Augmented 6th Chord Calculator: Notes and Resolution

An augmented 6th chord calculator identifies the notes in an Italian, French, or German augmented sixth chord from a chosen key and chord type. Enter the key’s tonic pitch class and select the chord type to get its notes, including the characteristic augmented sixth interval.

Formula

For this calculator, the tonic is represented by an integer pitch class: C = 0, C-sharp/D-flat = 1, and so on up to B = 11. The selected chord type determines which notes accompany the tonic and which of the other two chord members a and d represents. The formula for the characteristic augmented-sixth note is a = (t + 8) mod 12, eight semitones above the tonic; the dominant target is d = (t + 7) mod 12, seven semitones above it.

• t is the tonic pitch class, in semitones from C.
• c selects Italian, French, or German; it changes the chord’s internal notes, not the tonic or target.
• a is the pitch class a minor sixth above the tonic, enharmonically equivalent to an augmented fifth.
• b is the tonic pitch class.
• d is the dominant pitch class, the usual resolution target in the key.

The block’s first output is the pitch class of the characteristic upper note, not a complete spelling of the chord. Pitch classes describe equal-tempered semitone positions; they do not distinguish enharmonic spellings such as G-sharp and A-flat. The selected type is useful for identifying the chord’s other notes: Italian adds the raised fourth, French adds the second scale degree, and German adds the lowered sixth, using the conventional scale-degree descriptions for a major-key augmented sixth.

Worked Example

Use the default input, C = 0, and the default chord type, Italian:

1. Characteristic note: (0 + 8) mod 12 = 8, which is G-sharp as a pitch class (or A-flat enharmonically).
2. Tonic: 0 mod 12 = 0, or C.
3. Dominant target: (0 + 7) mod 12 = 7, or G.

The calculator’s headline result is 8 semitones for the characteristic note. In a C-major context, the correctly spelled Italian augmented sixth is A-flat–C–F-sharp: A-flat and F-sharp form the augmented sixth and resolve outward to G, while C commonly remains or moves according to the voice leading. The pitch-class result alone cannot show that A-flat is preferable to its enharmonic spelling G-sharp in this context.

What an Augmented Sixth Chord Is

An augmented sixth chord is a chromatic predominant chord: it commonly appears before the dominant, rather than functioning as a dominant chord itself. Its defining interval is an augmented sixth between the lowered sixth scale degree and raised fourth scale degree in a major-key setting. Those notes lie a total of ten semitones apart in equal temperament, but their spelling and tendency tones matter as much as their sounding distance.

For example, in C major the interval is A-flat to F-sharp. A-flat tends down to G, and F-sharp tends up to G. Both voices therefore converge on the dominant note G. This distinctive resolution is why an augmented-sixth chord is often discussed alongside secondary dominants and other chromatic approaches to the dominant.

How the Three Types Differ

The standard three types share the same augmented-sixth pair but differ in the added note or notes. In C major, the conventional spellings are:

• Italian (It+6): A-flat, C, F-sharp. It has three distinct pitch classes and doubles the tonic scale degree in common four-part writing.
• French (Fr+6): A-flat, C, D, F-sharp. The D adds a distinctive tritone-related sound within the chord.
• German (Ger+6): A-flat, C, E-flat, F-sharp. The E-flat makes its sound resemble a dominant seventh chord in equal temperament, though its spelling and resolution are different.

These examples are in C major. In a minor key, the chord is also built in relation to the key’s tonic and scale degrees, but the exact spelling and surrounding harmony should be checked in context. The calculator’s pitch-class model deliberately does not pretend to settle that notation question.

Using the Calculator and Reading Its Output

Enter the tonic as a number from 0 to 11, following the C-based mapping shown in the input label, then choose the chord type. The first result gives the characteristic note’s pitch class; the next gives the tonic, and the last gives the dominant target. For C, the outputs are 8, 0, and 7. For a tonic of D (2), they are 10, 2, and 9: the characteristic pitch class is A-sharp/B-flat, and the target is A.

Because the calculator returns numbers rather than note names or octave registers, use an instrument, notation program, or theory reference to confirm the intended enharmonic spelling. The chosen chord type does not alter the three numerical outputs: it describes which chord form you want, while a full chord-note listing would require note spelling and tonal context beyond pitch-class arithmetic.

Common Mistakes and Limitations

• Confusing the interval’s name with its semitone count: an augmented sixth is spelled as a sixth but sounds like eight semitones in equal temperament. The characteristic note is eight semitones above the tonic in this calculator’s major-key pitch-class model.
• Using the wrong tonic number: the mapping starts at C = 0, not C = 1. A one-step input error changes every result by one semitone.
• Treating enharmonic spellings as interchangeable in notation: G-sharp and A-flat can share a pitch class, but their harmonic roles and written intervals differ.
• Assuming the chord resolves to the tonic: its characteristic voices typically resolve outward to the dominant, a fifth above the tonic.

The results are pitch classes, not frequencies, staff positions, chord voicings, or a guarantee that a progression is stylistically appropriate. Equal temperament is assumed for the semitone arithmetic. Actual spellings and voice leading depend on key, musical context, and the notation convention being used.

Frequently Asked Questions

What does an augmented 6th chord calculator do?
It works out pitch-class relationships for an augmented-sixth chord from a tonic and chord type. This calculator reports the characteristic note, tonic, and dominant target; it does not generate a fully spelled score.

How many semitones are in an augmented sixth?
In equal temperament, an augmented sixth spans 10 semitones when measured from its lower note. The calculator’s characteristic note is eight semitones above the tonic because it calculates a different relationship: the tonic to the note a minor sixth above it, which forms the upper member of the usual augmented-sixth pair in the stated model.

What is the difference between Italian, French, and German augmented sixth chords?
They share the characteristic augmented-sixth pair and differ in their added chord tones. In C major, the Italian has C, the French adds D, and the German adds E-flat alongside A-flat and F-sharp.

Why does a German augmented sixth resemble a dominant seventh?
In equal temperament, the German chord’s notes can sound like those of a dominant seventh chord with enharmonic respelling. The written notes and harmonic function distinguish them: the augmented-sixth chord commonly resolves to the dominant through outward motion of its sixth.

Does this calculator give the correct note spelling?
No. It gives pitch classes, which collapse enharmonically equivalent notes into one number. Choose spellings from the key and progression—for example, A-flat rather than G-sharp in the usual C-major augmented-sixth chord.

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in t | Tonic pitch class (C=0, C#=1, D=2...) | semitones | 0 | 0
sel c | Chord type | Italian=1, French=2, German=3
out a | Augmented sixth chord notes (pitch classes) | semitones | (t + 8) % 12 | 0
out b | Tonic | semitones | t % 12 | 0
out d | Dominant target | semitones | (t + 7) % 12 | 0