In modern musical notation and tuning, an enharmonic equivalent is a note (enharmonic tone), interval (enharmonic interval), or key signature which is equivalent to some other note, interval, or key signature, but "spelled", or named, differently. Thus, the enharmonic spelling of a written note, interval or chord is an enharmonic equivalent to the way that note, interval or chord would be written under the current key signature. In other words, if two notes have the same pitch but are represented by different letter names and accidentals, they are enharmonic. Enharmonic equivalence is not to be confused with octave equivalence, nor are enharmonic intervals to be confused with inverted or compound intervals. "Enharmonic equivalents are tones that have the same pitch but different letter names....Two tones having the same pitch but different spelling." "Enharmonic intervals are intervals with the same sound that are spelled differently...[resulting], of course, from enharmonic tones."
For example, in twelve-tone equal temperament (the modern system of musical tuning in the West), the notes C♯ and D♭ are enharmonically equivalent - that is, they are the same key on a keyboard - and thus are identical in pitch, although they have different names and diatonic function, or role in harmony and chord progressions.
In a given diatonic scale, an individual note name may only occur once. In the key of F for example, the major scale is: 'F, G, A, B♭, C, D, E, (F)'. Thus, the 'B' is called 'B♭' rather than 'A♯' as we already have a note named 'A' in the scale. The scale of F♯ major is: 'F♯, G♯, A♯, B, C♯, D♯, E♯, (F♯)'; thus we use the term 'A♯' instead of 'B♭' as we need the name 'B' to represent the 'B' note in the scale, and 'E♯' instead of 'F' as we need the name 'F' to represent the 'F♯' note in the scale.
Some key signatures also have an enharmonic key signature that represents a scale identical in sound but spelled differently. The number of sharps and flats of enharmonic keys sum to twelve. For example, the key of B Major, with 5 sharps, is enharmonically equivalent to the key of C-flat major with 7 flats, and 5 (sharps) + 7 (flats) = 12. Keys past 7 sharps or flats exist only theoretically and not in practice. The enharmonic keys are six pairs, three major and three minor: B Major/C-flat Major, G-Sharp Minor/A-flat Minor, F-sharp Major/G-flat Major, D-sharp Minor/E-flat Minor, C-sharp Major/D-flat Major and A-sharp Minor/B-flat Minor. There are no works composed in keys that require double sharping or double flating in the key signature, except in jest. In practice, musicians learn and practice 15 major and 15 minor keys, three more than 12 due to the enharmonic spellings.
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