This post is one of a 2-part series of free basic music theory lessons on my blog, musictheoryde-mystified.com. You can see the complete list here. Please feel welcome to make a comment or ask a question.
Keys and key relationships are two of the most important concepts in music theory. If you’re not sure about these, please visit 11. Introduction To Keys and Key Signatures: Major Keys and the following two posts.
Interval names are equally important. Among other uses, interval names form the basis for understanding chords and chord names.
Melodic and Harmonic Intervals
An interval is the pitch difference between two notes. Intervals occur both as consecutive notes in a melody, or as two notes sounding together such as a melody and harmony. When more than two notes sound together, such as in a chord, there are multiple intervals between the various notes.
Not surprisingly, the interval between consecutive notes is called a melodic interval and that between two notes sounding together is called a harmonic interval (some call it a vertical interval). We count and name intervals the same way in both cases, from the lower note to the higher note.
Intervals are counted from the lower note to the higher note, even if the higher note comes before the lower note in a melody.
Singing A Scale
Trained musicians, including musicians who play by ear, are able to count the intervals from one note to the next in a melody or chord by mentally (or physically) singing the notes of a scale, starting on the lower note and finishing on the higher note. This is actually a very useful skill worth developing. Such general musical skills are called musicianship and form a bridge between theory and practice.
In the coming lessons I intend to look a a few basic musicianship skills including how to count intervals by singing.
Naming Intervals By Counting Scale Notes
So far we have described the interval between two notes in two ways; by counting letters and by counting semitones. Neither are enough.
- Counting letters doesn’t distinguish between sharps, flats or naturals so the number of semitones can vary: A-C and A-C# are not the same interval.
- Counting semitones doesn’t guarantee that we end up with the right note names: A-C# and A-Db have the same number of semitones but use different note names.
As we’ll continue to find out, note names are important. The choice of note name reflects how that note functions in a given context. We want a way of measuring the size of an interval that also tracks the note names; a method that counts both semitones and letters. Scale notes do just that.
To count in scale notes we use a major and a minor scale whose root note is the same as the lower note of the interval; the parallel major and minor. If the lower note is A, we use A major and A minor.
However, instead of using the aeolian mode, the natural minor, we use the phrygian mode. The phrygian mode has four notes that differ from the major instead of three; the 2nd, 3rd, 6th and 7th notes, as opposed to just the 3rd, 6th and 7th notes.
Think of the phrygian mode as being more minor than minor, or the super-minor…
Even though we’re now using the phrygian mode we still call it “minor” for interval names. I will mark this minor with an asterisk * as a reminder that it’s the phrygian rather than aeolian mode.
The Interval Ruler
We can hone this down a little: the 2nd, 3rd, 6th and 7th notes of the minor are 1 semitone lower than the major, so as a shortcut we can just write out the major scale and flatten the 2nd, 3rd, 6th and 7th note to find the minor intervals. I call this an interval ruler.
Remember that to flatten a note we lower it by 1 semitone without changing its letter. A sharp becomes a natural, a natural becomes a flat and a flat becomes a double flat.
Here is the interval ruler for an interval whose lower note is A. The degree numbers are written below. Each scale degree shows the number of semitones from the root note to that note.
Major, Minor and Perfect Intervals
There are three main types of interval names; major, minor and perfect, based upon the following conditions:
- If the upper note of the interval is only in the major scale on the lower note, the interval is major.
- If the upper note of the interval is only in the *minor scale on the lower note, the interval is minor.
- If the upper note of the interval is common to both scales, the interval is perfect.
We call this part the quality of the interval.
Perfect-type intervals are marked in green and major/minor type intervals in blue.
The other part of the interval name is the degree of the interval; the number of scale notes or letters including the first and last.
For instance, in the interval A to C#, the upper note, C#, is the 3rd note of the major scale on A, the lower note. A-C# is a major 3rd.
How To Name An Interval:
- Write the lower note of the interval in the ruler as the root note and add the notes of the major key.
- Now flatten the 2nd, 3rd, 6th and 7th note for the *minor as indicated by the red arrows.
