Diatonic and chromatic

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Melodies may be based on a diatonic scale and maintain its tonal characteristics but contain many accidentals up to all twelve tones of the chromatic scale, such as the opening of Henry Purcell's "Thy Hand, Belinda", Dido and Aeneas (1689) (About this sound Play , About this sound Play  with figured bass) which features eleven of twelve pitches while chromatically descending by half steps,[1] the missing pitch being sung later.
Bartok - Music for Strings, Percussion and Celesta, mov. I, fugue subject: diatonic variant About this sound Play .[2]

Diatonic (Greek: διατονική) and chromatic (Greek: χρωματική) are terms in music theory that are most often used to characterize scales, and are also applied to musical instruments, 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.[3]

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).[4] 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).[5] Chromatic most often refers to structures derived from the chromatic scale, which consists of all semitones. 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 music of the 14th through 16th centuries.

History[edit]

Tetrachord genera of the four-string lyre, from The History of the Arts and Sciences of the Antients, Charles Rollin (1768). The text gives a typically fanciful account of the term chromatic.

Greek genera[edit]

In ancient Greece there were three standard tunings (known by the Latin word genus, plural genera)[6] of a lyre.[7] These three tunings were called diatonic,[8] chromatic,[9] and enharmonic,[10] and the sequences of four notes that they produced were called tetrachords ("four strings").[11] 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 Gdouble flat F E (where F is F lowered by a quarter tone). For all three tetrachords, only the middle two strings varied in their pitch.[12]

Medieval coloration[edit]

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.[13] 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).[14][15] Similarly, in the 16th century, notation in a 4/4 time signature[citation needed] 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.[16] These uses for the word have no relationship to the modern meaning of chromatic, but the sense survives in the current term coloratura.[17]

Renaissance chromaticism[edit]

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,[18] 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.[19]

Diatonic scales[edit]

Diatonic scale on C About this sound Play  equal tempered and About this sound Play  just.
Gamut as defined by George William Lemon, English Etymology, 1783.

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. 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).

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 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][20]

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.[vague] (For simplicity, throughout this article equal temperament tuning is assumed unless otherwise noted.) This would include the major scale, and the 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/B.

Modern meanings[edit]

There are specific applications in the music of the Common Practice Period, and later music that shares its core features.

All writers accept the major scale as diatonic.[citation needed] Most, but not all,[21] accept the natural minor as diatonic.[vague] 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.[22]
  • "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[23] of the minor) or chromatic.[24]
  • "Mixed" usage
Still other writers[weasel words] 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.[25]

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.[26]

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[edit]

Chromatic scale on C: full octave ascending and descending About this sound Play .

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).[27]

Musical instruments[edit]

Some instruments, such as the violin, can be played in 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.

Diatonic Pixiphone, a brand of glockenspiel 
Chromatic Pixiphone 
Chromatic (rear) and diatonic harmonicas 

Intervals[edit]

The diatonic intervals are usually understood as those between some pair of notes both drawn from the same diatonic scale.[citation needed] Intervals that cannot be so derived are then called chromatic intervals[citation needed]. Because diatonic scale is itself ambiguous, 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.

In different systems of tuning[edit]

Pythagorean diatonic and chromatic interval: E-F and E-E About this sound Play .

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 (E–E) are smaller than diatonic semitones (E–F),[31] and with consonant intervals such as the major third the enharmonic 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).[citation needed]

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.[citation needed]

Chords[edit]

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 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–D) would be chromatic or altered in C minor.[34] Some writers[weasel words] use the phrase "diatonic to" as a synonym for "belonging to". Therefore a chord can be said to be diatonic if its notes belong to the underlying diatonic scale of the key.[vague]

Harmony[edit]

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]

However,

  • Chromatic harmony may be defined as "the use of two successive chords which belong to two different keys and therefore contain tones represented by the same note symbols but with different accidentals".[38] Four basic techniques produce chromatic harmony under this definition: modal interchange, secondary dominants, melodic tension, and chromatic mediants.[38]

Miscellaneous usages[edit]

Notes[edit]

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.

Inflection[edit]

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.[39]
  • Melodic movement between a diatonic note and a chromatically altered variant (from C to C in G major, or vice versa, for example).[40]

Progression[edit]

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).[41]
  • The same as the second sense of chromatic inflection, above.[42]
  • 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.[43]

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).[44]
  • 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.[43][vague]

Modulation[edit]

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

Pentatonic scale[edit]

  • 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.[46]

Modern extensions[edit]

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.[citation needed] 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.

Extended pitch selections[edit]

The selection of pitch classes can be generalised to encompass formation of non-traditional scales from the underlying twelve chromatic pitch classes.[26] 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[47] 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[edit]

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).[48]

See also[edit]

Notes and references[edit]

  1. ^ Benward & Saker (2003). Music: In Theory and Practice, Vol. I, p.38. Seventh Edition. ISBN 978-0-07-294262-0.
  2. ^ a b Leeuw, Ton de (2005). Music of the Twentieth Century, p.93. ISBN 90-5356-765-8.
  3. ^ 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.
  4. ^ This definition encompasses the natural minor scale (and equivalently the descending melodic minor), the major scale, and the ecclesiastical modes.
  5. ^ For inclusion of the harmonic minor and the ascending melodic minor see the section Modern meanings of "diatonic scale" in this article.
  6. ^ Translating the term used by Greek theorists: γένος, génos; plural γένη, génē.
  7. ^ 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. 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. 62–64). Many 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.
  8. ^ 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). 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 Solon Michaelides, The Music of Ancient Greece: An Encyclopaedia (London; Faber and Faber, 1978), pp. 335–40: "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.
  9. ^ 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 Greek lexicon). For more information, especially concerning the various exact tunings of the chromatic tetrachord, see Chromatic genus.
  10. ^ 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.
  11. ^ 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").
  12. ^ 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" (Chromaticism, Barsky, Vladimir, Routledge, 1996, p. 2). 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.
  13. ^ 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 [... .] 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 [... .] On occasions coloured notes could appear singly to denote imperfect value, especially to inhibit unwanted perfection and alteration," Roger Bowers, "Proportional notation", 2. Coloration, New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell (London: Macmillan Publishers, 2001).
  14. ^ Parrish, Carl, The Notation of Medieval Music, Pendragon, New York, 1978, pp. 147ff.
  15. ^ Harvard Dictionary of Music, 2nd ed., "Chromatic".
  16. ^ Grout, Donald J, and Palisca, Claude, A History of Western Music, 6th ed., Norton, New York, 2001, pp. 188–190.
  17. ^ "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").
  18. ^ 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:

