Diatonic and chromatic

Diatonic and chromatic are important terms in music theory. They are applied first of all to scales, but are often used in characterising intervals, chords, individual notes, general musical styles, kinds of harmony, etc. When treated as an opposing pair, the terms are especially used in discourse concerning modern Western music.^[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.

History

Greek genera

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<s>♭</s> E (where F<s>♭</s> is F♮ lowered by a quarter tone). For all three tetrachords, only the middle two strings varied in their pitch.^[9]

Medieval coloration

The term cromatico (Italian) was occasionally used in the Medieval and Renaissance periods to refer to coloration of certain notes (i.e. written in solid red or black ink). In works of the Ars Nova from the 14th century, this was used to indicate a change in duration. It was discontinued in the 15th century as the use of open white noteheads came into use (see white mensural notation).^[10]^[11] Similarly, in the 16th century, notation in a 4/4 time signature was referred to as "chromatic" notation because of its abundance of "colored in" black notes, as opposed to the open white notes of the more common 2/2 metre.^[12] These uses for the word have no relationship to the modern meaning of chromatic, but the sense survives in the current term coloratura.^[13]

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,^[14] 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.^[15]

See also: Chromaticism

Diatonic scales

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.^[16]

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: <blockquote>...-T-T-T-S-T-T-S-T-T-T-S-T-...</blockquote> 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: <blockquote>T-S-T-T-S-T-T [five T; two S]^[17]</blockquote>

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.^[18] 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.

Modern meanings of "diatonic scale"

Given the background presented above, and moving now to address the description of music of the Common Practice Period:^[19]

Many writers (especially music theorists and musicologists) 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.

Many writers (especially in musical pedagogy or otherwise engaged with practical music outside of academia) consistently include the melodic and harmonic minor scales as diatonic also. For this group, every Western scale in standard use^[20] is either diatonic (the major, and all forms of the minor) or chromatic.^[21]

Still other theorists 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.^[22]

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.^[23]

Diatonic and chromatic notes

In modern use, the meanings of the terms diatonic note and chromatic note vary according to the meaning allocated to the term diatonic scale. Generally, but not universally, a note is understood to be diatonic in a certain context if it belongs to the diatonic scale that is in use in that context; otherwise it is chromatic.

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).^[24]

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.^[25] Because diatonic scale is itself ambiguous (see above), this way of distinguishing intervals is also ambiguous.^[26] 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;^[27] but it is considered chromatic if the harmonic minor scale is not considered diatonic.^[28]

Intervals in different systems of tuning

In equal temperament, there is no difference between the tuning of 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 sound difference between intervals that are enharmonically equivalent, and these alternatives may be labeled as diatonic or chromatic intervals.

This distinction most commonly arises in tuning systems that are based on a cycle of fifths, such as Pythagorean tuning, and meantone temperament, which were common before the Classical period of music. Under these systems the cycle of fifths isn't 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♭), which is 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♭),^[29] and with consonant intervals such as the major third the chromatic equivalent is generally less consonant.

In tuning systems derived from a cycle of fifths the classification of intervals as diatonic or chromatic is not ambiguous. All intervals that are either augmented or diminished, excepting the tritone (of which both forms, the augmented fourth and diminished fifth, are tuned the same), are chromatic, and the rest are diatonic. This definition is consistent with the "drawn from the same diatonic scale" definition above as long as the harmonic minor and ascending melodic minor scale variants are not included.

Diatonic and chromatic chords

Diatonic chords are generally understood as those that are built using only notes from the same diatonic scale, all others then being considered chromatic chords. But given the ambiguity of diatonic scale, this definition too is ambiguous. For some, the augmented triad E♭-G-B♮ is always diatonic, because it occurs in C minor, using notes from C harmonic minor. For others, chords are only ever diatonic relatively: the augmented triad E♭-G-B♮ is diatonic "to" or "in" C minor.^[30] On this understanding the diminished seventh chord built on the leading note is accepted as a diatonic chord in minor keys.^[31] 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 interpreted as not diatonic in C minor.^[32]

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".^[33] 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.^[34]

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.

''Diatonic'' excludes the harmonic and melodic minor scales

1. The Oxford Companion to Music (Online [7]; 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, Chapters I and XI The diatonic scale comprises the tones of the major mode. Upon examination it is found that the contiguous intervals of the diatonic scale, unlike those of the natural scale (a scale of rising fifths from F to B, the keynote being C), are not uniform, but differ as follows:

[A diagram is shown of a C major scale with slurs pointing out the semitone placement between scale steps 3-4 & 7-8]

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 [Goetschius considers the harmonic minor scale as the only legitimate 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.

