Intervals: the alphabet of harmony
Learn the names, sizes and fretboard shapes of every interval inside an octave, how intervals invert, and how to start hearing them.
Why intervals come first
Every chord symbol, scale formula and voicing in this course is a list of intervals measured from a root. "The 3rd of F7", "a b9 on the V chord", "move that voicing up a minor 3rd": none of those instructions mean anything until you can see and hear the distance between two notes. Intervals are also the smallest unit your ear can learn. Players who can hear a major 3rd against a minor 3rd can tell a major chord from a minor chord, which is the beginning of learning tunes by ear.
This lesson gives you the vocabulary (names and semitone sizes), the shapes (where each interval lives relative to a root on strings 6, 5 and 4), the rule of inversion, and a daily routine for hearing them. You need the note names from the fretboard lesson to get the most out of it.
Two parts to every interval name
An interval has a number and a quality.
The number counts letter names, including both ends. From C up to E is a 3rd (C, D, E: three letters). From C up to A is a 6th. From C to the next C is an 8th, usually called an octave. Counting letters is why the number never depends on sharps or flats: C to Eb and C to E are both 3rds, just different kinds of 3rd.
The quality says exactly how big the interval is in semitones (frets). Unisons, 4ths, 5ths and octaves are called perfect when they are their normal size. 2nds, 3rds, 6ths and 7ths come in major and minor flavours, the minor being one semitone smaller than the major. Any interval made one semitone bigger than major or perfect is augmented; one semitone smaller than minor or perfect is diminished.
The engine-generated table below is the reference you should memorise. Note the "Inversion" column; we come back to it.
| Symbol | Name | Semitones | From C | Inversion |
|---|---|---|---|---|
| P1 | perfect unison | 0 | C → C | P8 |
| m2 | minor second | 1 | C → Db | M7 |
| M2 | major second | 2 | C → D | m7 |
| m3 | minor third | 3 | C → Eb | M6 |
| M3 | major third | 4 | C → E | m6 |
| P4 | perfect fourth | 5 | C → F | P5 |
| A4 | augmented fourth | 6 | C → F# | d5 |
| P5 | perfect fifth | 7 | C → G | P4 |
| m6 | minor sixth | 8 | C → Ab | M3 |
| M6 | major sixth | 9 | C → A | m3 |
| m7 | minor seventh | 10 | C → Bb | M2 |
| M7 | major seventh | 11 | C → B | m2 |
| P8 | perfect octave | 12 | C → C | P8 |
Read the table in frets: a minor 2nd is one fret, a major 2nd is two frets, a minor 3rd is three frets, and so on up to the octave at twelve frets. The augmented 4th (six frets, exactly half an octave) is the famous tritone, and it has two legal names: from C, six semitones up is F# if you count it as a 4th (C to F is four letters) and Gb if you count it as a 5th (C to G). The name you use depends on the key and the chord; the sound is identical.
P = perfect, M = major, m = minor, A = augmented, d = diminished, followed by the number: P5, M3, m7, A4, d5. Chord symbols use their own shorthand (b9 means a minor 9th, #11 an augmented 11th); you will meet those in later modules.
Interval shapes from a root on the 6th string
The fastest way to see an interval is to fix a root and learn where each interval sits relative to it. Here is every interval inside an octave from C at the 8th fret of the 6th string. Each pair is played root then interval note, so you also hear the sound. The whole exercise sits between frets 6 and 10; shift your hand slightly rather than stretching.
alphaTex source
\tempo 72
.
\ts 4 4
:4 8.6{txt "R"} 9.6{txt "m2"} 8.6 10.6{txt "M2"} | 8.6 6.5{txt "m3"} 8.6 7.5{txt "M3"} | 8.6 8.5{txt "P4"} 8.6 9.5{txt "A4"} | 8.6 10.5{txt "P5"} 8.6 6.4{txt "m6"} | 8.6 7.4{txt "M6"} 8.6 8.4{txt "m7"} | 8.6 9.4{txt "M7"} 8.6 10.4{txt "P8"} |Look at the map and you will see the logic of the fretboard: the next string up is a perfect 4th (same fret), so every interval on string 5 is "a 4th plus something". The 5th is one string up and two frets higher; the major 3rd is one string up and one fret back; the octave is two strings up and two frets higher, the shape you already know. This map is movable: slide the root to any fret on string 6 and every interval moves with it.
The same shapes from a root on the 5th string
Strings 5, 4 and 3 are also tuned in 4ths, so the whole map moves across unchanged. Here the intervals are played as harmonic intervals (both notes together), which is how you will meet them inside chords. The root is C at the 3rd fret of the 5th string.
alphaTex source
\tempo 60
.
