View source for Diatonic and chromatic

{{short description|Terms in music theory to characterize scales}}
{{redirect|Chromatic}}
<!-- Style: this article was originated in and is stable in British English, and also uses spaced en dashes (not em dashes), serial commas, BCE and CE (not BC and AD). -->
[[File:Purcell diatonic chromaticism.png|thumb|upright=1.8|Melodies can be based on a diatonic scale and maintain its tonal characteristics but contain multiple [[accidentals]], up to all twelve tones of the chromatic scale, such as the opening of [[Henry Purcell]]'s "[[Dido's Lament|Thy Hand, Belinda]]" from ''[[Dido and Aeneas]]'' (1689) with [[figured bass]]), which features eleven of twelve pitches while chromatically descending by half steps,<ref>Benward & Saker (2003). ''Music: In Theory and Practice'', Vol. I, p. 38. 7th ed. {{ISBN|978-0-07-294262-0}}.</ref> the missing pitch being sung later.[[File:Purcell diatonic chromaticism.mid|thumb|center|Melody]][[File:Purcell diatonic chromaticism fb.mid|thumb|center|With figured bass]]]]
[[File:Bartok - Music mov. I fugue subject chromatic.png|thumb|upright=1.8|[[Béla Bartók]]: ''[[Music for Strings, Percussion and Celesta]]'', movement I, [[fugue]] [[subject (music)|subject]]: chromatic.<ref name="Leeuw">[[Ton de Leeuw|Leeuw, Ton de]] (2005). ''Music of the Twentieth Century'', p. 93. {{ISBN|90-5356-765-8}}</ref> [[File:Bartok - Music mov. I fugue subject chromatic.mid]]]]
[[File:Bartok - Music mov. I fugue subject diatonic.png|thumb|upright=1.8|Bartók: ''Music ...'', movement I, fugue subject: diatonic variant<ref name="Leeuw"/>[[File:Bartok - Music mov. I fugue subject diatonic.mid]]]]

'''Diatonic''' and '''chromatic''' are terms in [[music theory]] that are used to characterize [[Scale (music)|scales]]. The terms are also applied to musical instruments, [[Interval (music)|intervals]], [[Chord (music)|chords]], [[Musical note|note]]s, [[musical style]]s, and kinds of [[harmony]]. They are very often used as a pair, especially when applied to contrasting features of the [[Common practice period|common practice]] music of the period 1600–1900.{{efn|Often ''diatonic'' and ''chromatic'' are treated as mutually exclusive opposites, concerning common practice music. This article deals mainly with common practice music, and later music that shares the same core features (including the same particular use of [[tonality]], harmonic and melodic idioms, and types of scales, chords, and intervals). Where other music is dealt with, this is specially noted.}}

These terms may mean different things in different contexts. Very often, ''diatonic'' refers to musical elements derived from the modes and transpositions of the "white note scale" C–D–E–F–G–A–B.{{efn|This definition encompasses the natural [[minor scale]] (and equivalently the descending melodic minor), the [[major scale]], and the ecclesiastical [[Mode (music)|modes]].}} In some usages it includes all forms of [[heptatonic scale]] that are in common use in Western music (the major, and all forms of the minor).{{efn|For inclusion of the harmonic minor and the ascending melodic minor see the section [[#Modern meanings of "diatonic scale"|Modern meanings of "diatonic scale"]] in this article.}}

''Chromatic'' most often refers to structures derived from the [[chromatic scale]] in [[12-tone equal temperament]], which consists of all [[semitone]]s. Historically, however, it had other senses, referring in Ancient Greek music theory to a particular tuning of the [[tetrachord]], and to a rhythmic notational convention in [[Mensural notation|mensural music]] of the 14th to 16th centuries.

== History ==
[[File:Tetrachord Genera 1768.png|right|thumb|300px|Tetrachord genera of the four-string lyre, from [https://books.google.com/books?id=-MMCAAAAYAAJ&pg=PA261 ''The History of the Arts and Sciences of the Antients'']<!-- In this title, the spelling "Antients" is correct.—https://archive.org/details/historyofartssci02roll -->, Charles Rollin (1768). The text gives a typically fanciful account of the term ''chromatic''.]]

