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Scales and Keys, -1-

SCALES AND KEYS

Terms defined:chromatic alteration, §8 degree, §2 degree names, §12 key, §14 key signature, §15 leading tone, §9

major scale, §2, 3, 5 minor scale, §2, 3, 7 mode, §19 parallel, §7 major pentatonic scale, §20 minor pentatonic scale, §20

relative major, §13 relative minor, §13 scale, §1 solfege, §13 tonic, §2

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Major and minor scales

§1. A scale is a series of pitches arranged in ascending or descending order. §2. We’ll deal chiefly with two kinds of scales: major and minor. For these scales

♦ there are seven different pitches, or degrees, numbered in ascending order; ♦ the letter names of the successive pitches are consecutive; ♦ the first degree—the tonic—is “home.”

§3. Major and minor scales take their names from their tonics. The G major scale, for example, is the major scale whose tonic is G; the F# minor scale is the minor scale whose tonic is F#. §4. Scale degrees are sometimes notated as numerals with carets on top, as on Example 1. ascending descending G major: 1̂ 2̂ 3̂ 4̂ 5̂ 6̂ 7̂ 1̂ 1̂ 7̂ 6̂ 5̂ 4̂ 3̂ 2̂ 1̂

Eb major:

Example 1. G major and Eb major scales.


Major scales

§5. As Example 1 shows, major scales create a particular pattern of half and whole steps among their seven degrees:

♦ half steps lie between 3̂- 4̂, and between 7̂- 1̂ ; between all other adjacent degrees lie whole steps.

The half steps are marked on the example, which shows G major scales and Eb major scales, ascending and descending.

§6. Example 2 spells out all standard major scales. The scales are arranged so that each scale after C includes all the accidentals from the preceding scale, and adds one. C major G major

D major A major

E major B major

F# major C# major C major F major Bb major Eb major

Ab major Db major

Gb major Cb major

Example 2. Major scales.


Minor scales

§7. Minor scales, in turn, create a similar pattern:

♦ half steps lie between 2̂- 3̂, and between 5̂- 6̂; between all other adjacent degrees lie whole steps.

The half steps are marked on Example 3, which shows G minor and Eb minor scales. The major scales on the same tonics are also shown so that you may compare them with their minor counterparts.

♦ Major and minor scales that share the same tonic are parallel. ascending descending G minor: 1̂ 2̂ 3̂ 4̂ 5̂ 6̂ 7̂ 1̂ G major: Eb minor:

Eb major:

Example 3. G minor and Eb minor scales, with their parallel major scales.

Note that the degrees which differ between parallel major and minor are 3̂, 6̂, and 7̂. Each of these is a chromatic half-step lower in the minor scale compared to the parallel major scale. §8. In many pieces based on minor scales, 6̂ and 7̂ are altered slightly so that they do not conform strictly to the pattern shown above, the so-called natural form of the scale. These degrees are chromatically raised to be half step higher than in that pattern. Example 4 illustrates.


♦ To raise or lower a scale degree chromatically, apply an accidental—either a sharp or a natural, as appropriate.

a) natural form:

b) with 7̂ raised:

(this is often called the harmonic minor scale form) c) with 6̂ and 7̂ raised:

(this is often called the ascending melodic minor scale form)

Example 4. G minor scales, in natural form, and with 6̂ and/or 7̂ raised.

♦ In general, raising a scale degree chromatically gives it an ascending tendency; it “wants” to go up. Likewise, lowering a degree chromatically makes it “want” to go down.

§9. In a minor scale, when 7̂ is raised chromatically to lie a half step below the tonic instead of a whole step, as in Examples 4b and 4c, it leads more powerfully up to the tonic.

♦ When 7̂ lies a half step below the tonic, as it does in the major scale, it’s called the leading tone.

§10. The leading tone—the raised 7th degree of the minor scale—lies three half steps above the 6th degree. This interval of three half steps, marked with a square bracket on Example 4b (and here called an augmented second), can be an angular interval in a melody.

To soften this angular interval, the 6th degree of the scale is also sometimes chromatically raised, so that the interval between 6̂ and 7̂ becomes a whole step, as in Example 4c. The chromatically raised 6th degree leads more powerfully up to the raised 7th, which in turn points up to the tonic.


