Английская Википедия:Enharmonic equivalence
Шаблон:Short description Шаблон:Distinguish Шаблон:Technical
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 Шаблон:Lang-la, in turn from Late Latin Шаблон:Lang-la, from Ancient Greek Шаблон:Lang-grc (Шаблон:Transliteration), from Шаблон:Lang-grc ('in') and Шаблон:Lang-grc ('harmony').
Definition
Шаблон:Image frame The predominant tuning system in Western music is twelve-tone equal temperament, where each octave is divided into twelve equivalent half-steps. Since all half steps are equivalent, FШаблон:Music (one half step above F) and GШаблон:Music (one half step below G) indicate the same pitch, since F and G are a whole step apart. These written notes are enharmonic, or enharmonically equivalent. In many other systems, this would not be the case. The choice of notation for a pitch can depend on its role in harmony; this notation keeps modern music compatible with earlier tuning systems, such as meantone temperaments. The choice can also depend on the note's readability in the context of the surrounding pitches. Multiple accidentals can produce other enharmonic equivalents; for example, FШаблон:Music (double-sharp) is enharmonically equivalent to GШаблон:Music. 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. For example, in most tuning systems other than the modern 12-tone equal temperament, GШаблон:Music is Шаблон:Em the same pitch as AШаблон:Music.[1] Шаблон:Image frame
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 CШаблон:Music major and DШаблон:Music 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 GШаблон:Music, or as an augmented fourth (C to FШаблон:Music). Representing the C as a BШаблон:Music leads to other enharmonically equivalent notational options.
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 GШаблон:Music (the sharp 5 of an augmented C chord) becomes an ehnarmonically equivalent AШаблон:Music (the third of an F minor chord) at the beginning of the returning "A" section.[3][4]
Beethoven's Piano Sonata in E Minor, Op. 90, contains a passage where a BШаблон:Music becomes an AШаблон:Music, altering its musical function. The first two bars of the following passage unfold a descending BШаблон:Music major scale. Immediately following this, the BШаблон:Musics become AШаблон:Musics, the leading tone of B minor:
Файл:Beethoven Sonata in E minor Op 90, first movement, bars 37-45.wav
Chopin's Prelude No. 15, known as the "Raindrop Prelude", features a pedal point on the note AШаблон:Music throughout its opening section.
Файл:Chopin Prelude No. 15, opening 01.wav
In the middle section, these are changed to GШаблон:Musics 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:
Файл:Chopin Prelude Op. 28, No. 15, bars 28-29.wav
The concluding passage of the slow movement of Schubert's final piano sonata in BШаблон:Music (D960) contains a dramatic enharmonic change. In bars 102–3, a BШаблон:Music, the third of a GШаблон:Music major triad, transforms into CШаблон:Music as the prevailing harmony changes to C major:
Файл:Schubert Piano Sonata D960 second movement, bars 98-106.wav
Other tuning conventions
The standard tuning system used in Western music is twelve-tone equal temperament tuning, where the octave is divided into 12 equal semitones. In this system, written notes that produce the same pitch, such as CШаблон:Music and DШаблон:Music, are called enharmonic. In other tuning systems, such pairs of written notes do not produce an identical pitch.[5]
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 AШаблон:Music, the thirteenth note in the series, GШаблон:Music is higher than the seventh octave (octave = ratio of 1 to 2, seven octaves is 1 to 27 = 128) of the AШаблон:Music by a small interval called a Pythagorean comma. This interval is expressed mathematically as:
- <math>\frac{\hbox{twelve fifths}}{\hbox{seven octaves}}
=\frac{\left(\tfrac32\right)^{12}}{2^7} = \frac{3^{12}}{2^{19}} = \frac{531\,441}{524\,288} = 1.013\,643\,264... \approx 23.46 \hbox{ cents} \!</math>
Meantone
Шаблон:Main In quarter-comma meantone, there will be a discrepancy between, for example, GШаблон:Music and AШаблон:Music. If middle C's frequency is x, the next highest C has a frequency of 2x. The quarter-comma meantone has perfectly tuned ("just") 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, AШаблон:Music and the C above it must be in the ratio 4 to 5, so AШаблон:Music needs to have the frequency
- <math>\frac {4}{5}(2x) = \frac{8}{5}x = 1.6 x. </math>
To form a just major third above E, however, GШаблон:Music 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 GШаблон:Music
- <math>\left(\frac{5}{4}\right)^2x = \frac{25}{16}x = 1.5625 x</math>
This leads to GШаблон:Music and AШаблон:Music being different pitches; GШаблон:Music 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 Шаблон:Sfrac. On a piano tuned in equal temperament, both GШаблон:Music and AШаблон:Music are played by striking the same key, so both have a frequency
- <math>2^\frac{8}{12}x = 2^\frac{2}{3}x \approx 1.5874 x</math>
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.
Enharmonically equivalent pitches can be referred to with a single name in many situations, such as the numbers of integer notation used in serialism and musical set theory and employed by the MIDI interface.
Enharmonic genus
In ancient Greek music the enharmonic was one of the three Greek genera in music in which the tetrachords are divided (descending) as a ditone plus two microtones. The ditone can be anywhere from Шаблон:Sfrac to Шаблон:Sfrac (3.55 to 4.35 semitones) and the microtones can be anything smaller than 1 semitone.[6] Some examples of enharmonic genera are
- Шаблон:Sfrac Шаблон:Sfrac Шаблон:Sfrac Шаблон:Sfrac
- Шаблон:Sfrac Шаблон:Sfrac Шаблон:Sfrac Шаблон:Sfrac
- Шаблон:Sfrac Шаблон:Sfrac Шаблон:Sfrac Шаблон:Sfrac
- Шаблон:Sfrac Шаблон:Sfrac Шаблон:Sfrac Шаблон:Sfrac
- Шаблон:Sfrac Шаблон:Sfrac Шаблон:Sfrac Шаблон:Sfrac
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-flat major|CШаблон:Music major]], [[G-sharp minor|GШаблон:Music minor]]/[[A-flat minor|AШаблон:Music minor]], [[F-sharp major|FШаблон:Music major]]/[[G-flat major|GШаблон:Music major]], [[D-sharp minor|DШаблон:Music minor]]/[[E-flat minor|EШаблон:Music minor]], [[C-sharp major|CШаблон:Music major]]/[[D-flat major|DШаблон:Music major]] and [[A-sharp minor|AШаблон:Music minor]]/[[B-flat minor|BШаблон:Music 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.
F flat major - (E major)
G sharp major - (A flat major)
D flat minor - (C sharp minor)
E sharp minor - (F minor)
See also
- Enharmonic keyboard
- Music theory
- Transpositional equivalence
- Diatonic and chromatic
- Enharmonic modulation
References
Further reading
- Eijk, Lisette D. van der (2020). "The difference between a sharp and a flat".
- Шаблон:Cite book
- Шаблон:Cite journal
External links
- ↑ Шаблон:Cite book
- ↑ Шаблон:Cite book
- ↑ Kern, J. and Hammerstein, O. (1939, bars 23-25) "All the things you are", New York, T. B. Harms Co.
- ↑ Archived at GhostarchiveШаблон:Cbignore and the Wayback MachineШаблон:Cbignore: Шаблон:Cite webШаблон:Cbignore
- ↑ Шаблон:Cite book
- ↑ Шаблон:Cite journal
