Chords are simply combinations of three or more notes. Thus, the simplest type of chord is the triad, which is a three-note combination. Chords are built on a root, which is the bottom note when the chord is in root position. For now, all you need to know is that the root position is the original position of a chord. It can then be inverted, as described later on in this lesson.
Other than having a root, a triad has a third, which is the middle note, and a fifth, which is the top note. Triads are built so that the root, third, and fifth are on consecutive lines or spaces.
There are four kinds of triads, similar to the four kinds of intervals. These are major, minor, augmented, and diminished. Remember that all triads have the same generic form of being on three consecutive lines or spaces when in root position. The only differences that are made with the four different qualities should be made with accidentals (to maintain correct spelling).
Major triads consist of the root, the note a major third up from the root, and the note a perfect fifth up from the root. For example, the C major triad consists of C, E, and G.
Minor triads consist of the root, the note a minor third up from the root, and the note a perfect fifth up from the root. For example, the A minor triad consists of A, C, and E.
You may have noticed that the general rule for major and minor triads is that you use the first, third, and fifth degrees of the major/minor scale (major for the major triad, minor for the minor triad).
To create a diminished triad, however, we use the root, the minor third above the root, and the diminished fifth above the root. For example, the E diminished triad consists of E, G, and Bb.
Augmented triads are created with the root, the major third above the root, and the augmented fifth above the root. For example, the D augmented triad consists of D, F#, and A#.
Triads have a special set of symbols that are useful as shorthand.
Major triads are notated in uppercase. For example, the G major triad may simply be referred to as G.
Minor triads are notated in lowercase (A minor becomes a) or are uppercase followed by a lowercase m (A minor could be Am).
Diminished triads are uppercase followed by a ° (C# diminished becomes C#° ).
Augmented triads are uppercase followed by a + (Gb augmented becomes Gb+).
So far, we have seen chords (specifically triads) in their root positions. There are two other positions: first inversion and second inversion.
First Inversion is when the root is moved from the bottom of the triad to the top (up an octave) so that the chord starts on the third degree. Thus, a C major triad in first inversion is E, G, and C.
Second Inversion is when the fifth is moved from the top to the bottom of the triad so that the chord starts on the fifth degree. Thus, a G minor triad in second inversion is D, G, and Bb.
The most popular way to notate inverted chords is the figured bass (or thoroughbass) method.
MAKE NUMBERS VERTICAL
Triad Notation (with G as the example triad)
Root Position G or G53
First Inversion G6 or G63
Second Inversion G64
The top number refers to the interval between the bottom note and the top note. The bottom number refers to the interval between the bottom note and the second note.
Insert cute diagram here
Seventh Chord Notation will be covered in the Seventh Chord section.
Diatonic chords are created by making generic triads out of every scale degree of the scale. For example, C major would look like this.
We then analyze each triad and determine what kind of triad it is. We use the Roman numeral notation a major triad is notated with capitals (ex. if the triad with the tonic is a major triad, it is notated as I), a minor triad is notated with lowercases (ex. a minor triad on the fourth degree would be iv), a diminished triad is notated with lowercases and a ° (a diminished triad on the seventh degree would be viiš), and an augmented triad is notated with capitals and a + (an augmented third degree would be III+).
The tonality of the triads will depend on the tonality of the key. If the key is major then:
I ii iii IV V vi viiš I
A natural minor:
i iiš III iv v VI VII i
A minor with a leading tone (raised 7th) or a harmonic minor:
I iiš III+ iv V VI viiš i
A melodic minor:
i ii III+ IV V vi viiš i
These are created, essentially, by taking a triad and adding in the seventh degree. Of course with all the different combinations of triads (major, minor, diminished, and augmented) and all the different types of seventh degrees (maj., min., dim., aug.) we can create numerous types of seventh chords.
|Dominant seventh chords (Mm7) ||major triad ||minor seventh|
|Major seventh chords (MM7) ||major triad ||major seventh|
|Minor seventh chords (mm7) ||minor triad ||minor seventh|
|Minor Major seventh chords (mM7) ||minor triad ||major seventh|
|Major Minor seventh chords (Mm7) ||major triad ||Minor seventh|
|Fully Diminished seventh chords (dd7) ||diminished triad ||diminished seventh|
|Half Diminished (minor seventh flat five, Tristan Chord) ||seventh chords (dm7) ||diminished triad|| minor seventh|
|Half Augmented seventh chords (AM7) ||augmented triad ||major seventh|
|Fully Augmented seventh chords (AA7) ||augmented triad ||augmented seventh|
The dominant seventh chord is one of the most important chords in musical composition. The reason for this is that its major chord helps it make a strong sound of finality. Composers use it often as a concluding chord.
