Diatonic and chromatic

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Diatonic and chromatic are terms in music theory that are most often used to characterise scales, and are also applied to intervals, chords, notes, musical styles, and kinds of harmony. They are very often used as a pair, especially when applied to contrasting features of the common practice music of the period 1600–1900.^[1]

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 (see details below).^[2] 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).^[3] Chromatic refers to structures derived from the chromatic scale, which consists of all semitones.

Contents 1 History 1.1 Greek genera 1.2 Medieval coloration 1.3 Renaissance chromaticism 2 Diatonic scales 2.1 Background: the Medieval gamut 2.2 Modern meanings of "diatonic scale" 3 Chromatic scale 4 Diatonic and chromatic intervals 4.1 Intervals in different systems of tuning 5 Diatonic and chromatic chords 6 Diatonic and chromatic harmony 7 Miscellaneous usages 7.1 Diatonic and chromatic notes 7.2 Chromatic inflection 7.3 Chromatic progression 7.4 Diatonic progression 7.5 Diatonic and chromatic modulation 7.6 Diatonic pentatonic scale 8 Modern extensions of the diatonic idea 8.1 Extended pitch selections 8.2 Diatonic rhythms 9 Notes 10 Published sources for "diatonic", in Common Practice music 10.1 Diatonic excludes the harmonic and melodic minor scales 10.2 Diatonic includes the harmonic and melodic minor scales 10.3 Diatonic used vaguely, inconsistently, or anomalously 11 See also

[edit] History

[edit] Greek genera

Main article: Tetrachord

In ancient Greece there were three standard tunings (known by the Latin word genus, plural genera)^[4] of the four-string lyre – an instrument that was accepted as a model for other instrumental and vocal music. These three tunings were called diatonic,^[5] chromatic,^[6] and enharmonic,^[7] and the sequences of four notes that they produced were called tetrachords ("four strings").^[8] 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♭, so that the two lower intervals in the tetrachord were semitones, making the pitches A G♭ F E. In the enharmonic tetrachord the tuning had two quarter tone intervals at the bottom: A F F♭ E (where F♭ is F♮ lowered by a quarter tone). For all three tetrachords, only the middle two strings varied in their pitch.^[9]

[edit] 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.^[10] 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 (see white mensural notation).^[11][12] Similarly, in the 16th century, notation in a 4/4 time signature was referred to as "chromatic" notation 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 of the more common 2/2 metre.^[13] These uses for the word have no relationship to the modern meaning of chromatic, but the sense survives in the current term coloratura.^[14]

[edit] Renaissance chromaticism

The term chromatic began to approach its modern usage in the 16th century. For instance Orlando Lasso's Prophetiae Sibyllarum opens with a prologue proclaiming, "these chromatic songs,^[15] 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.^[16]

See also: Chromaticism

[edit] Diatonic scales

Main article: Diatonic scale

[edit] Background: the Medieval gamut

Medieval theorists defined scales in terms of the Greek tetrachords. The gamut was the series of pitches from which all the Medieval "scales" (or modes, strictly) are notionally derived, and it may be thought of as constructed in a certain way from diatonic tetrachords.^[17]

The intervals from one note to the next in this Medieval gamut are all tones or semitones, 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 random string of ascending notes (starting with F, in fact) from the gamut:

... –T–T–T–S–T–T–S–T–T–T–S–T– ...

And here are the intervals for one random ascending octave (the seven intervals separating the eight notes A–B–C–D–E–F–G–A, in fact) from the gamut:

T–S–T–T–S–T–T [five tones and two semitones]^[18]

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 thereof): the modern equivalent of the gamut.^[19] This would include the major scale, the natural minor scale (same as the descending form of the melodic minor), and the old ecclesiastical church modes.

[edit] Modern meanings of "diatonic scale"

Given the background presented above, we now move on to address the music of the Common Practice Period, and later music that shares its core features (see note 1, above).

