musicand notation, an enharmonic equivalent is a note(enharmonic tone), interval (enharmonic interval), or key signaturewhich 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 enharmonic equivalent to the way that note, interval or chord would be written under the current key signature. In other words, if two notes have the same pitch but are represented by different letter names and accidentals, they are enharmonic. Enharmonic equivalence is not to be confused with octaveequivalence, nor are enharmonic intervals to be confused with inverted or compound intervals.
For example, in twelve-tone
equal temperament(the modern system of musical tuningin the West), the notes Cmusic|sharp and Dmusic|flat are "enharmonically equivalent" - that is, they are the same key on a keyboard - and thus are identical in pitch, although they have different names and diatonic function, or role in harmony and chord progressions.
In a given
diatonic scale, an individual note name may only occur once. In the key of F for example, the major scale is: 'F, G, A, Bmusic|flat, C, D, E, (F)'. Thus, the 'B' is called 'Bmusic|flat' rather than 'Amusic|sharp' as we already have a note named 'A' in the scale. The scale of Fmusic|sharp major is: 'Fmusic|sharp, Gmusic|sharp, Amusic|sharp, B, Cmusic|sharp, Dmusic|sharp, Emusic|sharp, (Fmusic|sharp)'; thus we use the term 'Amusic|sharp' instead of 'Bmusic|flat' as we need the name 'B' to represent the 'B' note in the scale, and 'Emusic|sharp' instead of 'F' as we need the name 'F' to represent the 'Fmusic|sharp' note in the scale.
key signatures also have an infinite number of enharmonic key signatures that sound identical. The most common interchanges occur between key signatures with more than 4 sharps or flats. For example, the key of B, with 5 sharps, is enharmonically equivalent to the key of Cmusic|flat, with 7 flats. Keys past 7 sharps or flats exist; they are, however, normally impractical, and are enharmonically equivalent to keys with fewer sharps or flats; normally the less complex key signature is used. For example, the key of Amusic|flat, with 4 flats, is equivalent to the key of Gmusic|sharp, with 8 sharps, the first of which is double-sharped (order of sharps: Fx Cmusic|sharp Gmusic|sharp Dmusic|sharp Amusic|sharp Emusic|sharp Bmusic|sharp), just as the diatonic major scale corresponding to the key of Amusic|sharp, with 11 sharps is Amusic|sharp, Bmusic|sharp, Cx, Dmusic|sharp, Emusic|sharp, Fx, Gx, Amusic|sharp, which is equivalent to the diatonic major scale of the key of Bmusic|flat, with two flats, Bmusic|flat, C, D, Emusic|flat, F, G, A, Bmusic|flat.
The modern musical use of the word "enharmonic" to mean identical tones is correct only in
equal temperament. This is in contrast to the ancient use of the word in the context of unequal temperaments, such as 1/4 comma meantoneintonation, in which enharmonic notes differ slightly in pitch. It should be noted, however, that enharmonic equivalences occur in any equal temperament system, such as 19 equal temperamentor 31 equal temperament, if it can be and is used as a meantone temperament. The specific equivalences define the equal temperament. 19 equal is characterized by Emusic|sharp = F♭ and 31 equal by Dmusic|sharpmusic|sharp = F♭♭, for instance; in these tunings it is "not" true that Emusic|sharp = F, which is characteristic only of 12 equal temperament.
In 1/4 comma meantone, on the other hand, consider Gmusic|sharp and A♭. Call middle C's frequency . Then high C has a frequency of . The 1/4 comma meantone has perfect major thirds, which means
major thirds with a frequency ratio of exactly 4 to 5.
In order to form a perfect major third with the C above it, A♭ and high C need to be in the ratio 4 to 5, so A♭ needs to have the frequency
In order to form a perfect 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 cents lower in pitch (41% of a semitone, not quite a quarter of a tone). The difference is the interval called the enharmonic
diesis, 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.
