A chord is a handful of notes at fixed distances above a root. The calculator gives the distances in semitones for every chord, along with the notes and the intervals with their frequency ratios, on any root from octave 1 to 6. On a synthesizer each note gets its own oscillator, and the semitones are exactly the transposition it needs. There is also a tip for a wide, beating sound.
A chord built from several oscillators: gives the transposition in semitones for each, plus a hint for a wide, drifting sound.
In the generator Oscillator: frequency, transpose, detune · Mixer
The keys show two octaves from C, the root is orange. In brackets the frequency ratio to the root: the simpler it is, the calmer the interval sounds. The formula: note = (root + semitones) mod 12, frequency × 2^(semitones / 12).
The notes of a chord lie a fixed number of semitones above the root: 4 (major third) and 7 (fifth) in a major chord, 3 (minor third) and 7 in a minor chord. To find a note, count on from the root; after twelve semitones the octave starts again:
The simpler the frequency ratio, the calmer the interval sounds: the fifth (3/2) almost merges, the tritone (≈ √2) grinds. Equal temperament does not quite hit the pure ratios: at 24/12 ≈ 1.260 the major third lies about 14 cents above 5/4. Example: C3 is 130.81 Hz; a second oscillator fine-tuned by 7 cents beats against it about 0.53 times per second.
| Chord | Semitones | Intervals | On C |
|---|---|---|---|
| Major | 0 · 4 · 7 | major third (5/4), fifth (3/2) | C E G |
| Minor | 0 · 3 · 7 | minor third (6/5), fifth (3/2) | C E♭ G |
| sus2 | 0 · 2 · 7 | major second (9/8), fifth (3/2) | C D G |
| sus4 | 0 · 5 · 7 | fourth (4/3), fifth (3/2) | C F G |
| Diminished | 0 · 3 · 6 | minor third (6/5), tritone (≈ √2) | C E♭ G♭ |
| Augmented | 0 · 4 · 8 | major third (5/4), augmented fifth (8/5) | C E G♯ |
| Seventh (7) | 0 · 4 · 7 · 10 | major third (5/4), fifth (3/2), minor seventh (16/9) | C E G B♭ |
| Major 7 (maj7) | 0 · 4 · 7 · 11 | major third (5/4), fifth (3/2), major seventh (15/8) | C E G B |
| Minor 7 (m7) | 0 · 3 · 7 · 10 | minor third (6/5), fifth (3/2), minor seventh (16/9) | C E♭ G B♭ |
| Fifth (power chord) | 0 · 7 | fifth (3/2) | C G |
| Fifth + octave | 0 · 7 · 12 | fifth (3/2), octave (2/1) | C G C |
Notes on C. For another root, shift everything by the same distance; the semitones stay the same.
ModuloOne is a modular synthesizer that runs in your browser: connect modules with cables and hear what comes out. A chord is built there from several oscillators: all at the same frequency, each with the transposition from the table (−24 to 24 semitones). The mixer has two inputs; for three or four notes, chain two mixers. Open the generator