In previous tutorials we learned about notes Notes that are the basic sounds in music. We then learned that it’s a good idea to group them into scales… the most important of which is the Major Scale.

The next level is to understand the relationships between notes. The relationships are viewed as the distance between notes. In this tutorial we learn about the intervals.

What’s an interval?

• In music an interval is the distance between two notes
• There are melodic intervals where you play one note and then the next
• There are harmonic intervals where the two notes are played together
• Being able to name and identify intervals is useful for a better understanding of music

The Major Scale and Intervals

• In the Major Scale Tutorial you learned all about the Major Scale
• It turns out the major scale is used to understand a lot of other music theory
• Interval names are based on the major scale steps

C	D	E	F	G	A	B	C
unison	2nd	3rd	4th	5th	6th	7th	octave

• The simplest way of naming intervals is in relation to the major scale (The C major scale is shown above)
• The distance from the tonic (the first note) to any other step is the numerical distance. So above C to E is a 3rd, C to A is a 6th, C to B is a 7th, etc.
• C to the same octave C is called unison (this pair can’t be played on a piano but is possible on a guitar for e.g.)
• C to the next highest C is called an octave

• There are also in between intervals that are not part of the major scale
• We need a way to say that “this interval is in the major scale” or “this interval is not in the major scale”
• As with a lot of music theory it is a bit more involved than you’d expect

C	D	E	F	G	A	B	C
perfect unison	2nd	3rd	perfect 4th	perfect 5th	6th	7th	perfect octave

• For historical reason the unison, 4th, 5th and octave were considered special
• They are called “perfect” intervals
• Above the “perfect” intervals have been labeled
• Remember that when you see “perfect” in front of those intervals it means that the note for that interval is part of the major scale

C	D	E	F	G	A	B	C
perfect unison	major 2nd	major 3rd	perfect 4th	perfect 5th	major 6th	major 7th	perfect octave

• To indicate that the 2nd, 3rd, 6th or 7th are in the major scale they are simply called major
• The diagram above has been labeled with all the perfect and major intervals. The picture for intervals in the major scale is complete

• Just as there there are notes that are named based on the notes around them the same applies to intervals that are not in the major scale
• We change the name to indicate if an interval is above or below the major scale step. But as you might have guessed the “major” and “perfect” in between steps are named differently

• To lower a perfect interval you “diminish” it
• To raise a perfect interval you “augment” it
• Using the 5th of the C major scale above for example:
  • G♭ is a “diminished 5th”
  • G# is an “augmented fifth”

• The naming for major interval adjustment is a little different
• To lower a major interval you make it “minor”
• To raise a major interval you also “augment” it
• Just using the 3rd of the C major scale as an example:
  • E♭ is a “minor third”
  • E# is an “augmented third”
• Some intervals are more common than others

• There are short forms to make naming intervals more compact
• The table below summarizes the short forms

Perfect	P
Major	M
Minor	m
Diminished	d
Augmented	A

• Notice that some letters are capital and others not

• The diagram above shows the intervals for the C major scale (which runs down the center)
• Top left of each box is the interval quality (using the short form)

• The diagram was created with the Interval Explorer tool found in both Smart Interval Trainer and Smart Piano Keyboard Interval Trainer. It lets you explore the intervals in all keys

Perfect 5th	P5	5
Minor 3rd	m3	3
Augmented 4th	A4	#4
Minor 6th	m6	♭6
Major 3rd	M3	3
Diminished 5th	d5	♭5

• There are other short hand methods of naming intervals
• One that is common is to use the scale degree plus sharp/flat
• The table above shows some examples

Summary:

• An interval is the distance between two notes
• Intervals are named relative to the Major scale
• There are ways of indicating an interval is in or out of the Major scale
• The unison, 4th, 5th and octave are called “perfect” intervals
• The 2nd, 3rd, 6th and 7th are “major” intervals
• A perfect (P) interval can be augmented (A) or diminished (d)
• A major (M) interval is made minor (m) or augmented (A)

Apps to assist you:

Having memorized the intervals in all keys opens the doors to a lot of theory and will take you to the next step in your understanding of music. A future tutorial will explain all the reasons intervals are useful. We have two apps specially designed to help you to learn the intervals:

• Smart Interval Trainer: Learn the intervals by note name independent on any instrument. This ensures you know your intervals by name and not just visually
• Smart Piano Keyboard Interval Trainer: Learn the intervals on a piano keyboard

Back: The Major Scale  Next: Why Intervals?