Heptatonic Scales
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A heptatonic scale is a musical scale that has seven pitches, or tones, per
octave In music, an octave ( la, octavus: eighth) or perfect octave (sometimes called the diapason) is the interval between one musical pitch and another with double its frequency. The octave relationship is a natural phenomenon that has been refer ...
. Examples include the
major scale The major scale (or Ionian mode) is one of the most commonly used musical scales, especially in Western music. It is one of the diatonic scales. Like many musical scales, it is made up of seven notes: the eighth duplicates the first at double i ...
or
minor scale In music theory, the minor scale is three scale patterns – the natural minor scale (or Aeolian mode), the harmonic minor scale, and the melodic minor scale (ascending or descending) – rather than just two as with the major scale, which also ...
; e.g., in
C major C major (or the key of C) is a major scale based on C, consisting of the pitches C, D, E, F, G, A, and B. C major is one of the most common keys used in music. Its key signature has no flats or sharps. Its relative minor is A minor and ...
: C D E F G A B C—and in the
relative minor In music, relative keys are the major and minor scales that have the same key signatures (enharmonically equivalent), meaning that they share all the same notes but are arranged in a different order of whole steps and half steps. A pair of major an ...
,
A minor A minor is a minor scale based on A, with the pitches A, B, C, D, E, F, and G. Its key signature has no flats and no sharps. Its relative major is C major and its parallel major is A major. The A natural minor scale is: : Changes ...
, natural minor: A B C D E F G A; the
melodic minor scale In music theory, the minor scale is three scale patterns – the natural minor scale (or Aeolian mode), the harmonic minor scale, and the melodic minor scale (ascending or descending) – rather than just two as with the major scale, which also ...
, A B C D E FGA ascending, A G F E D C B A descending; the
harmonic minor scale In music theory, the minor scale is three scale patterns – the natural minor scale (or Aeolian mode), the harmonic minor scale, and the melodic minor scale (ascending or descending) – rather than just two as with the major scale, which als ...
, A B C D E F GA; and a scale variously known as the Byzantine, and Hungarian,''The New Grove Dictionary of Music and Musicians'', second edition, edited by Stanley Sadie and John Tyrrell (London, 2001) scale, C D E F G A B C. Indian classical theory postulates seventy-two seven-tone scale types, collectively called ''
thaat A Thaat () is a "Parent scale" in North Indian or Hindustani music. It is the Hindustani equivalent of the term ''Melakartha raga'' of Carnatic Music. The concept of the ''thaat'' is not exactly equivalent to the western musical scale because t ...
'', whereas others postulate twelve or ten (depending on the theorist) seven-tone scale types. Several heptatonic scales in
Western Western may refer to: Places *Western, Nebraska, a village in the US *Western, New York, a town in the US *Western Creek, Tasmania, a locality in Australia *Western Junction, Tasmania, a locality in Australia *Western world, countries that id ...
, Roman, Spanish, Hungarian, and Greek music can be analyzed as juxtapositions of tetrachords.Dupré, Marcel (1962). ''Cours Complet d'Improvisation a l'Orgue'', v.2, p. 35, trans. John Fenstermaker. Paris: Alphonse Leduc. ASIN: B0006CNH8E. All heptatonic scales have all
intervals Interval may refer to: Mathematics and physics * Interval (mathematics), a range of numbers ** Partially ordered set#Intervals, its generalization from numbers to arbitrary partially ordered sets * A statistical level of measurement * Interval e ...
present in their
interval vector In musical set theory, an interval vector is an array of natural numbers which summarize the intervals present in a set of pitch classes. (That is, a set of pitches where octaves are disregarded.) Other names include: ic vector (or interva ...
analysis,Hanson, Howard. (1960) ''Harmonic Materials of Modern Music'', p. 362 ff. New York: Appleton-Century-Crofts. LOC 58-8138. and thus all heptatonic scales are both hemitonic and
tritonic A tritonic scale is a musical scale or mode with three notes per octave. This is in contrast to a heptatonic (seven-note) scale such as the major scale and minor scale, or a dodecatonic (chromatic 12-note) scale, both common in modern Western ...
. There is a special affinity for heptatonic scales in the Western
key signature In Western musical notation, a key signature is a set of sharp (), flat (), or rarely, natural () symbols placed on the staff at the beginning of a section of music. The initial key signature in a piece is placed immediately after the clef at ...
system.


Diatonic scale

A
diatonic scale In music theory, a diatonic scale is any heptatonic scale that includes five whole steps (whole tones) 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, ...
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 In music theory, the tritone is defined as a musical interval composed of three adjacent whole tones (six semitones). For instance, the interval from F up to the B above it (in short, F–B) is a tritone as it can be decomposed into the three a ...
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 Mode ( la, modus meaning "manner, tune, measure, due measure, rhythm, melody") may refer to: Arts and entertainment * '' MO''D''E (magazine)'', a defunct U.S. women's fashion magazine * ''Mode'' magazine, a fictional fashion magazine which is ...
of the
major scale The major scale (or Ionian mode) is one of the most commonly used musical scales, especially in Western music. It is one of the diatonic scales. Like many musical scales, it is made up of seven notes: the eighth duplicates the first at double i ...
( Ionian, Dorian, Phrygian, Lydian,
Mixolydian Mixolydian mode may refer to one of three things: the name applied to one of the ancient Greek ''harmoniai'' or ''tonoi'', based on a particular octave species or scale; one of the medieval church modes; or a modern musical mode or diatonic scal ...
, Aeolian, and Locrian).


