Enharmonic

In modern musical notation and tuning, an enharmonic equivalent is a note, interval, or key signature that 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 alternative way to write that note, interval, or chord. For example, in twelve-tone equal temperament (the currently predominant system of musical tuning in Western music), the notes C♯ and D♭ are enharmonic (or enharmonically equivalent) notes. Namely, they are the same key on a keyboard, and thus they are identical in pitch, although they have different names and different roles in harmony and chord progressions. Arbitrary amounts of accidentals can produce further enharmonic equivalents, such as B, although these are much rarer and have less practical use. In modern musical notation and tuning, an enharmonic equivalent is a note, interval, or key signature that 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 alternative way to write that note, interval, or chord. For example, in twelve-tone equal temperament (the currently predominant system of musical tuning in Western music), the notes C♯ and D♭ are enharmonic (or enharmonically equivalent) notes. Namely, they are the same key on a keyboard, and thus they are identical in pitch, although they have different names and different roles in harmony and chord progressions. Arbitrary amounts of accidentals can produce further enharmonic equivalents, such as B, although these are much rarer and have less practical use. In other words, if two notes have the same pitch but are represented by different letter names and accidentals, they are enharmonic. 'Enharmonic intervals are intervals with the same sound that are spelled differently… , of course, from enharmonic tones.' Prior to this modern meaning, 'enharmonic' referred to notes that were very close in pitch—closer than the smallest step of a diatonic scale—but not identical in pitch, such as F♯ and a flattened note such as G♭, as in an enharmonic scale. 'Enharmonic equivalence is peculiar to post-tonal theory.' 'Much music since at least the 18th century, however, exploits enharmonic equivalence for purposes of modulation and this requires that enharmonic equivalents in fact be equivalent.' Some key signatures have an enharmonic equivalent that represents a scale identical in sound but spelled differently. The number of sharps and flats of two enharmonically equivalent keys sum to twelve. For example, the key of B major, with 5 sharps, is enharmonically equivalent to the key of C♭ 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♭ major, G♯ minor/A♭ minor, F♯ major/G♭ major, D♯ minor/E♭ minor, C♯ major/D♭ major and A♯ minor/B♭ minor. There are practically no works composed in keys that require double sharps or double flats in the key signature. In practice, musicians learn and practice 15 major and 15 minor keys, three more than 12 due to the enharmonic spellings. Enharmonic equivalents can also be used to improve the readability of a line of music. For example, a sequence of notes is more easily read as 'ascending' or 'descending' if the noteheads are on different positions on the staff. Doing so may also reduce the number of accidentals that must be used. Thus, in the key of B♭ major, the sequence B♭-B♮-B♭ is more easily read using the enharmonic spelling C♭ instead of B♮. For example, the intervals of a minor sixth on C, on B♯, and an augmented fifth on C are all enharmonic intervals Play (help·info). The most common enharmonic intervals are the augmented fourth and diminished fifth, or tritone, for example C–F♯ = C–G♭. Enharmonic equivalence is not to be confused with octave equivalence, nor are enharmonic intervals to be confused with inverted or compound intervals. In principle, the modern musical use of the word enharmonic to mean identical tones is correct only in equal temperament, where the octave is divided into 12 equal semitones. In other tuning systems, however, enharmonic associations can be perceived by listeners and exploited by composers. In Pythagorean tuning, all pitches are generated from a series of justly tuned perfect fifths, each with a frequency ratio of 3 to 2. If the first note in the series is an A♭, the thirteenth note in the series, G♯ is higher than the seventh octave (octave = ratio of 1 to 2, seven octaves is 1 to 27 = 128) of the A♭ by a small interval called a Pythagorean comma. This interval is expressed mathematically as: