User:Hucbald.SaintAmand/Diatonic and Chromatic

I intend to assemble here definitions of "Diatonic" and "Chromatic" in different sources. I try always to read texts in their original language: unless otherwise stated, translations are mine.

Johann Nicolaus Forkel, Ueber die Theorie der Musik. Göttingen, Wittwe Vandenhoeck, 1777
"But so much as the colours can be brought in closer or more remote relations, when the space found between the principal colours is either filled with intermediate colours or left empty, so may the musical sounds be so little or so large, so near or so far apart, that the space between them in their progression can be more or less perceptible. From this arise different genres of progressions and of sound scales, that one properly names sound genres (genera). One has three different types of these: the diatonic, the chromatic and the enharmonic. (p. 17)" It is striking that Forkel describes this in terms of filling in spaces between "principal" elements.

Johann Georg Albrechtsberger, Anweisung zur Komposition. Leipzig, Breitkopf, 1790
In Chapter 4, "Of the Musical Genres and Tonalities", Albrechtsberger first describes the six diatonic modes, Dorian, Phrygian, Lydian, Mixolydian, Aeolian and Ionian, and their plagal version, forming twelve "genres". "When they added some foreign semitones in one of the mentioned 12 genres, the genre became genus Chromaticus, named the semitonal genre [halbtönige Geschlecht]; and if they added quarter tones, one named the result quartertonal genre, genus enharmonicum. Because they made little use of these rarities, which are very usual in our times, and satisfied themselves with the tone scales shown above, so their composition was almost fully in whole tones and that was called natural, plain, uniform genre (genus diatonicum). When however they made use of all three genres in one single composition (which happened only rarely), this was called genus mixtum, the mixed genre." The chromatic and enharmonic genres are described as resulting from the addition of accidental semitones or quarter tones to the diatonic genre. This type of description soon becomes standard. The diatonic is defined as "almost fully in whole tones": this also is a definition that will often be proposed.

Georg Joseph Vogler, Handbuch zur Harmonielehre. Prag, Karl Barth, 1802
"One names chromatic the colourful scale of 12 tones, diatonic the simple one of 7 tones, which counts no more tones as the tonality itself. For there exists no chromatic tonality because no more than 7 tones can have a claim on the tonic, while the 12 tones are in reciprocal relation with all tonalities. [... weil nicht mehr als 7 Töne Anspruch auf den Hauptton haben können, aber die 12 Töne im wechselseitigen Bezug mit allen Tonarten stehen.] (p. 3)"

John W. Calcott, A Musical Grammar in Four Parts. London, Birchall, 1817
The Diatonic Scale includes all the different Intervals formed by the Natural Notes and also those which are produced in transposing the Natural Scale higher or lower, by the employment of Sharps and Flats. [...] Those Intervals which are less than the Diatonic Semitone, as from F to F sharp, &c. will be distributed, with all other Intervals derived from them, into proper classes in the third Chapter of this Part, upon the Genera. (pp. 88-89) Calcott identifies fourteen diatonic intervals: Unison; Minor Second ("sometimes called the Flat Second") [he also names it "Diatonic Semitone"]; Major Second or Tone, which "although composed of two Semitones, does not consist of two equal parts [he further explains the notational difference between "Diatonic Semitone", changing one degree, and the "Chromatic Semitone", remaining on the same degree, the former being larger that the latter]; Minor Third; Major Third (The Major and Minor Thirds "formerly called Sharp and Flat Thirds"); Perfect Fourth; Sharp Fourth, "called by the Ancients [...] Tri-tone; Flat Fifth; Perfect Fifth; Minor Sixth; Major Sixth; Minor Seventh; Major Seventh; and Octave. "That Scale of Music which proceeds chiefly by Tones, called Diatonic, [...] constitutes the principal part of every piece of Music. When all the artificial Sounds are inserted between the natural Sounds, a Scale is formed of Semitones alone, and called Chromatic. When a Scale yet smaller in its Intervals is formed, which contains in some places Quarter Tones, it is called Enharmonic. (p. 109)" The definition of the diatonic as "chiefly by tones" is characteristic.

