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In music, two written notes haveenharmonic equivalence if they produce the samepitch but arenotated differently. Similarly, writtenintervals,chords, orkey signatures are consideredenharmonic if they represent identical pitches that are notated differently. The term derives from Latinenharmonicus, in turn fromLate Latinenarmonius, from Ancient Greekἐναρμόνιος (enarmónios), fromἐν ('in') andἁρμονία ('harmony').
The predominanttuning system in Western music istwelve-tone equal temperament (12TET), where eachoctave is divided into twelve equal half-steps, orsemitones; each half-step is both achromatic semitone (asharp or aflat) and adiatonic semitone (a minor step between twodiatonic notes). The notes F and G are a whole step apart, so the note one semitone above F (F♯) and the note one semitone below G (G♭) indicate the same pitch. These written notes areenharmonic, orenharmonically equivalent. The choice of notation for a pitch can depend on itsrole in harmony; this notation keeps modern music compatible with earlier tuning systems, such asmeantone temperaments. The choice can also depend on the note's readability in the context of the surrounding pitches. Multiple sharps or flats can produce other enharmonic equivalents; for example, F 
(double-sharp) is enharmonically equivalent to G♮.
When other tuning systems were in use, prior to the adoption of12TET, the termenharmonic referred to notes that were very close in pitch — closer than the smallest step of adiatonic scale — but not quite identical. In a tuning system without equal half steps, F♯ and G♭ do not indicate the same pitch, although the two pitches would be called enharmonically equivalent.
Sets of notes that involve pitch relationships — scales, key signatures, or intervals,[1]for example — can also be referred to asenharmonic (e.g., in12TET the keys ofC♯ major andD♭ major contain identical pitches and are therefore enharmonic). Identical intervals notated with different, enharmonically equivalent, written pitches are also referred to as enharmonic. The interval of atritone above C may be written as adiminished fifth from C to G♭, or as anaugmented fourth (C to F♯). In modern12TET, notating the C as a B♯ leads to other enharmonically equivalent notations, an option which does not exist in most earlier notation systems.
Enharmonic equivalents can be used to improve the readability of music, as when a sequence of notes is more easily read using sharps or flats. This may also reduce the number of accidentals required.
At the end of thebridge section ofJerome Kern's "All the Things You Are", a G♯ (the sharp 5th of an augmented C chord) becomes an enharmonically equivalent A♭ (thethird of an F minor chord) at the beginning of the returningA section.[2][3]
Beethoven'sPiano Sonata in E Minor, Op. 90, contains a passage where a B♭ becomes an A♯, altering its overt musical function. The first two bars of the following passage contain a descending B♭ major scale. Immediately following this, the B♭s become A♯s, theleading tone ofB minor:
Chopin'sPrelude No. 15, known as the "Raindrop Prelude", features apedal point on the note A♭ throughout its opening section.
In the middle section, these are changed to G♯s as the key changes toC♯ minor. The new key is not notated asD♭ minor because that key signature would require a double-flat:
The concluding passage of the slow movement ofSchubert's final piano sonata inB♭ (D960) contains an enharmonic change in bars 102–103, where there is a B♯ that functions as the third of a G♯ major triad. When the prevailing harmony changes toC major that pitch is notated as C♮:
Intwelve-tone equal temperament tuning, the standard tuning system of Western music, an octave is divided into 12 equal semitones. Written notes that produce the same pitch, such as C♯ and D♭, are calledenharmonic. In other tuning systems, such pairs of written notes do not produce an identical pitch, but can still be called "enharmonic" using the older sense of the word.[4]
In Pythagorean tuning, all pitches are generated from a series ofjustly tunedperfect 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♯ ishigher than the seventh octave (1 octave = frequency ratio of 2 to 1 = 2 ; 7 octaves is 27 to 1 = 128 ) of the A♭ by a small interval called aPythagorean comma. This interval is expressed mathematically as:
In quarter-comma meantone, there will be a discrepancy between, for example, G♯ and A♭. Ifmiddle C's frequency isf, the next highest C has a frequency of 2f . The quarter-comma meantone has perfectly tuned ("just")major thirds, which means major thirds with a frequency ratio of exactly 5 / 4 . To form a just major third with the C above it, A♭ and the C above it must be in the ratio 5 to 4, so A♭ needs to have the frequency
To form a just major third above E, however, G♯ needs to form the ratio 5 to 4 with E, which, in turn, needs to form the ratio 5 to 4 with C, making the frequency of G♯
This leads to G♯ and A♭ being different pitches; G♯ is, in fact 41 cents (41% of a semitone) lower in pitch. The difference is the interval called the enharmonicdiesis, or a frequency ratio of 128 / 125. On a piano tuned in equal temperament, both G♯ and A♭ are played by striking the same key, so both have a frequency
Such small differences in pitch can skip notice when presented as melodic intervals; however, when they are sounded as chords, especially as long-duration chords, the difference between meantone intonation and equal-tempered intonation can be quite noticeable.
Enharmonically equivalent pitches can be referred to with a single name in many situations, such as the numbers ofinteger notation used inserialism andmusical set theory and as employed byMIDI.
Inancient Greek music theenharmonic was one of the three Greekgenera in music; in theenharmonic genus, thetetrachords are divided (in descending pitch order) as aditone (M3) plus twomicrotones. The ditone can be anywhere from16/ 13 (359.5 cents) to9/ 7 (435.1 cents) (3.55 to 4.35 semitones) and the microtones can be anything smaller than 1 semitone.[5] Some examples of enharmonic genera in modern ascending pitch order are
| Tonic | Lower µ‑tone | Higher µ‑tone | ( wide gap ) | Ditone |
| 1/ 1 | 36/ 35 | 16/ 15 | 4/ 3 | |
| 1/ 1 | 28/ 27 | 16/ 15 | 4/ 3 | |
| 1/ 1 | 64/ 63 | 28/ 27 | 4/ 3 | |
| 1/ 1 | 49/ 48 | 28/ 27 | 4/ 3 | |
| 1/ 1 | 25/ 24 | 13/ 12 | 4/ 3 |
Somekey signatures have an enharmonic equivalent that contains the same pitches, albeit spelled differently. In twelve-tone equal temperament, there are three pairs each of major and minor enharmonically equivalent keys:B major/C♭ major,G♯ minor/A♭ minor,F♯ major/G♭ major,D♯ minor/E♭ minor,C♯ major/D♭ major andA♯ minor/B♭ minor.
If a key were to use more than 7 sharps or flats it would require at least one double flat or double sharp. These key signatures are extremely rare since they have enharmonically equivalent keys with simpler, conventional key signatures. For example,G sharp major would require eight sharps (six sharps plus F double-sharp), but would almost always be replaced by the enharmonically equivalent key signature ofA flat major, with four flats.
(with lyrics)Also archivedArchived 2021-12-05 at Ghost Archive
The dictionary definition ofenharmonic equivalence at Wiktionary
Media related toEnharmonic at Wikimedia Commons