=== Greek genera ===
{{main|Genus (music)}}
In ancient Greece there were three standard tunings (known by the Latin word ''[[Genus (music)|genus]]'', plural ''genera''){{efn|Translating the term used by Greek theorists: γένος, ''génos''; plural γένη, ''génē''.}} of a lyre.<ref>It is unclear whether the lyre in question was itself a presumed four-stringed instrument ("τετράχορδον ὄργανον"), as some have suggested (see Peter Gorman, ''Pythagoras, a Life'' (London: Routledge & K. Paul, 1979), p.&nbsp;162: "The fundamental instrument of early Greek music was the tetrachord or four-stringed lyre, which was tuned in accordance with the main concordances; the tetrachord was also the foundation of Greek harmonic theory"). The number of strings on early lyres and similar instruments is a matter of much speculation (see Martin Litchfield West, ''Ancient Greek music'' (Oxford and New York: Oxford University Press, 1994), especially pp.&nbsp;62–64). Multiple later instruments had seven or perhaps more strings, and in that case the tetrachord must be thought of as based on a selection of four adjacent strings.</ref> These three tunings were called ''diatonic'',{{efn|The English word ''[[wikt:diatonic|diatonic]]'' is ultimately from the Greek διατονικός (''diatonikós''), itself from διάτονος (''diátonos''), of disputed etymology. Most plausibly, it refers to the intervals being "stretched out" in that tuning, in contrast to the other two tunings, whose lower two intervals were referred to as πυκνόν (''[[pyknon|pyknón]]''), from πυκνός (''pyknós'', "dense, compressed"). For more information, especially concerning the various exact tunings of the diatonic tetrachord, see [[Diatonic genus]].}} ''chromatic'',{{efn|''Chromatic'' is from Greek χρωματικός (''khrōmatikós''), itself from χρῶμα (''khrṓma''), which means ''complexion'', hence ''colour'' – or, specifically as a musical term, "a modification of the simplest music" (Liddell and Scott's ''[http://archimedes.fas.harvard.edu/pollux Greek lexicon]''). For more information, especially concerning the various exact tunings of the chromatic tetrachord, see [[Chromatic genus]].}} and ''enharmonic'',<ref>Occasionally, as in the Rollin excerpt shown in this section, spelt ''inharmonic''; but in OED this is only given as a distinct word with a distinct etymology ("Not harmonic; not in harmony; dissonant,..."). The motivation and sources of the Greek term ἐναρμονικός (''enarmonikós'') are little understood. But the two roots are ἐν (''en'': "in") and ἁρμονία (''harmonía'': "good placement of parts", "harmony", "a scale, mode, or τόνος [in one sense; see notes above]"). So in some way the term suggests harmoniousness or good disposition of parts, but not in the modern sense of ''[[harmony]]'', which has to do with simultaneous sounds. (See Solon Michaelides, ''The Music of Ancient Greece: An Encyclopaedia'' (London: Faber and Faber, 1978); Liddell and Scott; etc.) For more information, especially concerning the various exact tunings of the enharmonic tetrachord, see [[Enharmonic genus]].</ref> and the sequences of four notes that they produced were called ''tetrachords'' ("four strings").{{efn|In practice ''tetrachord'' (τετράχορδον; ''tetrákhordon'') also meant the instrument itself. And it could also mean the interval of a perfect fourth between the pitches of the fixed top and bottom strings; therefore the various tunings were called ''divisions of the tetrachord'' (see [[OED]], "Tetrachord".}} A diatonic tetrachord comprised, in descending order, two whole tones and a semitone, such as A G F E (roughly). In the chromatic tetrachord the second string of the lyre was lowered from G to G{{music|flat}}, so that the two lower intervals in the tetrachord were semitones, making the pitches A G{{music|flat}} F E. In the enharmonic tetrachord the second string of the lyre was lowered further to G{{music|doubleflat}}, so that the two lower interval in the tetrachord were [[quarter tone]]s, making the pitches A G{{music|doubleflat}} F{{music|d}} E (where F{{music|d}} is F{{music|natural}} lowered by a quarter tone). For all three tetrachords, only the middle two strings varied in their pitch.{{efn|For general and introductory coverage of Greek theory see ''Tuning and Temperament, A Historical Survey'', Barbour, J. Murray, 2004 (reprint of 1972 edition), {{ISBN|0-486-43406-0}}.}}{{efn|These meanings in Greek theory are the ultimate source of the meanings of the words today, but through a great deal of modification and confusion in Medieval times. It would therefore be a mistake to consider the Greek system and the subsequent Western systems (Medieval, Renaissance, or contemporary) as closely similar simply because of the use of similar terms: "...&nbsp;the categories of the diatonic, chromatic and enharmonic genera developed within the framework of monodic musical culture and have little in common with the corresponding categories of modern music theory."<ref>''Chromaticism'', Barsky, Vladimir, Routledge, 1996, p. 2.</ref> There were several Greek systems, in any case. What is presented here is merely a simplification of theory that spans several centuries, from the time of [[Pythagoras]] (c. 580 BCE – c. 500 BCE), through [[Aristoxenus]] (c. 362 BCE – after 320 BCE), to such late theorists as [[Alypius of Alexandria]] ([[floruit|fl.]] 360 CE). Specifically, there are more versions of each of the three tetrachords than are described here.}}

=== Medieval coloration ===
The term ''cromatico'' (Italian) was occasionally used in the medieval and Renaissance periods to refer to the ''coloration'' (Latin ''coloratio'') of certain notes. The details vary widely by period and place, but generally the addition of a colour (often red) to an empty or filled head of a note, or the "colouring in" of an otherwise empty head of a note, shortens the duration of the note.{{efn|Details of the practice for certain periods: "The device that was both the simplest and the most stable and durable was that known as ''coloratio''. In principle, any note or group of notes subjected to coloration or blackening was reduced to two-thirds of the value that it would have enjoyed in its pristine state. In respect of any note in mensural notation that was equal in duration to two of that next smaller in value, the coloration of three in succession caused each to undergo reduction to two-thirds of its erstwhile value, so creating a triplet&nbsp;... In the case of any note that was equal in duration to three of that next smaller, the coloration of three together likewise effected a proportional reduction in the value of each to two-thirds, so reducing perfect value to imperfect and commonly creating the effect called hemiola&nbsp;... On occasions coloured notes could appear singly to denote imperfect value, especially to inhibit unwanted perfection and alteration."<ref>Roger Bowers, "Proportional notation", 2. Coloration, ''New Grove Dictionary of Music and Musicians'', second edition, edited by [[Stanley Sadie]] and [[John Tyrrell (musicologist)|John Tyrrell]] (London: Macmillan, 2001).</ref>}} In works of the [[Ars Nova]] from the 14th century, this was used to indicate a temporary change in metre from triple to duple, or vice versa. This usage became less common in the 15th century as open white noteheads became the standard notational form for minims (half-notes) and longer notes called [[white mensural notation]].<ref>Parrish, Carl, ''The Notation of Medieval Music'', Pendragon, New York, 1978, pp. 147ff.</ref><ref>''Harvard Dictionary of Music'', 2nd ed., "Chromatic".</ref> Similarly, in the 16th century, a form of notating secular music, especially madrigals in {{Music|cut-time}} was referred to as "chromatic" because of its abundance of "coloured in" black notes, that is semiminims (crotchets or quarter notes) and shorter notes, as opposed to the open white notes in {{Music|common-time}}, commonly used for the notation of sacred music.<ref>{{cite book|last1=Grout|first1=Donald J.|author1-link=Donald Grout|last2=Palisca|first2=Claude|author2-link=Claude V. Palisca|title=A History of Western Music|edition=6th|publisher=W. W. Norton|location=New York|year=2001|pages=188–190}}</ref> These uses for the word have no relationship to the modern meaning of ''chromatic'', but the sense survives in the current term ''[[coloratura]]''.<ref>"The root of the Italian term is that of 'colour', and it is probably related through its use of diminution (the little notes that 'rush' to the next long note, as Bernhard writes) to the mensural practice of coloration" (''New Grove'', "Coloratura").</ref>

