Heptatonic scale

A heptatonic scale is a musical scale with seven pitches per octave. Among the most famous of these are the "diatonic scale", C D E F G A B C; the "melodic minor scale", C D Eb F G A B C ascending, C Bb Ab G F Eb D C descending; the "harmonic minor scale", C D Eb F G Ab B C; and a scale variously known as the "Byzantine", "Hungarian" [The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell (London, 2001)] , "gypsy" [Ibid.] , or "Egyptian" scale, C D Eb F# G Ab B C. South Indian (Carnatic music) classical theory postulates seventy-two "melakarta", seven-tone scale types, whereas Hindustani classical music postulates twelve or ten (depending on the theorist) seven-tone scale types collectively called " thaat".

Diatonic scale

The term "diatonic scale" refers to a pitch collection and does not imply any particular tonal center or note of especial emphasis. It is in this respect different from the term "major scale", which does imply a tonal center.

Melodic minor scale

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 Bela Bartok 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.

Harmonic minor scale

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 more commonly derived from it than from either the natural minor scale or the melodic minor scale. The augmented second between its sixth degree and its raised (“leading tone”) seventh degree, usually traditionally considered undesirable, is easily avoided by distributing these pitches among voices. In the chord progression, D F Ab, B F G, C Eb G, (ii⁰, V7, i in C minor) for example, the Ab in the upper voice never ascends to B, and the B in the lower voice never descends to Ab.

Heptonia Prima and Secunda

The rather unwieldy name of Heptonia Prima and Heptonia Secunda are given to the various seven-note scales which can be formed using tones and semitones but without two semi-tones appearing in succession. Some are more theoretical than others. They are

Heptonia Prima

Beginning on keynote A and working up the notes of the 'natural minor' scale (A,B,C,D,E,F,G,A), the seven modes are:

Aeolian mode (natural minor) t-s-t-t-s-t-t

Locrian mode s-t-t-s-t-t-t

Ionian Mode (major) t-t-s-t-t-t-s

Dorian Mode t-s-t-t-t-s-t

Phrygian Mode s-t-t-t-s-t-t

Lydian Mode t-t-t-s-t-t-s

It may be noted that the Dorian is exactly the same descending as ascending. The less common series is

Heptonia Secunda

The difference between this and the diatonic modes is that they have two and three tones between each semitone, while these latter 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:

'Melodic ascending minor' t-s-t-t-t-t-s

'Phrygian raised sixth' s-t-t-t-t-s-t combines the Phrygian flat second and Dorian raised sixth

'Lydian raised fifth' t-t-t-t-s-t-s combines the Lydian fourth with a raised fifth

'Acoustic' or 'Lydian-Myxolydian' Scale t-t-t-s-t-s-t So-called because close to the scale built on natural overtones and combines Lydian raised fourth with Myxolydian flat seventh

'Major minor' scale t-t-s-t-s-t-t Like natural minor (aeolian) but with a major third

'Half diminished' or 'Locrian sharp 2' scale t-s-t-s-t-t-t This is like the Locrian with a raised second

'Altered scale' s-t-s-t-t-t-t Like Locrian with flat 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 given them unstable tonality while the fourth mode not only has an augmented fourth a la the Lydian mode but also an augmented fifth making the dominant and subdominant unusable.

Heptonia Tertia

The last group of seven note tone/semitone scales are known as Heptonia Tertia and consist of scales with two adjacent semitones which amounts to a whole-tone scale but with an additional note somewhere in its sequence ie b c d e f# g# a#

Other Heptatonic scales

If the interval of the augmented second is used, many other scales become possible. These includeGypsy I-bII-III-IV-V-bVI-VIIHungarian I-II-bIII-#IV-V-bVI-VIIThe scales are symmetrical about the tonic and dominant respectively and the names are sometimes used interchangeably.

Phrygian Major or Dominant Harmonic Minor I-bII-III-IV-V-bVI-bVIIThis differs from the Phrygian in having a major third. It may also be considered to be built on the dominant of the harmonic minor scale.

Harmonic minor I-II-bIII-IV-V-bVI-VII

Major Flat 6 I-II-III-IV-V-bVI-VII

Verdi's Scale Enigmatica I-bII-III-#IV-#V-#VI-#VII ie G Ab B C# D# E# F# which is similar to the Heptonia Tertia mentioned above differing only in that the second degree here is flattened.

Melakarta

The postulated number of melakarta derives from arithmetical calculation and not from Carnatic practice, which employs 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 seventh chromatic tones, are invariable in inflection, and the fourth melakarta tone, corresponding to the fifth or sixth chromatic tone, is allowed one of two inflections only, a natural ("shuddah") position and a raised ("tivra") position. 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:

$2cdotleft(frac\{4!\}\{2!cdot2!\}\; ight)^2\; =\; 2cdot6^2=\; 2cdot36\; =72$

Thaat

Hindustani heptatonic theory additionally stipulates that the second, third, sixth and seventh degrees of heptatonic scale forms ("septak") 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.

ee also

Diatonic and chromatic

References