Calcott proceeds describing five degrees which form "another species of Intervals, called Extreme or Chromatic. Of these, the Chromatic Semitone, extreme sharp second, flat Third, and flat Fourth, are simple or primitive; the extreme sharp Fifth, sharp Sixth, flat Seventh and flat Eighth, are compound or derivative." This obviously makes eight chromatic intervals, but Calcott had deduced the number of five from a deduction of the seven diatonic intervals from the twelve of the chromatic scale; several of his chromatic intervals appear redundant (by enharmony, we'd say today) with some of the diatonic ones. He reviews each of these in turn, with examples, and notes the identity of some of them, "upon keyed instruments", with diatonic intervals.

Calcott further describes the Enharmonic Scale as resulting from "the Interval formed between the sharpened Note and the Flat of the next succeding Note above."

M. Castil-Blaze, Dictionnaire de musique moderne. Paris, Magasin de Musique de la Lyre moderne, 2e éd., 1825
"C HROMATIC, adj. sometimes taken substantively. Music genre that proceeds through several successive semitones. The word comes from the Greek Chroma that means colour, either because the Greek marked this genre with red characters or otherwise coloured, or, the authors say, because the chromatic genre is the mean between the two others, as the colour is mean between the white and the black; or according to others, because this genre varies and embellishes the diatonic by its semitones, which in music make the same effect that the variety of colours makes in painting. One calls chromatic bass, chromatic scale, a harmonic progression that proceeds through semitones in the low, a scale that ascends or descends by semitones.(vol. I, p. 111)" "D IATONIC, adj. The diatonic genre proceeds through tones and natural semitones, i.e. without alteration; so, the two semitones that are found in the scale are of the diatonic genre; and the scale, either ascending or descending, is called diatonic gamut or scale. Even although, in the diatonic genre, the least interval is of a conjunct degree, this does not prevent that the parts could proceed through larger intervals, provided that they all be taken from the diatonic degrees. This word comes from the Greek dia, through, and from tonos, tone; that is passing from one tone to another. (vol. I, p. 187)" These definitions come from Jean-Jacques Rousseau's Dictionnaire, slightly shortened. Where Castil-Blaze mentions the "chromatic bass", Rousseau spoke of the chromatic fundamental bass, which makes more sense.

Simon Sechter, Die richtige Folge der Grundharmonien, Leipzig, Breitkopf und Härtel, 1853
"To progress diatonically means to use only those tones which are contained in the choosen tone scale, for instance in the scale of C major only the tones C d e f g a b c. [...] The chromatic progression in the major and minor scales consists in that, to the tones belonging to the scale, one adds tones from related scale degrees, without really leaving the choosen principal tone scale. [...] Finally comes the enharmonic mixtures [Verwechslungen], where one tone presents itself under two different signs and lets itself reasonably be related to different tone scales. (p. 1)" This gives the outline of the treatise, the four parts of which are titled "I. Diatonic progressions in major"; "II. Diatonic progressions in minor"; "III. Diatonic modulation and chromatic progressions in major"; and "IV. Chromatic progressions in minor and the enharmonic mixtures".

