![Comparison of unisons](https://upload.wikimedia.org/wikipedia/commons/1/19/Comparison_of_unisons.png)
In modern
musical notation
Music notation or musical notation is any system used to visually represent aurally perceived music played with instruments or sung by the human voice through the use of written, printed, or otherwise-produced symbols, including notation fo ...
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. The enharmonic spelling of a written note, interval, or chord is an alternative way to write that note, interval, or chord. The term is derived from Latin ''enharmonicus'', from
Late Latin
Late Latin ( la, Latinitas serior) is the scholarly name for the form of Literary Latin of late antiquity.Roberts (1996), p. 537. English dictionary definitions of Late Latin date this period from the , and continuing into the 7th century in t ...
''enarmonius'', from Ancient Greek ἐναρμόνιος (''enarmónios''), from ἐν (''en'') and ἁρμονία (''harmonía'').
Definition
For example, in any twelve-tone equal
temperament
In psychology, temperament broadly refers to consistent individual differences in behavior that are biologically based and are relatively independent of learning, system of values and attitudes.
Some researchers point to association of temperam ...
(the predominant system of
musical tuning
In music, there are two common meanings for tuning:
* Tuning practice, the act of tuning an instrument or voice.
* Tuning systems, the various systems of pitches used to tune an instrument, and their theoretical bases.
Tuning practice
Tun ...
in Western music), the notes C and D are ''enharmonic'' (or ''enharmonically equivalent'') notes. Namely, they are the same key on a
keyboard
Keyboard may refer to:
Text input
* Keyboard, part of a typewriter
* Computer keyboard
** Keyboard layout, the software control of computer keyboards and their mapping
** Keyboard technology, computer keyboard hardware and firmware
Music
* Musi ...
, and thus they are identical in pitch, although they have different names and different
roles
A role (also rôle or social role) is a set of connected behaviors, rights, obligations, beliefs, and norms as conceptualized by people in a social situation. It is an expected or free or continuously changing behavior and may have a given indivi ...
in harmony and chord progressions. Arbitrary amounts of
accidentals
In music, an accidental is a note of a pitch (or pitch class) that is not a member of the scale or mode indicated by the most recently applied key signature. In musical notation, the sharp (), flat (), and natural () symbols, among others, ma ...
can produce further enharmonic equivalents, such as B (meaning B-double sharp), although these are much rarer and have less practical use.
In other words, if two notes have the same
pitch but have different letter names, we call them enharmonic.
"''Enharmonic intervals'' are intervals with the same sound that are spelled differently…
esulting 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
Diatonic and chromatic are terms in music theory that are most often used to characterize Scale (music), scales, and are also applied to musical instruments, Interval (music), intervals, Chord (music), chords, Musical note, notes, musical sty ...
scale—but not identical in pitch. One such example is G, which is not the same note and sound as A in many temperaments of more than twelve tones, as in an
enharmonic scale
In music theory, an enharmonic scale is "an maginarygradual progression by quarter tones" or any " usicalscale proceeding by quarter tones". The enharmonic scale uses dieses (divisions) nonexistent on most keyboards,John Wall Callcott (1833). ...
. "Enharmonic equivalence is peculiar to post-tonal theory." "Much music since at least the 18th century, however, exploits enharmonic equivalence for purposes of
modulation
In electronics and telecommunications, modulation is the process of varying one or more properties of a periodic waveform, called the ''carrier signal'', with a separate signal called the ''modulation signal'' that typically contains informatio ...
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
Flat or flats may refer to:
Architecture
* Flat (housing), an apartment in the United Kingdom, Ireland, Australia and other Commonwealth countries
Arts and entertainment
* Flat (music), a symbol () which denotes a lower pitch
* Flat (soldier), ...
of two enharmonically equivalent keys sum to twelve. For example, the key of
B major
B major (or the key of B) is a major scale based on B. The pitches B, C, D, E, F, G, and A are all part of the B major scale. Its key signature has five sharps. Its relative minor is G-sharp minor, its parallel minor is B minor, and its ...
, with five sharps, is enharmonically equivalent to the key of
C major
C major (or the key of C) is a major scale based on C, consisting of the pitches C, D, E, F, G, A, and B. C major is one of the most common keys used in music. Its key signature has no flats or sharps. Its relative minor is A minor and ...
with seven flats, so that gives five (sharps) + seven (flats) = 12. Keys past seven sharps or seven flats exist only theoretically and not in practice. The enharmonic keys are six pairs, three major pairs and three minor pairs:
B major
B major (or the key of B) is a major scale based on B. The pitches B, C, D, E, F, G, and A are all part of the B major scale. Its key signature has five sharps. Its relative minor is G-sharp minor, its parallel minor is B minor, and its ...
/
C major
C major (or the key of C) is a major scale based on C, consisting of the pitches C, D, E, F, G, A, and B. C major is one of the most common keys used in music. Its key signature has no flats or sharps. Its relative minor is A minor and ...
,
G minor/
A minor
A minor is a minor scale based on A, with the pitches A, B, C, D, E, F, and G. Its key signature has no flats and no sharps. Its relative major is C major and its parallel major is A major.