=== Renaissance chromaticism ===
{{See also|Chromaticism}}
The term ''chromatic'' began to approach its modern usage in the 16th century. For instance [[Orlande de Lassus|Orlando Lasso]]'s ''[[Prophetiae Sibyllarum]]'' opens with a prologue proclaiming, "these chromatic songs,<ref>Rendered by many as ''Carmina chromatico'', though this is incorrect Latin; the title is given as ''Carmina chromatica'' (which is plural of Latin ''carmen chromaticum'') in ''New Grove Online''. The entire passage is relevant to present points in this article:
{{quote|Each tetrachord or hexachord is a diatonic entity, containing one diatonic semitone; but the tight overlapping of hexachordal segments – some as small as an isolated ''coniuncta'' – to produce successive or closely adjacent semitones did not necessarily compromise their diatonic status. The tenor of Willaert's so-called chromatic duo is entirely diatonic in its progressions (Bent, 1984), as are Lowinsky's examples of 'secret chromatic art' (Lowinsky, 1946) and indeed almost the entire repertory. True chromatic progressions (e.g. F–F{{music|sharp}}–G) are occasionally allowed in theory (Marchetto, ''GerbertS'' {{sic}}, iii, 82–3) and prescribed in manuscript sources. Except where a melodic chromatic interval is introduced in the interests of vertical perfection (e.g. Old Hall, no. 101; see ex. 2d), musica ficta is by nature diatonic.

Even music liberally provided with notated sharps is not necessarily chromatic. This has been called 'accidentalism'. Increasingly explicit use of accidentals and explicit degree-inflection culminates in the madrigals of Marenzio and Gesualdo, which are remote from medieval traditions of unspecified inflection, and co-exists in the 16th century both with older hexachordal practices and with occasional true melodic chromaticism. It is the small number of chromatic intervals in Lassus's [{{=}} Lasso's] Sibylline Prophecies (Carmina chromatica), for example, that determine its chromatic status, not the large number of sharps that give it 'chromatic' colouring according to looser modern usage.|''New Grove Online'', "Musica Ficta", I, ii}}</ref> heard in modulation, are those in which the mysteries of the Sibyls are sung, intrepidly," which here takes its modern meaning referring to the frequent change of key and use of chromatic intervals in the work. (The ''Prophetiae'' belonged to an experimental musical movement of the time, called [[musica reservata]]). This usage comes from a renewed interest in the [[Greek genera]], especially its chromatic tetrachord, notably by the influential theorist [[Nicola Vicentino]] in his treatise on ancient and modern practice, 1555.{{sfn|Grout|Palisca|2001|p=188}}

== Diatonic scales ==<!--this section is linked to from #REDIRECT Gamut (music)-->
{{Image frame
|content =<score sound="1"> {
\new Staff \with { \remove "Time_signature_engraver" }
\relative c'{ c d e f g a b c\fermata \bar "||" }
}
</score>
|width=|caption = Diatonic scale on C equal tempered and just.}}
{{main|Diatonic scale}}

[[File:Gammut etymology Lemon 1783.png|right|thumb|300px|''Gamut'' as defined by George William Lemon, ''English Etymology'', 1783.]]
[[File:Chromatic notes diagram.png|thumb|300px|The diatonic scale notes (above) and the non-scale chromatic notes (below)<ref name="Forte">{{cite book|last=Forte|first=Allen|author-link=Allen Forte|title=Tonal Harmony|edition=3rd|location={{abbr|[[sine loco|s.l.]]|without place}}|publisher=Holt, Rinehart, and Wilson|year=1979|pages=4–5|isbn=0-03-020756-8}}. "It is not an independent scale, but derives from the diatonic scale."</ref>]]

Medieval theorists defined scales in terms of the Greek tetrachords. The ''gamut'' was the series of pitches from which all the Medieval "scales" (or [[Mode (music)|modes]], strictly) notionally derive, and it may be thought of as constructed in a certain way from ''diatonic'' tetrachords. The origin of the word ''gamut'' is explained in the article [[Guidonian hand]]; here the word is used in one of the available senses: the all-encompassing gamut as described by [[Guido d'Arezzo]] (which includes all of the modes).

The [[Interval (music)|intervals]] from one note to the next in this medieval gamut are all [[Whole tone|tones]] or [[semitone]]s, recurring in a certain pattern with five tones (T) and two semitones (S) in any given [[octave]]. The semitones are separated as much as they can be, between alternating groups of three tones and two tones. Here are the intervals for a string of ascending notes (starting with F) from the gamut:
:... –T–T–T–S–T–T–S–T–T–T–S–T– ...
And here are the intervals for an ascending octave (the seven intervals separating the eight notes A–B–C–D–E–F–G–A) from the gamut:
:T–S–T–T–S–T–T (five tones and two semitones){{efn|Some theorists{{Weasel-inline|date=September 2010}} derive such a scale from a certain series of pitches rising by six perfect fifths: F–C–G–D–A–E–B. These pitches are then rearranged by transposition to a single-octave scale: C–D–E–F–G–A–B[–C] (the standard C major scale, with the interval structure T–T–S–T–T–T[–S]). A few theorists{{Weasel-inline|date=September 2010}} call the original untransposed series itself a "scale". Percy Goetschius calls that series the "natural scale";<ref>Goetschius, Percy. ''The Theory and Practice of Tone-Relations'', Schirmer, 1931 edition, p. 3.</ref> see further citation [[#Diatonic excludes the harmonic and melodic minor scales|below]]{{dead link|date=September 2019}}).}}

The white keys are the modern analog of the gamut. In its most strict definition, therefore, a diatonic scale is one that may be derived from the pitches represented in successive white keys of the piano (or a [[Transposition (music)|transposition]] thereof). This would include the [[major scale]], and the [[minor scale|natural minor scale]] (same as the descending form of the [[melodic minor]]), but not the old ecclesiastical [[church modes]], most of which included both versions of the "variable" note B{{Music|natural}}/B{{Music|flat}}.