A note on notation: it is common to write a seventh chord with the letter of the root of the triad and a 7, i.e. C7, would be a Dominant 7th with a C major triad.
- CMa7 would be a Major Seventh with a C major triad
- Cmi7 would be a Minor seventh
- Cš7 would be a fully diminished seventh
- Cmi7(flat5) would be a half diminished seventh
Learning the process of voice leading is a good way to learn chord progressions, as it is harmonic progression. Chord progressions are present in all compositions, even if the composer is unaware of their existence. In music theory, we study voice leading to gain a better grasp of different styles and forms of music.
For voice leading we need to create a range for the four voices, for the purposes of this site we will use these constraints:
|Soprano ||C4 (middle C) to G5 (Two Gs above middle C)|
|Alto ||G3 (G below middle C) to D5 (Two Ds above middle C)|
|Tenor ||C3 (C below middle C) to G4 (G above middle C)|
|Bass ||C2 (Two Cs below middle C) to C4 (middle C)|
There are certain rules that one must follow with voice leading and harmonies:
- One cannot have more than an octave between the soprano and alto or between the alto and tenor.
- Parallel unisons, perfect 5th, and octaves are not allowed
- Voices must not cross or overlap each other (i.e. soprano stays above the alto)
- No melodic augmented or diminished intervals (one voice moving into a diminished or augmented interval)
Closed and Open Structures
There are two different structures of chords that are applicable to voice leading.
Closed: the soprano, alto, and tenor are as close as they can get. In other words, there are no other notes within the chord in between the upper three voices that are not being used.
Open: there is a gap between two of the three upper voices. In other words, there is a note between the three voices that is in the chord, but is not being used.
Voice Leading: Harmonic progressions
for now we will be repeating the root in the chords for the four voices (four voices + three notes in a triad = a note needs to be repeated) unless noted
Moving from I to IV and V and back to I:
For now, the bass will always move to the new root
Keep the common tone in its current voice (for IāV that would be SO, for IāIV that would be DO)
Move the other two voices in step (if you did everything correctly the last two voices should only have to move one step to get to the correct notes)
*A note: in minor, always use a major V chord with a leading tone so that TI can go to DO
- Moving in thirds (i.e. IāIII, IVāVI, etc)
- Move the bass to the new root
- Keep TWO common tones in their current voices (if two chords are thirds apart there should be two tones in common, always)
- Move the last voice by step
Moving by seconds:
Move the bass to the new root
Move all other voices in contrary motion to the bass to the closest note of the new chord (there should be no common tones if moving by seconds)
*Moving in contrary motion will prevent any rule-breaking (i.e. parallel octaves, augmented melodic intervals, etc.)
*exception: when moving from V to VI (deceptive cadence)
- Move the bass to the new root
- Move TI to DO (deceptive cadence)
- Move all other voices in contrary motion
- Repeat the third degree instead of the root in VI chord
The harmonic series are created by different wavelengths with frequencies that are always multiples of each other:
The second series has half the wavelength and twice the frequency of the first (fundamental), the third series has a third of the wavelength and three times the frequency of the first, etc.
With the harmonic series, you can see the ratio of the frequencies between certain intervals with the harmonic series:
Thus we can see that the ratio between the octaves is 1:2 and ratio between a fifth is 2:3, etc.
The harmonic series is one of the most important aspects of the physics of sound for brass players. Brass players, instead of changing part of their instrument to change the fundamental frequency (i.e. pressing a different key on the piano, or pressing a different part of the string for string instruments); they change the shape of their lips to change the vibrations so that a harmonic sounds out instead of the fundamental.
Adding valves to brass instruments allows players to manipulate their instruments, thus creating an even greater range. Each valve opens an extra length of tube of their instrument, thus creating a new set of harmonic series so that this new set could overlap with all the other sets of the valves to create all the chromatic notes in a comfortable range. If brass instruments did not have valves then they would be stuck with certain notes in very high octaves that are difficult to play.