All writers accept the major scale as diatonic. Most, but not all,^[20] accept the natural minor (and the descending melodic minor) as diatonic. As for other forms of the minor:

• "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.^[21]
• "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^[22] of the minor) or chromatic.^[23]

• "Mixed" usage: Still other writers mix these two meanings of diatonic (and conversely for chromatic), and this may lead to confusions and misconceptions. Sometimes, though not always, the context makes it clear which meaning is intended.

For print sources employing each of these usages (for scales, and derived usages for intervals, etc.), see the list of sources, below.^[24]

There are a few other meanings of the term diatonic scale, some of which take the extension to harmonic and melodic minor even further, to be even more inclusive.^[25]

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.

[edit] Chromatic scale

Main article: Chromatic scale

A chromatic scale consists of an ascending or descending sequence of pitches proceeding always by semitones. Such a sequence of pitches would, for example, be produced by playing black and white keys of a piano in order, without leaving any out. 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).^[26]

[edit] Diatonic and chromatic intervals

The diatonic intervals are usually understood as those between some pair of notes both drawn from the same diatonic scale. Intervals that cannot be so derived are, by this way of thinking, called chromatic intervals.^[27] Because diatonic scale is itself ambiguous (see above), this way of distinguishing intervals is also ambiguous.^[28] For example, the interval B♮–E♭ (a diminished fourth, occurring in C harmonic minor) is considered diatonic if the harmonic minor scale is considered diatonic;^[29] but it is considered chromatic if the harmonic minor scale is not considered diatonic.^[30]

Additionally, the label chromatic or diatonic for an interval may be sensitive to context. For instance, in a passage in C major, the interval C–E♭ 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 as above, e.g. in the B♮–E♭ example above, classification would still depend on whether the harmonic minor scale is considered diatonic.

[edit] Intervals in different systems of tuning

In equal temperament, there is no difference in tuning (and therefore in sound) between intervals that are enharmonically equivalent. For example, the notes F and E♯ represent exactly the same pitch, so the diatonic interval C–F (a perfect fourth) sounds exactly the same as its enharmonic equivalent – the chromatic interval C–E♯ (an augmented third). In systems other than equal temperament, however, there is often a difference in tuning between intervals that are enharmonically equivalent. In tuning systems that are based on a cycle of fifths, such as Pythagorean tuning and meantone temperament, these alternatives are labelled as diatonic or chromatic intervals.

Under these systems the cycle of fifths is not circular in the sense that a pitch at one end of the cycle (e.g. G♯) is not tuned the same as the enharmonic equivalent at its other end (A♭); they are different by an amount known as a comma. This broken cycle causes intervals that cross the break to be written as augmented or diminished chromatic intervals. In meantone temperament, for instance, chromatic semitones (C–C♯) are smaller than diatonic semitones (C–D♭),^[31] and with consonant intervals such as the major third the chromatic equivalent is generally less consonant.

The exception to this classification is the tritone, of which both enharmonic forms (e.g. C–F♯ and C–G♭) are equally distant along the cycle of fifths, making them inversions of each other at the octave. Because of this the ambiguity cannot be resolved where octave equivalence is assumed, and the label diatonic or chromatic for either form of tritone is not useful in the context of tuning (the choice is arbitrary, and therefore unspecific).

If the tritone is assumed diatonic, the classification of written intervals by this definition is not significantly different from the "drawn from the same diatonic scale" definition given above as long as the harmonic minor and ascending melodic minor scale variants are not included. Aside from tritones, all intervals that are either augmented or diminished are chromatic, and the rest are diatonic.

[edit] Diatonic and chromatic chords

Diatonic 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♭–G–B♮ is diatonic "to" or "in" C minor.^[32] On this understanding, the diminished seventh chord built on the leading note is accepted as diatonic in minor keys.^[33] If the strictest understanding of the term diatonic scale were adhered to, even a major triad on the dominant scale degree in C minor (G–B♮–D) would be chromatic or altered in C minor.^[34] Some writers use the phrase "diatonic to" as a synonym for "belonging to".

