Intervals - Fundamentals of Music Theory

Intervals - Fundamentals of Music Theory

Now that we have introduced you to the basics of music theory, let's take a look at one of the most fundamental building blocks of music theory, the interval. If you are already confident with intervals, feel free to jump into a later section using the navigation below.

What is an Interval?

An interval is a distance between two notes represented by a name which consists of a word describing its quality and a number to help identify the end note's letter name.

Intervals can be classed as Melodic or Linear if the notes of the interval are different (so ascending or descending in pitch), and are played one after the other. If the two notes of an interval are played at the same time, as in a chord, then it is classed as a Harmonic interval. If the notes are the same i.e. you play the same note twice, the interval is classed as a Unison.

Interval Number

Without getting into too much detail about scales and modes (covered in the next sections), the most commonly used scales such as Major scale, Natural minor scale, and all of the modes, are all known as diatonic. One of the main characteristics of a diatonic scale is that it has 7 notes, 8 if you include the octave note. So it follows that there are 8 intervals in a diatonic scale, including the root itself and the octave, that describe the distance from the root note of the scale to each of the notes.

Let's take for example a Major 3rd interval in the C Major scale (C, D, E, F, G, A, B). The root note of the scale is C. The number of letters starting from the root note is 3. So if we count 3 notes of the scale, starting from the root, then our 3rd would be an E.

But wait, there are twelve chromatic notes available in an octave including the sharp/flat notes, each a semitone apart. How can we apply this diatonic number that only has seven numbers in an octave? This is where the quality of the interval comes in.

Interval Quality

Continuing with this same example of a Major 3rd interval in the C Major scale (C, D, E, F, G, A, B), let's break the scale down into its scale pattern of T, T, S, T, T, T, S. (Don't worry, this is covered in more detail later) This tells us that there is a tone (1 tone = 2 semitones) between the first root note and the second note (C, C♯, D). This is followed by another tone to get to the third note (D, D♯, E). So it can be said that a Major 3rd interval is 2 tones or 4 semitones.

Let's look at another example. Again a 3rd, but this time in the C Natural Minor scale (C, D, E, F, G, A, B). The pattern for this scale is T, S, T, T, S, T, T. This tells us that there is a tone between the first root note and the second note (C, D, D) and is followed by a semitone to get to the third note (D, E). So this time around the 3rd interval is only 3 semitones compared with 4 semitones in the previous Major scale example. So how can we distinguish between these two intervals? Both are 3rds but the end note is different. In this case the interval is called a minor 3rd.

Interval quality helps us to identify these differences in sizes when we use a diatonic number (1 to 7) to express an interval across the 12 chromatic notes. So far we have used Major and minor qualities. We also have Perfect, Diminished and Augmented qualities, the latter two of which aren't found in the Major scale. There are of course many scales and chords and these additional qualities help us to express those intervals. Diminished means lowered by a semitone, Augmented raised by a semitone. It is also worth noting that every Major, minor or Perfect interval can also be expressed as a Diminished or Augmented interval.

The following table details all the common Major, minor and Perfect intervals and their Diminished / Augmented equivalents. The abbreviated name for each is shown in brackets afterwards.

Semitones From RootMajor, minor & Perfect IntervalsDiminished & Augmented IntervalsNote Example
0Perfect Unison (P1)Diminished 2nd (d2)C > C
1minor 2nd (m2)Augmented Unison (A1)C > C♯
2Major 2nd (M2)Diminished 3rd (d3)C > D
3minor 3rd (m3)Augmented 2nd (A2)C > D♯
4Major 3rd (M3)Diminished 4th (d4)C > E
5Perfect 4th (P4)Augmented 3rd (A3)C > F
6Diminished 5th (d5 or Tritone)C > F♯
Augmented 4th (A4 or Tritone)
7Perfect 5th (P5)Diminished 6th (d6)C > G
8minor 6th (m6)Augmented 5th (A5)C > G♯
9Major 6th (M6)Diminished 7th (d7)C > A
10minor 7th (m7)Augmented 6th (A6)C > A♯
11Major 7th (M7)Diminished OctaveC > B
12Perfect Octave (P8)Augmented 7th (A7)C > C (+1 Octave)

A couple of points to note here:

Firstly, did you notice that minor intervals are shown with a lowercase m in both the long and abbreviated versions? In contrast, Major and Perfect intervals are shown with a capital letter. This isn't a hard and fast rule when it comes to the long names (although it is very common), but it is an accepted standard for the abbreviations. Same goes for the diminished and Augmented abbreviations.

The second thing of note is what we find for a 6 semitones interval. As the 4th (5 semitones) and 5th (7 semitones) intervals are normally expressed as Perfect, and not Major or minor, this interval must be expressed as either an Augmented 4th or a Diminished 5th. It is also known as the Tritone, Tri meaning 3, in other words 3 tones which is equivalent to 6 semitones. Another point of interest is that the Tritone is right in the middle of the 12 note Chromatic scale of all notes.

Compound Intervals

So far we have discussed only simple intervals that fit within one octave. Generally, scales within Western music all fit within one octave and then the scale pattern repeats. There are scales, particularly in Eastern music, that span multiple octaves but we won't be discussing those here. So, how do we describe intervals that are larger than an octave but still follow the repeating pattern of a scale? We simply continue with the same numbering as before and apply the same qualities as we did in the first octave.

Semitones From RootMajor, minor & Perfect IntervalsDiminished & Augmented IntervalsNote Example
12Perfect Octave (P8)Diminished 9th (d9)C > C (+1 Octave)
13minor 9th (m9)Augmented Octave (A8)C > C♯ (+1 Octave)
14Major 9th (M9)Diminished 10th (d10)C > D (+1 Octave)
15minor 10th (m10)Augmented 9th (A9)C > D♯ (+1 Octave)
16Major 10th (M10)Diminished 11th (d11)C > E (+1 Octave)
17Perfect 11th (P11)Augmented 10th (A10)C > F (+1 Octave)
18Diminished 12th (d12)C > F♯ (+1 Octave)
Augmented 11th (A11)
19Perfect 12th (P12)Diminished 13th (d13)C > G (+1 Octave)
20minor 13th (m13)Augmented 12th (A12)C > G♯ (+1 Octave)
21Major 13th (M13)Diminished 14th (d14)C > A (+1 Octave)
22minor 14th (m14)Augmented 13th (A13)C > A♯ (+1 Octave)
23Major 14th (M14)Diminished 15th (d15)C > B (+1 Octave)
24Perfect 15th (P15)Augmented 14th (A14)C > C (+2 Octave)

These compound intervals are known as such because they can also be described as a combination of two or more intervals. For example a Major 10th (16 semitones) can be expressed as a compound Major 3rd. In other words an Octave plus a Major 3rd (12 semitones + 4 semitones). Another way of looking at compound intervals is to subtract 7 from the interval number to help find what the end note is, then play that note one octave higher.

Whilst you may come across compound intervals in a melody, you will rarely see them used to describe the intervals within a scale that is popular in Western music as those scales mostly only span one octave. You will however see compound intervals a lot when expressing harmony, in particular within chords.

Inverted Intervals

Just as we can describe the distance between a root note and another note above it, we can also describe an interval between the root note and a note below it. This is known as an inverted interval. Once again, let's use the C Major Scale as an example but across two octaves this time.

C, D, E, F, G, A, B, C, D, E, F, G, A, B, C

This distance from the root C (shown in the middle) to the E above it is a Major 3rd (4 semitones). But we can also say that the inverted interval from the root C to the E below it is a minor 6th (8 semitones).

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