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A chord is a juxtaposition of a minimum of 3 sounds (notes), therefore of 2 intervals.
Chords can vary in harmonic density :
- triads, with three sounds
- tetrads, with four sounds
- five-sound chords, called "ninth" chords
- six-sound chords, called "eleventh" chords
- seven-sound chords, called "thirteenth" chords
- etc... (a pianist has ten fingers, but a guitarist only has six strings...)
Construction
In tonal music, a chord is built by stacking thirds (F - 3 - 5 - 7) up to the extensions (9 - 11 - 13).
They can therefore :
- include extensions (2/9, 4/11, 6/13)
- be played with the root in the bass or be played inverted (1st inversion = third in the bass, 2nd inversion = fifth in the bass, 3rd inversion = seventh in the bass)
Relative naming : degree
In a given context defined by a key (chord sequence, entire piece), a chord can be notated as a "degree" relative to this tonal context.
In a piece in C major, Dm7 can be called "II" or "second degree" and G7 can be called "V" or "fifth degree". C will of course be the "I" (thus the first degree whose root also defines the key).
We can talk about constitutive alteration, accidental alteration or an altered chord and these are three different things.
An altered chord (sometimes noted "alt.") is a dominant 7th chord (with a major 3rd and minor 7th) whose fifth is a b5 or a #5, or whose ninth is a b9 or a #9.
An accidental alteration is the use in a chord of a note that is not part of the scale in the current harmonic context.
It is a transient tension that can call for a resolution, foreshadow a modulation, or just simulate it and maintain this tension in the auditory impression.
This alteration can also participate in horizontal writing, voice leading, and allow parallel melodic movements within your harmonic movement.
A constitutive accidental, or key accidental is a sign (♯ sharp, ♭ flat or ♮ natural) that changes the pitch of the notes in a line/space on a staff.
A cadence is a melodic and harmonic formula that punctuates a phrase, a section, or an entire musical piece and (re)affirms its key.
In classical music, the word "cadence" is reserved for harmonic resolution movements, at the conclusion of a harmonic narrative, while the term "formula" designates other non-conclusive forms of harmonic progressions.
In Jazz, the word "cadence" designates any form of harmonic progression (conclusive or not).
A harmonic cadence therefore articulates chords!
Between these chords, notes are articulated since a chord is made of notes : a chord progression therefore makes voice movements (stepwise, by leap, ascending, descending) "sing" between their notes.
The succession of these chords can give an impression of resolution of a more or less significant harmonic tension, or else only provoke a more or less temporary suspension effect.
Here are some essential cadences:
Perfect cadence (Strong conclusive cadence - leading tone towards tonic)
| V | I | (root position = non-inverted)
often preceded by IV or II, or sometimes VI and rarely III
Complete cadence (strong conclusive cadence - with preceding subdominant)
| II | V | I | or | IV | V | I |
Italian cadence (complete cadence amplified by a preparatory movement including a subdominant like IV or II or a secondary subdominant like II7 or a Neapolitan sixth chord: a IIb in 1st inversion, for example Db/F in C)
| IV | I | V | I | or | VI | V | I | or | VI | II7 | V | I | or | IIb /bassIV | V | I |
Imperfect cadence (weak conclusive cadence)
| V | I | (1st inversion state -third in the bass- for one of the two, example: V/3 - I or V - I/3
Incomplete cadence (progression of two tonal functions among IV V I)
| IV | V | or | V | I | or | IV | I |
Plagal cadence (from the subdominant to the I)
| IV | I | or | II | I |
Deceptive cadence (restarts the musical phrase or surprises)
| V | VI | or | V | III | or | V | "any chord other than I" |
Half cadence (suspensive cadence to V in root position)
| IV | V | or | II | V | (IV or II in root position or 1st inversion)
An extension is a note that is not part of the "basic" chord consisting of 3 or 4 sounds.
It is a note added to this chord to enrich it, to give it a unique color.
It is, in the context of harmonization by thirds, a note located in the gaps of the stacking of constituent thirds (root + third + fifth + seventh) of a chord :
- a second (m2 or M2)
- a fourth (P4, A4 or d4)
- a sixth (M6 or m6)
To respect a certain spacing between notes and add color without too much tension, these extensions can be played in higher octaves and, when a seventh is present or when one wants to signify that they are played at the octave, they are then called :
- ninth (b9 for m2, 9 for M2)
- eleventh (11 for P4, #11 for A4, b11 for d4)
- thirteenth (13 for M6, b13 for m6)
Extensions bring unique colors to chords, sometimes brilliance (9), sometimes tension (b9), sometimes a mysterious light (#11 on a M7 chord) or a shadow (#11 on an m7 or 7 chord), etc...
