Harmony is the vertical htmlect of music. Western harmony is based upon the 3rd, 4th, and 5th harmonics of the overtone series. Greek mathematician, Pythagoras, theorized that these three harmonics had the most pleasant sound qualities. In examples #90 are the first five notes of the overtone series, followed by the 3rd, 4th, and 5th harmonics played together as a chord:
- The note name of the bottom note of this chord is the fundamental of the overtone series. This note is called the root of the chord.
- The middle note is a third away from the root. This note is called the third of the chord.
- The top note is a fifth away from the root. This note is called the fifth of the chord.
- Visually, these three notes appear to be stacked together by an interval of a third. Three note chords created by superimposing, or stacking thirds are called triads.
Composers established tonality through triads by superimposing thirds above scale degrees. The result was a “musical pallet” of seven triads. In example:
- The bottom note of each triad forms the Bl Major scale. Notice that that key signature matches this scale.
- Each scale degree forms one triad.
- The root of every triad is a scale degree (more on this later).
Triads do not always have to be written in neatly "stacked thirds." In example #91:
- Measure 1: A triad written in neatly "stacked thirds:"
- D is the root
- Fs is the third
- A is the fifth
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Measure 2:
- Same pitches as measure 1, but Fs is lowered to
Fs3
- Moving triad pitches to a different octave will not affect its overall sound
- The triad names "root, third, and fifth" do not change when notated in a different order. "D" is still the root,
"Fs" is the third, and "A" is the fifth
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Measure 3:
- Same pitches as measure 1, but with an additional "D"
- Adding one additional triad called Doubling. In this case, "D" is the doubled note.
- Triads with doubled notes will not affect the triad’s sound quality.
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Measure 4:
- Same pitches as measure 1, but with two additional "Ds" and one additional "A"
The "A" is doubled, and the "D" is tripled
- The number of doubled or tripled notes does not affect the triad’s sound quality.
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Measure 5:
- Same pitches as measure 1, but the "D" is tripled and the "A" is omitted
- Even though the fifth of the triad (A) is missing, it is considered to be a triad because it is still constructed of stacked thirds and it is “tonic heavy.”
- Tripled roots, with an omitted fifth, does not affect the triad’s sound quality.
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Measure 6:
- Same pitches as measure 1, but the "D" and "A" are doubled, the
"Fs" is omitted
- This chord is not a triad
- Without the third (Fs), this chord is not constructed of “stacked third.” This chord’s sound quality is much different than the previous measures. It has an "open" sound, similar to the sound of perfect intervals.
- Only the fifth of a triad can be omitted without changing its overall sound. Omitting the root or third changes the triad's sound
There are two different ways to visually identify a triad:
- By its root
- By its sound quality, also called color, quality, or type
Different combinations of Major and/or minor thirds determine a triad's colors. The triads in Example #92 illustrate the four possible triad colors:
- The Major triad
- Formed by superimposing a Major third below a minor third
- The two outside notes form a Perfect fifth
- The major triad is a consonant triad because all of the intervals formed in the triad are consonant
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The minor triad
- Formed by superimposing a minor third below a Major third
- The two outside notes form a Perfect fifth
- The minor triad is a consonant sounding triad because all of the intervals formed in the triad are consonant
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The diminished triad
- Formed by superimposing two minor thirds
- It is a dissonant triad because the two outside notes form a diminished fifth
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The augmented triad
- Formed by superimposing two Major thirds
- It is a dissonant triad because the two outside notes form an augmented fifth
Roman numerals are used to analyze the seven triads formed from a scale:
- The numeral itself indicates the root of the chord. For example,
"I" is the triad whose root (scale
degree) is the tonic (Ý)
- Upper case numerals indicate a major triad. Example: "V" is a Major triad whose root is the dominant (á)
- Upper case numerals with a plus sign (+) indicate an augmented triad. Example:
"III+" is an augmented triad whose root is the mediant (ß)
- Lower case numerals indicate a minor triad. Example: "iv" is a minor triad whose root is the subdominant (à)
- Lower case numerals with a circle (o) indicate a diminished triad. Example:
"viio" is a diminished triad whose root is the leading tone (ã)
The seven triads formed from a major scale, as shown in Example #93, result in the following triad colors:
- The tonic triad, "I," is always major.
- The supertonic triad, "ii," always is minor.
- The mediant triad, “iii,” triad is always minor.
- The subdominant triad, “IV,” is always major.
- The dominant triad, “V,” is always major.
- The submediant triad, “vi,” is always minor.
- The leading tone triad, “viio,” is always diminished.
- The upper case "C:" below the first system indicates totality, C Major.
The seven triads formed from a harmonic minor scale, as shown in Example #93, result in the following triad colors
- The tonic triad, "I," is always minor.
- The supertonic triad, "ii," always is diminished.
- The mediant triad, “III+,” is always augmented.
- The subdominant triad, “iv,” is always minor.
- The dominant triad, “V,” is always major.
- The submediant triad, “VI,” is always major.
- The leading tone triad, “viio,” is always diminished.
- The lower case "c:" below the the second and third systems indicates totality, c minor.
Composers primarily used harmonic minor when composing in a minor key. There are two exceptions:
- In natural minor, the mediant triad, “III,” is always major.
- Also in natural minor, the subtonic triad, “VII,” is always major.
Changing of tonality will change a triad’s analysis. In Example #94, the analysis of an F major triad is:
- Subdominant (IV) in the key of C major
- Tonic (I) in the key of F major
- Submediant (IV) in the key of a minor
Triads can be written in which the bottom note is the root, third, or fifth. Triads written with either the third or fifth on the bottom are inverted triads (Example #95):
- A triad with the root on the bottom is called root position. It is labeled with its Roman
numeral analysis.
- A triad with the third on the bottom is called first inversion. It is labeled with its Roman numeral analysis along with a superscript “6.” When written in close position, the interval between the top and bottom note
is a 6th.
- A triad with the fifth on the bottom is called second inversion. It is labeled with its Roman numeral analysis along with a superscript “6” and a subscript “4.” When written in close position, the interval between the top and bottom note is a 6th and between the middle and bottom note is a 4th.
- Traditionally, root position triads are acoustically stronger than inverted triads (more on this later).
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