Harmony
Contents
Keys
A tonality or key refers to the fundamental tone (the keynote) of a theme or piece, defined by a note, regardless of its octave pitch. A theme in C, for example, defines the note C as the fundamental tone of the theme, its key. The tonality determines a note as central, a reference note that can qualify the other notes according to their distance or interval from it. Dynamically, the central note takes the function of pole of attraction on the other notes: melodic pole of a mode, called Tonic, harmonic pole of a chord, called Root.
The octave being divided in 12 intervals of semitones, thus 12 degrees, there will be 12 different possible tonalities. The C major scale is composed of the notes C, D, E, F, G, A and B. By transposing this major scale into another key, altered notes will appear (sharp notes or flat notes) which will be indicated by the key signature.
In the tonal system, there are 2 main modes: the major mode and the minor mode. The major scale of C is composed, as we have seen, of the C, D, E, F, G, A and B notes. The relative minor scale of C is the minor scale of A, made of the same notes, but with the note A as tonic: A, B, C, D, E, F, G. Each major scale has its relative minor scale (by definition made of the same notes) built on its 6th degree. The 2 relative scales also have the same key signature.
In practice, the minor mode is often a mixed mode, borrowing its degrees from several different minor scales: natural or Aeolian, melodic minor and harmonic minor..
Intervals
In the western musical system, the fundamental interval is the octave. This one is divided into 12 semitones and as many degrees. We have therefore 12 different possible intervals between 2 degrees included in an octave.
An interval is therefore the distance between 2 degrees, the first serving as a reference point. This interval is defined by a name, designating the number of notes covered by the interval, and by a qualifier, designating the quality of the interval, i.e. its size in number of semitones.
There are 2 types of intervals: simple intervals, less than or equal to the octave; and compound intervals, greater than the octave. We also distinguish the melodic intervals, distance between 2 successive notes; and the harmonic intervals, distance between 2 simultaneous notes.
Scales or modes being defined within an octave, the distance between their degrees will be measured in terms of simple intervals and melodic intervals. For chords on the other hand, the distance between their degrees will be measured in terms of harmonic intervals and simple or even compound intervals for 9th chords and more.
We also specify 2 specific relations between intervals :
- intervals whose sum equals an octave are called complementary intervals.
- intervals with a different name but of the same size are called enharmonic intervals.
(The latter have the same sonority but not the same musical meaning).
Chords
A chord can be defined here as a set of 3 notes minimum played simultaneously.
In a tonal context (or functional harmony), the chords used are built by superimposing thirds. These chords have a structure and a dynamic that allows them to be linked together in a cascade of resolutions, characteristic of tonal contexts.
In modal contexts, on the other hand, chords often incorporate fourth intervals, making them more static, more ambiguous and producing more complex harmonic "colors".
In the case of a stack of thirds, we can distinguish roughly 3 kinds of chords:
- 3 notes chords, called triads,
- 4 notes chords, called tetrads,
- 5 notes chords and more.
The structure of the chord is then described as follows:
- 1: root, pole of the chord,
- 3rd, 5th and 7th: structure, with harmonic function (voices resolution),
- 9th, 11th and 13th: extensions, mainly melodic function (voices linking).
A scale is a stock of notes that can be used in the form of a sequence of notes (improvised melody or not). This same stock can be used in the form of a chord, i.e. a set of simultaneous notes. The chords of a scale are built by stacking thirds (in the desired number) on each of its degrees. The main triads and tetrads are thus obtained by harmonizing the major, melodic minor and harmonic minor scales.
Modes-Chords
The scale is a sequence of degrees whose spacing is defined in number of tones. The major scale, for example, is defined by the following structure: 1 - 1 - 1/2 - 1 - 1 - 1/2. In the scale, we consider the degrees apart from their pitch, so they have no name.
As the octave has 12 degrees, we can build a major scale on each of them, taking one of the degrees as the beginning of the structure described above. We go from the major scale to the C major scale for example, starting from the note C. This gives us the following series: C D E F G A and B.
