# AI Wiki - Music - Intervals ## Overview An interval is the distance between two notes. Every chord and scale is a set of intervals measured from a root, so intervals are the vocabulary the rest of theory is written in: a major triad is "root, major third, perfect fifth", a major scale is "whole, whole, half, whole, whole, whole, half", a dominant seventh adds a minor seventh. The smallest step in Western music is the **semitone** (half step): one fret on the guitar, one key on the piano (black keys included). Two semitones make a **whole tone** (whole step). On the piano the white-key pairs E–F and B–C are only a semitone apart because there is no black key between them; every other pair of neighbouring white keys is a whole tone. When the two notes sound together it's a **harmonic interval** (a double stop, a chord); one after the other it's a **melodic interval** (a melody, an arpeggio). ## How intervals are named An interval name has two parts: a **number** (generic size) and a **quality**. **The number counts letter names, inclusively.** C to E is a third because C, D, E spans three letters. C to G is a fifth (C D E F G). Unison (same note) is a "first", the octave an "eighth". Accidentals don't change the number: C to E♭ and C to E♯ are both thirds. **The quality is fixed by the exact semitone count.** Unisons, fourths, fifths and octaves are **perfect**; seconds, thirds, sixths and sevenths are **major** or **minor** (minor = one semitone smaller than major). One semitone larger than perfect or major is **augmented**; one smaller than perfect or minor is **diminished**. | Semitones | Interval | Short | From C | From A | Guitar (same string) | |---|---|---|---|---|---| | 0 | Perfect unison | P1 | C | A | same fret | | 1 | Minor second | m2 | D♭ | B♭ | +1 fret | | 2 | Major second | M2 | D | B | +2 | | 3 | Minor third | m3 | E♭ | C | +3 | | 4 | Major third | M3 | E | C♯ | +4 | | 5 | Perfect fourth | P4 | F | D | +5 | | 6 | Augmented fourth / diminished fifth (tritone) | A4 / d5 | F♯ / G♭ | D♯ / E♭ | +6 | | 7 | Perfect fifth | P5 | G | E | +7 | | 8 | Minor sixth | m6 | A♭ | F | +8 | | 9 | Major sixth | M6 | A | F♯ | +9 | | 10 | Minor seventh | m7 | B♭ | G | +10 | | 11 | Major seventh | M7 | B | G♯ | +11 | | 12 | Perfect octave | P8 | C | A | +12 | The chromatic scale from C, labelled by interval from the root, shows the whole table on one octave of keys. Chord symbols use the same shorthand: `b3` is a minor third, `b7` a minor seventh, `b5` the diminished fifth. ```keyboard scale: C chromatic labels: intervals range: C4-C5 ``` **Spelling matters.** C–F♯ (augmented fourth) and C–G♭ (diminished fifth) are the same six semitones and sound identical on a guitar or piano, but they are spelled from different letters and play different roles. These are **enharmonic** intervals. The six-semitone interval is the **tritone**: three whole tones, exactly half an octave, and the tense interval at the heart of the dominant seventh chord (see [[AI Wiki - Music - Seventh Chords]]). ## The intervals of the major scale Measured from the tonic, every note of a major scale forms a major or perfect interval: M2, M3, P4, P5, M6, M7, P8. That is why the major scale is the yardstick: "minor third" means "one semitone below the third of the major scale". The flatted labels in chord formulas (b3, b7) are relative to this reference. See [[AI Wiki - Music - Major Scale]] and [[AI Wiki - Music - Minor Scales]]. ```keyboard scale: C major labels: intervals range: C4-C5 ``` ## Inversion and compound intervals **Inverting** an interval puts the lower note an octave up. The two numbers always add up to nine and the two semitone counts to twelve; major becomes minor, augmented becomes diminished, perfect stays perfect. C up to E is a major third (4 semitones); E up to C is a minor sixth (8). C up to G is a perfect fifth; G up to C is a perfect fourth. This is why a fourth and a fifth feel related, and why a tritone inverts to another tritone. **Compound intervals** are wider than an octave: an octave plus a simple interval. A ninth is an octave plus a second (a major ninth is 14 semitones), an eleventh an octave plus a fourth, a thirteenth an octave plus a sixth. They keep the quality of their simple interval. Chord names use them: Cadd9 adds D (the ninth), not because D is far away on the keyboard but to say "this is an extension above the chord, not a replacement for the third". See [[AI Wiki - Music - Suspended and Added-Tone Chords]]. ## Consonance and dissonance Which intervals sound stable depends on style, but in tonal music the octave, fifth, fourth, and major and minor thirds and sixths are treated as consonant; seconds, sevenths and the tritone as dissonant, creating tension that tends to resolve to a consonance. The third is the interval that makes a chord major or minor; the fifth gives it weight and stability (a power chord is just root and fifth). See [[AI Wiki - Music - Triads]] and [[AI Wiki - Music - Power Chords]]. ## On guitar On one string, an interval is just a fret count. Across strings, standard tuning makes adjacent strings a **perfect fourth** apart (5 frets), except **G to B, which is a major third** (4 frets). So an interval shape