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Scales and generic scales

A scale is a stepwise sequence (usually upward) of pitches. The term is also connected to the concept of musical key and tonality; the notes of a melody in a certain key can form a scale. Notes outside the scale are perceived as non-harmonic.

A need to classify pitches gave rise to the concept of a scale. If only a certain part of all possible pitches is applied in music, it is practical and sensible to create an abstraction of these pitches and name it.

Ancient Greeks, especially Plato, saw a strong connection between musical scales and human emotions (ethos). Even today, musical scales are more than just "schemes of pitches". It is typical in several scales that one of the notes is more important than the others; it begins and gives a name to the scale (for example, C major). This note is usually called the tonic or the tonal centre. There is a hierarchy between the other notes of a scale; for example, some of them have a semitonal relationship (capability of leading) to the tonal centre.  In the Phrygian mode, the leading note is the second note of the scale; in a major scale, it is the 7th note.

Related keys differ from each other in terms of the keynote; C major and A natural minor share pitches but not the keynote. Pitches are also shared by the D Dorian, E Phrygian, F Lydian modes, and so on.

Thus, these scales can be considered to be part of the same generic scale. For example, modes (also major scale and natural minor) are part of the diatonic scale, perhaps the most important generic scale of Western music.

Diatonic scales:

Notation is based on the diatonic scale. It has no beginning or end, but it includes tones and semitones in a certain order. Between semitones (S), two or three tones take turns (T): ...T T S T T T S... (cf. a keyboard, for example).

  F G A B C D E F G A B C D E
Lydian T T T S T T S              
Ionian (= major scale)         T T S T T T S      
Mixolydian   T T S T T S T            
Aeolian (= minor scale)           T S T T T S T    
Dorian     T S T T S T T          
Phrygian             S T T T S T T  
Lochrian       S T T S T T T        

The notes of a generic scale are related by certain intervals, but there is no tonal centre to name the scale. Different scales can be formed from the generic scale by naming the tonal centre. Naming is possible if one of the notes is perceived as the tonic, which is a natural note, for example, on which to end a melody.

Generic diatonic scale (...TTSTTTS...)

Generic diatonic scale

The pentatonic scale is also a generic scale. While the prefix "penta" refers to any scale with five pitches, the most typical pentatonic scale looks like this: ...T T m3 T m3 ..., where m3 stands for a minor third (1 ½ steps).

The most common pentatonic scales are the major pentatonic (T T m3 T m3), which resembles a major scale with semitones replaced by minor thirds, and the minor pentatonic (m3 T T m3 T), which is the basic structure for the minor scale and the blues scale.

Pentatonic scales are considered to be the oldest scale structures and the basis for scales with more pitches.

Pentatonic scale (...T T m3 T m3...)

Pentatonic scale

A chromatic scale consists of semitones (...S S S S S...). The meaning of the Greek word "khrôma" is colour; originally the chromatic scale was formed on the "colourings" of the diatonic scale. For example, in medieval music, the notes B and B flat stood for the same pitch, interpreted either high, "b durum" (= hard), or low "b molle " (= soft), depending on the hexachord. Gradually, chromaticism became the standard for other pitches as well.

An extension of the diatonic scale, the chromatic scale can be written in several enharmonic sequences. It is necessary to make a distinction between the concepts of a chromatic semitone (C-C sharp) and a diatonic semitone (E-F). In the former, the notes are situated on the same level of the staff; in the latter, they are on different levels

A long, historical line can be perceived in the formation of scales: pentatonic > diatonic > chromatic. Through this development, the size of intervals has diminished. At the beginning of the 20th century, Czech Alois Hába developed ideas about scales with 24 or even 36 pitches and intervals of one-fourth or one-sixth steps. Other composers have experimented with microintervals. The experiments did not, however, bear fruit; the standard today is the chromatic, equal-tempered scale of 12 pitches, the basis for all other scales.

Several of the scales used in 20th-century music are symmetrical. Symmetry can mean that the intervals are read in the same way, from the beginning to the end, as they are when read the other way round (Dorian scale: T S T T T S T). It can also mean that a certain structure is repeated and fits an octave, as in the two following scales:

Whole tone scale consists of tones (T T T T T T). It divides an octave into six equal parts.

Whole tone scale

Because of the lack of leading note relationships, there is no tonal centre. Thus, whole tone scales C, D, E, F sharp, G sharp, and B flat are defined as one whole tone scale, complemented by pitches outside the scale which form a second whole tone scale. The scale is a mode of limited transposition since different pitches can be created only by transposing m2, m3, 4, 5, M6, and M7.