[edit] Diatonic and chromatic harmony

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

• Often musicians call diatonic harmony any kind of harmony inside the major–minor system of 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".^[35] 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.^[36]
• 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.^[37]

[edit] Miscellaneous usages

[edit] Diatonic and chromatic notes

In modern usage, the meanings of the terms diatonic note and chromatic note 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.

[edit] 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.^[38]
• Melodic movement between a diatonic note and a chromatically altered variant (from C to C# in G major, or vice versa, for example).^[39]

[edit] Chromatic 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#–F#–A, for example).^[40]
• The same as the second sense of chromatic inflection, above.^[41]
• 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.^[42]

[edit] Diatonic progression

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).^[43]
• 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♯–G–A♭.^[44]

[edit] Diatonic and chromatic modulation

• Diatonic modulation is modulation via a diatonic progression.^[45]
• Chromatic modulation is modulation via a chromatic progression, in the first sense given above.^[46]

[edit] Diatonic pentatonic scale

• One very common kind of pentatonic scale that draws its notes from the diatonic scale (in the exclusive sense, above) is sometimes called the diatonic pentatonic scale: C–D–E–G–A[–C], or some other 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.^[47]

[edit] Modern extensions of the diatonic idea

Traditionally, and in all uses discussed above, the term diatonic has been confined to the domain of pitch, and in a fairly restricted way. The common idea in those uses is that a specific selection is made from an underlying superset of pitches. A particular subset of seven pitch classes is selected from a superset of twelve semitonally incrementing pitch classes, to yield a particular heptatonic scale. Exactly which heptatonic 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.

[edit] Extended pitch selections

The selection of pitch classes can be generalised to encompass formation of non-traditional scales from the underlying twelve chromatic pitch classes.^[48] 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^[49] 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.

[edit] Diatonic 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 African rhythms, for example. Some selection or other is made from an underlying superset of metrical beats, 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).^[50]

[edit] Notes

[edit] Published sources for "diatonic", in Common Practice music

Notes:

• The sources cited below are sorted into three groups, depending on what they say about the term diatonic:

• those that explicitly or implicitly exclude the harmonic and melodic minors, along with the consequences for intervals, etc.;
• those that include the harmonic and melodic minors, with consequences; and
• those that are ambiguous, inconsistent, or anomalous.

• In cited text below, relevant portions have been highlighted in bold, which has been added for emphasis.

[edit] Diatonic excludes the harmonic and melodic minor scales

1. The Oxford Companion to Music (Online [1]; current print edition is the same: ISBN 0198662122, p. 1106)

Scale [...] 3. Diatonic Scale: [...] The sixth and seventh degrees of the minor scale are unstable and result in two forms, neither of them diatonic: the harmonic minor, with the characteristic interval of an augmented 2nd; and the melodic minor [...]

[But see the same source, and an older edition (same as the first edition), below in other categories.]

2. Grove Music Online (see p. 295 in the print version)

Diatonic (from Gk. dia tonos: 'proceeding by whole tones').

Based on or derivable from an octave of seven notes in a particular configuration, as opposed to chromatic and other forms of scale. A seven-note scale is said to be diatonic when its octave span is filled by five tones and two semitones, with the semitones maximally separated, for example the major scale (T–T–S–T–T–T–S). The natural minor scale and the church modes (see Mode) are also diatonic.

[But see the same source, Grove Music Online, below also.]

3. The Harvard Dictionary of Music 4th edition, p. 239

Diatonic: (1) A scale with seven pitches (heptatonic) that are adjacent to one another on the circle of fifths; thus, one in which each letter name represents only a single pitch and which is made up of whole tones and semitones arranged in the pattern embodied in the white keys of the piano keyboard; hence, any major or pure minor scale and any church mode as distinct from the chromatic scale.