Melodic minor scale

In traditional classical theory, the
melodic minor scale In music theory, the minor scale is three scale patterns – the natural minor scale (or Aeolian mode), the harmonic minor scale, and the melodic minor scale (ascending or descending) – rather than just two as with the major scale, which also ...
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 Béla Viktor János Bartók (; ; 25 March 1881 – 26 September 1945) was a Hungarian composer, pianist, and ethnomusicologist. He is considered one of the most important composers of the 20th century; he and Franz Liszt are regarded as H ...
and to bop and post-bop
jazz Jazz is a music genre that originated in the African-American communities of New Orleans, Louisiana in the late 19th and early 20th centuries, with its roots in blues and ragtime. Since the 1920s Jazz Age, it has been recognized as a major ...
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 In music theory, the minor scale is three scale patterns – the natural minor scale (or Aeolian mode), the harmonic minor scale, and the melodic minor scale (ascending or descending) – rather than just two as with the major scale, which als ...
is so called because in tonal music of the
common practice period In European art music, the common-practice period is the era of the tonal system. Most of its features persisted from the mid- Baroque period through the Classical and Romantic periods, roughly from 1650 to 1900. There was much stylistic evoluti ...
(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 In classical music from Western culture, an augmented second is an interval that, in equal temperament, is sonically equivalent to a minor third, spanning three semitones, and is created by widening a major second by a chromatic semitone.Ben ...
between its sixth
degree Degree may refer to: As a unit of measurement * Degree (angle), a unit of angle measurement ** Degree of geographical latitude ** Degree of geographical longitude * Degree symbol (°), a notation used in science, engineering, and mathematics ...
and its raised seventh degree (the "
leading tone In music theory, a leading-tone (also called a subsemitone, and a leading-note in the UK) is a note or pitch which resolves or "leads" to a note one semitone higher or lower, being a lower and upper leading-tone, respectively. Typically, ''the ...
"), traditionally considered undesirable in melodic progression, is avoided by placing these pitches in different voices in adjacent chords, as in this progression: F A D, F G B, F A C (ii°b–V7d–iv in C minor). 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, the major-minor, and altered scales.


Heptatonia prima

In these scales the semi-tones are maximally separated. They are known most commonly as the
diatonic Diatonic and chromatic are terms in music theory that are most often used to characterize Scale (music), scales, and are also applied to musical instruments, Interval (music), intervals, Chord (music), chords, Musical note, notes, musical sty ...
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: * 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 * Mixolydian mode t-t-s-t-t-s-t


Heptatonia secunda

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: * '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 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 * 'Major minor' scale t-t-s-t-s-t-t Like natural minor (aeolian) but with a major third * '
Half diminished scale The half diminished scale or Sisyphean Scale is a seven-note musical scale. It is more commonly known as the Locrian 2 scale, a name that avoids confusion with the diminished scale and the half-diminished seventh chord (minor seventh, diminishe ...
' or 'Locrian sharp 2' scale t-s-t-s-t-t-t This is like the Locrian with a raised second * '
Altered scale In jazz, the altered scale, altered dominant scale, Palamidian Scale, or Super Locrian scale is a seven-note scale that is a dominant scale where all non-essential tones have been altered. This means that it comprises the three irreducibly ess ...
' 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.


Heptatonia tertia

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 In music, a whole-tone scale is a scale in which each note is separated from its neighbors by the interval of a whole tone. In twelve-tone equal temperament, there are only two complementary whole-tone scales, both six-note or ''hexatonic'' s ...
, 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

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. Phrygian major 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. The
harmonic major scale In music theory, the harmonic major scale is a musical scale found in some music from the common practice era and now used occasionally, most often in jazz. In George Russell's '' Lydian Chromatic Concept'' it is the fifth mode (V) of the Lydian ...
differs from the major scale by having a flat sixth degree: I-II-III-IV-V-VI-VII. Verdi's
Scala Enigmatica The enigmatic scale ( it, scala enigmatica) is an unusual musical scale, with elements of both major and minor scales, as well as the whole-tone scale. It was originally published in a Milan journal as a musical challenge, with an invitation t ...
I-II-III-IV-V-VI-VII i.e. G A 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

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 () position and a raised () 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: : 2\cdot\left(\frac\right)^2 = 2\cdot6^2 =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.


Chinese Gongche notation

Gongche notation ''Gongche'' notation or ''gongchepu'' is a traditional musical notation method, once popular in ancient China. It uses Chinese characters to represent musical notes. It was named after two of the Chinese characters that were used to represen ...
heptatonic scale gives a do, re, mi, (between fa and fa), sol, la, (between ti and ti) heptatonic scale.


See also

*
Diatonic and chromatic Diatonic and chromatic 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, ...
* Modes of the ancohemitonic heptatonic scales and the key signature system


References

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