=== Modern meanings ===
There are specific applications in the music of the [[common practice period|Common Practice Period]], and later music that shares its core features.

Most, but not all writers,<ref>Goetschius, as cited [[#Diatonic excludes the harmonic and melodic minor scales|below]]{{dead link|date=September 2019}}, accepts only the major as diatonic.</ref> accept the [[natural minor]] as diatonic.{{Failed verification|date=April 2015}}<!--Goetschius, as cited, is specifically said not to consider the natural minor scale at all, and his rejection is of the harmonic minor scale. Who, then, rejects the natural minor as diatonic, and what is the difference between natural minor and descending melodic minor?--> As for other forms of the minor:{{efn|The first "exclusive" usage seems to be gaining greater currency. Certainly it is becoming close to standard in academic writing, as can be seen by querying online archives (such as [[JSTOR]]) for recent uses of the term ''diatonic''. Equally certainly, the second "inclusive" meaning is still strongly represented in non-academic writing (as can be seen by online searches of practically oriented music texts at, for example, [[Amazon.com]]). Overall, considerable confusion remains; on the evidence presented in the list of sources, there are very many sources in the third category: ''Diatonic used vaguely, inconsistently, or anomalously''.}}

*"Exclusive" usage
:Some writers consistently classify the other variants of the minor scale – the [[melodic minor]] (ascending form) and the [[harmonic minor]] – as ''non''-diatonic, since they are not transpositions of the white-note pitches of the piano. Among such theorists there is no agreed general term that encompasses the major and all forms of the minor scale.{{efn|A very clear statement of the "exclusive" stance is given in the excerpt from "The leading tone in direct chromaticism: from Renaissance to Baroque", Clough, John, 1957, [[#Diatonic_excludes_the_harmonic_and_melodic_minor_scales|below]]{{dead link|date=September 2019}}. The excerpt acknowledges and analyses the difficulties with logic, naming, and taxonomy in that stance.}}
*"Inclusive" usage
:Some writers consistently include the melodic and harmonic minor scales as diatonic also. For this group, every scale standardly used in common practice music and much similar later music is either ''diatonic'' (the major, and ''all'' forms{{efn|A few exclude only the harmonic minor as diatonic, and accept the ascending melodic, because it comprises only tones and semitones, or because it has all of its parts analysable as tetrachords in some way or other.}} of the minor) or ''chromatic''.{{efn|However, ''beyond'' analysis of common practice music, even these writers do not typically consider non-standard uses of some familiar scales to be ''diatonic''. For example, unusual modes of the melodic or harmonic minor scale, such as used in early works by [[Stravinsky]], are almost never described as "diatonic".}}
*"Mixed" usage
:Still other writers mix these two meanings of ''diatonic'' (and conversely for ''chromatic''), and this can lead to confusions and misconceptions. Sometimes context makes the intended meaning clear.

Some other meanings of the term ''diatonic scale'' take the extension to harmonic and melodic minor even further, to be even more inclusive.<ref name=gould2000>{{cite journal |jstor=833660 |url=http://www.accessmylibrary.com/coms2/summary_0286-28765351_ITM |pages=88–105 |last1=Gould |first1=M. |title=Balzano and Zweifel: Another Look at Generalized Diatonic Scales |volume=38 |issue=2 |journal=[[Perspectives of New Music]]|year=2000 |doi=10.2307/833660|url-access=subscription }}
An explicit example of such an extended general use of ''diatonic scale'' and related terms:{{quote|Throughout this paper, I use the terms "diatonic," "pentatonic" and "chromatic" in their generic senses, as follows:
#A "diatonic" scale is a scale formed from two intervals of different sizes, such that groups of several adjacent instances of the larger interval are separated by single instances of the smaller interval.
#A "pentatonic" scale is a scale formed from two intervals of different sizes, such that groups of several adjacent instances of the smaller interval are separated by single instances of the larger interval. Therefore a generic "pentatonic" can contain more than five tones.
#"Chromatic" refers to the interval formed between adjacent pitch-classes of any equal-tempered scale.}}
See also [[#Extended pitch selections]], in this article. See also an exceptional usage by Persichetti, in a note to [[#Diatonic_pentatonic_scale]], below.</ref>

In general, ''diatonic'' is most often used inclusively with respect to music that restricts itself to standard uses of traditional major and minor scales. When discussing music that uses a larger variety of scales and modes (including much jazz, rock, and some tonal 20th-century concert music), writers often adopt the exclusive use to prevent confusion.

== Chromatic scale ==
{{main|Chromatic scale}}
<score sound="1">
{
  \new Staff \with { \remove "Time_signature_engraver" }
  \relative c' { \time 13/4
c cis d dis e f fis g gis a ais b c b bes a aes g ges f e es d des c \bar "|" }
}
</score>
Chromatic scale on C: full octave ascending and descending

A ''chromatic'' scale consists of an ascending or descending sequence of pitches, always proceeding by [[semitone]]s. Such a sequence of pitches is produced, for example, by playing all the black and white keys of a piano in order. The structure of a chromatic scale is therefore uniform throughout—unlike major and minor scales, which have tones and semitones in particular arrangements (and an augmented second, in the harmonic minor).<ref>It is not usual to use ''chromatic scale'' in any other sense. A rare exception is found in ''Elements of Musical Composition'', Crotch, William, 1830. (See the quotation from this text, [[#Diatonic excludes the harmonic and melodic minor scales|below]]{{dead link|date=September 2019}}. See also extensive analysis in the excerpt from "The leading tone in direct chromaticism: from Renaissance to Baroque", Clough, John, 1957, in the same subsection below.) Outside of music altogether, ''chromatic scale'' may refer to [[Von Luschan's chromatic scale]].</ref>

