Standard 4: Intervals
Our objectives:
- Determine the size and quality of a given interval, from perfect unison to perfect octave.
- Complete a given interval by adding either a note above or below a given note.
4.1 What's an "interval"?
An interval is the distance between two pitches, usually measured in two components: 1) the size, and 2) the quality.
The term interval regularly refers both to:
- The distance between two pitches on a scale, as described by the size and quality (e.g. major 2nd), and;
- Two pitches that are separated by that distance (e.g. G and A).
A melodic interval describes the distance between two pitches that are sounded one after another (as in a melody). A harmonic interval describes the distance between two pitches that are sounded together, at the same time (as in harmony).
4.2 Interval Size
We can describe the interval between two notes first by stating its size, which is the number of letters that we can count from the the bottom pitch to the top pitch, including both pitches in the count.
For example, here are two examples of a 2nd: both as a melodic interval and a harmonic interval
To find the size, begin with the letter names only. That is, treat C, C-sharp, and C-flat all as C for the time being. Next, count the number of steps (different letters) between the two pitches in question, including both pitches in your count. Start from the bottom pitch and count up the musical alphabet to the top pitch. Remember, you must include both pitches of the interval in your count!
Here's an example of a 4th. The letters are C-D-E-F. We are igoring the F# here when we count the size of this interval.
Review this interactive demonstration on counting interval size. Note: in this demonstration, "generic interval" means the same thing as interval size.
Your Turn: Try this exercise to identify the size of an interval.
4.3 Interval Quality
Often more specificity is needed than what the interval size can provide. That specificity comes in the form of an interval's quality. Combining the size and quality gives us the full description of that interval.
There are five possible interval qualities:
- augmented (A)
- major (M)
- perfect (P)
- minor (m)
- diminished (d)
We will begin with the major and perfect intervals.
4.4 Diatonic Intervals
The term "diatonic interval" describes the interval between two notes, where the top pitch is part of the major scale built on the bottom pitch. For example, here are eight different harmonic intervals all built on the C major scale, with C as the bottom note:
The names of the intervals above are as follows, from left to right. These are called diatonic intervals:
- Perfect Unison (P1)
- Major 2nd (M2)
- Major 3rd (M3)
- Perfect 4th (P4)
- Perfect 5th (P5)
- Major 6th (M6)
- Major 7th (M7)
- Perfect Octave (P8)
When you count the number of half-steps between each pair of notes, use the piano keyboard to help you. Start with the bottom pitch, and move up by half-steps until you reach the top pitch. In counting the half-steps, make sure that you start with the first pitch as "zero" (i.e. with just one note, there are no half steps), and count up from there.
The number of half steps in each diatonic interval is as follows:
| Interval Name | Half-Steps |
|---|---|
| Perfect Unison (P1) | 0 |
| Major 2nd (M2) | 2 |
| Major 3rd (M3) | 4 |
| Perfect 4th (P4) | 5 |
| Perfect 5th (P5) | 7 |
| Major 6th (M6) | 9 |
| Major 7th (M7) | 11 |
| Perfect Octave (P8) | 12 |
We will be referring to these diatonic intervals as we describe minor, diminished and augmented intervals. So it's a good idea to memorize the relationship between a given diatonic interval and the number of half-steps that it includes.
4.5 Minor, Diminished and Augmented intervals
To round out our tools for describing the quality of an interval, we will also use three additional qualities: minor, diminished, and augmented.
Major Intervals:
- When a major interval is decreased by a half-step, it becomes a minor interval.
- When a minor interval is decreased by a half-step, it comes a diminished interval.
- When a major interval is increased by a half-step, it becomes an augmented interval.
Perfect Intervals:
- When a perfect interval is decreased by a half-step, it becomes a diminished interval.
- When a perfect interval is increased by a half-step, it becomes an augmented interval.
Take a look at the example below:
All three are examples of a third:
- The first interval, with the notes C - E, yields four half-steps, and therefore is described as a Major 3rd.
- The second interval, with the notes C - Eb, yields only three half-steps, and therefore is described as a Minor 3rd. (Note that this is still a third, because the letter names are the same.)
- The third interval, with the notes C# - Eb, yeilds only two half-steps (a half-step smaller than a Minor 3rd). This is an example of a diminished 3rd.
Remember: the size and quality of an interval depends entirely on how the notes are written on the staff. For example, even though the diminished 3rd in the example above are enharmonically equivalent to C# and D#, since the notes are written as C# and Eb, the interval must be described as a third.
Here is a chart that shows the correspondence between the half-step count, the size, and the resulting quality.
| Half-Steps | Unis. | 2nd | 3rd | 4th | 5th | 6th | 7th | Octave |
|---|---|---|---|---|---|---|---|---|
| 0 | P1 | d2 | ||||||
| 1 | A1 | m2 | ||||||
| 2 | M2 | d3 | ||||||
| 3 | A2 | m3 | ||||||
| 4 | M3 | d4 | ||||||
| 5 | A3 | P4 | ||||||
| 6 | A4 | d5 | ||||||
| 7 | P5 | d6 | ||||||
| 8 | A5 | m6 | ||||||
| 9 | M6 | d7 | ||||||
| 10 | A6 | m7 | ||||||
| 11 | M7 | d8 | ||||||
| 12 | A7 | P8 |
Take a look at this interactive demonstration on combining interval size and interval quality.
Your turn:
- Identify these intervals. (major and perfect intervals only.)
- Now, identify these intervals. (all intervals)
Having trouble? Use this Interval Calculator to help reveal the process of identifying an interval. Enter the first note of the interval (this could be either the top or bottom note), then click on the up arrow to identify the ascending interval from this note, or the down arrow to identify the descending interval from this note.
4.6 Notating Intervals
Given an interval (say, "Minor 3rd") and one pitch, we can determine what the other pitch needs to be, either below or above the given note. Here are the steps to notate a given interval:
- Write down the number of half steps that are contained in the given interval (e.g. a minor 3rd has three half steps).
- Find the letter name of the second pitch of the interval by either counting above (if it's an "ascending" interval) or below (if it's a "descending" interval) the given note, according to the given interval size, and using the musical alphabet.
For example, if we are trying to find a minor third above a C, the letter name of the second pitch must be an "E" (C - D - E). If we're trying to find a minor third below a C, the letter name of the second pitch would be an "A" (C - B - A). - Head to the keyboard. Find the given pitch (C in this example), and count the number of half steps that are contained in the given interval in the same direction as step two (e.g. either "ascending" or "descending").
- Once you arrive at the note, describe this note in terms of the letter name from step two. In our case, a minor 3rd above C would be E-flat. A minor 3rd below C would be A.