A mode is a scale in which one of the degrees takes the function of pole, the central degree (tonic) polarizing all the other degrees, and is therefore numbered: 1. The major scale polarized on its 2nd degree, for example, produces the Dorian mode; polarized on its 4th degree, the Lydian mode, etc. A scale therefore has as many different modes as degrees.
Similarly, the C major scale for example, polarized on its 2nd degree produces the D Dorian mode; polarized on its 4th degree, the F Lydian F, etc.
A chord built on one of the degrees of a scale functions as a pole, and makes that scale sound like the specific mode of that degree. The chord of the 2nd degree of the C scale for example, is Dm7, polarizes the scale on the note D, and thus produces the D Dorian mode.
In the end, we obtain the Mode-Chord relations for each degree of the scales (if we disregard their tonality). The chord of the mode is obtained by harmonizing (by stacking thirds) the first degree (the pole or tonic) of the considered mode. The mode of a chord is the set of notes of a scale polarized by this chord.
Pentatonic modes
The main scales, major, melodic minor and harmonic minor, are 7 notes scales (heptatonic). Other scales are possible, notably the 5-note scales (pentatonics), very much used in Rock and also in Jazz. We will only mention here the anhemitonic pentatonics, literally: without semitones. Composed only of intervals of M2 and m3, these scales have a characteristic ambiguous and floating sound which makes them usable in very varied harmonic contexts.
The pentatonic scale is obtained by removing the 2 degrees forming semitone intervals from the heptatonic scales. From the major scale, we obtain the major pentatonic by removing the degrees 4 and 7. The major pentatonic is then numbered: 1 2 3 5 6.
From the melodic minor scale, we obtain the melodic minor pentatonic by removing the degrees 2 and 7. The melodic minor pentatonic is thus numbered: 1 b3 4 5 6. The harmonic minor scale (with 3 semitones) does not allow to obtain a pentatonic scale without semitones (only 2 degrees can be deleted).
As for the heptatonic scales, the pentatonic scales can be polarized in turn on each of their degrees, thus producing 5 different modes, sometimes widely used. The major pentatonic polarized on its 5th degree, for example, is none other than the minor pentatonic (1 b3 4 5 b7) extensively used in Rock and Blues.
Heptatonic modes
A heptatonic mode is a mode with 7 notes. The modes come essentially from the main scales: major, melodic minor and harmonic minor. These scales, whose degrees are distributed fairly evenly over the octave, can be harmonized with third chords, which are functional in a tonal context.
Other, rarer scales, such as Phrygian major, Harmonic major, minor Hungarian, etc., produce modes that work better in a modal context.
The heptatonic modes can be divided into 2 groups: minor modes (with minor third) and major modes (with major third). Each group is divided into 2 subgroups: with a major 7th and with a minor 7th. We thus obtain 4 main groups which have in common a perfect 5th, strong degree of the mode. The modes with a major 7th are more dynamic because the major 7th functions as a lower leading-tone, i.e. as a semitone lower approach to the tonic and intensifying the latter. A leading-tone and its target note form a dynamic couple: the leading-tone is attracted by its target and intensifies it.
Within these 4 groups, there are modes with the b2 degree, upper leading-tone or upper approach of the tonic. The modes with major 7th and b2 degree, combining the 2 approaches of the tonic, are very dynamic.
There are also modes with the #4 degree , as a lower approach to the strong 5 degree. The fourth degree, usually strong, and here raised by a semitone, becomes weak and the lower leading-tone of the fifth. Some modes also have the b6 degree, a higher approach of the 5 degree.
We thus have a whole panel of modes with various leading-tone, more or less dynamic, and whose leading-tone (approach) degrees are very mobile and replaceable.
Apart from these 4 main groups, there are 2 other groups of altered fifth modes. The 5 degree, the strongest after the tonic, becomes weak degree: major modes with #5 degree and minor modes with b5 degree.