January 2021 – inalbis

Modulation

January 25, 2021 by inalbis

Blog, Functional harmony key system, Harmony, Modulation

To modulate means to move from one key to another. This involves a change in what the listener perceives to be the tonic chord. This means that the qualities of the tonic chord must thus be transferred to a new chord. When this new chord has been established as the tonic, the music is said to have changed key. There are different Types of Modulation. Some methods are suitable for closely related keys—such as diatonic and chromatic modulation—while there are others that are only suitable for distantly related keys, such as abrupt and enharmonic modulation.

Diatonic Modulation

The process of modulation has two main features. There is the journey that is taken from one key to another, and there is the way in which we get there. The journey itself concerns the distance traveled between keys. Diatonic Modulation This is to do with the fact that there are some keys that represent a relatively short journey, while others require a more extended or even abrupt journey. In a traditional sense, the distance traveled is measured by how closely related the two keys are. This closeness of relationship is generally determined by how many notes the two keys have in common.

Diatonic modulation is where the change of key is effected through use of chords that belong to both keys. This common chord is thus used as a pivot chord in order to create a bridge to cross over to the new key. Because this type of modulation necessitates that the two keys share some chords in common, it is only really suitable for modulation to the more closely related keys.

Closely Related Keys

Looking at the key of C major at the top of the circular diagram, we can immediately see that the two most closely related major keys are those whose keynotes are a fifth up (G major) and a fifth down (F major). This is because the key of G major requires only one sharp, which means that the other six notes are identical to the C major scale. Similarly, the key of F major requires only one flat. So again, F major has six notes that are identical to the C major scale.

Common-Chord Modulation

A common chord, meaning a chord that is common to each of two keys, offers a smooth introduction to the new key, since it is diatonic to both the old and the new key. This common chord is often called a pivot chord because it becomes a sort of middle ground between the two keys. Common-chord modulation is the name given to a modulation where a common chord (or chords) exists.

The Relative Major/Minor Connection

The circle of fifths also shows us that there is another important key that is closely related to the key of C major. This is the relative minor key of A. The closeness of the relationship between these two keys can be gauged from the fact that they both use the same set of notes, the difference between them lying in the note that is perceived as the tonic. This key relationship is different than the relationship with F and G major by the fact that it also involves a change of mode. To change key from C major to the relative minor is also to change mode—from major to minor. The Relative Major Minor Connection

Because the key of C major has a close relationship to the relative minor key of A, C major also shares a close relationship with those keys whose tonic notes lie a fifth above and below the key of the relative minor. This is because a fifth above the tonic of the relative minor, we have the tonic of the key of E minor, which, like G major, uses only one sharp. And a fifth below the tonic of A minor, we have the tonic of the key of D minor, which, like F major, only uses one flat. Summarizing these observations then gives us a picture of those keys that can be considered to be most closely related to the key of C. To find the relative minor of any major scale, proceed to the sixth degree of that scale. This tone is the tonic of the relative minor

The Parallel Major/Minor Connection

Another criterion that can be used to demonstrate a link between keys is the strong connection between those keys that share the same tonic note. Therefore, for example, the key of C major uses exactly the same tonic as the key of C minor. On these grounds, there is a common link between the two keys. This link is strengthened by the fact that both keys possess the primary roots of C, F, and G as well as having the same dominant seventh chord.

This link between keys that share the same tonic is called the parallel major/minor link. Therefore, the key of C minor is the parallel minor key to C major, and the key of C major is the parallel major to the key of C minor. However, because a modulation is said to be a change of key, this being qualified as a change of tonal center, then to move between C major and minor is perhaps not a true modulation. Nonetheless, it can be a great way to achieve contrast in our music.

Distantly Related Keys

All keys that are diametrically opposite to one another on the circle of fifths represent a maximum possible distance between keys. Although the two keys are therefore distantly related, this does not prevent a modulation between them. It is just that a modulation of this sort is more radical and tricky, and achieving such a modulation often requires ingenuity on behalf of the composer/songwriter.

The Process of Modulation

The Initial Key

It is not essential that the tonic chord should appear, but the dominant must be made to sound as such.