4. Elements of Musical Composition, Crotch, William, 1830 [reproduced 1991, Boethius Press, Aberystwyth, Wales], pp. 21–22

In modern music, the seventh note Si is often made one semitone higher, and then the scale of the minor key becomes chromatic. [...] The sixth and seventh notes are both occasionally altered at the same time, and then also the scale is chromatic. [...] This is the usual method of ascending the minor key, but in descending, the ancient diatonic scale is commonly used.

[A rare instance of classifying the harmonic minor and the ascending melodic minor as chromatic.]

5. The Theory and Practice of Tone-Relations, Goetschius, Percy, Schirmer, 1931 edition

[p. 4] This diatonic scale comprises the tones of the major mode, so designated for reasons given later. Upon examination it is found that the contiguous intervals of the diatonic scale, unlike those of the natural scale [Goetschius's term for a series of pitches rising by fifths, starting from F and ending and B, with C identified as the "keynote"; see p. 3], are not uniform, but differ as follows:

[A diagram is shown of a C major scale with slurs pointing out the semitones between scale steps 3 and 4, and 7 and 8.]

[p. 33] The line of research and argument [above] proves that, of the two modes recognized and employed in modern music, that one known as major (because its prin. triads have a major third) is the natural one.

The other, i.e., the minor mode, is consequently to be regarded as an unnatural or artificial mode, and is accounted for as an arbitrary modification of the natural major mode.

[...]

The scale thus obtained is called the harmonic minor mode. It is the only theoretically accurate minor scale, [... .]

[Goetschius's stance is unusual in not recognising any scale other than the major as diatonic; he does not mention the so-called "natural" minor scale as an entity in its own right, but considers the harmonic minor as the basic minor form, derived directly from the major by alteration of the third and sixth scale-steps. Later (pp. 104–106) he discusses the melodic minor scale, and the fact that the third scale-step is "the only distinctive tone between the major form and the various minor forms" (p. 105).]

6. The Leading Tone in Direct Chromaticism: From Renaissance to Baroque, John Clough, Journal of Music Theory, Vol. 1, No. 1. (1957), pp. 2–21. Excerpt is from pp. 3–4.

Chromaticism being essentially the antonymn [sic] of the more restrictive term diatonicism, its precise definition rests on a series of definitions beginning with the concept diatonic system:

diatonic system – a succession of whole steps and half steps, of indefinite compass, in which the half steps are separated alternately by two whole steps and three whole steps

diatonic – comprised entirely of tones from a single diatonic system

diatonicism – the use of diatonic collections of tones

chromatic – not comprised entirely of tones from a single diatonic system

chromaticism – the use of chromatic collections of tones

[... During] the past two hundred and fifty years, when extensive deviation from it and abandonment of it have become the norm of practice, the [diatonic] system has persisted as an important framework of tonal organization. Without doubt, this simple succession of whole and half steps is among the most deeply rooted facts of our musical culture.

In view of its historical pre-eminence alone, the system deserves to be represented in its pure form by such a basic theoretical concept as diatonic. Modern abstractions such as the harmonic minor and so called "ascending melodic" minor scales, which are sometimes referred to as diatonic, cannot be reconciled with the above definitions without the term diatonic becoming an unwieldy and theoretically useless catch-all. [Reference to footnote.]

[Footnote:] 1. In this connection much confusion derives from the accepted meaning of the expression chromatic scale. (Clearly, the harmonic minor scale is not the chromatic scale; it is therefore diatonic, or so the reasoning goes.) If the presently accepted meaning of chromatic scale is to be retained, we must content ourselves with the paradox that the harmonic minor and "ascending-melodic" minor scales, while inherently chromatic, are not "chromatic scales".

Here it might be stated also that, while I am entirely convinced of the soundness of the above definitions, the reader must realize that any doubts he may entertain regarding them can be in no way damaging to the principle to be derived by their use. So long as the concept of chromaticism, as defined above, is clearly understood, I have no essential objection to the reader's substituting his own term for it throughout the article. Universally accepted nomenclature is a desirable objective, but, unfortunately, it sometimes lags behind theoretical thought.