The A natural minor scale is:
:
Changes ...
,
F major
F major (or the key of F) is a major scale based on F, with the pitches F, G, A, B, C, D, and E. Its key signature has one flat. Its relative minor is D minor and its parallel minor is F minor
F minor is a minor scale based on F, consis ...
/
G major
G major (or the key of G) is a major scale based on G, with the pitches G, A, B, C, D, E, and F. Its key signature has one sharp. Its relative minor is E minor and its parallel minor is G minor.
The G major scale is:
Notable compositi ...
,
D minor
D minor is a minor scale based on D, consisting of the pitches D, E, F, G, A, B, and C. Its key signature has one flat. Its relative major is F major and its parallel major is D major.
The D natural minor scale is:
Changes needed for t ...
/
E minor,
C major
C major (or the key of C) is a major scale based on C, consisting of the pitches C, D, E, F, G, A, and B. C major is one of the most common keys used in music. Its key signature has no flats or sharps. Its relative minor is A minor and ...
/
D major and
A minor
A minor is a minor scale based on A, with the pitches A, B, C, D, E, F, and G. Its key signature has no flats and no sharps. Its relative major is C major and its parallel major is A major.
The A natural minor scale is:
:
Changes ...
/
B minor
B minor is a minor scale based on B, consisting of the pitches B, C, D, E, F, G, and A. Its key signature has two sharps. Its relative major is D major and its parallel major is B major.
The B natural minor scale is:
:
Changes neede ...
. 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
B major (or the key of B) is a major scale based on B. The pitches B, C, D, E, F, G, and A are all part of the B major scale. Its key signature has five sharps. Its relative minor is G-sharp minor, its parallel minor is B minor, and its ...
, 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 . 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
In music, an octave ( la, octavus: eighth) or perfect octave (sometimes called the diapason) is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon that has been refer ...
equivalence, nor are enharmonic intervals to be confused with
inverted or
compound intervals
In music theory, an interval is a difference in pitch between two sounds.
An interval may be described as horizontal, linear, or melodic if it refers to successively sounding tones, such as two adjacent pitches in a melody, and vertical or h ...
.
Examples in practice
An example in popular music occurs in melody line of
Jerome Kern
Jerome David Kern (January 27, 1885 – November 11, 1945) was an American composer of musical theatre and popular music. One of the most important American theatre composers of the early 20th century, he wrote more than 700 songs, used in over ...
's song “
All the things you are
"All the Things You Are" is a song composed by Jerome Kern with lyrics written by Oscar Hammerstein II.
The song was written for the musical ''Very Warm for May'' (1939) ”, where the note G sharp that concludes the
bridge
A bridge is a structure built to span a physical obstacle (such as a body of water, valley, road, or rail) without blocking the way underneath. It is constructed for the purpose of providing passage over the obstacle, which is usually somethi ...
section repeats, over changing harmony, as an A flat, the first note of the returning “A” section.
Beethoven
Ludwig van Beethoven (baptised 17 December 177026 March 1827) was a German composer and pianist. Beethoven remains one of the most admired composers in the history of Western music; his works rank amongst the most performed of the classical ...
's Piano
Sonata in E Minor, Op. 90, contains a passage where the lowest note, B-flat, becomes an A-sharp, altering its musical meaning and significance. The first two bars of the following passage unfold a simple descending scale of B-flat major. However, according to
Wilfrid Mellers
Wilfrid Howard Mellers (26 April 1914 – 17 May 2008) was an English music critic, musicologist and composer.
Early life
Born in Leamington, Warwickshire, Mellers was educated at the local Leamington College and later won a scholarship to Dow ...
, the B-flats here "turn out to be a
pun, for they change enharmonically into A-sharps, part of a dominant ninth leading to B minor."
Chopin's
Prelude No. 15, known as the "Raindrop Prelude", features a
pedal point
In music, a pedal point (also pedal note, organ point, pedal tone, or pedal) is a sustained tone, typically in the bass, during which at least one foreign (i.e. dissonant) harmony is sounded in the other parts. A pedal point sometimes function ...
on the note A-flat throughout its opening section.
"The repeated A-flats ... become enharmonically changed into G-sharps in the middle section of this Prelude, and take on a brooding, ominous character."
One of the most spectacular enharmonic changes in all music occurs in the concluding passage of the slow movement of one of
Schubert's last sonatas, his final piano sonata, in B-flat, D960. Here, in bars 102-3, the note B-sharp transforms into C natural as part of a progression, where the chord of G sharp, the dominant chord of C sharp minor, "melts with breathtaking effect into a C major chord."
Tuning enharmonics
In principle, the modern musical use of the word ''enharmonic'' to mean identical tones is correct only in
equal temperament
An equal temperament is a musical temperament or tuning system, which approximates just intervals by dividing an octave (or other interval) into equal steps. This means the ratio of the frequencies of any adjacent pair of notes is the same, wh ...
, 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.