The Pivot Chord

The pivot chord selected is preferably not the V of the second key. In the second stage we are still at the point where only the composer is aware that a modulation is to take place. The sounding of the dominant chord of the new key belongs to a later stage, when the hearer is made to realize that a new tonal center is being felt. To put it a little more techrocaHy, the pivot chord should be’ placed in advance of the appearance of the dominant chord of the new key.

The New Key

Establishment of the new key is accomplished by means of the cadence which ends the phrase, although there may occur strong progressions in the key before the cadence. The cadence may be either a half cadence or an authentic cadence.

Phrase Modulation (Abrupt Modulation)

Abrupt modulation is a sudden change of key that comes without warning or preparation. As such, abrupt modulation represents the simplest type of modulation that is possible. Phrase modulation, also known as direct modulation, occurs between phrases, periods, or larger sections where a phrase cadences in one key, and the next phrase begins immediately in a different key.

Chromatic Modulation

A chromatic modulation occurs at the point of a chromatic progression (a progression that involves the chromatic inflection of one or more tones). Chromatic modulations often occur in passages where the two keys involved are not closely related. They are somewhat less smooth than the common chord modulation and, on occasion, can call attention to the modulation. Chromatic modulation is effected through introducing chromatic alterations of diatonic scale degrees. By chromatic, I mean notes that do not belong to the diatonic scale of the key in question. The letter name remains the same in a chromatic progression.

By including these chromatic notes, along with the regular diatonic notes of the scale of C major, we obtain a complete chromatic scale. Notice, however, that the scale is notated differently depending upon whether it is rising or falling. This type of chromatic scale is called the melodic form of chromatic scale, and for a very good reason. Notice that any chromatic note preceded by a sharp is a rising chromatic note obtained by sharpening the previous note. Rising chromatic notes are notated in this way because they are assumed to be chromatic passing notes that are leading smoothly up to the note that follows. In contrast to this, any chromatic note preceded by a flat is a falling chromatic note obtained by flattening the previous note. And it is notated as a flat because it, too, is assumed to be a chromatic passing note that is falling down to the degree that follows. So the chromatic notes are written in such a way as to reflect their use as passing notes either to the scale degree above them or to the scale degree below them. In this way, a rising chromatic auxiliary would be written as a flat, and a falling chromatic auxiliary would be written as a sharp.

Chromatic modulation is most commonly effected by using these chromatic notes as part of a tritone that acts as a dominant agent of the new key (they are acting as agents of dominant function). To be a true chromatic modulation, the chord progression must not cadence to the new tonic, but also depart from it as a new tonic chord. Otherwise, the modulation is said to be transitory—a brief visit to another key as a means of broadening the horizon of a chord progression.

Enharmonic Modulation

Enharmonic modulation is used to modulate to remote keys. This type of modulation is termed enharmonic because it largely depends upon the process of the enharmonic respelling of chords such as the dominant seventh, diminished seventh, and augmented triad. These chords are therefore being used as an enharmonic pivot chord between the two keys. Let us first consider the principle behind enharmonic modulation, which is the process of enharmonic respelling. This is based on the idea that the same note—B, for example—can also be written as note Cb. Although in terms of their pitch, notes B and Cb are the same note, in terms of their place in the scheme of key relations, they are very distant from one another. Therefore, while we can find note B in the key of C, in the circle of fifths we only encounter the note Cb when we reach the key of Gb major. And from the standpoint of the scheme of key relations represented by the circle of fifths, the key of Gb major is about as far from the key of C as it is possible to get.

Now that you understand the principle of enharmonic respelling, let us see how and why it applies to certain chords. It applies to the dominant seventh and the diminished seventh chord because they contain the interval of the tritone. The tritone is probably the most tonally unstable musical interval that there is. This instability is used to good effect when it is employed as an agent of dominant tension. Through enharmonically respelling the tritone, we can actually redirect its tension and harness it to a dominant chord from a different key. Let us now see how.

