Harmony and Tonality
Harmony is the musical combination of tones or chords. The organized
relationship of tones in music is referred to as tonality. Modality
refers to the choice of tones from this relationship. Modality is
synonymous with scale, and tonality with key.
The Overtone Series
The overtone series provides an explanation for consonance and dissonance.
The lower and more audible spectrum of the three primary intervals, octaves,
fifths, and thirds, are most prominent. Triads are created from these.
Note also the intervallic spread between the lowest notes of the spectrum
and how these intervals narrow as the pitches increase. This may
also explain orchestrational issues of generally avoiding clusters in the
lower pitch ranges for clarity.
The overtone series also provides an explanation of diatonic scales.
From the following diagram, it can be seen how the scale emerged from the
overtones of the fundamental tone and its nearest neighbors:
Consonance and Dissonance
Consonance is the combination of two or more tones that are pleasing in
and of themselves, and require not further progression. Consonant
intervals include:
- Unisons
- Octaves
- Fourths
- Fifths
- Major Thirds
- Minor Thirds
Dissonance is the combination of two or more tones that require some
sort of resolution to a consonance. A dissonant chord contains one or more
dissonant intervals. Dissonant intervals include:
- Major seconds
- Minor seconds
- Major sevenths
- Minor sevenths
- Diminished intervals
- Augmented intervals
Keys
Key refers to all of the intervallic relationships within a piece of music
that define one pitch
as the tonic. All other pitches function in
relation to this tonic. A key is a network of intervallic relationships,
while a scale is simply a list of the diatonic pitches of a key.
There are two scale degrees that define the key. The tonic is
the center of a key; all the other notes revolve around it. The dominant
degree requires resolution to the tonic to give completeness of finality.
These factors are what defines the pitches in the vocabulary of tonality.
Tonality defines these pitches as diatonic, and those that are not in this
vocabulary as chromatic. Melodies are described to be scales of ordered
intervals.
The dominant and subdominant degrees give the impression of support
for the tonic degree. These three degrees are called the tonal degrees,
as they are the defining aspect of tonality. These degrees are the
functionally the same in both major and minor modes.
The mediant and submediant are called the modal degrees, as they have
little effect on tonality, but suggest a mode, since they’re different
in major and minor. The supertonic is usually treated as the dominant of
the dominant degree, but tends to function as a modified subdominant.
Perhaps the strongest factor in tonal music is the function of the dominant,
as it seems to decisively determine the key center even more than the tonic
itself. The seventh degree above the root of the dominant creates
dissonances and tendencies that lead to the tonic. This helps to
establish and confirm a key center.
Music the revolves around a central note (a tonic) is called tonal.
All of the notes in a piece of music are related to that tonic. There
is also music that has no tonic. The relationships between the notes
have nothing to do with a key center. This type of music is called
atonal (without a tonic). The term atonal doesn’t describe the way
in which this type of music is constructed, so other concepts will have
to be developed for that purpose.
The Circle of Fifths
One of the bases of our notational system is the Circle of Fifths, which
shows the relationships between keys. The circle is arranged by successive
ascending dominants in one direction, and successive subdominants in the
other direction. Adjacent keys differ by the addition or subtraction
of one sharp or flat. Keys near each other are said to be closely
related; those far apart are distantly related.
Scales
To construct a major scale, we are able to generalize a succession of major
and minor seconds. This formula can start on any pitch
class. Transposition is the process by which a group of notes is exactly reproduced
at a higher or lower pitch level. When changing a group of notes
to another pitch level, sharps or flats must be added to maintain the relationships
of whole and half steps. The particular set of sharps or flats that
define the pitches of a particular scale is called a key signature.
The Major Mode
The various notes in the construction of a scale are known as degrees of
the scale. They are identified by names, Arabic numerals, and sol-fa
syllables.
The following table of root progressions contains generalizations based
on usage, and is not a set of rules to be strictly followed:
- I is followed by IV or V, sometimes VI, occasionally II or III
- II is followed by V, sometimes IV or VI, occasionally I or III
- III is followed by VI, sometimes IV, occasionally I, II, or V
- IV is followed by V, sometimes I or II, occasionally III or VI
- V is followed by I, sometimes IV or VI, occasionally II or III
- VI is followed by II or V, sometimes III or IV, occasionally I
- VII is followed by III, sometimes I
The Minor Mode
The major mode is defined by a standard set of pitches, whereas the minor
mode is not. Several types of triads and scales are used, usually
depending on the current context. The tonic triad is always
minor; other than that, the other triads are defined in a flexible manner.
The melodic minor scale includes the major sixth and seventh degrees
in ascending motion, and the minor sixth and seventh degrees in descending
motion. The melodic motion of minor-mode music often matches the
interval pattern of this scale.
The natural minor scale is the same as the descending melodic minor
scale. It has the same notes as the relative major scale.
The harmonic minor scale includes the leading-tone, or major-seventh
degree. Much of the harmony used in minor-mode music is made of triads
based on this scale.
Other Modes
The Dorian mode, starting on the note D, contains the same pitch
classes as C major and A minor, but in a different order. Likewise,
using the same pitch class as C major, Mixolydian mode starts on the note
G, and Phrygian on the note E.
Chords/Triads
The combination of two or more intervals
creates a chord. The simplest
chord is constructed of the combination of two thirds, which makes a triad.
These three pitches of the triad are called root, third, and fifth.
A triad with the root as its lowest tone is said to be in root position.
A triad with the third as its lowest tone is in first inversion.
A triad with the fifth as its lowest tone is in second inversion.
- A major triad is composed of a major third and perfect fifth.
- A minor triad is composed of a minor third and perfect fifth.
- An augmented triad is composed of a major third and augmented fifth.
- A diminished triad is composed of a minor third and diminished fifth.
Interval Strengths
The strength of the various intervals
generally follows the order of the scale:
- Octave
- Fifth
- Fourth
- Third
- Sixth
- Second
- Seventh
Roots
Roots are usually defined as being the lowest note of odd-numbered intervals,
and the highest note of even-numbered intervals.
In the following triad example, the strongest interval is the fifth,
its lowest note is the root:
The strongest interval in these examples is the fourth, the upper note
of this interval is the root of these triads. The first triad is
in first inversion, the second triad in second inversion:
In the following dissonant chords, the same principles apply.
In each chord the quarter note is the root:
Progression Strengths
Chord progression strengths are defined by a combination of interval strengths
and dissonance. The strength of the root intervals and if the chord
is in root position are considerations in determining a weak or strong
progression (quarter note is the root).
In a tonal context, chromaticism can add variation, direction, and
motion by increasing tension. However, when the context becomes
chromatic, motion and direction can be achieved by means such as interval
strength and controlled dissonance. The overtone series can
be used in similar ways.
The following musical passage becomes more and more chromatic as it
progresses:
Musical variety, motion, and interest in progressions can be created
with variations in root placements (horizontal and vertical),
texture,
consonance and dissonance, and chromaticism.
|
|