A whole tone scale can be written enharmonically in several ways; a diminished third (C sharp, D sharp, F) can be used instead of a whole tone (or C sharp, D sharp, E sharp).

Octatonic scales consist of eight notes. The most common version is a regular sequence of tones and semitones. It is also called a diminished scale. The terms whole-half and half-whole are used to denote the starting note.  A scale starting with a half step (S T S T S...) is also called a dominant diminished scale, as most of its notes are guide tones (flat9, #9, #11 and 13) to the dominant chord. In addition to the C7 in the example below, the same scale suits chords Eflat7, F#7, Gflat7, and A7. For reasons of symmetry, they share the colourings: the "#9" of C7 is the "13" of F#7 and vice versa. The diminished scale starting with a whole step (T S T S T S...) is suitable for use with diminished chords.

Oktatonic scale

The octatonic scale divides the octave in four parts and each of these parts into two steps of different sizes. It is a mode of limited transposition, which means that transposing it by, for example, a minor third produces the same notes: in other words, C, E flat, F sharp and A octatonic scales consist of the same pitches. Two diminished four-note chords form an octatonic scale; the complements of this scale (the notes that are not included in the scale) form a diminished tetrachord. These features can be perceived in a circle of notes (see circle of notes).

Other scales

Identical to a whole step scale, an augmented scale consists of six notes. In an augmented scale, minor thirds and augmented seconds alternate with half steps, depending on the notation used. An augmented scale can also be perceived as two augmented triads a half step apart.

Augmented scale

An ascending melodic minor or jazz minor scale can also be considered to be a generic scale since the same order of steps (... T S T T T T S ...) is seen in the overtone and the altered scales. The only difference is the placement of the starting note (cf. diatonic scales).  

Upward melodic minor

An overtone scale is the fourth mode of the jazz minor scale, in other words a scale with the keynote on the fourth note of a minor scale. The notes of an ascending melodic G minor are identical to the C overtone scale. The name "overtone" derives from the fact that the seven first notes of the overtone series are similar to the overtone scale, differing from a major scale with a raised 4th and lowered 7th.

Overtone scale

Altered scale is the 7th mode of a melodic minor. The name derives from the fact that it consists of all the notes of a corresponding major scale, altered. Therefore, the jazz minor scale has seven modes (see "Modes of the jazz minor scale"), the four most common below.

melodic minor   T S T T T T S            
overtone scale         T T T S T S T      
altered scale S T S T T T T S            
Mixolydian B6           T T S T S T T    

E alt scale

The in sen scale is sometimes encountered in jazz literature. It is a pentatonic scale including all intervals smaller than a fourth (m2, M3, M2, and m3). It forms a part of both the diatonic scale and the jazz minor scale.

For example, notes G, A flat, C, D, and F are part of the E sharp major (2nd, 3rd, 4th, 6th, and 7th) and the F jazz minor scales. Similarly, they are part of the F Dorian, G Phrygian, and so on.

In sen scale

The in sen scale is always presented as beginning with a half step; this may be the reason for ignoring the connection to the scales mentioned above. The in sen scale can also be perceived as a pitch class set forming the overall structure of a chord. The said notes are included, for example, in chords Bflast13 and E7#9#5, Dm7flat5, and Fm69.

We have already discussed limited transposition, a term coined by Olivier Messiaen (1908 -1992). Segments are the fundamental element of his scales. They are divided in two, three, or four parts with the same interval structure. Messiaen's modes can be formed in several ways; the following example displays only one form of the fifth mode.

mode 1 T T T T T T (= whole step scale)
mode 2 ST ST ST ST (= octatonic)
mode 3 TSS TSS TSS (or SST SST or STS STS)
mode 4 SSSm3 SSSm3 (also, e.g., m3SS m3SS)
mode 5 SM3S SM3S (also, e.g., SSM3 SSM3)
mode 6 SSTT SSTT

Messiaen scale

The eighth symmetrical mode is the augmented scale (Sm3 Sm3 Sm3), already discussed, for some reason omitted from the list by Messiaen.

With the help of the scales, it is possible to illustrate the Western tonal system in a general manner, keeping in mind, however, that they can be presented in other ways than in an order by degrees. A pentatonic scale can be seen as a series of fifths (C - G - D - A - E). The chromatic scale can also be presented in a similar manner (for example, F sharp-B-…-A flat-D flat, cf. the circle of fifths and the circle of notes).

Chords and scales:

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