Indian classical theory postulates seventy-two seven-tone scale types, collectively called melakarta or thaat, whereas others postulate twelve or ten (depending on the theorist) seven-tone scale types.
A diatonic scale is any seven-note scale constructed sequentially using only whole tones and half tones, repeating at the octave, having a tonal center, and comprising only one tritone interval between any two scale members, which ensures that the half tone intervals are as far apart as possible. In Western music, there are seven such scales, and they are commonly known as the modes of the major scale (Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, and Locrian).
In traditional classical theory, the melodic minor scale has two forms, as noted above, an ascending form and a descending form. Although each of these forms of itself comprises seven pitches, together they comprise nine, which might seem to call into question the scale's status as a heptatonic scale. In certain twentieth-century music, however, it became common systematically to use the ascending form for both ascending and descending passages. Such a use has been notably ascribed to the works of Béla Bartók and to bop and post-bop jazz practice. The traditional descending form of the melodic minor scale is equivalent to the natural minor scale in both pitch collection (which is diatonic) and tonal center.
The harmonic minor scale is so called because in tonal music of the common practice period (from approximately 1600 to approximately 1900) chords or harmonies are derived from it more than from the natural minor scale or the melodic minor scale. The augmented second between its sixth degree and its raised seventh degree (the "leading tone"), traditionally considered undesirable in melodic progression, is avoided by placing these pitches in different voices in adjacent chords, as in this progression: FA♭D, FGB, FA♭C (ii°b–V7d–iv in Cminor). The A♭ in the middle voice does not ascend to B, and the B in the upper voice does not descend to A♭.
Heptatonia prima and secunda
The names heptatonia prima and heptatonia secunda apply to seven-note scales that can be formed using five tones (t) and two semi-tones (s), (also called whole-steps and half-steps), but without two semi-tones in succession. Throughout history and to the present day, some have occurred much more commonly than others, namely Ionian (also called the major scale), Aeolian (also called the natural minor scale), melodic ascending minor, Dorian, Mixolydian, Lydian, Lydian dominant, Aeolian dominant, and altered scales.
Heptatonia prima
In these scales the semi-tones are maximally separated. They are known most commonly as the diatonic modes. Beginning on keynote C and working up the notes of the 'natural minor' scale (A, B, C, D, E, F, G, A), the seven modes are:
While the diatonic modes have two and three tones on either side of each semitone, the heptatonia secunda modes have one and four. These are sometimes called modes of the melodic ascending minor since that is the most commonly used scale of this type, but other modes can be produced by starting on the different scale notes in turn. Thus starting on keynote A as above and following the notes of the ascending melodic minor (A, B, C, D, E, F♯, G♯) yields these seven modes:
Acoustic scale or Lydian dominant scale t-t-t-s-t-s-t So-called because it is close to the scale built on natural overtones and combines Lydian raised fourth with Mixolydian (Dominant) flat seventh
Aeolian dominant scale or Mixolydian ♭6 scale t-t-s-t-s-t-t Like natural minor (aeolian) but with a major third
Altered scale s-t-s-t-t-t-t Like Locrian with diminished fourth
These modes are more awkward to use than those of the diatonic scales due to the four tones in a row yielding augmented intervals on one hand while the one tone between two semitones gives rise to diminished intervals on the other. For example, the last two modes listed above both have 'Locrian' diminished triads built on their tonics, giving them unstable tonality, while the third mode not only has an augmented fourth a la the Lydian mode but also an augmented fifth making the dominant and subdominant essentially unusable.
The last group of seven-note tone/semitone scales is heptatonia tertia, and consists of scales with two adjacent semitones—which amounts to a whole-tone scale, but with an additional note somewhere in its sequence, e.g., B C D E F♯ G♯ A♯. One such example is the Neapolitan major scale.
Other heptatonic scales
Hungarian Gypsy scale
If the interval of the augmented second is used, many other scales become possible. These include Gypsy I-♭II-III-IV-V-♭VI-VII Hungarian I-II-♭III-♯IV-V-♭VI-VII The scales are symmetrical about the tonic and dominant respectively and the names are sometimes used interchangeably.
The double harmonic scale, also known as the Byzantine or Hungarian,[3] scale, contains the notes C D E♭ F♯ G A♭ B C.
Phrygian dominant or dominant harmonic minor I-♭II-III-IV-V-♭VI-♭VII This differs from the Phrygian in having a major third. It may also be considered built on the dominant of the harmonic minor scale.
Neapolitan minor differs from the Phrygian in having a major seventh.
Verdi's Scala Enigmatica I-♭II-III-♯IV-♯V-♯VI-VII i.e. G A♭ B C♯ D♯ E♯ F♯, which is similar to the heptatonia tertia mentioned above, differing only in that the second degree here is flattened.
