Inversion Basics

Inversion Basics

An interval is the distance between two notes. When you reverse the direction of an interval, you create its inversion.

An interval is not the same when moving up and down. For example, if you move up a perfect 5ᵗʰ, moving down a perfect 5ᵗʰ will not return you to the starting note. Instead, you must move down a perfect 4ᵗʰ, the inversion of a perfect 5ᵗʰ. (The tritone is the only exception and is discussed below.)

Interval Numbers

Inverting an interval changes its number. The original interval and its inversion always add up to 9.

• 2ⁿᵈ ↔ 7ᵗʰ (2 + 7 = 9)
• 3ʳᵈ ↔ 6ᵗʰ (3 + 6 = 9)
• 4ᵗʰ ↔ 5ᵗʰ (4 + 5 = 9)

Interval Qualities

Inverting an interval usually changes its quality.

• Major ↔ Minor
• Augmented ↔ Diminished
• Perfect ↔ Perfect

Perfect intervals keep their perfect quality but change their number.

Example: Perfect 4ᵗʰ ↔ Perfect 5ᵗʰ

Examples

• Up a Perfect 5ᵗʰ → Down a Perfect 4ᵗʰ
• Up a Major 3ʳᵈ → Down a Minor 6ᵗʰ
• Up a Minor 7ᵗʰ → Down a Major 2ⁿᵈ

The Tritone

The Augmented 4ᵗʰ and Diminished 5ᵗʰ are inversions of each other.

Both span 6 half-steps, making the tritone the only interval whose inversion has the same half-step distance.

Although the distance remains the same, the quality changes:

• Augmented 4ᵗʰ ↔ Diminished 5ᵗʰ

This is the only interval that returns to the starting pitch when moved by the same number of half-steps in either direction.

Interval Inversions

• Minor 2ⁿᵈ ↔ Major 7ᵗʰ
• Major 2ⁿᵈ ↔ Minor 7ᵗʰ
• Minor 3ʳᵈ ↔ Major 6ᵗʰ
• Major 3ʳᵈ ↔ Minor 6ᵗʰ
• Perfect 4ᵗʰ ↔ Perfect 5ᵗʰ
• Augmented 4ᵗʰ ↔ Diminished 5ᵗʰ

Minor Second/Major Seventh
1♭2
2
♭3
3
4
♭5
5
♭6
6
♭7
7
1
1→♭2 = 1 half-step (min2)♭2→1 = 11 half-steps (Maj7)1+11 half-steps = 1 octave
Major Second/Minor Seventh
1
♭2
2
♭3
3
4
♭5
5
♭6
6
♭7
7
1
1→2 = 2 half-steps (Maj2)2→1 = 10 half-steps (min7)2+10 half-steps = 1 octave

Minor Third/Major Sixth
1
♭2
2
♭3
3
4
♭5
5
♭6
6
♭7
7
1
1→♭3 = 3 half-steps (min3)♭3→1 = 9 half-steps (Maj6)3+9 half-steps = 1 octave
Major Third/Minor Sixth
1
♭2
2
♭3
3
4
♭5
5
♭6
6
♭7
7
1
1→3 = 4 half-steps (Maj3)3→1 = 8 half-steps (min6)4+8 half-steps = 1 octave
Perfect Fourth/Perfect Fifth
1
♭2
2
♭3
3
4
♭5
5
♭6
6
♭7
7
1
1→4 = 5 half-steps (Perf4)4→1 = 7 half-steps (Perf5)5+7 half-steps = 1 octave
Diminished Fifth/Augmented Fourth
1
♭2
2
♭3
3
4
♭5
5
♭6
6
♭7
7
1
1→♭5 = 6 half-step (dim5)♭5→1 = 6 half-steps (aug4)6+6 half-steps = 1 octave

The interval inversions shown above will become important throughout the NANDI Method, where many fretboard patterns are derived by inverting known interval relationships.