Harmony
Harmony is the musical result of tones sounding together. Whereas melody implies the linear or horizontal aspect of music, harmony refers to the vertical dimension of music.
Chord
A chord is a harmonic unit with at least three different tones sounding simultaneously.
The term includes all possible such sonorities.
Triad
Strictly speaking, a triad is any three-tone chord. However, since western European music of the seventeenth through the nineteenth centuries is tertian (chords containing a superposition of harmonic thirds), the term has come to be limited to a three-note chord built in superposed thirds.
Triad Root
The term root refers to the note on which a triad is built. "C major triad" refers to a major triad whose root is C. The root is the pitch from which a triad is generated. Four types of triads are in common use. They are identified by the quality names major, minor, diminished, and augmented.
Major Triad
A major triad consists of a major third and a perfect fifth.
Minor Triad
A minor triad consists of a minor third and a perfect fifth.
Diminished Triad
A diminished triad consists of a minor third and a diminished fifth.
Augmented Triad
An augmented triad consists of a major third and an augmented fifth.
Triad Stability
A triad that is a combination of the strongest intervals is the most stable. The perfect fifth is by far the strongest interval, and this accounts for the superior stability of the major and minor triads.
Strongest and most stable Major triad
Strong and quite stable Minor triad
Weak and unstable Diminished triad
Weak and unstable Augmented triad
Triad Names
You can construct a triad on any of the scale degrees. The triad has the same function name as the individual pitch.
Primary Triads
The triads built on the tonic, subdominant, and dominant are often referred to as the primary triads because of their strong relationship to each other. The tonic stands in the center of the tonal system, with the dominant a perfect fifth above and the subdominant a perfect fifth below.
Triad Position
Triad position identifies the note of the chord that appears as the lowest-sounding pitch of the harmony. Any of the three notes of the triad can appear as the lowest-sounding pitch.
Root Position
No matter what the arrangement of the third and fifth factors, the triad is in root position if the root of the triad is the lowest-sounding pitch. All the triads in Figure 4.9 are in root position.
Triad Inversion
An inversion of a triad occurs when the root is not the lowest-sounding pitch.
First Inversion
No matter what the arrangement of the root and fifth factors, the triad is in first inversion if the third factor is the lowest-sounding pitch.
Second Inversion
No matter what the arrangement of the root and third factors, the triad is in second inversion if the fifth factor is the lowest-sounding pitch.
Other Tertian Chords
Triads by no means exhaust the possible tertian sonorities. We can continue adding thirds to tertian chords, resulting in seventh chords, ninth chords, eleventh chords, and thirteenth chords.
Seventh Chords
A seventh chord is formed by adding another third above the fifth of a triad. The seventh chord built on the dominant is the most common seventh chord in tonal
music.
APPLICATIONS
Musicians analyze harmonic elements in music using sets of symbols to identify chord types, function, and relationships. A chord's connection to a key center, or perceived forward motion in a composition, can often be explained through harmonic analysis. Two analytical methods, Roman numeral analysis and macro analysis, are presented throughout this volume as tools for categorizing tonal harmonies and chord relationships. Symbols are not limited to analysis. Composers and arrangers use both the baroque figured-bass system and modern-day popular music symbols as shorthand systems to reveal harmonic vocabulary to performers.
Roman Numeral Analysis
In analysis, Roman numerals are used to distinguish triads based on scale degrees (Arabic numerals with carets are used for scale degrees themselves). Memorize the type of triads that appear on each tone of the major scale and the three forms of the minor scale.
Capital Roman numerals Major triads Examples: I, I V, V
Lowercase Roman numerals Minor triads Examples: ii, iii, vi
Lowercase Roman numerals with ° Diminished triads Examples: ii°, VII°
Capital Roman numerals with + Augmented triads Example: III+
Triad Position Symbols
Root-position triads are indicated with Roman numerals without additional symbols. First inversion triads are indicated with a superscript 6 to the right of the Roman numeral. Second-inversion triads are indicated with a superscript 4 to the right of the Roman numeral. When triads are reduced to three notes spaced as close together as possible, we say they are in simple position.
Although 6 and 4 accompany Roman numerals to indicate inversions, they are shorthand symbols to represent intervals above the lowest sounding note. Figure below illustrates the complete interval figures for triads, along with the abbreviated symbols.
Seventh-Chord Position Symbols
We indicate root-position seventh chords by adding a small superscript 7 to the right of the Roman numeral.
The dominant seventh chord can appear in various inversions, including third inversion, as shown in Figure below.