keeps its form as you move it around, but every shape that crosses the G–B pair shifts **one fret higher** on the B string. | Interval up from a root | Shape (strings below the G–B pair) | Crossing G → B | |---|---|---| | Major third | next string up, one fret lower | next string up, same fret | | Perfect fourth | next string up, same fret | next string up, one fret higher | | Perfect fifth | next string up, two frets higher | next string up, three frets higher | | Octave | two strings up, two frets higher | two strings up, three frets higher | Example with A: low E string fret 5 (A2), octave on the D string fret 7 (A3); from there the next octave is on the B string fret **10** (A4), not 9, because the shape crosses G–B. The perfect fifth of A2 is E on the A string fret 7: the power-chord shape. Root, fifth and octave together form the **L** shape; [[AI Wiki - Music - Fretboard Interval Shapes|Fretboard Interval Shapes]] covers every interval shape on the neck, with diagrams and drills. Every A on the neck (octave shapes): ```fretboard notes: A frets: 0-12 ``` Root and fifth everywhere for A (the A5 power chord): note the fifth sits one fret further on the B string. ```fretboard chord: A5 frets: 0-12 labels: intervals ``` More on mapping these shapes in [[AI Wiki - Music - Guitar Fretboard Navigation]]. ## On piano Count keys, black and white, starting from the key after the lower note: C to E = C♯, D, D♯, E = 4 semitones = major third. White-key thirds from C, F and G (C–E, F–A, G–B) are major; from D, E, A and B they're minor. White-key fifths are all perfect except B–F, a diminished fifth. With the hand, a third usually spans fingers 1–3, a fifth 1–5. See [[AI Wiki - Music - Piano Keyboard Layout]]. ## How to practise 1. **Learn the table cold**: name the interval from any two notes, and the note from any root and interval (C up a minor sixth = A♭). 2. **On the fretboard**: from a root on the low E and A strings, find the third, fifth and octave without counting. Then do it across the G–B pair. 3. **On the piano**: play every major third and perfect fifth starting on each white key; notice which come out minor or diminished. 4. **By ear**: sing intervals against a drone, and tie each to a reference melody. Common ones (ascending): m2 *Jaws*; M2 *Happy Birthday*; m3 *Greensleeves*; M3 *When the Saints Go Marching In*; P4 *Here Comes the Bride*; tritone *The Simpsons*; P5 *Star Wars* (main theme); M6 *My Bonnie Lies Over the Ocean*; P8 *Somewhere Over the Rainbow*. See [[AI Wiki - Music - Interval Recognition]] and [[AI Wiki - Music - Ear Training]]. ## Common mistakes - Counting semitones from 1 instead of 0 (the starting note is zero). - Counting interval numbers exclusively (C to E is a third, not a second). - Ignoring spelling: in A major the third is C♯, not D♭, even if the key is the same. - Forgetting the G–B shift when moving a shape across strings. ## Key Points - Interval = number (letter count, inclusive) + quality (perfect, major, minor, augmented, diminished), fixed by semitones. - Semitones: m3 = 3, M3 = 4, P4 = 5, tritone = 6, P5 = 7, m7 = 10, M7 = 11, octave = 12. - Major-scale intervals from the tonic are all major or perfect; "b3", "b7" are measured against them. - Inversion: numbers sum to 9, semitones to 12; major ↔ minor, augmented ↔ diminished, perfect stays perfect. - On guitar, adjacent strings are a fourth apart except G–B (a third): shapes crossing that pair move up one fret. ## Open Questions - Which reference songs stick best for descending intervals? - How fast does interval naming on the fretboard become automatic with daily drills? ## References - Interval (music) — Wikipedia: https://en.wikipedia.org/wiki/Interval_(music) - Generic Intervals — musictheory.net: https://www.musictheory.net/lessons/30 - Specific Intervals — musictheory.net: https://www.musictheory.net/lessons/31 - Interval Inversion — musictheory.net: https://www.musictheory.net/lessons/33 - Song references for interval ear training — JustinGuitar: https://www.justinguitar.com/modules/ear-training-reference ## Related - [[AI Wiki - Music - Triads]] - [[AI Wiki - Music - Seventh Chords]] - [[AI Wiki - Music - Suspended and Added-Tone Chords]] - [[AI Wiki - Music - Major Scale]] - [[AI Wiki - Music - Minor Scales]] - [[AI Wiki - Music - Power Chords]] - [[AI Wiki - Music - Guitar Fretboard Navigation]] - [[AI Wiki - Music - Piano Keyboard Layout]] - [[AI Wiki - Music - Ear Training]] - [[AI Wiki - Music - Interval Recognition]] - [[AI Wiki - Music - Arpeggios]] - [[AI Wiki - Music - Reading Standard Notation]] - [[AI Wiki - Music - Alternate Tunings]] - [[AI Wiki - Music - Blues Music]] - [[AI Wiki - Music - CAGED System]] - [[AI Wiki - Music - Capo and Transposition]] - [[AI Wiki - Music - Chord Quality Recognition]] - [[AI Wiki - Music - Circle of Fifths]] - [[AI Wiki - Music - Diatonic Chords and Roman Numerals]] - [[AI Wiki - Music - Functional Ear Training]] - [[AI Wiki - Music - Guitar Lead Techniques]] - [[AI Wiki - Music - Keys and Key Signatures]] - [[AI Wiki - Music - Pentatonic Scale]] - [[AI Wiki - Music - Relative and Perfect Pitch]] - [[AI Wiki - Music - Solfege and Singing]] - [[AI Wiki - Music - Fretboard Interval Shapes]]