[A rare detailed articulation of the "exclusive" stance, exceptional for its mentioning and analysing the alternative "inclusive" stance.]

[edit] Diatonic includes the harmonic and melodic minor scales

1. Oxford Companion to Music, ed. Scholes, Percy, "Diatonic and chromatic", 9th edition, 1955, p. 291

Diatonic and Chromatic: [...] The diatonic scales are the major and minor, made up of tones and semitones (in the case of the harmonic minor scale, also an augmented second), as distinct from the chromatic [...]

2. Oxford Concise Dictionary of Music (Online [2]; current print edition is the same)

For the older European scales, used in the Church's plainsong and in folk song, see modes. Two of these ancient modes remained in use by composers, when the other 10 were almost abandoned, and these are our major and minor scales – the latter, however, subject to some variations in its 6th and 7th notes. Taking C as the keynote these scales (which have provided the chief material of music from about AD 1600 to 1900) run as follows: [than the first figure in the article, showing the major scale on C, then the harmonic minor on C, then the ascending and descending melodic on C; text continues immediately with:] The major and minor scales are spoken of as DIATONIC SCALES, as distinct from a scale using nothing but semitones, which is the CHROMATIC SCALE, [...]

3. Music Notation and Terminology, Gehrkens, Karl Wilson, Barnes, NY, 1914

[p. 79] There are three general classes of scales extant at the present time, viz.: (1) Diatonic; (2) Chromatic; (3) Whole-tone.

[p. 80] The word diatonic means "through the tones" (i.e., through the tones of the key), and is applied to both major and minor scales of our modern tonality system. In general a diatonic scale may be defined as one which proceeds by half-steps and whole-steps. There is, however, one exception to this principle, viz., in the progression six to seven in the harmonic minor scale, which is of course a step-and-a-half.

4. Tonal Harmony in Concept and Practice, Forte, Allen, NY, Holt, Rinehart, and Winston, 3rd edition, 1979, p. 14

The diatonic minor scale therefore has three forms: natural, melodic, and harmonic.

5. The New Penguin Dictionary of Music, Jacobs, Arthur, Penguin, 4th edition (1977) reprinted with revisions (1986)

[p. 108] diatonic, pertaining to a given major or minor key (opposite of CHROMATIC); so diatonic scale, any one of the major or minor scales; [...]

[pp. 246–247] major, minor, [...] The minor scale is divided for theoretical purposes into three types, [followed by an equal treatment of natural, melodic, and harmonic minor scales, with figures showing each form]

6. Harmony: Its Theory and Practice, Prout, Ebenezer, Augener, 16th edition 1901, Chapter I, p. 3

8. A SCALE is a succession of notes arranged according to some regular plan. Many different kinds of scales have been used at various times and in various parts of the world; in modern European music only two are employed, which are called the diatonic and the chromatic scale.

9. The word "diatonic" has already been explained in §6 as meaning "through the degrees". A diatonic scale is a succession of notes in which there is one note, neither more nor less, on each degree of the staff – that is to say, on each line and space. [Reference to Chapter II, p. 17, where the sources of the modern scales in the old system of modes are explained.] There are two varieties of the diatonic scale, known as the major (or greater) and minor (or less) scale from the nature of the interval between the first and third notes of the scale. [Two figures, showing an ascending octave of the C major scale (Ex. 4) and of the C harmonic minor scale (Ex. 5).] Other forms of the minor scale frequently to be met with will be explained later. [The melodic is introduced and explained in Chapter VII, pp. 80–83, §§ 206–210.]

7. Music History and Theory, Clendinnen, William, Doubleday, 1965, p. 23

Western music made from about 1680–1880 made use of a system of diatonic scales, comprising certain arrangements of whole tones (T) and semitones (S) such as the major [...] the melodic minor [...] and the harmonic minor (T-S-T-T-S-T½-S).