    New Grove Online, "Musica Ficta", I, ii

  19. ^ Grout et al., 2001, p. 188.
  20. ^ Some theorists[weasel words] 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 words] 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).
  21. ^ Goetschius, as cited below, accepts only the major as diatonic.
  22. ^ 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, below. The excerpt acknowledges and analyses the difficulties with logic, naming, and taxonomy in that stance.
  23. ^ 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.
  24. ^ 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".
  25. ^ 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.
  26. ^ a b Gould, M. (2000). "Balzano and Zweifel: Another Look at Generalized Diatonic Scales". Perspectives of New Music 38 (2): 88–105. doi:10.2307/833660. JSTOR 833660.  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.

    See also #Extended pitch selections, in this article. See also an exceptional usage by Persichetti, in a note to #Diatonic_pentatonic_scale, below.

  27. ^ 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. (See the quotation from this text, below. 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.
  28. ^ There are several other understandings of the terms diatonic interval and chromatic interval. There are theorists[weasel words] 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, 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"). 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. 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. For example, the term chromatically, as used in: "The trill rises chromatically by step above this harmonic uncertainty, forming a chromatic fourth, ..." (Robin Stowel, Beethoven: Violin Concerto (Cambridge Music Handbooks), Cambridge and New York: Cambridge University Press, 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.
  29. ^ See for example William Lovelock, The Rudiments of Music, 1971.[full citation needed]
  30. ^ See for example the citation from Grove Music Online ("Diatonic"), below.
  31. ^ 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.
  32. ^ Kostka, Stefan, and Payne, Dorothy, Tonal Harmony, McGraw-Hill, 5th edition, 2003, pp. 60–61.
  33. ^ "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).
  34. ^ This is because 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 alone, 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).
  35. ^ 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.
  36. ^ 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.
  37. ^ "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" Music for Our Time, Winter, Robert, Wadsworth, 1992, p. 35. (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–A in C major, for example. But the intention is clearly that such harmonies are chromatic.)
  38. ^ a b Tischler, H. (1958). "Re: Chromatic Mediants: A Facet of Musical Romanticism". Journal of Music Theory 2 (1): 94–97. doi:10.2307/842933. JSTOR 842933. 
  39. ^ "... 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.
  40. ^ "A chromatic progression is one between harmonies having no diatonic relationship, harmonies which 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.
  41. ^ Wallace Berry, Form in Music (Prentice-Hall, 1966), pp. 109–110, note 5.
  42. ^ "In [an example] the change from major to minor is supported by the chromatic progression ... in the bass" Structural Functions of Harmony, Schoenberg, Arnold, Faber & Faber, 1983, p. 54.
  43. ^ a b See New Grove Online, "Musica Ficta", I, ii, cited earlier.
  44. ^ 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.
  45. ^ a b Berry, Form in Music, p. 125, note 2.
  46. ^ 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 ...".
  47. ^ Zweifel, P. F. (1996). "Generalized Diatonic and Pentatonic Scales: A Group-Theoretic Approach". Perspectives of New Music 34 (1): 140–161. doi:10.2307/833490. JSTOR 833490. 
  48. ^ Rahn, J. (1996). "Turning the Analysis around: Africa-Derived Rhythms and Europe-Derived Music Theory". Black Music Research Journal 16 (1): 71–89. doi:10.2307/779378. JSTOR 779378. 

Bibliography[edit]

Diatonic[edit]

Published sources for "diatonic", in Common Practice music.

  • 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.

Exclusive[edit]

Excluding harmonic and melodic minor scales:

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 ...

  • Grove Music Online (see p. 295 in the print version)[full citation needed]
    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.]
  • The Harvard Dictionary of Music 4th edition, p. 239[full citation needed]
    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.
  • 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.]
  • 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).]
  • Clough, J. (1957). "The Leading Tone in Direct Chromaticism: From Renaissance to Baroque". Journal of Music Theory 1 (1): 2–21. JSTOR 843089. 
    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
      consisting entirely of tones from a single diatonic system
    • diatonicism
      the use of diatonic collections of tones
    • chromatic
      not consisting 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.]

Inclusive[edit]

Including harmonic and melodic minor scales:

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...

  • Oxford Concise Dictionary of Music (Online [1]; 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, ...
  • 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.
  • 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.
  • 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]
  • 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.]
  • 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).
  • 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.

Other[edit]

Vague, inconsistent, or anomalous use:

  • 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).
  • 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.
  • The Cambridge History of Western Music Theory, ed. Thomas Christensen, 2004
    [Records different usages by different major theorists.]
  • 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.]
  • 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".]
  • 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.]

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.
  • 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.]
  • Theory of Harmony Schoenberg, Arnold, (translation of 3rd edition, 1922), 1983, p. 32[citation needed]
    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.]
  • 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.]
  • 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".]