They can sound like a pleasant, more or less sophisticated release, or create tension, a call towards a future resolution; they participate in the "dramaturgy" of questions/answers & tensions/releases of your harmony.
Extensions can therefore result from stacking thirds above the seventh (extensions planned by harmonization) or be accidental alterations allowing surprising tension, or a melodic and/or chromatic voice leading in your chord progression (extensions outside the skeleton of the harmonization)
It's the note that gives the chord its name.
The root of an A minor chord (Am) will be the note "A" (A).
The root allows referencing by intervals:
- all the notes of a chord (for a C root: P4 or 11 for F, M7 for B, m2 or b9 for Db, ...)
- melodic elements of a phrase
It is therefore a vertical reference (as opposed to the tonic, which is a horizontal reference for naming the key of a set of chords, a piece...).
If no bass note is specified, this root note (notated "1") will most often be played in the bass to reinforce the chord's foundation.
But one can play a C/E chord ("C major with E bass") whose root is C and whose bass is E (E is the third of C, the C/E chord is therefore the first inversion of the C major chord).
We speak of scale or mode harmonization when we try to determine the chords resulting from a given scale or mode.
System of harmonization by thirds (example in C major)
To harmonize the first chord of a C major scale (with 7 sounds), we stack thirds starting from:
- its root (C),
- its third in the scale (E),
- then the third of this third, so the fifth (G),
- then if we want a 4-sound chord, we also add the third of this fifth, so the seventh (B).
The stacking of these 4 sounds constitutes the harmonization of the first degree of the C major scale : a CM7 chord with a major third M3, a perfect fifth P5, and a major seventh (M7).
We can continue to stack thirds above this seventh to determine the nature of the chord's extensions:
- the third of the seventh is the ninth (D),
- the third of the ninth is the eleventh (F)
- the third of the eleventh is the thirteenth (A)
For the chord of the second degree of C major (root = D, degree = ii), this gives us :
R - m3 - P5 - m7 (- 9 - 11 - 13) so a Dm7 chord with possible extensions 9, 11, 13
These harmonized chords will serve as skeletons for the musical staging of your cadences, skeletons to make dance among themselves, to dress with extensions, to mask with accidentals, to tile with chromatics, sometimes also to strip of their obviousness, to offer emotions, surprise, and grandeur to the ball of your harmonies.
Coming soon :
- harmonization by fourths,
- by "search for significant degree" as in pentatonic scales where the division of the octave into notes and the range of their intervals do not offer the same scales as in 7-note scales, not allowing to stick to a single harmonization matrix (1357) if one wants to obtain degrees somewhat "coherent" with our 21st-century ears.
An interval designates a distance separating two notes:
"Perfect" is used for fourths and fifths.
"Minor" and "Major" are used for seconds, thirds, sixths, and sevenths.
"Diminished" and "Augmented" are used for all intervals, but their use is rare (except for 5d, 7d, and 2A, 3A, 4A, and 5A).
It is also common to use ♯ and ♭ as modifiers.
| Intervals | Distances | Names | Extension | Other equivalents | Complementary Interval |
|---|
| R, T | 0 tone | root, tonic (notions of unison, enharmonics...) | | these are not intervals in the strict sense, but references | octave |
| m2 | 1/2 tone | minor second | ♭9 | | M7 |
| M2 (or 2) | 1 tone | major second (second) | 9 | diminished third, d3 | m7 |
| m3 | 1 1/2 tones | minor third | ♯9 | augmented second, A2, ♯2 | M6 |
| M3 | 2 tones | major third | ♭11 | diminished fourth, d4, ♭4 | m6 |
| P4 | 2 1/2 tones | perfect fourth | 11 | augmented third, A3 | P5 |
| A4 | 3 tones | augmented fourth | ♯11 | diminished fifth, tritone, d5, ♯4, ♭5 | d5 |
| P5 | 3 1/2 tones | perfect fifth | | diminished sixth, d6 | P4 |
| A5 | 4 tones | augmented fifth | ♭13 | minor sixth, m6, ♯5 | M3 |
| M6, 6 | 4 1/2 tones | major sixth, sixth | 13 | diminished seventh, d7, ♭7 | m3 |
| m7, 7 | 5 tones | minor seventh | ♯13 | augmented sixth, A6, ♯6 | M2 |
| M7 | 5 1/2 tones | major seventh, leading tone | | | m2 |
A mode is a sequence of notes played starting from one of the notes of its original scale : a 7-note scale therefore has 7 different modes.