Henry C. Banister, Music. Cambridge, Deighton. Bell, and Co., 1873
Banister explains the name "diatonic" as coming from the Greek dia, "through", and tonos, "a tone", "i. e. through the tones or sounds consisting of two precisely similar Tetrachords". He gives the following definition: "A Diatonic scale may be defined as a series of eight notes, proceeding alphabetically from any note to its octave by five tones and two semitones. [...] The first or initial note of a Diatonic scale is termed its T ONIC, or K EY-NOTE ; also its F INAL . [...] Any note may be taken as the Tonic of a scale. If, however, a scale of natural notes–(white keys on the Pianoforte) be formed, commencing with any other note than C, the order of the tones and semitones will vary; the scale will not be a Major scale. (pp. 22-23)" As one can see, Banister is not entirely at ease distinguishing the scale from the "mode" (or key) defined by a tonic, a reference note. He further describes the natural minor scale as the relative to the major one, and adds that "it is now customary to raise the 7th note of the Minor scale one semitone, accidentally, to obtain a true leading-tone. [Example of A minor with G♯]. The scale, as thus altered, ceases to be purely Diatonic; having three tones, three semitones, and one distance of a tone and a half: F to G♯. (pp. 28-29)" "The distances between the notes that are a tone apart in the Diatonic scale, may be filled up by the insertion of the intermediate notes, thus producing a scale of semitones, termed the C HROMATIC scale (from chroma, colour; the origin of the term, as applicable to this scale, being uncertain, however.) [...] The raising or lowering the pitch of a note one semitone without changing its position on the stave, or its alphabetical name, is termed Chromatic alteration. [...] The semitone obtained by Chromatic alteration, occuring only in the Chromatic scale, and consisting, therefore, of two notes on the same position of the stave, is termed a C HROMATIC SEMITONE ; whereas that which is found in a Diatonic scale, consisting of two notes on different positions on the stave, is termed a D IATONIC SEMITONE . [...] The Chromatic semitone is also termed a Minor semitone, and, likewise, a Superfluous Prime, and an Augmented Unison, or Diminished Unison, according as it is obtained by a raising or lowering of the note. The Diatonic semitone is also termed a Major semitone; likewise a Minor 2nd ... (pp. 32-34)" "Intervals which occur in an unaltered Diatonic scale are termed D IATONIC INTERVALS ; i. e. the distance between any two notes in the same Diatonic scale is a Diatonic interval. Intervals that occur only in the Chromatic scale are termed Chromatic intervals. (p. 35)" Banister continues with lists, first of the diatonic intervals: minor and major seconds, minor and major thirds, perfect fourth, tritone, imperfect and perfect fifths, minor and major sixths, minor and major sevenths, perfect octave, minor and major ninths. Then of the chromatic intervals, "obtained by Chromatic alteration of one of the notes of the Diatonic intervals, either augmenting or diminishing it, by one semitone" (p. 37). He adds that augmented intervals are diversely named, but that the term "augmented" appears the best; he appears to have thought the same of "diminished". Chromatic intervals listed: augmented 2nd, diminished 3rd, diminished 4th, augmented 5th, augmented 6th, diminished 7th, diminished 8ve, augmented 8ve, augmentend 9th. "S TRICTLY speaking, a C HROMATIC C HORD is one that contains a Chromatic Interval, e. g. a Dominant 97 in the Minor key, which has a Diminished 7th. This, however, is not the sense in which the term is customarily used by musicians. By a Chromatic Chord is meant a chord in which one or more of the notes of a Diatonic Chord is chromatically altered. Thus, as will be seen, a chord which contains only Diatonic Intervals may be termed Chromatic; which is anomalous, but, nevertheless, customary. (p. 109)." Banister may not fully identify the cause of this "anomaly", which obviously is when a note, instead of an interval, is termed "chromatic". No isolated note is chromatic as such, it always is with respect to another note. To say that an isolated note is chromatically altered, one must first have considered another note, of which it is supposed to be an alteration. "The progression of a Chromatically raised note is to ascend, forming part of the ascending Chromatic scale. Therefore, these chords are usually followed as [follows an example, e.g. of augmended fifths resolving in ascending). (pp. 109-110)" One of the examples given is somewhat puzzling: where F♯ and C♯ are given by the key signature (two sharps), while D♯ is "accidental". Banister writes that in this example "the D♯ is simply a chromatic alteration of the Root, and is followed as the Diatonic note might be. [...] Thus, then, the chord on D♯ has a Chromatically altered note, but not a Chromatic Interval." Was it not for the key signature, however, it is not clear that D♯ is "chromatically altered", nor that it stands for an implied D♮.

