieu. Example 4 shows how these qualities are applied today. The left column shows that seconds, thirds, sixths, and sevenths are major and/or minor, while the right column shows that unisons, fourths, fifths, and octaves are perfect intervals.

Example 4. Interval qualities.

The "Major Scale" Method for Determining Quality

There are several different methods for learning to write and identify qualities of intervals. One method you may have heard of is counting half steps. We do not recommend this method, because it is time consuming and often inaccurate. Instead, we recommend using what you know about major scales to identify interval quality.

To identify an interval (size and quality) using this method, complete the following steps:

Determine size (by counting lines and spaces between the notes).

Imagine that the bottom note of the interval is the tonic of a major scale.

Determine whether or not the top note is in the bottom note's major scale (imagined in step 2) and assign the corresponding quality.

If it is: the interval is perfect (if it is a unison, fourth, fifth, or octave) or major (if it is a second, third, sixth, or seventh). If it is not: the interval could be minor (a lowered second, third, sixth, or seventh), or it could be augmented or diminished, which will be covered in the next section.

Example 5 shows two intervals. Try identifying their size and quality:

Example 5. Two intervals.

In Example 5a, the notes are F and C in treble clef. Here is how you would use the “Major Scale” method to identify the interval:

First

### Key Quote

Melodic intervals are played or sung separately, while harmonic intervals are played or sung together.

### Application Scenarios

A quality makes an interval specific when used in combination with a size. Unisons, fourths, fifths, and octaves form perfect intervals, while seconds, thirds, sixths, and sevenths form major and minor intervals.

Intervallic inversion occurs when two notes are "flipped." When you need to identify an interval where the lower note is the tonic of a difficult or imaginary major key, inverting the interval can help.

Intervals can be melodic (played or sung separately) or harmonic (played or sung together). In Example 1, the notes in the first measure sound together (harmonically), while in the second measure, they sound separately (melodically).

Example 1. A harmonic and a melodic interval.

### Key Terminology

intervallic inversion diminished intervals augmented intervals compound interval melodic interval simple intervals harmonically major scale wavelength interval measure milieu

### Related Links

https://viva.pressbooks.pub/app/uploads/sites/12/2019/05/simple-v-compound.png https://viva.pressbooks.pub/app/uploads/sites/12/2019/05/inversion-3.png https://viva.pressbooks.pub/app/uploads/sites/12/2019/05/imaginary.png Introduction to Species Counterpoint https://viva.pressbooks.pub/app/uploads/sites/12/2019/05/white-key-sevenths.png https://viva.pressbooks.pub/app/uploads/sites/12/2019/05/enh-eq.png Specific Intervals (musictheory.net)Interval Introduction (Robert Hutchinson)Intervals (Hello Music Theory)Diminished and Augmented Intervals (Open Textbooks)
Source: https://viva.pressbooks.pub/openmusictheory/chapter/intervals/
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