== Musical instruments ==
Some instruments, such as the [[violin]], can play any scale; others, such as the [[glockenspiel]], are restricted to the scale to which they are tuned. Among this latter class, some instruments, such as the piano, are always tuned to a chromatic scale, and can be played in any key, while others are restricted to a diatonic scale, and therefore to a particular key. Some instruments, such as the [[harmonica]], [[harp]], and glockenspiel, are available in both diatonic and chromatic versions (although it is possible to play chromatic notes on a diatonic harmonica, they require extended [[embouchure]] techniques, and some chromatic notes are only usable by advanced players). {{gallery|align=center
|File:Pixiphone diatonic.jpg|Diatonic [[Pixiphone]], a brand of glockenspiel
|File:Pixiphone chromatic.jpg|Chromatic Pixiphone
|File:16-hole chrom 10-hole diatonic.jpg|Chromatic (rear) and diatonic harmonicas
}}

== Intervals ==
<!--[[Diatonic interval]] and [[chromatic interval]] redirect directly here-->

{{Quote|When one note of an interval is chromatic or when both notes are chromatic, the entire interval is called chromatic. Chromatic intervals arise by raising or lowering one or both notes of a diatonic interval, so that the interval is made larger or smaller by the interval of half step ["altered diatonic intervals"].|[[Allen Forte]] (1979){{sfn|Forte|1979|pp=19–20}}}}

Because ''diatonic scale'' is itself ambiguous, distinguishing intervals is also ambiguous.{{efn|There are several other understandings of the terms ''diatonic interval'' and ''chromatic interval''. There are theorists{{Weasel-inline|date=September 2010}} who define all augmented and diminished intervals as ''chromatic'', even though some of these occur in scales that everyone accepts as diatonic. (For example, the diminished fifth formed by B and F, which occurs in C major.) There are even some writers who define all ''minor'' intervals as chromatic (Goetschius assesses all intervals as if the lower note were the [[Tonic (music)|tonic]], and since for him only the major scale is diatonic, only the intervals formed above the tonic in the major are diatonic;<ref>Goetschius, Percy, ''The Theory and Practice of Tone-Relations'', 1931, p. 6. {{pre-ISBN}}.</ref><ref>See also, for example, Harrison, Mark, ''Contemporary Music Theory – Level Two'', 1999, p. 5.</ref>). Some theorists take the ''diatonic interval'' to be simply a measure of the number of "scale degrees" spanned by two notes (so that F{{music|sharp}}–E{{music|flat}} and F{{music|natural}}–E{{music|natural}} represent the same "diatonic interval": a seventh); and they use the term ''chromatic interval'' to mean the number of semitones spanned by any two pitches (F{{music|sharp}} and E{{music|flat}} are "at a chromatic interval of nine semitones"). Some theorists use the term ''diatonic interval'' to mean ''an interval named on the assumption of the diatonic system of Western music'' (so that all perfect, major, minor, augmented, diminished intervals are "diatonic intervals"). It is not clear what ''chromatic interval'' would mean, if anything, in parallel with this usage for ''diatonic''. Some theorists use ''chromatic interval'' to mean simply ''[[semitone]]'', as for example in the article [[Chromatic fourth]].<ref>See also Williams, Peter F., ''The Chromatic Fourth during Four Centuries of Music'', OUP, 1997.</ref> Something close to this usage may be found in print. For example, the term ''chromatically'', as used in: "The trill rises chromatically by step above this harmonic uncertainty, forming a chromatic fourth&nbsp;..."<ref>Robin Stowel, ''Beethoven: Violin Concerto'' (Cambridge Music Handbooks), Cambridge and New York: Cambridge University Press, 2005, p. 66.</ref> The term as used in the phrase ''chromatic fourth'' itself perhaps means just what it means in ''chromatic scale'', but here applied to a melodic ''interval'' rather than a scale.}} For example, the interval B{{music|natural}}–E{{music|flat}} (a [[diminished fourth]], occurring in C harmonic minor) is considered diatonic if the harmonic minor scale is considered diatonic,<ref>{{Cite book|last=Lovelock|first=William|url=https://www.worldcat.org/oclc/1039070588|title=The rudiments of music.|date=1971|publisher=St. Martin's Press|location=New York|language=English|oclc=1039070588}}{{Page needed|date=November 2020}}</ref> but chromatic if the harmonic minor scale is ''not'' considered diatonic.<ref>{{cite Grove|last1=William|first1=Drabkin|date=2001|title=Diatonic|url=https://doi.org/10.1093/gmo/9781561592630.article.07727|url-access=subscription}}</ref>

Forte lists the chromatic intervals in major and natural minor as the augmented unison, diminished octave, augmented fifth, diminished fourth, augmented third, diminished sixth, diminished third, augmented sixth, minor second, major seventh, major second, minor seventh, doubly diminished fifth, and doubly augmented fourth.{{sfn|Forte|1979|p=21}}

Additionally, the label ''chromatic'' or ''diatonic'' for an interval may depend on context. For instance, in C major, the interval C–E{{music|flat}} could be considered a ''chromatic'' interval because it does not appear in the prevailing diatonic key; conversely, in C minor it would be ''diatonic''. This usage is still subject to the categorization of scales above, e.g. in the B{{music|natural}}–E{{music|flat}} example above, classification would still depend on whether the harmonic minor scale is considered diatonic.

=== In different systems of tuning ===
<score sound="1">
{
\new Staff \with { \remove "Time_signature_engraver" }
\relative c' {e!2 f e! eis}
}
</score>
Pythagorean diatonic and chromatic interval: E{{music|natural}}-F{{music|natural}} and E{{music|natural}}-E{{music|#}}
{| align=right
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| [[File:Just major third on C.mid|thumb|C–E]][[File:Just perfect fourth on C.mid|thumb|C–F]][[File:Pythagorean augmented third on C.mid|thumb|C–E{{music|#}}{{+}}{{+}}]]
|}

In cases where intervals are [[enharmonic]]ally equivalent, there is no difference in tuning (and therefore in sound) between them. For example, in [[12-tone equal temperament]] and its multiples, the notes F and E{{music|sharp}} represent the same pitch, so the diatonic interval C–F (a perfect fourth) sounds the same as its enharmonic equivalent—the chromatic interval C–E{{music|sharp}} (an augmented third).

