Intervals
In music, an interval is the relationship between two notes that are played simultaneously or in sequence. Knowing the basic theory about intervals is essential to understanding the fundamentals of scale and chord construction.
Interval Names
Intervals are classified in two steps: first the broad type is derived by stripping away all accidentals and counting how many scale steps the interval encompasses:
An easier method that doesn't require notation is to count the number of steps in the sequence of natural notes. C and A are a sixth apart, since C=1, D=2, E=3, F=4, G=5 and A=6. G and F are a seventh apart—G=1, A=2, B=3, C=4, D=5, E=6, F=7.
Intervals larger than an octave are referred to as compound intervals:
| Compound interval | Consists of |
|---|---|
| Ninth | Octave + 2nd |
| Tenth | Octave + 3rd |
| Eleventh | Octave + 4th |
| Twelfth | Octave + 5th |
| Thirteenth | Octave + 6th |
Interval Inversion
Inverting intervals means that you transpose either of the notes so that the note that was formerly at the bottom is now on top or vice versa:
This means that intervals appear in discrete pairs that have similar properties. Unisons and octaves tend to be discussed together, likewise with thirds and sixths, or fourths and fifths, and so on. [1]
Interval Quality
The quality of an interval, how it actually sounds, is determined by the actual physical distance between the notes, which is measured in semitones.
In musical notation, B, C and D are consecutive scale steps. However, on an instrument, B and C are adjacent and C and D are separated by the enharmonic note C sharp/D flat. This means that intervals are of varying sizes.
To determine the interval quality, we add any accidentals back into the equation.
The following table contains some commonly occuring intervals together with their actual spans in semitones:
| Semitones | Interval |
|---|---|
| 0 | Perfect unison |
| 1 | Minor 2nd |
| 2 | Major 2nd |
| 3 | Minor 3rd |
| 4 | Major 3rd |
| 5 | Perfect 4th |
| 6 | (See below.) |
| 7 | Perfect 5th |
| 8 | Minor 6th |
| 9 | Major 6th |
| 10 | Minor 7th |
| 11 | Major 7th |
| 12 | Perfect octave |
Perfect vs. Minor/Major Intervals
As you can see in the above table, certain intervals appear in one basic form only, whereas others have two.
The unison, fourth and fifth and octave are collectively termed perfect intervals. They appear in one basic form only. Perfect intervals are considered as such because they are the most consonant intervals, they have the simplest frequency ratios according to the harmonic overtone series, and also because when inverted (see below), they remain perfect.
The second, third, sixth and seventh are known as minor/major intervals. These are less consonant, have more complex frequency ratios, and in interval theory they appear in two basic forms. Music theory has no preference for either.
Major/minor intervals can never turn into perfect intervals and vice versa.
Inversion of Interval Qualities
Major intervals become minor upon inversion, and vice versa. Perfect intervals remain perfect:
Altering Intervals
When either or both notes of an interval are modified with an accidental (or a key signature), the semitone span of the interval shrinks or grows. Such an interval is said to be altered.
This can happen in two ways. If you add a sharp accidental to the higher note, the interval grows. If you add a flat, it shrinks. It works the other way around with the lower note: add a sharp and the interval shrinks, add a flat and it grows.
Altering Perfect Intervals
A perfect interval becomes diminished when shrunk by a semitone and augmented when grown:
Altering Major/Minor Intervals
A minor interval that is raised by a semitone becomes a major interval. If it is further raised, it becomes augmented.
A major interval that is lowered by a semitone becomes a minor interval. If lowered further, it becomes diminished.
The following example illustrates the progression of diminished to augmented:
Diminished and augmented intervals that are further altered become double-diminished and double-augmented, then triple ditto, and so on. Again: a minor/major interval can never become perfect and vice versa.
Inverting Altered Intervals
The quality of altered intervals also reverses upon inversion. An augmented interval becomes diminished when inverted, and vice versa. A double-augmented interval instead becomes double-diminished, and the other way around.