In the key of C major, there is only one tritone, and this uses the notes F and B. As a part of the dominant seventh chord of that key, the tritone tends to resolve in a certain way, the B—leading note—rising up to the tonic note C, and the F resolving stepwise down to the third of the tonic triad, which is E (or Eb in the case of the minor key). However, we could also respell the same tritone as F and Cb. Spelled in this way, we find the same interval being used in the dominant seventh chord of a totally different key—the key of Gb major. By enharmonically respelling the interval in this way, therefore, the triton acquires different implications for resolution. While the tritone F and B resolves outwardly to the sixth E and C—in other words, the tonic chord of C major the tritone Cb and F resolves inwardly to the notes Bb and Gb—that is, the tonic chord of Gb major .

The same tritone therefore effectively offers us a connection with both the keys of C major and Gb major. In this way, through the process of enharmonic respelling, the tritone gives us a subtle doorway that connects keynotes that are diametrically opposite on the circle of fifths. The same tritone therefore effectively offers us a connection with both the keys of C major and Gb major. In this way, through the process of enharmonic respelling, the tritone gives us a subtle doorway that connects keynotes that are diametrically opposite on the circle of fifths.

Wherever we find a chord that has a tritone in it, that tritone can be respelled in order to enter into the territory of a new key. In this sense, the chord that carries the tritone is being used as a pivot that links the two keys. An important chord for the process of enharmonic modulation, therefore, is the diminished seventh chord. This is because the diminished seventh chord consists of numerous equal interlocking tritones. Another chord that is susceptible to enharmonic respelling is the augmented triad on degree three of the harmonic form of the minor scale.

Common-tone modulation

Common-tone modulation uses a sustained or repeated pitch from the old key as a bridge between it and the new key. Usually, this pitch will be held alone before the music continues in the new key. For example, a held F from a section in B♭ major could be used to transition to F major. This is used, for example, in Schubert’s Unfinished Symphony.

Sequential modulation

Although a sequence does not have to modulate, it is also possible to modulate by way of a sequence. A sequential modulation is also called rosalia. The sequential passage will begin in the home key, and may move either diatonically or chromatically. Harmonic function is generally disregarded in a sequence, or, at least, it is far less important than the sequential motion. For this reason, a sequence may end at a point that suggests a different tonality than the home key, and the composition may continue naturally in that key.

Chain modulation

Distant keys may be reached sequentially through closely related keys by chain modulation, for example C to G to D or C to C minor to E♭ major.

Parallel key modulation

A parallel key modulation is a change of mode, but maintains the same tonal center. For example, one section of a composition may be in the key of E major and then modulate to E minor. This can be done directly or facilitated by the various modulation techniques described above. Depending on the length of the modulation and whether or not it returns to the original key, it may or may not be designated by a change of key signature.

Key Relationships

January 18, 2021 by inalbis

Blog, Functional harmony key system, Harmony

The more notes that two keys share in common, the closer the felt relationship between them. Therefore, because C major uses the same set of notes as A minor, the two keys are related in the closest possible way. The key of A minor is thus termed the relative minor of C major, while C major is termed the relative major of A minor. The closest connection between keys of the same kind—in other words, all major or all minor —lies in the key that is a perfect fifth above or below a given key. This is because the scales belonging to keys a fifth up or down from a given keynote only involve one change of note —an extra flat, as in the case of a key a fifth down, or an extra sharp in the case of a key a fifth up. This means that these keys all share six notes in common. Therefore, the most closely related keys to C major are G major, whose key signature has one sharp, and F major, whose key signature has only one flat (See circle of fifths above)

As a part of this network of key relationships, each key of the key system has its own particular scale. Each note of this scale is called a scale degree. Each degree is numbered with Roman numerals, because a triad can be built upon each degree of the scale. Each triad can then be identified by the degree of the scale that is its root note.