However, in the majority of other tunings (such as [[19 equal temperament|19-tone]] and [[31 equal temperament|31-tone]] equal temperament), there is a difference in tuning between notes that are enharmonically equivalent in 12-tone equal temperament. In systems based on a [[cycle of fifths]], such as [[Pythagorean tuning]] and [[meantone temperament]], these intervals are labelled ''diatonic'' or ''chromatic'' intervals. Under a generalized [[meantone]] tuning, notes such as G{{music|sharp}} and A{{music|flat}} are not enharmonically equivalent but are instead different by an amount known as a ''[[diesis]]''. Instruments limited to 12 pitches per octave can only produce a chain of 11 fifths, resulting in a "break" at the ends of the chain. This causes intervals that cross the break to be written as [[Augmented (music)|augmented]] or [[Diminished (music)|diminished]] ''chromatic'' intervals, with the most notable example being the "[[wolf interval|wolf fifth]]" (which is actually a [[diminished sixth]]) that occurs when 12-note-per-octave keyboards are tuned to meantone temperaments whose fifths are flatter than those in 12-tone equal temperament. In a generalized meantone temperament, chromatic [[semitone]]s (E–E{{music|sharp}}) are smaller than or equal to diatonic semitones (E–F) in size,<ref>Helmholtz, Hermann, trans. Alexander Ellis, ''On the Sensations of Tone'', Dover, New York, 1954, pp. 433–435 and 546–548. The two notes of a diatonic semitone have different letter names; those of a chromatic semitone have the same letter name.</ref> With consonant intervals such as the major third, the nearby interval (a diminished fourth in the case of a major third) is generally less consonant.

If the tritone is assumed diatonic, the classification of written intervals on this definition is not significantly different from the "drawn from the same diatonic scale" definition above as long as the harmonic minor and ascending melodic minor scale variants are not included.

== Chords ==
{{Quote|By chromatic linear chord is meant simply a chord entirely of linear origin which contains one or more chromatic notes. A great many of these chords are to be found in the literature.|Allen Forte (1979){{sfn|Forte|1979|p=352}}}}

[[File:Diatonic triads, seventh, and ninth chords (Ziehn 1907).png|thumb|500px|center|[[Bernhard Ziehn]]'s 1907 list of, "diatonic triads", diatonic seventh-chords," and two examples of, "diatonic ninth-chords," the "large" and "small" ninth chords; all from the C major or the C harmonic minor scale<ref>Ziehn, Bernhard (1907). ''[https://books.google.com/books?id=fb0PAAAAYAAJ&pg=PA3 Manual of Harmony: Theoretical and Practical, Volume 1]'', p.3. Wm. A Kaun Music Company. {{pre-ISBN}}. Macro and Roman numeral analysis not in the original.</ref>]]

''Diatonic [[Chord (music)|chords]]'' are generally understood as those that are built using only notes from the same diatonic scale; all other chords are considered ''chromatic''. However, given the ambiguity of ''diatonic scale'', this definition, too, is ambiguous. And for some theorists, chords are only ever diatonic in a relative sense: the [[augmented triad]] E{{music|flat}}–G–B{{music|natural}} is diatonic "to" or "in" C minor.<ref>Kostka, Stefan, and Payne, Dorothy, ''Tonal Harmony'', McGraw-Hill, 5th edition, 2003, pp. 60–61. {{ISBN|9780070358744}}.</ref>

On this understanding, the [[diminished seventh chord]] built on the [[leading note]] is accepted as diatonic in minor keys.<ref>"Because of the variability of [scale degrees] 6 and 7, there are sixteen possible diatonic seventh chords in minor&nbsp;... [One line in a table headed ''Common diatonic seventh chords in minor'':] __º7_____viiº<sup>7</sup>__" (''Tonal harmony'', Kostka, Stefan and Payne, Dorothy, McGraw-Hill, 3rd edition 1995, pp. 64–65).</ref>

If the strictest understanding of the term ''diatonic scale'' is adhered to – whereby only transposed 'white note scales' are considered diatonic – even a major triad on the dominant scale degree in C minor (G–B{{music|natural}}–D) would be chromatic or [[alteration (music)|altered]] in C minor.{{efn|This is because the third of the triad does not belong to the [[natural minor]] scale or [[mode (music)|Aeolian mode]]<!--Remove the reference to the Aeolian mode here? Doesn't it clutter the sentence?--> of C minor (C, D, E{{music|flat}}, F, G, A{{music|flat}}, B{{music|flat}}).

This highly restrictive interpretation is effectively equivalent to the idea that diatonic triads are those drawn from the notes of the major scale alone, as this source rather roughly puts it: "Diatonic chords are wholly contained within a major scale."<ref>Harrison, Mark, ''Contemporary Music Theory – Level Two'', 1999, p. 7.</ref>}} Some writers{{Weasel-inline|date=September 2010}} use the phrase "diatonic to" as a synonym for "belonging to". Therefore a chord is not said to be "diatonic" in isolation, but can be said to be "diatonic to" a particular key if its notes ''belong'' to the underlying diatonic scale of the key.