Pythagorean
In Pythagorean tuning, all pitches are generated from a series of
justly tuned perfect fifth
In music theory, a perfect fifth is the Interval (music), musical interval corresponding to a pair of pitch (music), pitches with a frequency ratio of 3:2, or very nearly so.
In classical music from Western culture, a fifth is the interval fro ...
s, 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 2
7 = 128) of the A by a small interval called a
Pythagorean comma. This interval is expressed mathematically as:
:
Meantone
In quarter-comma meantone, on the other hand, consider G and A. Call
middle C
C or Do is the first note and semitone of the C major scale, the third note of the A minor scale (the relative minor of C major), and the fourth note (G, A, B, C) of the Guidonian hand, commonly pitched around 261.63 Hz. The actual frequen ...
's frequency ''x''. Then high C has a frequency of 2''x''. The quarter-comma meantone has just (i.e., perfectly-tuned) major thirds, which means
major thirds with a frequency ratio of exactly 4 to 5.
To form a just major third with the C above it, A and high C must be in the ratio 4 to 5, 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. Thus the frequency of G is
:
Thus, G and A are not the same note; G is, in fact 41
cent
Cent may refer to:
Currency
* Cent (currency), a one-hundredth subdivision of several units of currency
* Penny (Canadian coin), a Canadian coin removed from circulation in 2013
* 1 cent (Dutch coin), a Dutch coin minted between 1941 and 1944
* ...
s lower in pitch (41% of a semitone, not quite a quarter of a tone). The difference is the interval called the enharmonic
diesis
In classical music from Western culture, a diesis ( , plural dieses ( , "difference"; Greek: δίεσις "leak" or "escape"Benson, Dave (2006). ''Music: A Mathematical Offering'', p.171. . Based on the technique of playing the aulos, where p ...
, or a frequency ratio of . 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 escape notice when presented as melodic intervals. However, when they are sounded as chords, the difference between meantone intonation and equal-tempered intonation can be quite noticeable, even to untrained ears.
One can label enharmonically equivalent pitches with one and only one name; for instance, the numbers of
integer notation
In music, a pitch class (p.c. or pc) is a set of all pitches that are a whole number of octaves apart; for example, the pitch class C consists of the Cs in all octaves. "The pitch class C stands for all possible Cs, in whatever octave positio ...
, as used in
serialism
In music, serialism is a method of Musical composition, composition using series of pitches, rhythms, dynamics, timbres or other elements of music, musical elements. Serialism began primarily with Arnold Schoenberg's twelve-tone technique, thou ...
and
musical set theory and employed by the
MIDI
MIDI (; Musical Instrument Digital Interface) is a technical standard that describes a communications protocol, digital interface, and electrical connectors that connect a wide variety of electronic musical instruments, computers, and re ...
interface.
Enharmonic genus
In
ancient Greek music
Music was almost universally present in ancient Greek society, from marriages, funerals, and religious ceremonies to theatre, folk music, and the ballad-like reciting of epic poetry. It thus played an integral role in the lives of ancient Greek ...
the enharmonic was one of the three Greek
genera
Genus ( plural genera ) is a taxonomic rank used in the biological classification of living and fossil organisms as well as viruses. In the hierarchy of biological classification, genus comes above species and below family. In binomial nomenclat ...
in music in which the
tetrachord
In music theory, a tetrachord ( el, τετράχορδoν; lat, tetrachordum) is a series of four notes separated by three intervals. In traditional music theory, a tetrachord always spanned the interval of a perfect fourth, a 4:3 frequency propo ...
s are divided (descending) as a
ditone
In music, a ditone (, from , "of two tones") is the interval of a major third. The size of a ditone varies according to the sizes of the two tones of which it is compounded. The largest is the Pythagorean ditone, with a ratio of 81:64, also cal ...
plus two
microtones. The ditone can be anywhere from to (3.55 to 4.35
semitones) and the microtones can be anything smaller than 1 semitone.
Some examples of enharmonic genera are
#
#
#
#
#
See also
*
Enharmonic keyboard An enharmonic keyboard is a musical keyboard, where enharmonically equivalent notes do not have identical pitches. A conventional keyboard has, for instance, only one key and pitch for C and D , but an enharmonic keyboard would have two different ...
*
Music theory
Music theory is the study of the practices and possibilities of music. ''The Oxford Companion to Music'' describes three interrelated uses of the term "music theory". The first is the "rudiments", that are needed to understand music notation (ke ...
*
Transpositional equivalence
*
Diatonic and chromatic
Diatonic and chromatic are terms in music theory that are most often used to characterize scales, and are also applied to musical instruments, intervals, chords, notes, musical styles, and kinds of harmony. They are very often used as a pair, ...
*
Enharmonic modulation
In music, modulation is the change from one tonality ( tonic, or tonal center) to another. This may or may not be accompanied by a change in key signature (a key change). Modulations articulate or create the structure or form of many pieces, as ...
References
Further reading
* Eijk, Lisette D. van der (2020).
The difference between a sharp and a flat.
*
*
External links
*
*
{{Pitch (music)
Intervals (music)
Musical notes