Capital Roman numerals indicate major chords, and lowercase Roman numerals stand for minor chords. The numeral itself stands for the note on the major scale the chord is built on. For example, in C major, the I would be a C major chord, the ii would be D minor, the iii would be E minor, and so on. The ° symbol indicates a diminished chord (lowercase Roman numeral plus the small circle), and the + symbol is used for augmented chords (uppercase Roman numeral plus the small plus sign). Thus, within a major scale, the seven chords are notated as follows: I ii iii IV V vi vii°. Each degree of the scale has a particular name—tonic, dominant, and so on. We can assign these names to the different chords, like this:

Functional harmony key system

January 11, 2021 by inalbis

Blog, Functional harmony key system, Harmony

Each such scale is built upon a principle note, which is called the tonic or keynote. The tonic is the first degree of the scale. Both the major and the minor scales of a given key take the notes that they need from a foundation scale, which is called the twelve-tone chromatic scale.

Because there are 12 possible keynotes and two basic scales, major or minor, this means that there are 24 basic keys belonging to the key system. Each key is named by the note that is taken to be the tonic or first degree of the scale in conjunction with the type of scale used—major or minor. Each key whose tonic is a fifth higher requires a further sharp in the key signature. Each key whose tonic is a fifth lower requires a further flat in the key signature.

The key is represented by the flat before the last flat

The best way to recognize the key signature is:
1. The key Signature of no sharps or flats is C major
2. The key signature of one flat is F major
3. For flat keys: If the key signature includes flats, you look at the next-to-last flat—the one that’s next to the farthest or last one on the right. This note determines the key signature.

The key is a half step above the last sharp

4. For sharp keys: If the key signature includes sharps, the method is different. What you want to remember here is that the last sharp in the key signature represents the seventh degree of that particular scale, so that the tonic of the scale is the next note up. In other words, look at the last sharp and the next note up is the key.

Each key is a complete scale system—whether major or minor—together with the various chords that can be derived from the notes of that particular scale. Many musicians and composers have spoken of particular emotional and coloristic associations with particular keys. Therefore, the key of C major is often associated with purity, Dmajor with feelings of triumph, while the key of F major speaks of the pastoral world of nature. Similarly, Bb minor is often described as being a key filled with darkness and despair, while C# minor is often linked to intimate religious feelings (Rita Steblin: A History of Key Characteristics in the 18th and Early 19th Centuries).

Use of function in cadence

January 4, 2021 by inalbis

Blog, Cadence, Harmony

A cadence is the characteristic way in which a musical phrase, section, or entire piece of music comes to a close. This feeling of a natural ending is called cadence. The longer you take to reach this point of cadence, the more tension you can build in your music.

Perfect Authentic Cadence

The perfect authentic cadence is a progression from V to I in major keys and V to i in minor keys. Both chords must be in root position. In this cadence the tonic note must also be the highest sounding pitch in the tonic triad. From the standpoint of finality, the perfect authentic cadence is the strongest cadence of all.

Imperfect Authentic Cadence

The imperfect authentic cadence is slightly weaker than the perfect authentic cadence. In these instances, you’re setting up an unresolved tension, typically by ending on the V (dominant) triad. A perfect authentic cadence becomes imperfect when:

The highest-sounding tone in the tonic triad is a tone other than the tonic note.
The viio triad is substituted for the V, making the cadence viio6 to I or viio6 to i.
One or both of the chords (V or I) is inverted. Examples are: V6 to I or V to i6.

Half Cadence

If the second chord of a cadence is V, it is a half cadence. This permits a large number of possibilities, but composers actually employ only a few. I to V, IV to V, or ii to V account for the vast majority of half cadences. A half cadence from iv6 to V in a minor key is sometimes called a Phrygian half cadence.

Plagal Cadence

The plagal cadence is nearly always one progression: IV to I in major keys, or its equivalent, iv to i in minor keys. Infrequently, the progression ii6 to I occurs as a plagal cadence.

Deceptive Cadence

If the first chord is V and the second is not I, the cadence is deceptive. Although there are a large number of possibilities, composers most often select vi (VI in minor).

Rhythmic Cadence

Phrase endings often contain characteristic rhythmic patterns that create a rhythmic cadence. Rhythmic cadences often end with a longer note than the prevailing note values or are followed by a rest, which, in effect, lengthens the final note. A rhythmic cadence pattern may recur several times throughout a given composition.

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