== Harmony ==
{{Quote|The chromatic expansion of tonality which characterizes much of nineteenth century music is illustrated in miniature by the substitution of a chromatic harmony for an expected diatonic harmony. This technique resembles the deceptive cadence, which involves the substitution of another diatonic chord for the expected diatonic goal harmony.{{sfn|Forte|1979|p=497}}&nbsp;...<br/>
In the major mode a substitute chromatic consonance often proves to be a triad which has been taken from the parallel minor mode. This process ["assimilation"]...is called ''mixture of mode'' or simply ''mixture''....Four consonant triads from the minor mode may replace their counterparts in the major mode. These we call ''chromatic triads by mixture''.{{sfn|Forte|1979|p=498}}|Allen Forte (1979)}}

The words ''diatonic'' and ''chromatic'' are also applied inconsistently to [[harmony]]:

* Often musicians call ''diatonic harmony'' any kind of harmony inside the [[Major and minor|major–minor]] system of [[Common practice period|common practice]]. When diatonic harmony is understood in this sense, the supposed term ''chromatic harmony'' means little, because chromatic chords are also used in that same system.
* At other times, especially in textbooks and syllabuses for musical composition or music theory, ''diatonic harmony'' means ''harmony that uses only "diatonic chords"''.{{efn|Often the content of "diatonic harmony" in this sense includes such harmonic resources as diminished sevenths on the leading note – possibly even in major keys – even if the text uses a classification for chords that should exclude those resources.}} According to this usage, ''chromatic harmony'' is then harmony that extends the available resources to include chromatic chords: the [[augmented sixth]] chords, the [[Neapolitan sixth]], chromatic [[seventh chords]], etc.{{efn|Some of these are chords "borrowed" from a key other than the prevailing key of a piece; but some are not: they are derivable only by chromatic [[alteration (music)|alteration]].}}
* Since the word ''harmony'' can be used of single classes of chords (''dominant harmony'', ''E minor harmony'', for example), ''diatonic harmony'' and ''chromatic harmony'' can be used in this distinct way also.{{efn|"''Diatonic harmonies'' are those built on the seven degrees of whatever major or minor diatonic scale is being used. ''Chromatic harmonies'' are those built on, or using, the five non-diatonic degrees of the scale."<ref>''Music for Our Time'', Winter, Robert, Wadsworth, 1992, p. 35.</ref> (Strictly, there is an uncertainty to be noted here, involving harmonies that would be diatonic because they are built on unaltered degrees of a diatonic scale, but chromatic because they include a non-diatonic note: D–F{{music|sharp}}–A in C major, for example. But the intention is clearly that such harmonies are chromatic.)}}
However,
* Chromatic harmony may be defined as the use of successive chords that are from two different keys and therefore contain tones represented by the same note symbols but with different [[accidentals]].<ref name="Tischler">{{cite journal |jstor=842933 |pages=94–97 |last1=Tischler |first1=H. |title=Re: Chromatic Mediants: A Facet of Musical Romanticism |volume=2 |issue=1 |journal=Journal of Music Theory |year=1958 }}</ref> Four basic techniques produce chromatic harmony under this definition: modal interchange, secondary dominants, melodic tension, and [[chromatic mediant]]s.<ref name="Tischler"/>

Instrumental compositions of the late [[Renaissance music|Renaissance]] and early [[Baroque music|Baroque]] periods also began experimenting with the expressive possibilities of contrasting diatonic passages of music with chromatic ones.  Here, for example is part of the [[Virginals|Virginal]] Piece ‘His Humour’ by [[Giles Farnaby]].  (The title ‘Humour’ should be interpreted as meaning ‘mood’, here.) The first four bars are largely diatonic.  These are followed by a passage exploiting chromatic harmony, with the upper part forming an ascending, followed by a descending [[chromatic scale]]:[[File:Farnaby - His Humour 01.wav|thumb|Farnaby - His Humour]][[File:Farnaby - His Humour.png|thumb|center|500px|Farnaby - His Humour]]

In the following passage from the slow movement of [[Beethoven]]'s [[Piano Concerto No. 4 (Beethoven)|Piano Concerto No. 4]], Op. 58., the long, flowing melody of the first five bars is almost entirely diatonic, consisting of notes within the scale of E minor, the movement's home key. The only exception is the G sharp in the left hand in the third bar. By contrast, the remaining bars are highly chromatic, using all the notes available to convey a sense of growing intensity as the music builds towards its expressive climax.[[File:Beethoven Piano Concerto 4 slow movement, bars 47-55.wav|thumb|Beethoven Piano Concerto 4 slow movement, bars 47–55]][[File:Beethoven Piano Concerto 4 slow movement opening.png|thumb|center|500px|Beethoven Piano Concerto 4 slow movement, bars 47–55]]

A further example may be found in this extract from act 3 of [[Richard Wagner]]'s opera ''[[Die Walküre]]''. The first four bars harmonize a descending [[chromatic scale]] with a rich, intoxicating chord progression. In contrast, the bars that follow are entirely diatonic, using notes only within the scale of E major. The passage is intended to convey the god Wotan putting his daughter Brünnhilde into a deep sleep.
[[File:Wagner, Die Walkure, Act III, magic sleep music.wav|thumb|Wagner, ''Die Walküre'', act 3, magic sleep music]]
[[File:Wagner, Die Walkure, Act III, magic sleep music.png|thumb|center|500px|Wagner, ''Die Walküre'', act 3, magic sleep music]]

== Miscellaneous usages ==

=== Tones ===
{{Quote|Notes which do not belong to the key [those "that lie within the major 2nds" of the diatonic scale] are called ''chromatic'' notes.|[[Allen Forte]] (1979)<ref name="Forte"/>}}

In modern usage, the meanings of the terms ''diatonic note/tone'' and ''chromatic note/tone'' vary according to the meaning of the term ''diatonic scale''. Generally – not universally – a note is understood as diatonic in a context if it belongs to the diatonic scale that is used in that context; otherwise it is chromatic.