8. Harmony, Piston, Walter, DeVoto, Mark, Norton, 5th edition, 1987, pp. 4–5

The tones that form the interval are drawn from scales. The most familiar of these are the two diatonic scales of seven notes each, called the major scale and the minor scale. Tonal music, which includes most music written between 1700 and 1900, is based on diatonic scales.

The difference between the major and minor scales is found in the distribution of whole steps and half steps above a given starting point. [... C major scale as one case; Example 1–2, showing the scale and its steps and half steps.]

There are three different forms of the minor scale. The natural minor scale has three tones that are different from corresponding tones in the major scale. Some of these same tones are also found in the other forms, as shown here. [Example 1–3, showing five forms of scales on C: major, natural minor, harmonic minor, melodic minor ascending (all shown ascending); and melodic minor descending.]

All of the possible pitches in common use, considered together, constitute the chromatic scale. [Example 1–4, showing an ascending and descending chromatic scale; explanation of the chromatic scale. ...]

Any particular diatonic scale is a seven-note subset of the twelve-note chromatic scale.

[edit] Diatonic used vaguely, inconsistently, or anomalously

1. Grove Music Online

Diatonic (same article as cited above) [...] An interval is said to be diatonic if it is available within a diatonic scale. The following intervals and their compounds are all diatonic: minor 2nd (S), major 2nd (T), minor 3rd (TS), major 3rd (TT), perfect 4th (TTS), perfect 5th (TTST), minor 6th (STTTS), major 6th (TTSTT), minor 7th (TSTTTS), major 7th (TTSTTT) and the octave itself. The tritone, in theory diatonic according to this definition, has traditionally been regarded as the alteration of a perfect interval, and hence chromatic; it may be either a semitone more than a perfect 4th (augmented 4th: TTT) or a semitone less than a perfect 5th (diminished 5th: STTS).

2. Grove Music Online

Minor (i). (1) The name given to a diatonic scale whose octave, in its natural form, is built of the following ascending sequence, in which T stands for a tone and S for a semitone: T–S–T–T–S–T–T). The note chosen to begin the sequence, called the key note, also becomes part of the name of the scale; a D minor scale, for instance, consists of the notes D–E–F–G–A–B♭–C–D. In practice, however, some notes of the scale are altered chromatically to help impart a sense of direction to the melody. The harmonic minor scale has a raised seventh, in accordance with the need for a major triad on the fifth step (the Dominant chord). The melodic minor scale has a raised sixth and a raised seventh when it is ascending, borrowing the leading-note function of the seventh step from the major scale; in descending, though, it is the same as the natural minor scale.

3. The Cambridge History of Western Music Theory, ed. Thomas Christensen, 2004

[Records different usages by different major theorists.]

4. Encyclopaedia Britannica (Online: consulted in April 2007; 2005 CD-ROM version is the same.)

Diatonic. [...] The "harmonic" minor that results is, strictly speaking, no longer a diatonic scale, unlike "melodic" minor, which simply borrows its upper tetrachord from the parallel major, i.e., the major scale beginning and ending on the same pitch.

[This accepts the ascending melodic as diatonic.]

5. Encyclopaedia Britannica (Online: consulted in December 2007.)

Diatonic. [I]n music, any stepwise arrangement of the seven "natural" pitches (scale degrees) forming an octave without altering the established pattern of a key or mode – in particular, the major and natural minor scales. Some scales, including pentatonic and whole-tone scales, are not diatonic because they do not include the seven degrees. [...] In the natural minor scale, the half steps occur at II-III and V-VI. Given the crucial importance of the so-called leading tone (the seventh degree of the major scale) in diatonic harmony, however, the natural minor scale regularly becomes subject to chromatic alteration (in this case, the raising by a half step) of its seventh degree (the harmonic minor form) and often the sixth degree as well (the melodic minor form of the scale, used in an ascending melody). The harmonic minor is, strictly speaking, not really a scale; it is used normally not melodically but as a source set for constructing harmony. The upper tetrachord of the ascending melodic minor scale is identical with that of the major scale. [...] The diatonic scale, as a model, is contrasted with the chromatic scale of 12 pitches, corresponding to the white and black notes of the piano keyboard considered together. [...] An accidental sign in front of a note normally signifies either that the tone is notated as the sixth or seventh degree of the minor scale, or that the tone is a chromatic tone (it does not belong to the particular diatonic scale being used in the harmony of the moment).

