Whole and half steps
Intervals are a core concept in music, but the two intervals that are most relevant to understanding scales are whole and half steps.
A half step, also called a semitone, is the smallest musical interval in existence. This is the span from one note to an adjacent note.
On a keyboard, every key is a half-step from the adjacent key.
On a guitar, any two adjacent frets on the same string are a semitone apart. Two notes on different strings can also be a semitone apart. For example, the fifth-fret Low E string is a half-step below the first-fret A-string.
Semitones are key to understanding musical intervals, as any musical interval can be measured as a specific number of half-steps.
For example, the interval from C to G is known as a perfect fifth (we’ll cover this in more depth later). However, let’s think about this interval in terms of semitones:
- C to C# is one semitone.
- C# to D makes two.
- D to D# is three.
- D# to E is four.
- E to F is five.
- F to F# is six.
- Finally, F# to G is seven.
In other words, a perfect fifth can also be viewed as an interval of seven semitones. This applies to all intervals; half-steps are the foundation of musical intervals.
A whole step is an interval of two semi-tones, and is also known as a tone.
On a piano a key is a whole step away from another if there is one key in between them.
Alternatively, you can think of a it as being two half-steps away.
All intervals are named for their relation to the tonic, or starting note. The intervals in this section are the most commonly used, and are known as simple intervals. These are intervals that are within an octave (or eighth) of the root note.
If the root note of an interval was C, the interval between that C and the C above it, or any note in between, would be considered simple.
We’ll look at every interval, from a half-step apart to a full octave, in order of increasing distance.
Any interval from one letter note to an adjacent one is considered a second. For example, from C to Db is an ascending second, as is D to E.
Remember that the musical alphabet spans from A to G and then loops back around, so an interval from G to A is also a second since these two notes are adjacent in music.
There are two kinds of seconds: Major and minor.
A minor second is formed by two notes a semitone apart, and is the smallest musical interval. The interval from C to C# is a minor second.
The major second is the next-largest musical interval, with a distance of two semitones.
An augmented second is a span of three semitones, such as the interval from C to D#.
A third occurs when two notes are two letter names apart. For example, from A to C is a third, as is the interval from C to E.
The minor third, like the augmented second, is an interval of three semitones. The difference is purely notational: Since C and D are adjacent letters, C to D# is a second, whereas C to Eb is a third.
Keep in mind, D# and Eb are enharmonic (the same note), so the actual interval is identical.
One half-step up from a minor third, the major third is an interval of four semitones. The interval from C to E is a major third.
A fourth is formed by two notes that are three letter names apart. For instance, the intervals between C and F, G and C, and A# and D are all fourths.
Just as an augmented second and minor third are the same, a diminished fourth is identical to a major third: It’s an interval of four semitones. In this instance, though, the notes are three letter-names apart rather than two (Fb and E are enharmonic).
The perfect fourth is an interval of five semitones, such as the one from C to F or F to Bb.
An augmented fourth spans six semitones. This musical interval is also sometimes referred to as a tritone, so named because it’s the equivalent of three adjacent whole steps (or tones).
The fifth is, the interval in which one note is on the fifth sequential letter from another. Some examples include the interval between F and C, D# and A, and C and G.
The sequence of C, D, E, F, G goes through five adjacent letters, and so the interval from C to G is a fifth.
The diminished fifth is enharmonic with the augmented fourth: it’s also a tritone, an interval of six half-steps.
A perfect fifth occurs between two notes that are seven semitones apart. Some examples of perfect fifths include the intervals from C to G, A to E, and B to F#.
The augmented fifth is one half-step farther than a perfect fifth, or an interval of eight semitones.
As you probably guessed, a sixth is an interval between notes that are five letter-names apart, such as C and A, E and C, or G and E.
The minor sixth is the smallest sixth interval, a span of eight semitones. It’s enharmonic with the augmented fifth.
One half-step up from the minor sixth is the major sixth, an interval of nine semitones.
The penultimate simple interval, the seventh occurs between a root note and the seventh note in a consecutive sequence.
Examples of seventh intervals include that from C to B, E to D, or F# to E.
As with every other interval, we see that the first and seventh note of a major or minor scale produce an interval of a seventh.
Since the musical alphabet is circular, you can also think of a seventh as the interval from the root note to an octave above the previous letter.
That may seem complex, but it’s actually quite simple. Let’s consider an example.
We know that the interval from C to B is a seventh because we can think of the sequence of the notes between these two:
C, D, E, F, G, A, B
In other words, B is the seventh letter in the sequence, and thus forms a seventh.
But we could have also started with C and gone to the left…
…And gotten the same result. This is much quicker, but it’s important to remember that you have to add an octave. In other words, this interval is not a seventh:
whereas this one is:
A diminished seventh is formed by two notes that are 9 semitones apart.
A minor seventh is formed by two notes that are 10 semitones apart.
A half-step above the minor seventh comes the major seventh, an interval of 11 semitones.
The eighth, also known as the octave, is the largest simple interval. It spans from one letter note to the next instance of that note.
For instance, the interval from one C to the next one is an octave.
The diminished octave is enharmonic with the major seventh; they’re the same interval, just notated differently, a span of 11 semitones. To look at it differently, a diminished octave is the interval from a note to its flat an octave above (i.e. from C to Cb).
The most common quality of octave by far, the perfect octave is formed by two notes that are 12 semitones apart (this is why the guitar fretboard has two dots at the twelfth fret).
Last but not least, we have the augmented octave, an interval of 13 semitones, or the interval from a note to its sharp an octave above.
Anything greater than an octave is considered a compound interval. You might find it easier to think of these in terms of their corresponding simple interval. To do this, simply subtract seven from the interval.
Here’s an example: Consider a major ninth starting on C. Let’s count it out: C, D, E, F, G, A, B, C, D. Since D is the ninth note in the C major scale, this is the note that gives us a major ninth above C.
If we take 9-7, we get 2. In other words, a major second is the same as a major ninth, just an octave higher.
This applies to any interval: a minor tenth is just a minor third raised an octave.
Compound intervals typically only go up to fifteenths (an interval of two octaves) and they rarely even make it that high. Focus on becoming comfortable with all of the simple intervals first and use the subtract-seven rule to figure out the rest.
A Graph of the Musical Intervals
We’ve put together a graph of every musical interval through the augmented octave. Above this, just use the subtract-seven rule to figure out what notes an interval is made up of.
|Number of Semitones||Interval Name||Example|
|1||Minor Second||C to Db|
|2||Major Second||C to D|
|3||Augmented Second||C to D#|
|3||Minor Third||C to Eb|
|4||Major Third||C to E|
|4||Diminished Fourth||C to Fb|
|5||Perfect Fourth||C to F|
|6||Augmented Fourth||C to F#|
|6||Diminished Fifth||C to Gb|
|7||Perfect Fifth||C to G|
|8||Augmented Fifth||C to G#|
|8||Minor Sixth||C to Ab|
|9||Major Sixth||C to A|
|9||Diminished Seventh||C to Bbb|
|10||Minor Seventh||C to Bb|
|11||Major Seventh||C to B|
|11||Diminished Octave||C to Cb|
|12||Perfect Octave||C to C|
|13||Augmented Octave||C to C#|