Melakarta is a South Indian classical method of organizing Raagas based on their unique heptatonic scales. The postulated number of melakarta derives from arithmetical calculation and not from Carnatic practice, which uses far fewer scale forms. Seven-pitch melakarta are considered subsets of a twelve-pitch scale roughly analogous to the Western chromatic scale. The first and fifth melakarta tones, corresponding to the first and eighth chromatic tones, are invariable in inflection, and the fourth melakarta tone, corresponding to the sixth or seventh chromatic tone, is allowed one of two inflections only, a natural (shuddah) position and a raised (tivra) position. The second and third melakarta tones can be picked from the 4 chromatic tones (second through fifth), and similarly for the sixth and seventh. Thus the number of possible forms is equal to twice the square of the number of ways a two-membered subset can be extracted from a four-membered set:
Hindustani heptatonic theory additionally stipulates that the second, third, sixth and seventh degrees of heptatonic scale forms (saptak) are also allowed only two inflections each, in this case, one natural position, and one lowered (komal) position. Arithmetically this produces 25, or thirty-two, possibilities, but Hindustani theory, in contradistinction to Carnatic theory, excludes scale forms not commonly used.
Chinese Gongche notation
Gongche notation heptatonic scale gives a do, re, mi, (between fa and fa♯), sol, la, (between ti♭ and ti) heptatonic scale.
In music theory, a diatonic scale is any heptatonic scale that includes five whole steps and two half steps (semitones) in each octave, in which the two half steps are separated from each other by either two or three whole steps, depending on their position in the scale. This pattern ensures that, in a diatonic scale spanning more than one octave, all the half steps are maximally separated from each other.
In music theory, the term mode or modus is used in a number of distinct senses, depending on context.
A jazz scale is any musical scale used in jazz. Many "jazz scales" are common scales drawn from Western European classical music, including the diatonic, whole-tone, octatonic, and the modes of the ascending melodic minor. All of these scales were commonly used by late nineteenth and early twentieth-century composers such as Rimsky-Korsakov, Debussy, Ravel and Stravinsky, often in ways that directly anticipate jazz practice. Some jazz scales, such as the bebop scales, add additional chromatic passing tones to the familiar diatonic scales.
B, also known as Si, Ti, or, in some European countries, H, is the seventh note and the twelfth semitone of the fixed-Do solfège. Its enharmonic equivalents are C♭ (C-flat) and A.
A or La is the sixth note and the tenth semitone of the fixed-do solfège.
In music, the major Locrian scale, also called the Locrian major scale, is the scale obtained by sharpening the second and third notes of the diatonic Locrian mode. With a tonic of C, it consists of the notes C D E F G♭ A♭ B♭. It can be described as a whole tone scale extending from G♭ to E, with F introduced within the diminished third interval from E to G♭. The scale therefore shares with the Locrian mode the property of having a diminished fifth above the tonic.
D is a musical note a whole tone above C, and is known as Re within the fixed-Do solfege system. Its enharmonic equivalents are C and E. It is the third semitone of the solfège.
E is the third note and the fifth semitone of the C major scale, and mi in fixed-do solfège. It has enharmonic equivalents of F♭ [(F-flat) which is by definition a diatonic semitone above E♭] and D, amongst others.
F is a musical note, the fourth above C or fifth below C. It is the fourth note and the sixth semitone of the solfège. It is also known as fa in fixed-do solfège. It has enharmonic equivalents of E♯ (E-sharp) and G, amongst others.
Sol, so, or G is the fifth note of the fixed-do solfège starting on C. It is the fifth note and the eighth semitone of the solfège. As such it is the dominant, a perfect fifth above C or perfect fourth below C.
F♯ is the seventh semitone of the solfège.
G♯ (G-sharp) or sol dièse is the ninth semitone of the solfège. In the German pitch nomenclature, it is known as gis.
A♯ is the eleventh semitone of the solfège. In some countries, it is also called B.
D♯ (D-sharp) or re dièse is the fourth semitone of the solfège. It lies a chromatic semitone above D and a diatonic semitone below E, thus being enharmonic to mi bémol or E♭. However, in some temperaments, it is not the same as E♭. E♭ is a perfect fourth above B♭, whereas D♯ is a major third above B.
C♯ (C-sharp) is a musical note lying a chromatic semitone above C and a diatonic semitone below D; it is the second semitone of the solfège. C-sharp is thus enharmonic to D♭. It is the second semitone in the French solfège and is known there as do dièse. In some European notations, it is known as Cis. In equal temperament it is also enharmonic with B.
B♭ (B-flat), or, in some European countries, B, is the eleventh step of the Western chromatic scale . It lies a diatonic semitone above A and a chromatic semitone below B, thus being enharmonic to A♯, even though in some musical tunings, B♭ will have a different sounding pitch than A♯. B-flat is also enharmonic to C.
A♭ is the ninth semitone of the solfège.
D♭ (D-flat) is a musical note lying a diatonic semitone above C and a chromatic semitone below D. It is thus enharmonic to C♯. In the French solfège it is known as re bémol. It is the second semitone of the solfège.
E♭ (E-flat) or mi bémol is the fourth semitone of the solfège.
G♭ is the seventh semitone of the solfège.
References
↑ Dupré, Marcel (1962). Cours Complet d'Improvisation a l'Orgue, v.2, p. 35, trans. John Fenstermaker. Paris: Alphonse Leduc. ASIN: B0006CNH8E.
↑ Hanson, Howard. (1960) Harmonic Materials of Modern Music, p. 362 ff. New York: Appleton-Century-Crofts. LOC 58-8138.
↑ The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell (London, 2001)
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