Intervals
An interval is the distance between two pitches, measured in half steps.
The 13 Simple Intervals
| Interval | Half Steps | Sound |
|---|---|---|
| Perfect Unison (P1) | 0 | Identity |
| Minor 2nd (m2) | 1 | Tense, dissonant |
| Major 2nd (M2) | 2 | Open, whole step |
| Minor 3rd (m3) | 3 | Sad, minor quality |
| Major 3rd (M3) | 4 | Happy, major quality |
| Perfect 4th (P4) | 5 | Stable, open |
| Tritone (TT) | 6 | Maximum tension |
| Perfect 5th (P5) | 7 | Strong, consonant |
| Minor 6th (m6) | 8 | Bittersweet |
| Major 6th (M6) | 9 | Warm, sweet |
| Minor 7th (m7) | 10 | Bluesy, dominant |
| Major 7th (M7) | 11 | Bright, leading tone tension |
| Perfect Octave (P8) | 12 | Same note, higher |
Consonance and Dissonance
Perfect consonances: unison, octave, perfect 5th. These are the most stable intervals, anchoring harmony since ancient times. Imperfect consonances: major and minor 3rds and 6ths. These define chord quality (major vs. minor) and form the basis of triadic harmony. Dissonances: 2nds, 7ths, and the tritone. These create tension that demands resolution. The tritone (augmented 4th / diminished 5th) is the most unstable interval and drives dominant-to-tonic resolution.Compound Intervals
Any interval wider than an octave is compound. A 9th is an octave + a 2nd (14 half steps). An 11th is an octave + a 4th (17 half steps). A 13th is an octave + a 6th (21 half steps). These are critical in jazz harmony as chord extensions.
Interval Inversion
Subtracting an interval from an octave gives its inversion. Major inverts to minor, perfect stays perfect, augmented inverts to diminished. A major 3rd (4 semitones) inverts to a minor 6th (8 semitones). The two always sum to 12.
On the Guitar in P4
In fourths tuning, every interval has exactly one shape across any pair of adjacent strings. A major 3rd is always the same fret pattern regardless of where you play it. This is the fundamental geometric advantage of uniform tuning.