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Scale degree names and solfege §11. In addition to the numbers 1̂-7̂, scale degrees may be identified by names or by solfege syllables.

§12. Scale degree names for major and natural minor scales are shown in example 5.

G major:

G minor:

Example 5. Scale degree names.

Note that the 7th degree is called the “leading tone” only in its higher version (a half step below the tonic).

♦ The lower version of the 7th scale degree is the subtonic.

(The term “leading tone” derives from the particular tendency of the high 7th degree to lead to the tonic, as noted above; the subtonic has no such tendency and is just as “happy” to descend.) If raised 7̂ is used in minor, it is called the leading tone, as in major. The terms “mediant” and “submediant” are used for both versions (major and minor) of these degrees. If it is necessary to specify, use the qualifiers major/raised or minor/lowered, for example, “Bb is the minor mediant of G,” or “the ascending melodic minor scale uses the raised submediant.” §13. Solfege syllables are shown in example 6.

G major:

G minor:

Example 6. Solfege.

Note that the minor (lowered) forms of scale degrees 3̂, 6̂, and 7̂, me, le, and te, use different vowels from their major counterparts. When raised (major) 6̂ and 7̂ appear in minor music, they take the major solfege syllables la and ti.

Pronunciation is from Latin, so re, me, le and te rhyme with “Che”, while mi and ti rhyme with “ski”.


Keys

§14. A key is a system of pitch relationships based on a particular major or minor scale. A piece in a certain key

♦ draws most of its pitches from the scale of the same name, and ♦ the tonic of that scale is the musical goal of the piece.

A piece in E major, for example, will draw most of its pitches from the E major scale, and the pitch E will be the musical home, on which the piece ultimately comes to a conclusive end.

Key signatures

§15. The key signature indicates which notes are to be sharped or flatted in the following music; accordingly, it signifies which scale is to be used, hence the key of the music. Key signatures are given in Example 7. C major G major D major A major E major B major F# major C# major A minor E minor B minor F# major C# major G# major D# major A# major C major F major Bb major Eb major Ab major Db major Gb major Cb major A minor D minor G minor C minor F minor Bb minor Eb minor Ab minor

Example 7. Signatures for major and minor keys. §13. To each key signature belong two scales (and keys), one major and one minor. These two scales (and the corresponding keys), which use the same pitches, are related. The one is the relative major or relative minor of the other: they share the same pitches.


Here’s a diagram of this relationship: degrees of relative major scale: degrees of relative minor scale:

Figure 1. Scale relationship.

♦ The tonic of a minor scale is always the 6th degree of its relative major. In turn, the tonic of a major scale is always the 3d degree of its relative minor.

§14. In a major scale, how do I find the tonic of its relative minor?

► Start on the tonic of the major scale, boxed on the upper left of the diagram,

► follow the arrows, counting down to its 6th degree: that’s the tonic of the relative minor, circled on the lower left.

§15. In a minor scale, how do I find the tonic of its relative major?

► Start on the tonic of the minor scale, circled on the lower right of the diagram,

► follow the arrows, counting up to its 3d degree: that’s the tonic of the relative major, boxed on the upper right.

§16. Key signatures do not mix sharps and flats. When the 6th and 7th degrees are altered in minor scales, the accidentals are applied to the notes themselves. They are not included in the key signature.

Writing key signatures

§17. As Example 5 shows, keys are arranged so that once a sharp or flat appears in the signature, it appears in the same position in all the following signatures. Compare Examples 5 and 2. The logic according to which the sharps and flats are added is shown in Figure 2.

. . . 6̂ 7̂ 11̂ 2̂ 3̂ 4̂ 5̂ 6̂ 7̂ 1̂ . . . . . . 1̂ 2̂ 3̂ 4̂ 5̂ 6̂ 7̂ 1̂ 2̂ 3̂ . . .


→ (1st) (2d) (3d) (4th) (5th) (6th) (7th)

B C D E F G A B C D E F G A B C D E F (7th) (6th) (5th) (4th) (3d) (2d) (1st) ←

Figure 2. Building key signatures. The series runs alphabetically from B to F. Every fourth letter is bolded.

► Apply flats: the key signature with one flat has Bb, the key signature with two flats has Bb and Eb, and so on.