[The status of the harmonic and melodic minor as diatonic is left uncertain. Treatment of the alteration of the sixth and seventh degrees in minor is self-contradictory: at first those degrees are "subject to chromatic alteration"; but later such alterations are mentioned separately from and distinguished from "chromatic tones".]

6. Elementary Training for Musicians Hindemith, Paul, 2nd edition, 1949, p. 58

[...] (diatonic = consisting of whole- and half-tone steps) [... .]

[This definition fails to exclude the ascending melodic as diatonic, and fails to include the harmonic minor.]

7. Oxford Companion to Music (Online [3]; current print edition is the same)

diatonic (from Gk. dia tonikos, 'at intervals of a tone). In the major–minor tonal system, a diatonic feature – which may be a single note, an interval, a chord, or an extended passage of music – is one that uses exclusively notes belonging to one key. In practice, it can be said to use a particular scale, but only with the proviso that the alternative submediants and leading notes of harmonic and melodic minor allow up to nine diatonic notes, compared with the seven available in a major scale.

[The exact intention with regard to classification of the harmonic and melodic minor scales is unclear, and likely to be inconsistent.]

8. Collins Pocket Dictionary of Music, Collins, 1982 [abridged from Collins Encyclopedia of Music, eds. Westrup, J, and Harrison, F, revised edition 1976]

Diatonic [...] In minor keys [the] sharpened sixth and seventh are in such common use, though not strictly proper to [the] key, that they are also regarded as diatonic [...]

Scale [...] Modern diatonic scale as 2 modes: major [...] and minor (TSTTSTT). Latter only has theoretical existence; in practice has 2 forms, both of which involve element of chromaticism in treatment of leading note: [forms of harmonic and ascending and descending melodic are given].

[See note for the entry immediately above.]

9. Theory of Harmony Schoenberg, Arnold, (translation of 3rd edition, 1922), 1983, p. 32

In the seven chords that we build on the seven tones of the major scale we use no tones other than these same seven – the tones of the scale, the diatonic tones.

[Harmonic and melodic minor scales aren't necessarily excluded. The intention is unclear.]

10. A Dictionary of Musical Terms Baker, Theodore, 1923 edition

Diatonic: (In modern usage) By, through, with, within, or embracing the tones of the standard major or minor scale.

[The phrase "standard major or minor scale" is ambiguous, and could include all forms of the minor.]

11. Music for Our Time, Winter, Robert, Wadsworth, 1992, pp. 28–29

[...] Western music settled on two diatonic patterns, known today as the major scale and the minor scale. [...] The minor scale results from flatting (lowering by half a step) the third and sixth degrees of the major scale. [...] it is frequently smoothed out by [alterations to the sixth and seventh degree. ...] this form of the minor scale is called the melodic minor scale.

[The precise interpretation of patterns in two diatonic patterns is open to dispute. On one reading, these patterns are more general and flexible, and the minor pattern remains diatonic when it is varied as the author describes. By that reading, the definition of diatonic scale is not anomalous, but includes all standard forms of the minor scale. On another reading, pattern is taken to mean "exact configuration of tones and semitones"; by that reading, the definition is barely coherent (since a scale constrained to conform to such a strict configuration cannot be "smoothed out" by the alterations mentioned and yet retain the pattern that the author identifies as "the minor scale"). This second reading entails that among the minors only the harmonic form is "diatonic".]

[edit] See also

• Diatonic scale
• Chromatic scale
• Pentatonic scale
• Chromaticism
• Major and minor
• Semitone