- Next, look in the ruler for the upper note of the interval.
- The interval name is made up of the quality; major, minor or both (=perfect), and the degree.
In the above example, A-C# is a major 3rd (= 4 semitones).
Similarly, A-C is a minor 3rd (= 3 semitones), A-D is a perfect 4th (= 5 semitones), etc.
- 1st, 4th, 5th and 8th are perfect-type intervals.
- 2nd, 3rd, 6th and 7th are major/minor type intervals, depending on which scale the upper note is in.
As well as the octave, we’ve already met three intervals:
- Minor 3rd (3 semitones to the 3rd letter) – the interval between the root notes of relative major and minor keys.
- Perfect 5th (7 semitones to the 5th letter) – the interval from any key to the next key in the cycle of 5ths.
- Perfect 4th (5 semitones to the 4th letter)- the interval from any key to the previous key in the cycle of 5ths.
An Interval Name Is Based On The Lower Note
All the examples so far assume that A is the lower note of the interval, hence we’ve used A scales for our ruler. If we want to measure an interval with a different lower note we want the interval ruler to start on that note. For example, to name the interval from G to E we would need G scales and to name the interval from Bb to Db we would need Bb scales.
G-E
E is the 6th note of G major, so G – E is a major 6th (9 semitones).
Bb-Db
Db is the 3rd note of Bb minor, so Bb – Db is a minor 3rd (3 semitones).
By now you’ll see why I was so keen on learning key signatures of major scales: knowing them makes this process a lot quicker than having to work it out on the fly! Every time we look at the interval between a pair of notes with a different lower note, we need to use a different scale for our interval ruler.
At least by using the interval ruler we only need to learn the major scale, as we can flatten the 2nd, 3rd, 6th and 7th to find the *minor (phrygian mode).
Try These…
Name the following major, minor and perfect intervals:
- F-Bb
- F-E
- F-Db
- G-B
- G-D
- G-F
- Bb-G
Answers at the end of this post.
Interval Names In Reverse: finding the upper note
So far we’ve named an existing interval. Now let’s recreate an interval from its name. We’ll pick a note to be our lower note and name the higher note based on the interval name.
For instance, let’s find the note that’s a minor 6th above E.
- First we’ll create our interval ruler on E. We’ll start with E major. The key signature of E major is 4 sharps: F#, C#, G# and D#, so the scale of E major is E, F#, G#, A, B, C#, D#, E.
- Now we’ll write E *minor below it by flattening the 2nd, 3rd, 6th and 7th notes.
- Next we look for the interval, in this case a minor 6th. Minor 6th means the upper note is the 6th note of the minor built on the lower note, so we look for the 6th note of E *minor on our interval ruler.
Minor 6th above E
An interval name means:
The higher note of the interval is the …th (degree name) note of the … (major or minor or both) scale built on the lower note.
Saying it in this way may help to remember how interval names work.
Try These…
Find the upper note in the following major, minor or perfect intervals:
- a minor 3rd above C
- a major 6th above C
- a minor 2nd above E
- a perfect 4th above E
- a minor 7th above E
- a major 2nd above Eb
- a major 7th above Eb
Interval Names As Scale Degrees
The different notes of a scale are called degrees. So far I have used the note’s position in the scale to indicate the degree, such as 3rd or 5th. We can refine this by calling the third note of a major scale the major 3rd, the 5th note of either scale the perfect 5th and so on.
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NEXT LESSON: 17. Listen & Sing: How To Sing The Major Scale
PART 1 CONTENTS: Basic Music Theory Course Contents
Answers To Try These…
- F-Bb = perfect 4th
- F-E = major 7th
- F-Db = minor 6th
- G-B = major 3rd
- G-D = perfect 5th
- G-F = minor 7th
- Bb-G = major 6th
- a minor 3rd above C = Eb
- a major 6th above C = A
- a minor 2nd above E = F
- a perfect 4th above E = A
- a minor 7th above E = D
- a major 2nd above Eb = F
- a major 7th above Eb = D