The tools on Chord-Calculator.com perform exact calculations based on established music theory definitions. No microphone, no audio capture, no signal processing, no estimation. Every result is derived directly from the interval mathematics that defines chord and scale structure in Western tonal theory.
This page explains how each tool works — the mathematical and theoretical logic behind its results, what inputs it requires, and what its output means.
Written and maintained by Liam, founder of Chord-Calculator.com.
The Foundation: Intervals and the Chromatic Scale
Before explaining how each tool works, it is necessary to understand the system they all share: the chromatic scale and interval measurement.
Western tonal music divides the octave into twelve equal steps called semitones (also called half steps). Each semitone represents a frequency ratio of the 12th root of 2 (approximately 1.0595) — the same equal temperament mathematics that governs piano tuning, guitar frets, and all standard Western instruments.
The twelve pitch classes of the chromatic scale, ascending from C:
C — C#/Db — D — D#/Eb — E — F — F#/Gb — G — G#/Ab — A — A#/Bb — B — C
An interval is the distance between two notes measured in semitones. Each interval has a standard name:
| Semitones | Interval name | Abbreviation |
|---|---|---|
| 0 | Perfect unison | P1 |
| 1 | Minor second | m2 |
| 2 | Major second | M2 |
| 3 | Minor third | m3 |
| 4 | Major third | M3 |
| 5 | Perfect fourth | P4 |
| 6 | Tritone (aug. 4th / dim. 5th) | A4 / d5 |
| 7 | Perfect fifth | P5 |
| 8 | Minor sixth | m6 |
| 9 | Major sixth | M6 |
| 10 | Minor seventh | m7 |
| 11 | Major seventh | M7 |
| 12 | Perfect octave | P8 |
All tools on this site derive their results by counting semitones from a given root note according to the interval patterns that define each chord or scale type.
Part 1 — The Chord Calculator
How It Works
The Chord Calculator takes two inputs: a root note (any of the twelve pitch classes) and a chord quality (major, minor, dominant 7th, etc.). From these, it derives the complete chord — every note, the interval each note forms with the root, and all possible inversions.
Chord Construction: Interval Formulas
Every chord quality is defined by a specific pattern of intervals from the root. These patterns are fixed in Western tonal theory — they do not vary by root note. The interval formula determines the quality; the root note determines the specific pitches.
Triads (three-note chords):
| Quality | Interval formula | Example (root C) |
|---|---|---|
| Major | M3 + P5 (4 + 7 semitones) | C — E — G |
| Minor | m3 + P5 (3 + 7 semitones) | C — Eb — G |
| Diminished | m3 + d5 (3 + 6 semitones) | C — Eb — Gb |
| Augmented | M3 + A5 (4 + 8 semitones) | C — E — G# |
| Suspended 2nd | M2 + P5 (2 + 7 semitones) | C — D — G |
| Suspended 4th | P4 + P5 (5 + 7 semitones) | C — F — G |
Seventh chords (four-note chords):
| Quality | Interval formula | Example (root C) |
|---|---|---|
| Major 7th | M3 + P5 + M7 (4 + 7 + 11) | C — E — G — B |
| Dominant 7th | M3 + P5 + m7 (4 + 7 + 10) | C — E — G — Bb |
| Minor 7th | m3 + P5 + m7 (3 + 7 + 10) | C — Eb — G — Bb |
| Minor-major 7th | m3 + P5 + M7 (3 + 7 + 11) | C — Eb — G — B |
| Half-diminished | m3 + d5 + m7 (3 + 6 + 10) | C — Eb — Gb — Bb |
| Fully diminished | m3 + d5 + d7 (3 + 6 + 9) | C — Eb — Gb — Bbb |
| Augmented 7th | M3 + A5 + m7 (4 + 8 + 10) | C — E — G# — Bb |
Extended chords (9ths, 11ths, 13ths) add further intervals above the seventh, continuing to stack thirds. A dominant 9th adds a major 9th (14 semitones = 2 semitones above the octave) to a dominant 7th chord.
Note Derivation
Once the interval formula for a chord quality is established, deriving the notes for any root is a mechanical semitone-counting operation.