A mode is defined by a fixed pattern of successive intervals of tones and semitones (or more for non-diatonic scales : 1 and a half tones, 2 tones, etc...).
A mode also has one or more "characteristic notes". These notes are "calculated" by comparing the mode's intervals with those of 2 reference modes:
- if the mode has a major third, its intervals are compared to those of the major scale (i.e. the Ionian mode of the major scale)
- if the mode has a minor third, its intervals are compared to those of the natural minor scale (i.e. the Aeolian mode of the major scale)
Example of characteristic notes for the modes of C major scale :
- major mode Ionian → reference mode for major modes
- minor mode Dorian → M6
- minor mode Phrygian → m2
- major mode Lydian → A4
- major mode Mixolydian → m7
- minor mode Aeolian → reference mode for minor modes
- minor mode Locrian → m2 and d5
To hear the colors of the modes, you could play different modes starting from the same root note (e.g. C Ionian, C Dorian, C Phrygian, C Lydian, C Mixolydian, C Aeolian, C Locrian for the modes of the major scale).
Example of using modes : play D Dorian (2nd mode of C major) over the ii-V part (Dm7-G7) of a ii-V-I.
Making a mode sound can involve placing its constituent notes (Root - 3rd note - 5th note and possibly the 7th note) on the accents of your rhythmic phrase, possibly incorporating its characteristic note to define the modal color. That's a good start ;)
The term
inversion can apply to an interval and a chord :
- an inverted
interval designates the complementary interval
(the major sixth for a minor third, the perfect fourth for a perfect fifth, ...)
- an inverted chord does not have its
root in the bass, the order of the notes has been changed
(the 1st inversion puts the third in the bass, the 2nd inversion : the fifth, the 3rd inversion : the seventh, ...)
In jazz and contemporary music, chord inversions are notated with the chord name, a slash, and the bass note name slightly lower, like C
/E (1st inversion of the C major chord).
Regarding
chords inversions :
| Chord Type | Inversion Name | Figured Bass Symbol | Example in C major | Intervals from the bass | Harmonic Function and Common Context |
|---|
| Triad | Root Position | (often omitted) | C-E-G (C in bass) | Major third (C-E) perfect fifth (C-G) | Tonic or dominant function in cadences. Example : V-I in classical music |
| Triad | 1st inversion | 6/3 or 6 | E-G-C (E in bass) | Minor third (E-G), minor sixth (E-C) | Used for smooth passages and to avoid abrupt leaps. Example : plagal cadences (IV-I) |
| Triad | 2nd inversion | 6/4 | G-C-E (G in bass) | Perfect fourth (G-C), major sixth (G-E) | Suspended cadence or 6/4 cadence before resolution. Example : V6/4-V-I in baroque motets |
| Tetrad | Root Position | M7, Maj7 or Δ7 | C-E-G-B (C in bass) | Major third (C-E), perfect fifth (C-G), major seventh (C-B) | Tonic chords (e.g. CMaj7 at the end of a jazzy phrase). Example : ending of a modal piece |
| Tetrad | 1st inversion | 6/5 | E-G-B-C (E in bass) | Minor third (E-G), perfect fifth (E-B), minor sixth (E-C) | Used in modal progressions or for smooth transitions. Example : Am7-Dm7-G7-CM7/E |
| Tetrad | 2nd inversion | 4/3 | G-B-C-E (G in bass) | Major third (G-B), perfect fourth (G-C), major sixth (G-E) | Part of open cadences. Example : plagal cadence with IV-I |
| Tetrad | 3rd inversion | 2 | B-C-E-G (B in bass) | Minor second (B-C), perfect fourth (B-E), minor sixth (B-G) | Used in modulations or for atonal effects. Example : unresolved cadence in contemporary music |
The tonic is the note that defines the key of a scale or mode (giving the "Tone" → Tonality → Tonic).
The tonic of the C major scale will therefore be C.
The tonic allows referencing by degree (in the key of C: IV for F, vii for B, bII for Db) all harmonic elements of a phrase, a group of measures, or a piece.
The tonic is a horizontal reference, as opposed to the root, which is a vertical reference for naming the intervals of a chord.
A scale or a mode can have several keys, so we specify the tonic note for :
- the scale (e.g. C major scale or G major scale)
- the mode (C Ionian or G Mixolydian are two modes of the C major scale)