\ts 4 4
:2 (3.5 1.4){txt "m3"} (3.5 2.4){txt "M3"} | (3.5 3.4){txt "P4"} (3.5 4.4){txt "A4"} | (3.5 5.4){txt "P5"} (3.5 1.3){txt "m6"} | (3.5 2.3){txt "M6"} (3.5 3.3){txt "m7"} | (3.5 4.3){txt "M7"} (3.5 5.3){txt "P8"} |Practise this block slowly, then play the same pairs from other roots on string 5 (try fret 1, fret 5 and fret 8) naming the actual notes: "C and E, major 3rd" becomes "F and A, major 3rd" when the root moves to fret 8.
Crossing to the B string
Because the 2nd string is tuned a major 3rd above the 3rd string instead of a 4th, every shape that crosses from string 3 to string 2 moves up one fret. Compare the major 3rd and perfect 4th from a root on string 4 with the same intervals from a root on string 3.
alphaTex source
\tempo 60
.
\ts 4 4
:2 (10.4 9.3){txt "M3 from str 4"} (10.4 10.3){txt "P4"} | (5.3 5.2){txt "M3 from str 3"} (5.3 6.2){txt "P4"} |Nothing changes for roots on string 2 moving to string 1: that pair is a 4th again. Memorise this one adjustment now and triad and chord shapes in the rest of the module will make sense immediately.
Inversion: flip the interval
If you take the lower note of an interval and move it up an octave, you have inverted it. The new interval is always found by two rules: the numbers add up to 9 (a 3rd inverts to a 6th, a 2nd to a 7th, a 4th to a 5th) and the quality flips (major becomes minor, minor becomes major, augmented becomes diminished, perfect stays perfect). Check these against the "Inversion" column of the table above.
alphaTex source
\tempo 66
.
\ts 4 4
:4 3.5{txt "C"} 2.4{txt "E (M3 up)"} (3.5 2.4).2 | :4 2.4{txt "E"} 5.3{txt "C (m6 up)"} (2.4 5.3).2 | :4 3.5{txt "C"} 5.4{txt "G (P5 up)"} (3.5 5.4).2 | :4 5.4{txt "G"} 5.3{txt "C (P4 up)"} (5.4 5.3).2 |Why does this matter? Guitar voicings constantly spread notes across octaves. The 3rd and 7th of a chord, which you will learn to call guide tones, sit a 5th apart in one voicing and a 4th apart in the next, but the names of the notes never change. Thinking in inversions lets you recognise the same two notes whatever order they appear in.
Intervals and the sound of chords
A quick preview of the next lessons: a major triad is a major 3rd with a minor 3rd stacked on top; a minor triad is the other way round. A dominant 7th chord contains a tritone between its 3rd and 7th, which is why it sounds unstable and wants to resolve. You will build these in the triads lesson; for now just notice when you play the harmonic intervals above which ones sound restful (the 3rds, 6ths, 5th and octave) and which ones are tense (the 2nds, 7ths and the tritone). Jazz uses the tense ones on purpose.
Hearing intervals
Knowing the shapes is half the job. Spend five minutes a day on the ear trainer with intervals in melodic mode (one note after the other). Start with four: P5, P4, M3 and m3. Add the octave and the M2 when those are reliable, then the 6ths and 7ths, and finally the tritone and the m2.
Two techniques help enormously:
- Sing before you play. Play a root, sing the interval, then check on the guitar. Your voice is the most honest ear-training device you own.
- Anchor on sounds you already know. A perfect 5th is the sound of a power chord; a perfect 4th is the sound of two adjacent open strings. For the others, make up a short two-note phrase of your own and keep it as a reference; a phrase you invented and play daily is more reliable than a half-remembered song opening.
Exercises
- Name the shape. Put your first finger on any 6th-string root. Without playing, point to the m3, M3, P4, P5, m7 and M7. Then play each and sing it. Move the root and repeat. Do this on string 5 as well.
- Interval on one string. Play a root, then play each interval from m2 to P8 on the same string (1 fret, 2 frets, 3 frets and so on). This connects the semitone count with the sound.
- Random intervals. Shuffle the thirteen interval names, pick a root and play them in the shuffled order, both melodically and harmonically, saying the second note's name aloud.
- Inversions. Play a M3 from a root on string 5, then invert it (lower note up an octave, as in the block above). Repeat with m3, P4, M2 and M7.
- Shapes (10 min): exercises 1 and 3 from roots C, F, Bb and Eb on strings 6 and 5, metronome at 60 bpm, one interval per beat.
- Ear (5 min): ear trainer, melodic intervals, start with P5, P4, M3, m3; add one new interval every two days.
- Singing (5 min): play a root, sing each interval of the "Harmonic intervals from C on string 5" block before you play it.
- Reading (5 min): play the "Intervals ascending from C on string 6" block from roots at frets 3, 5 and 10, naming both notes of each pair. Target by the end of the week: name and play any interval from any root on strings 6 and 5 within two seconds, and identify P5, P4, M3 and m3 by ear nine times out of ten.