Intervals and Enharmonicity
When you add altered intervals to the mix, it becomes a great deal more complicated. With single and double diminution and augmentation, there are several ways of notating what sounds the same (on an instrument with equal temperament). If you expand the interval quality table with the most common altered intervals in chord theory, it reads thus:
| Semitones | Interval |
|---|---|
| 0 | Unison |
| 1 | Minor 2nd |
| 2 | Major 2nd |
| 3 | Minor 3rd/Augmented 2nd |
| 4 | Major 3rd |
| 5 | Perfect 4th |
| 6 | Augmented 4th/Diminished 5th |
| 7 | Perfect 5th |
| 8 | Minor 6th/Augmented 5th |
| 9 | Major 6th/Diminished 7th |
| 10 | Minor 7th/Augmented 6th |
| 11 | Major 7th |
| 12 | Octave |
This table can be expanded indefinitely with all sorts of theoretical interval qualities of barely more than academic interest. An example is the triple-diminished third between C double-sharp and E double-flat, which sounds just like the unison D-D. Or the quadruple-augmented third between C double-flat and E double-sharp, which spans eight semitones and is equivalent to an augmented 5th or a minor 6th.
It is important to once again note that interval naming always starts with the notation. Between C and E, only thirds can be constructed no matter how many accidentals are added to the notes.
However, on an actual instrument, two notes that are n semitones apart are just that. If you play the notes C and E, they need the context of a key center in order to be C and E. It is far more likely that they will be C and E as opposed to B sharp and F flat, but otherwise, they're just two notes out of context.
The Tritone
The diminished fifth/augmented fourth between B and F is the only altered interval that occurs between natural notes. All others are perfect, major or minor.
This interval is known as the tritone, because it spans three [whole-] tones. It is also known as diabolus in musica (Lat. "devil in music"), because early theorists considered it an unpleasant-sounding interval that was to be avoided or at least swiftly resolved.
The tritone has many interesting properties. It consists of six semitone steps, which means that it is a division of the octave into two equal parts. It is also the only interval that remains identical when inverted. Since it is midway through the octave, it is also the largest possible interval class—the perfect fifth inverts to a perfect fourth, which is a smaller interval than the augmented fourth.
The tritone is one of the key components in the dissonance-consonance schemes that help establish the dominant-tonic relationship so essential to tonal music. How this works will be discussed in more detail in the essay on chord theory.
Learning the Intervals
It is not a bad idea to approach interval theory a bit like the multiplication table. If you know all possible pairings of natural notes by heart, it is easy to apply sharps and flats and determine the quality of any interval at a glance:
| C | D | E | F | G | A | B | |
|---|---|---|---|---|---|---|---|
| C | Unison | Major 2nd | Major 3rd | Perfect 4th | Perfect 5th | Major 6th | Major 7th |
| D | Minor 7th | Unison | Major 2nd | Minor 3rd | Perfect 4th | Perfect 5th | Major 6th |
| E | Minor 6th | Minor 7th | Unison | Minor 2nd | Minor 3rd | Perfect 4th | Perfect 5th |
| F | Perfect 5th | Major 6th | Major 7th | Unison | Major 2nd | Major 3rd | Aug 4th |
| G | Perfect 4th | Perfect 5th | Major 6th | Minor 7th | Unison | Major 2nd | Major 3rd |
| A | Minor 3rd | Perfect 4th | Perfect 5th | Minor 6th | Minor 7th | Unison | Major 2nd |
| B | Minor 2nd | Minor 3rd | Perfect 4th | Dim 5th | Minor 6th | Minor 7th | Unison |
1. Because of this, theorists sometimes use the term interval class. The shortest possible distance between two notes is calculated, with no regard to which note is higher or lower than the other. Octaves are treated as unisons, and the largest possible interval is a fourth, since the fifth inverts to a fourth, the sixth to a third, and so on. [Go back]