The reason that — despite the fact that in recent western music, A♭ is exactly the same pitch as G♯ — we label them differently is that in tonal music notes are named for their harmonic function, and retain the names they had in the meantone tuning era. This is called
diatonic functionality. One can however label enharmonically equivalent pitches with one and only one name, sometimes called integer notation, often used in serialismand musical set theoryand employed by the MIDIinterface.
ancient Greek music, the enharmonic scalewas a form of octavetuning, in which the first, second, and third notes in the octave were separated approximately by quarter tones, as were the fifth, sixth, and seventh.
An "enharmonic" is also one of the three Greek genera in music, in which the
tetrachordsare divided (descending) as a ditone plus two microtones. The ditone can be anywhere from 16/13 to 9/7 (3.55 to 4.35 semitones) and the microtones can be anything smaller than 1 semitone. Some examples of enharmonic genera are:1. 1/1 36/35 16/15 4/3:2. 1/1 28/27 16/15 4/3:3. 1/1 64/63 28/27 4/3:4. 1/1 49/48 28/27 4/3:5. 1/1 25/24 13/12 4/3
Enharmonic tetrachords in Byzantine music
Byzantine music, "enharmonic" describes a kind of tetrachordand the echoi that contain them. As in the ancient Greek system, enharmonic tetrachords are distinct from diatonicand chromatic. However Byzantine enharmonic tetrachords bear no resemblance to ancient Greek enharmonic tetrachords. Their largest division is between a whole-toneand a tone-and-a-quarter in size, and their smallest is between a quarter-toneand a semitone. These are called "improper diatonic" or "hard diatonic" tetrachords in modern western usage.
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Look at other dictionaries:
Enharmonic — En har*mon ic ([e^]n h[.a]r*m[o^]n [i^]k), Enharmonical En har*mon ic*al ([e^]n h[.a]r*m[o^]n [i^]*kal), a. [Gr. enarmoniko s, enarmo nios fitting, accordant; en in + armoni a harmony: cf. F. enharmonique.] 1. (Anc. Mus.) Of or pertaining to that … The Collaborative International Dictionary of English
enharmonic — [en΄här män′ik] adj. [L enharmonicus < Gr enarmonikos: see EN 1 & HARMONY] in equal temperament, designating or of tones, as C♯ and D♭, that are identical in pitch but are written differently according to the key in which each occurs:… … English World dictionary
enharmonic — англ. [инхамо/ник] enharmonique фр. [анармони/к] enharmonisch нем. [энхармо/ниш] энгармонический … Словарь иностранных музыкальных терминов
enharmonic — c.1600, from L.L. enharmonicus, from Gk. enharmonikos, from en (see EN (Cf. en ) (2)) + harmonikos (see HARMONIC (Cf. harmonic)) … Etymology dictionary
enharmonic — enharmonically, adv. /en hahr mon ik/, adj. Music. having the same pitch in the tempered scale but written in different notation, as G sharp and A flat. [1590 1600; < LL enharmonicus < Gk enarmónios ( icus r. ios), equiv. to en EN 1 + harmoní(a)… … Universalium
enharmonic — adjective Etymology: French enharmonique, from Middle French, of a scale employing quarter tones, from Greek enarmonios, from en in + harmonia harmony, scale Date: 1794 of, relating to, or being notes that are written differently (as A flat and G … New Collegiate Dictionary
enharmonic — adjective a) Describing two or more identical notes that are written differently when in different keys b) Of or pertaining to a tetrachord … Wiktionary
enharmònic — en|har|mò|nic Mot Pla Adjectiu variable … Diccionari Català-Català
enharmonic — adj. relating to tones that are identical in pitch but are written differently according to the key in which they occur (Music) … English contemporary dictionary
enharmonic — [ˌɛnhα: mɒnɪk] adjective Music relating to notes which are the same in pitch (in modern tuning) though bearing different names (e.g. F sharp and G flat). ↘of or having intervals smaller than a semitone (e.g. between notes such as F sharp and G… … English new terms dictionary