Enharmonic equivalence

One note, two names

The exercise page Enharmonic Matching explains the term: what is asked for is the enharmonic equivalent of a note, so the other name for the same pitch. In equal temperament, which became the standard over the course of the 19th century, the octave is divided into twelve exactly equal semitones. As a result notes coincide that are theoretically different: C♯ and D♭ sound identical, B♯ and C likewise.

The name follows the function

In practice the context decides the name. A note that wants to be resolved upwards is written as a raised note, one that strives downwards as a lowered one. That is why in a cadence to D major there is a C♯ and not a D♭. The page Name the Note adds: in A major the third note is called C♯ and not D♭, although both are the same key. The principle: a scale uses each note letter exactly once. If you wrote D♭, the letter D would occur twice and the letter C not at all. Notation therefore shows not only pitch but also intention.

At the lower edge of the circle

The page Circle of fifths shows three pairs of keys that describe the same notes but are notated differently. Composers choose, wherever possible, the spelling with fewer sharps or flats: D♭ major with five flats is almost always preferred to C♯ major with seven sharps. Keys with more than seven sharps or flats, such as G♯ major or F♭ major, exist only on paper and are rewritten to avoid double sharps or double flats. See D♭ major, F♯ major and G♯ major.

Reinterpretation as a means of modulation

The article The diminished seventh shows why enharmonic reinterpretation is more than hair-splitting: the same chord is written differently, and the spelling decides where it pulls. The chord C–E♭–G♭–A resolves to D♭ major if you take C as the leading tone, to E major if E♭ is read as D♯, to G major via G♭ as F♯ and to B♭ major via A. Four keys, one chord, not a single note changed.

Why it is not “the same”

The enharmonics page points out that the notes are in theory not equal: historical instruments with separate keys for C♯ and D♭ have existed. Equal temperament is a compromise that makes all keys playable and puts every one minimally out of tune. More under Pythagorean comma.

Common mistakes

• Paying attention only to the sound: C♯ and D♭ sound the same on the piano, in notation each spelling belongs in its own context.
• Dodging the double accidental: Such cases seem contrived, but follow inevitably from the system.
• Mixing both spellings in one key: A key is written with sharps or with flats.