''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 [8]; 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 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.]

''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 ([9] Print version is the same.) Also Concise Britannica, "Diatonic" ([10] Print version is the same.) 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. 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.]

6. Oxford Companion to Music (Online [11]; 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.]

7. 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. Not very clear.]

8. 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.]

Citations

[1] That is to say common practice music – the tonal music that dominated in the West from about 1600 to about 1900. But the terms are also relevant to a great deal of current music, since beyond art music Western music is still overwhelmingly tonal.
[2] This definition encompasses the natural minor scale (and equivalently the descending melodic minor), the major scale, and the ecclesiastical modes.
[3] For inclusion of the the harmonic minor and the ascending melodic minor see the section Modern meanings of "diatonic scale" in this article.
[4] Translating the term used by Greek theorists: γένος, génos; plural γένη, génē.
[5] The English word diatonic is ultimately from the Greek διατονικός (diatonikós), itself from διάτονος (diátonos), which may mean (as OED claims) "through the tones" (taking τόνος, tónos, to mean interval of a tone), or perhaps stretched out (as recorded in Liddell and Scott's Greek Lexicon). See also Barsky (Chromaticism, Barsky, Vladimir, Routledge, 1996, p. 2): "There are two possible ways of translating the Greek term 'diatonic': (1) 'running through tones', i.e. through the whole tones; or (2) a 'tensed' tetrachord filled up with the widest intervals". The second interpretation would be justified by consideration of the pitches in the diatonic tetrachord, which are more equally distributed ("stretched out") than in the chromatic and enharmonic tetrachords, and are also the result of tighter stretching of the two variable strings. It is perhaps also sounder on linguistic morphological grounds. (See also Merriam-Webster Online.) A completely separate explanation of the origins of the term diatonic appeals to the generation of the diatonic scale from "two tones": "Because the musical scale is based entirely on octaves and fifths, that is, two notes, it is called the 'diatonic scale' " (Phillips, Stephen, "Pythagorean aspects of music", in Music and Psyche, Vol. 3, available also online). But this ignores the fact that it is the element di- that means "two", not the element dia-, which has "through" among its meanings (see Liddell and Scott, op. cit.). There is a Greek term δίτονος (dítonos), which is applied to an interval equivalent to two tones. It yields the English words ditone and ditonic (see Pythagorean comma), but it is quite distinct from διάτονος. Yet another derivation assumes the sense "through the tones" for διάτονος, but interprets tone as meaning individual note of the scale: "The word diatonic means 'through the tones' (i.e., through the tones of the key)" (Gehrkens, 1914, see below; see also the Prout citation, at the same location). This is not in accord with any accepted Greek meaning, and in Greek theory it would fail to exclude the other tetrachords. The fact that τόνος itself has at least four distinct meanings in Greek theory of music contributes to the uncertainty of the exact meaning and derivation of διατονικός, even among ancient writers. (See The Music of Ancient Greece: An Encyclopaedia, Michaelides, Solon, Faber, 1978, pp. 335-340: "Tonos". Τόνος may refer to a pitch, an interval, a "key" or register of the voice, or a mode.) For more information, especially concerning the various exact tunings of the diatonic tetrachord, see Diatonic genus.
[6] Chromatic is from Greek χρωματικός (khrōmatikós), itself from χρῶμα (khrṓma), which means complexion, hence color – or, specifically as a musical term, "a modification of the simplest music" (Liddell and Scott's Greek lexicon). For more information, especially concerning the various exact tunings of the chromatic tetrachord, see Chromatic genus.
[7] 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. (See Michaelides, op. cit., Liddell and Scott, etc.) For more information, especially concerning the various exact tunings of the enharmonic tetrachord, see Enharmonic genus.
[8] 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").
[9] 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. 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: "[...] 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" (Barsky, loc. cit.). 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 (fl. 360 CE). Specifically, there are more versions of each of the three tetrachords than are described here.
[10] Parrish, Carl, The Notation of Medieval Music, Pendragon, New York, 1978, pp. 147-147
[11] Harvard Dictionary of Music, 2nd ed., "Chromatic"
[12] Grout, Donald J, and Palisca, Claude, A History of Western Music, 6th ed., Norton, New York, 2001, pp. 188-190
[13] "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").
[14] 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 our article: 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♯–G) are occasionally allowed in theory (Marchetto, GerbertS, 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)
[15] Grout et al., 2001, p. 188
