Intervals build scales and chords: a scale is a sequence of intervals above a root, and a chord is a stack of intervals above a root. The C major scale is built from the intervals 0, 2, 4, 5, 7, 9 and 11 semitones, and the C major chord is built from the intervals 0, 4 and 7.
How do intervals build scales and chords?
Intervals are the raw material of scales and chords, and the relationship is simple: a scale is a sequence of intervals above a root, and a chord is a stack of intervals above a root. The C major scale is the intervals 0, 2, 4, 5, 7, 9 and 11 semitones above C, which gives the notes C, D, E, F, G, A and B. The C major chord is the intervals 0, 4 and 7 semitones above C, which gives the notes C, E and G. The scale and the chord are built from the same material, and the chord is simply a selection of notes from the scale. That relationship explains why chords and scales fit together. A chord built from the notes of a scale will always sound at home in that scale, because every note of the chord is a note of the scale, and the intervals of the chord are intervals of the scale. The C major chord fits the C major scale because its intervals, 0, 4 and 7, are all in the scale's interval list. The D minor chord fits too, because its intervals above D, 0, 3 and 7, are the intervals of the D dorian mode, which is the C major scale starting on D. Once you see the connection, you can work out which chords belong to a scale and which scales fit over a chord.
How the interval patterns work
Every scale has an interval pattern, a list of semitone distances from the root, and every chord has one too. The major scale pattern is 0, 2, 4, 5, 7, 9, 11, which is the whole-tone and semitone pattern W, W, H, W, W, W, H. The natural minor scale pattern is 0, 2, 3, 5, 7, 8, 10, which is W, H, W, W, H, W, W. The major triad pattern is 0, 4, 7, the minor triad is 0, 3, 7, the dominant 7th is 0, 4, 7, 10, and the major 7th is 0, 4, 7, 11. Learn the patterns and you can build any scale or chord from any root, just by counting semitones. The patterns also explain the modes. The modes of the major scale are the same seven notes starting from different degrees, which means they are the same interval pattern rotated: dorian is 0, 2, 3, 5, 7, 9, 10, phrygian is 0, 1, 3, 5, 7, 8, 10, lydian is 0, 2, 4, 6, 7, 9, 11, mixolydian is 0, 2, 4, 5, 7, 9, 10, and locrian is 0, 1, 3, 5, 6, 8, 10. Each mode is a different selection of intervals, and each selection gives the mode its character. The C major scale shows the major pattern, the A minor scale shows the natural minor pattern, and the D dorian scale shows the dorian pattern.
Worked example — building the chords of C major from intervals. Start with the C major scale intervals, 0, 2, 4, 5, 7, 9, 11, and build a triad on each degree by stacking 3rds. On C, the intervals 0, 4 and 7 give C, E and G, a major triad. On D, the notes are D, F and A, and the intervals above D are 0, 3 and 7, a minor triad. On E, the notes are E, G and B, and the intervals above E are 0, 3 and 7, minor again. On F, the notes are F, A and C, intervals 0, 4 and 7, major. On G, the notes are G, B and D, intervals 0, 4 and 7, major. On A, the notes are A, C and E, intervals 0, 3 and 7, minor. On B, the notes are B, D and F, intervals 0, 3 and 6, diminished. That is the whole diatonic set, worked out from intervals alone, and the key of C major lists the same seven chords.
How to practise building scales and chords from intervals
Practise by building scales and chords from interval patterns, not by memorising note lists, so the skill transfers to every key.
- Write out the major scale interval pattern, 0, 2, 4, 5, 7, 9, 11, and build the scale on G by counting semitones from G for each interval.
- Build the triads of the key of G major from the interval patterns, and check that you get three major, three minor and one diminished triad.
- Take the C major guitar chord and work out its interval pattern above C, then build the same chord on F by counting the same intervals from F.
- Play the D dorian scale and work out its interval pattern above D, then compare it with the natural minor pattern to find the one interval that differs.
- Use the interval calculator and the scale finder to check your interval patterns before you use them in a chord or a scale.
Common mistakes
- Memorising note lists instead of interval patterns — Note lists work for one key only, while interval patterns work for all twelve. Learn the pattern, 0, 4, 7 for a major triad, and you can build the chord on any root; learn the notes of C major only, and you are stuck in C.
- Forgetting that chords come from scales — A chord that is not built from the notes of the scale will clash with it, unless the clash is deliberate. Check that every note of your chord belongs to the scale you are playing over, or the chord will sound wrong.
- Using the wrong interval pattern for the chord type — A major triad is 0, 4, 7 and a minor triad is 0, 3, 7, and mixing them up gives the wrong chord. Write the pattern down before you build the chord, and check the 3rd first, because it is the interval that decides the quality.
Quick reference
This table shows the C major scale as a list of intervals from the root, so you can see the scale and the chord built from it side by side. The first, third and fifth rows are the notes of the C major chord, C, E and G, and the interval column shows that they sit 0, 4 and 7 semitones above the root, which is the major triad pattern.
| Scale degree | Interval from C | Note | Semitones |
|---|---|---|---|
| 1st | Unison | C | 0 |
| 2nd | Major 2nd | D | 2 |
| 3rd | Major 3rd | E | 4 |
| 4th | Perfect 4th | F | 5 |
| 5th | Perfect 5th | G | 7 |
| 6th | Major 6th | A | 9 |
| 7th | Major 7th | B | 11 |
| 8th | Octave | C | 12 |
Copy the table with a different root, such as G, and fill in each column yourself: the interval name from the degree, the note by counting semitones from G, and the semitone count from the pattern. When you can build the table for any root without looking, you can build any scale and any chord, because they are all made from the same interval patterns.
Frequently asked questions
How do intervals build a scale?
A scale is a sequence of intervals above a root: the major scale is the intervals 0, 2, 4, 5, 7, 9 and 11 semitones above the root, which gives the notes of the scale. Change the intervals and you change the scale.
How do intervals build a chord?
A chord is a stack of intervals above a root: a major triad is the intervals 0, 4 and 7 semitones above the root, which gives the root, the major 3rd and the perfect 5th. Add more intervals and you get 7th chords and extended chords.
Why do chords and scales fit together?
Because a chord built from the notes of a scale contains only notes of that scale, and its intervals are intervals of the scale. The C major chord fits the C major scale because its intervals, 0, 4 and 7, are all in the scale's interval list.
What is the interval pattern of a major scale?
0, 2, 4, 5, 7, 9 and 11 semitones above the root, which is the whole-tone and semitone pattern W, W, H, W, W, W, H. The natural minor scale pattern is 0, 2, 3, 5, 7, 8 and 10, which is W, H, W, W, H, W, W.
Can I build any chord from intervals?
Yes. Every chord has an interval pattern, and counting semitones from any root using that pattern gives you the chord. A dominant 7th is 0, 4, 7, 10, a minor 7th is 0, 3, 7, 10, and a major 7th is 0, 4, 7, 11, on any root you choose.