=== Inflection ===
The term ''chromatic inflection'' (alternatively spelt ''inflexion'') is used in two senses:
* Alteration of a note that makes it (or the harmony that includes it) chromatic rather than diatonic.<ref>"... most chromatic harmony can be read as diatonic harmony with chromatic inflection", a view attributed to Simon Sechter in ''New Grove'', "Analysis", §II: History 3.</ref>
* Melodic movement between a diatonic note and a chromatically altered variant (from C to C{{music|sharp}} in G major, or vice versa, for example).<ref>"A ''chromatic progression'' is one between harmonies with no diatonic relationship, harmonies that do not coexist in any single diatonic system of key and mode. For this purpose, the harmonic form of the minor scale is considered the tonal-harmonic basis of its diatonic system. A usual characteristic of the chromatic progression is ''chromatic inflection'' – the change of one or more notes from one form (sharp, natural, or flat) to another" Wallace Berry, ''Form in Music'' (Prentice-Hall, 1966), pp. 109–110, note 5.</ref>

=== Progression ===
The term ''chromatic progression'' is used in three senses:
* Movement between harmonies that are not elements of any common diatonic system (that is, not of the same diatonic scale: movement from D–F–A to D{{music|sharp}}–F{{music|sharp}}–A, for example).<ref>Wallace Berry, ''Form in Music'' (Prentice-Hall, 1966), pp. 109–110, note 5.</ref>
* The same as the second sense of ''chromatic inflection'', above.<ref>"In [an example] the change from major to minor is supported by the chromatic progression&nbsp;... in the bass" ''Structural Functions of Harmony'', Schoenberg, Arnold, Faber & Faber, 1983, p. 54.</ref>
* In [[musica ficta]] and similar contexts, a melodic fragment that includes a chromatic semitone, and therefore includes a ''chromatic inflection'' in the second sense, above.<ref name="ReferenceA">See ''New Grove Online'', "Musica Ficta", I, ii, cited earlier.</ref>

The term ''diatonic progression'' is used in two senses:
* Movement between harmonies that both belong to at least one shared diatonic system (from F–A–C to G–B–E, for example, since both occur in C major).<ref>See ''Form in Music'', Berry, Wallace, Prentice-Hall, 1966, pp. 109–110, note 5. The author even includes movement between tonic and [[Neapolitan sixth]] harmonies (in both major and minor), because there exists some diatonic system in which both harmonies occur. With C major, for example, both occur in the subdominant minor, F minor.</ref>
* In musica ficta and similar contexts, a melodic fragment that does not include a chromatic semitone, even if two semitones occur contiguously, as in F{{music|sharp}}–G–A{{music|flat}}.<ref name="ReferenceA"/>{{Vague|date=September 2010}}<!--By the rules governing musica ficta, this sequence of notes may not occur (rule that mi may not mutate to fa, and vice-versa). In what way does this apply to ficta contexts, therefore?-->

=== Modulation ===
* Diatonic modulation is [[Modulation (music)|modulation]] via a diatonic progression.<ref name="Berry, p. 125">Berry, ''Form in Music'', p. 125, note 2.</ref>
* Chromatic modulation is modulation via a chromatic progression, in the first sense given above.<ref name="Berry, p. 125"/>

=== Pentatonic scale ===
* One very common kind of [[pentatonic scale]] that draws its notes from the diatonic scale (in the ''exclusive'' sense, [[#Modern_meanings|above]]) is sometimes called the ''diatonic pentatonic scale'': C–D–E–G–A[–C], or some other [[Musical mode|modal]] arrangement of those notes.
* Other pentatonic scales (such as the [[pelog]] scales) may also be construed as reduced forms of a diatonic scale but are not labelled ''diatonic''.<ref>''Twentieth-Century Harmony'', Persichetti, Vincent, Norton, 1961, pp. 50–51. Persichetti also makes an exceptional use of the term ''diatonic scale'' in this context: "Diatonic scales of five tones are harmonically limited&nbsp;...".</ref>

== Modern extensions ==
Traditionally, and in all uses discussed above, the term ''diatonic'' has been confined to the domain of pitch, and in a fairly restricted way. Exactly which scales (and even which ''modes'' of those scales) should count as diatonic is unsettled, as shown above. But the broad selection principle itself is not disputed, at least as a theoretical convenience.

=== Extended pitch selections ===
The selection of pitch classes can be generalised to encompass formation of [[Musical scale#Non-Western scales|non-traditional scales]].<ref name=gould2000/> Or a larger set of underlying pitch classes may be used instead. For example, the octave may be divided into varying numbers of equally spaced pitch classes. The usual number is twelve, giving the conventional set used in Western music. But Paul Zweifel<ref>{{cite journal |jstor=833490 |pages=140–161 |last1=Zweifel |first1=P. F. |title=Generalized Diatonic and Pentatonic Scales: A Group-Theoretic Approach |volume=34 |issue=1 |journal=[[Perspectives of New Music]]|year=1996 |doi=10.2307/833490}}</ref> uses a [[group-theoretic]] approach to analyse different sets, concluding especially that a set of twenty divisions of the octave is another viable option for retaining certain properties associated with the conventional "diatonic" selections from twelve pitch classes.

=== Rhythms ===
It is possible to generalise this selection principle even beyond the domain of pitch. The diatonic idea has been applied in analysis of some traditional [[Music of Africa|African rhythms]], for example. Some selection or other is made from an underlying superset of metrical [[beat (music)|beat]]s, to produce a "diatonic" rhythmic "scale" embedded in an underlying metrical "matrix". Some of these selections are diatonic in a way similar to the traditional diatonic selections of pitch classes (that is, a selection of seven beats from a matrix of twelve beats – perhaps even in groupings that match the tone-and-semitone groupings of diatonic scales). But the principle may also be applied with even more generality (including even ''any'' selection from a matrix of beats of ''any'' size).<ref>{{cite journal |jstor=779378 |pages=71–89 |last1=Rahn |first1=J. |title=Turning the Analysis around: Africa-Derived Rhythms and Europe-Derived Music Theory |volume=16 |issue=1 |journal=Black Music Research Journal |year=1996 |doi=10.2307/779378}}</ref>

== See also ==
* [[Major and minor]]
* [[Universal key]]

== Notes ==
{{Notelist}}

== References ==
{{Reflist}}

{{Chromaticism}}

{{DEFAULTSORT:Diatonic And Chromatic}}
[[Category:Ancient Greek music]]
[[Category:Byzantine music]]
[[Category:Musical scales]]
[[Category:Music of Greece]]
[[Category:Harmony]]
[[Category:Chromaticism]]