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1015:{\displaystyle {\frac {\ {\hbox{twelve fifths}}\ }{\ {\hbox{seven octaves}}\ }}~=~{\frac {1}{\ 2^{7}}}\left({\frac {3}{\ 2\ }}\right)^{12}~=~{\frac {\ 3^{12}}{\ 2^{19}}}~=~{\frac {\ 531\ 441\ }{\ 524\ 288\ }}~=~1.013\ 643\ 264\ \ldots ~\approx ~23.460\ 010{\hbox{ cents}}~.}
622:
551:
1546:
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.
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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
1964:
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:
425:
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.
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692:. In other tuning systems, such pairs of written notes do not produce an identical pitch, but can still be called "enharmonic" using the older, original sense of the word.
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566:
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:
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271:), where each octave is divided into twelve equivalent half steps or semitones. The notes F and G are a whole step apart, so the note one semitone above F (F
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tuning, where the octave is divided into 12 equal semitones. In this system, written notes that produce the same pitch, such as C
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383:
Sets of notes that involve pitch relationships — scales, key signatures, or intervals, for example — can also be referred to as
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1215:
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
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83:
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Enharmonically equivalent pitches can be referred to with a single name in many situations, such as the numbers of
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299:. The choice can also depend on the note's readability in the context of the surrounding pitches. Multiple
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1536:{\displaystyle \ 2^{\left(\ 8\ /\ 12\ \right)}\ f~=~2^{\left(\ 2\ /\ 3\ \right)}\ f~\approx ~1.5874\ f~.}
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17:
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1640:) and the microtones can be anything smaller than 1 semitone. Some examples of enharmonic genera are
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2202:
Kern, J. and
Hammerstein, O. (1939, bars 23-25) "All the things you are", New York, T. B. Harms Co.
479:, altering its musical function. The first two bars of the following passage unfold a descending B
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2212:
61:
2629:
2426:
2153:
442:
1329:{\displaystyle \left({\frac {\ 5\ }{4}}\right)^{2}\ f~=~{\frac {\ 25\ }{16}}\ f~=~1.5625\ f~.}
124:
if they represent identical pitches that are notated differently. The term derives from Latin
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2091:. They have enharmonically equivalent keys with simpler key signatures, so are rarely seen.
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238:
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8:
2137:
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1361:(41% of a semitone) lower in pitch. The difference is the interval called the enharmonic
2355:
Morey, Carl (1966). "The
Diatonic, Chromatic and Enharmonic Dances by Martino Pesenti".
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scale — but not quite identical. In a tuning system without equivalent half steps, F
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2366:
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306:
295:; this notation keeps modern music compatible with earlier tuning systems, such as
224:
109:
105:
2279:
Barbera, C. André (1977). "Arithmetic and
Geometric Divisions of the Tetrachord".
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2319:
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707:
232:
713:, each with a frequency ratio of 3 to 2. If the first note in the series is an A
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457:(the third of an F minor chord) at the beginning of the returning "A" section.
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In quarter-comma meantone, there will be a discrepancy between, for example, G
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451:(the sharp 5 of an augmented C chord) becomes an enharmonically equivalent A
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The same passage notated as sharps, requiring fewer canceling natural signs.
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1199:{\displaystyle {\frac {\ 4\ }{5}}\ (2f)={\frac {\ 8\ }{5}}\ f=1.6\ f~~.}
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In
Pythagorean tuning, all pitches are generated from a series of
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597:(D960) contains a dramatic enharmonic change. In bars 102–3, a B
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leads to other enharmonically equivalent options for notation.
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are played by striking the same key, so both have a frequency
508:
Beethoven Sonata in E Minor Op. 90, first movement, bars 37–45
1072:, which means major thirds with a frequency ratio of exactly
729:
than the seventh octave (1 octave = frequency ratio of
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Comparison of intervals near or enharmonic with the unison
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Keys that require more than 7 sharps or flats are called
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Enharmonic tritones: Augmented 4th = diminished 5th on C.