[16] The origin of the word gamut is explained at the article Hexachord; 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), but generalised as an unending string of pitches.
[17] Some theorists 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 call the original untransposed series itself a "scale". Percy Goetschius calls that series the "natural scale" (The Theory and Practice of Tone-Relations, Schirmer, 1931 edition, p. 3; see further citation below).
[18] For simplicity, throughout this article equal temperament tuning is assumed unless otherwise noted.
[19] This treatment covers also music after the Common Practice Period, including most popular music and indeed most Western music outside of art music (or contemporary "classical" music).
[20] Almost no writer uses diatonic to describe non-traditional or modal use of the melodic and harmonic minor scales, in ways that are outside of common practice.
[21] 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.
[22] Perhaps the more academic and "exclusive" usage is gainly greater currency; but hard evidence that this is pervasive or general is lacking. On the evidence presented in the list of sources, there are very many sources in the third category: Diatonic used vaguely, inconsistently, or anomalously.
[23] An explicit example of such an extended general use of diatonic scale and related terms: Throughout this paper, I use the terms "diatonic," "pentatonic" and "chromatic" in their generic senses, as follows: 1. 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. 2. 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. 3. "Chromatic" refers to the interval formed between adjacent pitch-classes of any equal-tempered scale. (Gould, Mark, "Balzano and Zweifel: another look at generalised diatonic scales", Perspectives Of New Music, vol. 38 no. 2, pp. 88-105; see introductory section online)
[24] It is not usual for chromatic scale to be used in any different sense from this. A rare exception is found in Elements of Musical Composition, Crotch, William, 1830 [reproduced 1991, Boethius Press, Aberystwyth, Wales], pp. 21-22. (See the quotation from this text, below.) Outside of music altogether, chromatic scale may refer to Von Luschan's chromatic scale.
[25] Of relevance in searching for the term chromatic interval, note that the phrase has distinct meanings outside of music theory. See for example ''The equivalent sphere and chromatic interval in astigmatism''.
[26] There are several other understandings of the terms diatonic interval and chromatic interval. There are theorists 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 writers who have defined all minor intervals as chromatic (Goetschius, Percy, The Theory and Practice of Tone-Relations, 1931, p. 6; Goetschius assesses all intervals as if the lower note were the tonic, and since for him only the major scale is diatonic, only the intervals formed above the tonic in the major are diatonic; see also, for example, Harrison, Mark, Contemporary Music Theory – Level Two, 1999, p. 5). Some theorists take the diatonic interval to be simply a measure of the number of "scale degrees" spanned by two notes (so that F♯-E♭ and F♮-E♮ 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♯ and E♭ 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"). This use of the term occurs in the Wikipedia table called Diatonic intervals. In that usage, it is not clear what chromatic interval would mean, if anything. Some theorists use chromatic interval to mean simply semitone, as for example in the article Chromatic fourth. See also Williams, Peter F., The Chromatic Fourth during Four Centuries of Music, OUP, 1997. Something close to this usage may be found in print. We see it in the term chromatically, in: "The trill rises chromatically by step above this harmonic uncertainty, forming a chromatic fourth,[...]" (Stowel, Robin, Beethoven: Violin Concerto (Cambridge Music Handbooks), Cambridge UP, 2005, p. 66). 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.
[27] See for example The Rudiments of Music, Lovelock, William, 1971.
[28] See for example the citation from Grove Music Online ("Diatonic"), below.
[29] Helmholtz, Hermann, trans. Alexander Ellis, On the Sensations of Tone, Dover, New York, 1954, pp. 433-435 and 546-548
[30] Kostka, Stefan, and Payne, Dorothy, Tonal Harmony, McGraw-Hill, 5th edition, 2003, pp. 60-61. In other usage, E♭-G-B♮ is diatonic not to C minor, but to the C harmonic minor scale.
[31] "Because of the variability of [scale degrees] 6 and 7, there are sixteen possible diatonic seventh chords in minor. [...] [One line in a table headed Common diatonic seventh chords in minor:] __º7_____viiº7__" (Tonal Harmony, Kostka, Stefan and Payne, Dorothy, McGraw-Hill, 3rd edition 1995, pp. 64-65).
[32] It would be counted as a chromatic or altered chord, since the third of the triad does not belong to the natural minor scale or Aeolian mode of C minor (C, D, E♭, F, G, A♭, B♭). This highly restrictive interpretation is effectively equivalent to the idea that diatonic triads are those drawn from the notes of the major scale only, as this source rather roughly puts it: "Diatonic chords are wholly contained within a major scale" (Harrison, Mark, Contemporary Music Theory – Level Two, 1999, p. 7).
[33] Often the content of "diatonic harmony" in this sense will include 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.
[34] 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.

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