Percy Goetschius, The Theory and Practice of Tone Relations. New York, Schirmer, 1900, 1917, 1931
Goetschius has an evolutionary conception of the scale, as appears to have been rather common in the early 20th century (e.g. Maurice Emmanuel, or even Schœnberg): "From the infinite multitude of possible tones perceptible to the ear, the intuition of man (in civilized countries), has singled out a limited number (at first 7, later 12), which with their reproduction or duplication in higher and lower registers, by the octave relation, represent the entire absolute tone-material of the art of music". Seven-note scales are deduced from the cycle of fifths, "the basis of the whole system of tone-combination, and the standard of measurement in harmony." He describes the ascending series of fifths from F to B as "the true natural scale [...]. For the sake of convenience, the seven tones are drawn into close proximity by simply transferring certain tones down or up by the octave-relation [...]. In this way the so-called diatonic scale is obtained. [...] This diatonic scale comprises the tones of the major mode. (pp. 3-4)" "DIATONIC INTERVALS. All those intervals which agree with the natural major scale [...] are called natural or diatonic intervals. (p. 6)" The example that follows illustrates the perfect unison, 8th, 5th and 4th, and the major 7th, 6th, 3d and 2d, all counted above E♭ in the key and the scale of E♭. "CHROMATIC INTERVALS. But the upper of two tones does not always agree thus with the major scale of the lower tone; for example [augmented 5th; minor 7th; augmented 3d; diminished 7th] etc. Such tone-relations are termed chromatic intervals, and are qualified as follows: Any perfect interval when extended by an accidental before the upper tone [...] becomes augmented; when similarly contracted, it becomes diminished. [...] Analogously, any major interval when extended by an accidental becomes augmented; when contracted by an accidental, a major interval becomes minor. One similar contraction of a minor interval, or two contractions of the corresponding major interval, will result in its diminution. (p. 6)" This is quite ambiguous. The statement that "those intervals which agree with the major scale are called diatonic" would appear to include all the intervals found in that scale; but only perfect and major ones are illustrated. And the statement that "the upper of two tones does not always agree with the major scale of the lower tone " appears to imply that diatonic intervals must be counted from the tonic of the scale. And again, the statement that "when contracted by an accidental, a major interval becomes minor" would appear to indicate that only major (or perfect) intervals are diatonic. When discussing diatonic melodic progressions, however, Goetschius does include minor seconds, thirds, etc. It seems difficult therefore to assume that he considered only perfect and major intervals to be diatonic, a position which in any case would soon become untenable.

François-Auguste Gevaert, Traité d'harmonie théorique et pratique, vol. 1, Paris, Lemoine, 1905
Gevaert considers that all intervals and all scales originate in a cycle of fifths. "In theory as in practice, the fifth is the true generator of the musical scale; it is the consonance which makes us discover all the sounds usable in the harmony. [...] Starting from G and ascending from fifth to fifth, one finds the 31 sounds comprised in each octave of the overall ambitus: first the four other sounds marked with a double flat, then the seven sounds with a flat, then the seven notes without sign of alteration, the seven sharpened notes and finally the five doubly sharpened notes. (p. 5)" Gevaert gives an example extending in the order of the cycle of fifths from G to A. He explains that the thirty fifths necessary for this would cover more than 17 octaves, but because sounds an octave apart have the same value in the system, the scale can be reduced to within the limits of one single octave.

Gevaert then proceeds to describe all the intervals in terms of the number of fifths or fourths necessary to produce them in ascending order: two fifths for the major second, two fourths for the minor seventh; three fifths for the major sixth, three fourths for the minor third; etc., up to sixteen fifths, doubly augmented second, or sixteen fourth, doubly diminished seventh. He then proceeds to a discussion of the "systems" (obviously refering to the Greek systems which he knew particularly well). As harmonic unit, the general system is not susceptible of practical application. [...] This general collection of the musical sounds is employed only in partial series, in fragmentary systems embracing a determined number of fifths, taken anywhere in the entire series.

There exists two systems of this kind, to which we will give the name of primary. The first and the principal is the diatonic, of which the entire domain is contained in a series of seven sounds (6 fifths), that is in the interval of a tritone (or of false fifth).