► Apply sharps: the key signature with one sharp has F#, the key signature with two

sharps has F# and C#, and so on.

Recognizing key signatures

§18. Figure 3 gives the number of sharps or flats in each major key.

Keys with Keys with SHARPS FLATS

C major has 0 sharps/flats.

G major [1] F major

D major [2] Bb major

A major [3] Eb major

E major [4] Ab major

B major [5] Db major

F# major [6] Gb major

C# major. [7] Cb major

Figure 3. Number of sharps or flats in major key signatures.

Modes

§19. Mode refers to the particular sequence of half steps and whole steps within a scale of 7 degrees. Major mode, for example, refers to the pattern of the major scale, and minor

APPLY FLATS

APPLY SHARPS


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mode refers to the pattern of the minor scale. There are other modes that are characterized by unique patterns of whole and half steps. The seven Church modes or white-note modes can be formed from the natural notes, just like the major and natural minor scales. They are shown on Example 8. The major scale is identified with the Ionian mode and the natural minor scale with the Aeolian mode.

Example 8. Church modes.

Modes are named for their modal tonic, also called the keynote or final, not for the major scale their pitches belong to. For example: the natural-note scale that starts and ends on D in ex. 8 above is D Dorian, not “C Dorian”. Sometimes musicians, especially in jazz, will refer to “the Dorian mode of A-flat”, for instance, because it uses the same notes as the A-flat major scale. That is, it is relative to A-flat major, just as F minor is the relative minor. However the proper name for this mode is B-flat Dorian, not “A-flat Dorian” (see ex. 9).

Example 9. Three modes of the Ab major scale.

Note that the various mode names (which are all called after ancient Greek tribes) should be capitalized.


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Pentatonic Scales

§20. As with the heptatonic (7-note) scales, we’ll deal chiefly with two kinds of pentatonic (5-note) scales: major and minor.

♦ The major pentatonic scale consists of the intervals WS, WS, m3, WS, m3. ♦ The minor pentatonic scale consists of the intervals m3, WS, WS, m3, WS

There are two easy methods for building these scales.

§21. To build a pentatonic scale by omission: For a major pentatonic scale, take the major scale on the tonic and omit degrees 4̂ and 7̂. For a minor pentatonic scale, take the natural minor scale on the tonic and omit 2̂ and 6̂.

Example 10. Pentatonic scales by omission.

♦ When using this method, remember to omit the correct degrees, which are different for the major and minor pentatonics.

♦ Pentatonic scales have the same sort of major/minor relative relationship as their “parent” 7-note scales, so the notes you skip to form the pentatonic counterparts of a major/minor relative pair are the same two pitches (though not the same scale degrees). This is illustrated in example 10.

The two “missing” notes in pentatonic music are the lower notes of each of the two half-steps in the major or natural minor scale. The pentatonic scales therefore have no half step, and are sometimes called anhemitonic. §22. To build a pentatonic scale by addition: For a major pentatonic scale, build a major triad with the tonic as root, then add the major second and major sixth, in other words, add the notes a whole step above the root and above the fifth. This is the same as the notes of a so-called 6/9 chord. For a minor pentatonic scale, build a minor seventh chord with the tonic as root, then “fill in” the middle third of this chord, that is, add the p4 above the tonic.

Example 11. Pentatonic scales by addition.


§23. Degree numbering: Pentatonic scale degrees are numbered as if they were 7-note scales with “gaps”. Thus the fourth tone of a major pentatonic scale is scale degree 5̂, for instance, and the fifth tone of a minor pentatonic scale is scale degree 7̂ (see ex. 10). Even though music that is pentatonic does not sound like it is “missing” notes, we number the scale degrees this way because the alternative would be even more confusing. §24. Key signatures: Typically, pentatonic music is notated using the key signature of the corresponding major or minor scale, even though the final sharp or flat of the key signature is superfluous. Note that the black keys on the piano form a pentatonic collection. We can say that the pentatonic collection is the complement of the major or natural minor scale with respect to the 12-note chromatic scale, that is, for any major or natural minor scale the “missing” five pitches form a pentatonic scale. Just as the 7-note diatonic collection has seven modes, the pentatonic has five modes (i.e. five unique patterns of whole steps and minor thirds), but we will focus only on the major and minor, which are the most commonly used.

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