Enharmonic equivalence
This article may be too technical for most readers to understand.(September 2019) |
In music, two written notes have enharmonic equivalence if they produce the same pitch but are notated differently. Similarly, written intervals, chords, or key signatures are considered enharmonic if they represent identical pitches that are notated differently. The term derives from Latin enharmonicus, in turn from Late Latin enarmonius, from Ancient Greek ἐναρμόνιος (enarmónios), from ἐν ('in') and ἁρμονία ('harmony').
Definition
The predominant
Sets of notes that involve pitch relationships — scales, key signatures, or intervals,[2] for example — can also be referred to as enharmonic (e.g., the keys of C♯ major and D♭ 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 a tritone above C may be written as a diminished fifth from C to G♭, or as an augmented fourth (C to F♯). Representing the C as a B♯ leads to other enharmonically equivalent options for notation.
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.
Examples
At the end of the bridge section of Jerome Kern's "All the Things You Are", a G♯ (the sharp 5 of an augmented C chord) becomes an ehnarmonically equivalent A♭ (the third of an F minor chord) at the beginning of the returning "A" section.[3][4]
In the middle section, these are changed to G♯s as the key changes to C-sharp minor. This is primarily a notational convenience, since D-flat minor would require many double-flats and be difficult to read:
The concluding passage of the slow movement of Schubert's final piano sonata in B♭ (D960) contains a dramatic enharmonic change. In bars 102–3, a B♯, the third of a G♯ major triad, transforms into C♮ as the prevailing harmony changes to C major:
Other tuning conventions
The standard tuning system used in Western music is
Pythagorean
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 (1 octave = frequency ratio of 2 to 1 = 2 ; 7 octaves is 27 to 1 = 128 ) of the A♭ by a small interval called a Pythagorean comma. This interval is expressed mathematically as:
Meantone
In quarter-comma meantone, there will be a discrepancy between, for example, G♯ and A♭. If
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 enharmonic diesis, 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 of
interface.Enharmonic genus
In
- 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
Enharmonic key
Some key signatures have an enharmonic equivalent that contains the same pitches, albeit spelled differently. 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 and A♯ minor/B♭ minor.
Theoretical key
Keys that require more than 7 sharps or flats are called theoretical keys. They have enharmonically equivalent keys with simpler key signatures, so are rarely seen.
See also
- Enharmonic keyboard
- Music theory
- Transpositional equivalence
- Diatonic and chromatic
- Enharmonic modulation
References
- ^
Elson, Louis Charlesb (1905). Elson's Music Dictionary. O. Ditson Company. p. 100.
The relation existing between two chromatics, when, by the elevation of one and depression of the other, they are united into one.
- ^
Benward, Bruce; Saker, Marilyn (2003). Music in Theory and Practice. Vol. I. p. 54. ISBN 978-0-07-294262-0.
- ^ Kern, J. and Hammerstein, O. (1939, bars 23-25) "All the things you are", New York, T. B. Harms Co.
- ^ Archived at Ghostarchive and the Wayback Machine: "Ella Fitzgerald - All The Things You Are (with lyrics)". YouTube.
- ^
ISBN 0-19-517067-9.
- JSTOR 843492.
Further reading
- Eijk, Lisette D. van der (2020). "The difference between a sharp and a flat Archived 2021-03-01 at the Wayback Machine".
- Mathiesen, Thomas J. (2001). "Greece, §I: Ancient". In ISBN 0-19-517067-9.
- Morey, Carl (1966). "The Diatonic, Chromatic and Enharmonic Dances by Martino Pesenti". JSTOR 932526.
External links
- The dictionary definition of enharmonic equivalence at Wiktionary
- Media related to Enharmonic at Wikimedia Commons