For C major (interval formula: M3 = 4 semitones, P5 = 7 semitones):
- Root: C
- Up 4 semitones from C: C → C# → D → D# → E = E
- Up 7 semitones from C: C → C# → D → D# → E → F → F# → G = G
- Result: C major = C, E, G
The same logic applies to every root and every chord quality.
Inversions
An inversion places a chord tone other than the root in the bass position. Every chord has as many inversions as it has notes (minus one — root position is not an inversion):
- Root position: Root in the bass (C–E–G for C major)
- First inversion: Third in the bass (E–G–C)
- Second inversion: Fifth in the bass (G–C–E)
- Third inversion (seventh chords only): Seventh in the bass (Bb–C–E–G for C7)
The notes of the chord do not change in an inversion — only their vertical arrangement (which note is lowest) changes. Inversions are used in voice leading to create smoother bass movement between chords.
Part 2 — The Chord Finder
How It Works
The Chord Finder reverses the chord construction process. You enter a set of notes; the tool identifies the chord name, quality, and — if the notes are in an inverted arrangement — the chord inversion.
The Identification Process
Step 1 — Pitch class normalisation. The entered notes are reduced to their pitch classes (note names without octave numbers) and any duplicate pitch classes are removed.
Step 2 — Root candidate testing. For each note in the set, the tool tests whether that note could function as the root of a recognisable chord quality. It does this by calculating the interval each other note forms with the candidate root and checking whether the resulting interval set matches a known chord formula.
Step 3 — Quality identification. When a candidate root produces an interval set matching a known chord formula, that root and quality are returned as a match. If multiple roots produce valid matches, all are returned — this reflects genuine harmonic ambiguity, which the tool documents rather than arbitrarily resolving.
Step 4 — Inversion identification. If the lowest-sounding note is not the identified root, the chord is in inversion. The inversion is identified by which chord tone (third, fifth, seventh) appears in the bass position.
Enharmonic Equivalents
Because C# and Db are the same pitch, a set of notes may have multiple theoretically valid chord names that are enharmonically equivalent. The tool handles this by returning both names with an explanation of the enharmonic relationship rather than choosing one arbitrarily.
Part 3 — The Interval Calculator
How It Works
The Interval Calculator takes two note inputs and returns the interval between them — the semitone count and the standard interval name.
Step 1 — Semitone counting. The calculator counts the number of semitones from the lower note to the higher note, ascending through the chromatic scale. This count is always between 0 and 12 (within one octave) or extended for compound intervals (13 semitones and above, for intervals larger than an octave).
Step 2 — Interval name lookup. The semitone count is matched against the standard interval name table. For compound intervals (larger than an octave), the compound name is derived: a 14-semitone interval is a minor ninth (minor second + octave); a 16-semitone interval is a major tenth (major third + octave).
Step 3 — Context note. The tool also notes whether the interval is consonant (stable, at rest) or dissonant (unstable, creating tension), and which chord and scale contexts commonly feature this interval.
What These Tools Cannot Determine
Harmonic context. The same chord can function differently in different keys and progressions. C major is the tonic in C major, the subdominant in G major, and the bVI in E minor. The tools calculate what a chord is — not what role it plays in a specific harmonic context. That requires musical analysis that goes beyond the chord itself.
Enharmonic intent. D# and Eb are the same pitch but carry different theoretical meanings depending on the key and voice leading context. The tools work with pitch classes — they note enharmonic alternatives but cannot determine which spelling is theoretically correct in a specific context without knowing the surrounding harmony.
Voicing and register. A chord’s notes can be distributed across registers in countless ways (close voicing, open voicing, drop-2, drop-3, etc.). The tools identify which notes belong to a chord — not how those notes should be arranged for a specific instrument, texture, or musical effect.
Related Pages
- Chord Calculator FAQ — common questions about chord theory and the tools
- About the Author — Liam’s background and expertise
- Editorial Guidelines — research standards for all content
- Contact — report a technical issue or inaccuracy
This How It Works page is written and maintained by Liam, founder of Chord-Calculator.com. Last updated: June 2026.