[Examples: from A{{flat)) to D, from F to B, from D to G{{sharp}}]

The second is the chromatic, which covers a series of twelve sounds (11 fifths), framed by the interval of an augmented third (or a diminished sixth).

[Examples: from G{{flat}} to B, from F to A{{sharp}}]

All the sounds of the two systems disposed in the form of a scale, one sees produced the two characteristic types of melodic successions: the diatonic scale, proceeding by major and minor seconds; the chromatic scale, proceeding by minor seconds and chromatic semitones. (p. 9)

Heinrich Schenker, Harmonielehre. 1906
Chapter IV, The Relations between Chromaticism and Diatony, of Section II, Of the Psychology of Chromaticism and the Alteration, in Part II, Practical Part, of the treatise, opposes the nouns Chromatik ("Chromaticism") and Diatonie ("Diatonic"). Elisabeth Mann Borgese's translation (perhaps under the guidance of Oswald Jonas), Relations Between Chromatic Change and Diatonic System, says more, associating "chromaticism" with modulation ("change") and "diatony" with a system. The usage of these terms by Schenker in Harmonielehre does not seem so heavily loaded and may merely reflect the difficulty of substantiving these two adjectives. Schenker however clearly sees chromaticism as a mere alteration of diatony, not necessarily creating a new system: "Chromaticism is an element which does not destroy diatony, rather one that reinforces it more espressly. [...] I may therefore advance the principle that for the sake of the diatony, one cannot enough write chromatically. (p. 380)" Schenker further explains that he is refering here to "chromaticism in the service of tonicization, that is of the degrees of the diatony." He reminds that other devices often named Chroma, particularly the combination of major with minor, is considered an independent principle of composition that he names "mixture". "Making this distinction," he adds, "leads more securely to an understanding of the point of view of the composer."

Schenker considers that the diatonic version of the minor scale is the so-called "natural" minor. It would be necessary, however, to reread in Harmonielehre what concerns the "mixture", which seems to concern the fact that the diatonic minor scale may borrow degrees from the major one, or inversely. This not only provides justifications for all forms of the minor scale, but it might also lead to the idea that all these forms are somehow diatonic.

Bruce Benward and Marylin Saker, Music in Theory and Practice, 8th edition. New York, McGraw Hill, 2009
"Diatonic (literally 'across the tones') defines a scale of mixed half and whole steps (and an occasional step and a half) in which each individual tone plays a role. The first tone of a scale, the tonic, is a point of rest and is considered to be the most stable. Other tones lead toward or away from it, creating varying degrees of tension or relaxation. Since the tonic  is  the  focal  point  of  the  scale,  the  most  stable  note,  and  the  point  of  greatest relaxation, diatonic melodies frequently end on the tonic note. At times the word diatonic is used to indicate a tone that is part of a particular scale pattern—as distin-guished from a nondiatonic tone that does not belong to the scale pattern. (p. 28)" There is an obvious confusion in this between the diatonic scale and the tonal scale. Benward and Saker continue listing the degrees of the scale that they call diatonic, "tonic", "supertonic", "mediant", "subdominant", "dominant", "submediant", "leading tone" and "subtonic", confirming the confusion. They describe this in the major and in the "natural" minor scales. They confirm (p. 32) that they consider that the various forms of the minor scale are all diatonic. "A scale that does not observe the interval sequence of the diatonic or pentatonic scales is called a nondiatonic scale. Many nondiatonic scales have no identifiable tonic. (p. 41)" It seems here that the "pentatonic" scale is considered a diatonic scale, even although that had not be said before. The pentatonic scale described on p. 40 is more precisely the anhemitonic scale. Benward and Saker first state that "It is convenient to think of the common pentatonic scale as an incomplete major scale", then that "The pentatonic scale in Figure 2.22 is based on the natural minor scale". The examples actually propose two of the five aspects of the anhemitonic pentatonic scale: first C D E G A C, then A C D E G A.