2222:"Ella Fitzgerald - All The Things You Are (with lyrics)"
404:
above C may be written as a diminished fifth from C to G
303:
can produce other enharmonic equivalents; for example, F
2326:
Mathiesen, Thomas J. (2001). "Greece, §I: Ancient". In
645:
Schubert Piano Sonata D960 second movement, bars 98–106
291:. The choice of notation for a pitch can depend on its
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and the C above it must be in the ratio 5 to 4, so A
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The standard tuning system used in
Western music is
283:) indicate the same pitch. These written notes are
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may be too technical for most readers to understand
2258:(2nd ed.). London, UK: Macmillan Publishers.
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1093:To form a just major third with the C above it, A
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1064:The quarter-comma meantone has perfectly tuned (
753:. This interval is expressed mathematically as:
311:(double-sharp) is enharmonically equivalent to G
2337:The New Grove Dictionary of Music and Musicians
2255:The New Grove Dictionary of Music and Musicians
1383:. On a piano tuned in equal temperament, both G
587:The concluding passage of the slow movement of
2340:(2nd ed.). London: Macmillan Publishers.
1209:To form a just major third above E, however, G
615:as the prevailing harmony changes to C major:
529:, known as the "Raindrop Prelude", features a
485:major scale. Immediately following this, the B
325:in pitch — closer than the smallest step of a
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560:In the middle section, these are changed to G
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2313:The difference between a sharp and a flat
84:Learn how and when to remove this message
68:, without removing the technical details.
1056:, the next highest C has a frequency of
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317:. Prior to this modern use of the term,
27:Distinct pitch classes sounding the same
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2178:Benward, Bruce; Saker, Marilyn (2003).
14:
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277:) and the note one semitone below G (G
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66:make it understandable to non-experts
40:
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410:, or as an augmented fourth (C to F
371:A musical passage notated as flats.
341:would not indicate the same pitch.
24:
2311:Eijk, Lisette D. van der (2020). "
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1604:. The ditone can be anywhere from
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573:Chopin Prelude No. 15, bars 28–29
96:In music, two written notes have
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1580:Genus (music) § Enharmonic
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1596:are divided (descending) as a
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609:major triad, transforms into C
546:Chopin Prelude No. 15, opening
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237:are enharmonic equivalents in
198:are enharmonic equivalents in
13:
1:
2397:The dictionary definition of
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749:by a small interval called a
674:twelve-tone equal temperament
589:Schubert's final piano sonata
263:twelve-tone equal temperament
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2180:Music in Theory and Practice
1105:needs to have the frequency
416:). Representing the C as a B
321:referred to notes that were
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7:
2182:. Vol. I. p. 54.
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2505:Scientific pitch notation
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2244:(2001). "Enharmonic". In
627:G-sharp to C progression.
465:Sonata in E Minor, Op. 90
289:enharmonically equivalent
100:if they produce the same
2485:Helmholtz pitch notation
660:Other tuning conventions
246:; both are the same as A
30:Not to be confused with
2282:Journal of Music Theory
2400:enharmonic equivalence
2154:Diatonic and chromatic
1592:in music in which the
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443:All the Things You Are
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98:enharmonic equivalence
2495:Piano key frequencies
2159:Enharmonic modulation
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297:meantone temperaments
139:, from Ancient Greek
2415:at Wikimedia Commons
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1357:is, in fact 41
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1032:Meantone temperament
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387:(e.g., the keys of C
261:in Western music is
2138:Enharmonic keyboard
1586:ancient Greek music
1562:and as employed by
603:, the third of a G
2318:2021-03-01 at the
1560:musical set theory
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433:At the end of the
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2625:Intervals (music)
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2531:Pitch circularity
2411:Media related to
2358:Acta Musicologica
2189:978-0-07-294262-0
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2365:(2–4): 185–189.
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1339:This leads to G
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2582:Musical tuning
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1956:Enharmonic key
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1578:Main article:
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527:Prelude No. 15
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74:September 2019
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2117:C sharp minor
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2541:Tonal memory
2526:Ear training
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2143:Music theory
2113:D flat minor
2108:A flat major
2095:F flat major
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739:2 to 1 = 128
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501:of B minor:
499:leading tone
473:becomes an A
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127:enharmonicus
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2500:Pitch class
2150:equivalence
1594:tetrachords
1002: cents
696:Pythagorean
531:pedal point
439:Jerome Kern
437:section of
393:major and D
301:accidentals
186:The notes F
161:('in') and
2619:Categories
2594:Pitch pipe
2577:Microtuner
2514:Perception
2480:Enharmonic
2413:Enharmonic
2165:References
1602:microtones
732:2 to 1 = 2
690:enharmonic
491:s become A
385:enharmonic
323:very close
319:enharmonic
285:enharmonic
173:Definition
150:enarmónios
143:ἐναρμόνιος
136:enarmonius
132:Late Latin
122:enharmonic
36:Inharmonic
32:Anharmonic
18:Enharmonic
2450:Frequency
1638:semitones
1600:plus two
1556:serialism
1513:≈
985:≈
979:…
463:'s Piano
461:Beethoven
110:intervals
2560:See also
2461:Notation
2334:(eds.).
2316:Archived
2252:(eds.).
2215:and the
2132:See also
2074:♭
2064:♯
2054:♭
2044:♯
2034:♭
2024:♯
2014:♭
2004:♯
1994:♭
1984:♯
1974:♭
1554:used in
1392:♭
1386:♯
1354:♯
1348:♭
1342:♯
1218:♯
1212:♯
1102:♭
1096:♭
1050:middle C
1045:♭
1039:♯
1026:Meantone
746:♭
743:of the A
722:♯
716:♭
685:♭
679:♯
612:♮
606:♯
600:♯
594:♭
563:♯
536:♭
494:♯
488:♭
482:♭
476:♯
470:♭
454:♭
448:♯
429:Examples
419:♯
413:♯
407:♭
396:♭
390:♯
338:♭
332:♯
327:diatonic
314:♮
280:♭
274:♯
249:♮
195:♭
189:♯
153:), from
104:but are
2587:Beating
2227:YouTube
2126:F minor
2099:E major
1967:B major
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497:s, the
402:tritone
165:ἁρμονία
106:notated
60:Please
2379:932526
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2295:843492
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1598:ditone
1590:genera
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1516:
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1312:1.5625
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523:Chopin
445:", a G
435:bridge
114:chords
2454:pitch
2375:JSTOR
2291:JSTOR
2077:minor
2067:minor
2057:major
2047:major
2037:minor
2027:minor
2017:major
2007:major
1997:minor
1987:minor
1977:major
1960:Some
1389:and A
1359:cents
1345:and A
1048:. If
1042:and A
961:1.013
682:and D
335:and G
287:, or
229:and B
192:and G
116:, or
102:pitch
2473:A440
2452:and
2342:ISBN
2260:ISBN
2184:ISBN
2059:and
1566:MIDI
1558:and
1377:125
591:in B
441:'s "
265:(12
2367:doi
2124:- (
2115:- (
2106:- (
2097:- (
1620:to
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1179:1.6
997:010
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967:643
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920:531
725:is
525:'s
268:TET
242:TET
239:12
203:TET
200:12
64:to
34:or
2621::
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2128:)
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2019:,
1999:,
1979:,
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1570:.
1436:12
1292:16
1285:25
1085:4
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1068:)
1058:2
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882:12
857:12
157:ἐν
112:,
2442:e
2435:t
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2381:.
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2192:.
2119:)
2110:)
2101:)
2071:B
2069:/
2061:A
2051:D
2049:/
2041:C
2031:E
2029:/
2021:D
2011:G
2009:/
2001:F
1991:A
1989:/
1981:G
1971:C
1969:/
1947:3
1944:/
1941:4
1929:/
1914:/
1902:1
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1498:)
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1470:(
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1458:=
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1443:)
1429:/
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1415:(
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1374:/
1324:.
1318:f
1306:=
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1273:=
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1259:2
1254:)
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1242:5
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1194:.
1185:f
1176:=
1173:f
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1146:)
1143:f
1140:2
1137:(
1129:5
1122:4
1091:.
1082:/
1062:.
1060:f
1054:f
1010:.
955:=
908:=
893:2
878:3
865:=
852:)
843:2
836:3
831:(
821:7
817:2
809:1
801:=
741:)
252:.
221:G
207:.
147:(
87:)
81:(
76:)
72:(
58:.
38:.
20:)
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