Download what is harmony

© 2007 Tony Crimlisk.
WHAT IS HARMONY IN MUSIC?
Harmony is the combination of two or more sounds. The effect of this combination can be
consonant (harmonious and pleasant) or dissonant (clashing and potentially unpleasant).
HARMONICS – a natural harmony
Although it’s hard to believe, any vibrating source (the string of a guitar or violin, or the
column of air in the tube of a trumpet or clarinet etc) produces, within a “single” note, a
mixture of several sounds called “harmonics”.
The main note, produced by vibrating the full length of the string etc., is called the
“fundamental”, and the other sounds (which are weaker) are called “harmonics”. In the
example below, a fundamental note of C will produce a first harmonic an octave higher (ie.
another C), a second harmonic of G above, another C (two octaves above the fundamental),
then an E as the 4th harmonic, and another G above that, and these notes; C: E: & G sound
harmonious when played together.
Fundamental
1st
2nd
3rd
4th
5th
=
1st, 2nd & 4th
Harmonics
The series continues getting higher in pitch and weaker so that it’s eventually possible
(although very difficult) to play actual tunes; in Bach’s time musicians who could do this
were very well paid! The use of harmonics is also how, for example, a bugle is able to
produce several notes from a single length of tubing.
The number of times per second that the string or column of air vibrates is called its
“frequency”. For example, the note A (in the middle of the piano keyboard) vibrates 440
times (or cycles) per second. It is this note (at what is called “concert pitch”) to which an
orchestra normally tunes. The A an octave (eight notes) higher doubles the number of
vibrations (or the “frequency”) to 880cps (cycles per second), whilst the note E a fifth (five
notes) higher vibrates at 660 cps (ie: a ratio of 3:2). Notes with the same letter-name (ie. all
“A’s”, all “B’s” etc.) double their frequency as they go up each octave. NB: The frequency
of notes and of tuning is rather more complicated than this; but we needn’t go into it here.
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TRIADS – the basis of Western harmony
As can be seen, the first four notes of the harmonic series include three-notes (in the above
example C: E: G) consisting of the first (“fundamental” or “tonic”) note plus the note a
“third” (three notes) and a “fifth” (five notes) higher. The same is true for any other
fundamental note. Because they form part of the naturally occurring harmonic series, our
ears find this combination of sounds harmonious, and it forms what is known as a “triad”.
The “triad” is the basis of all Western harmony.
SCALES AND KEYS
Western music uses the letter-names A:B:C:D:E:F:G to describe notes as they go up in pitch,
and then the letter names are repeated for each octave. Notes played one after another form
patterns called “scales”. There are many different scale patterns (jazz, pentatonic, ancient
modes etc), but the most common scales are the Major and Minor patterns.
NB: The smallest distance available in Western music between notes (ie. next door notes on
a piano or between next door frets on a guitar) is called a “semi-tone” (two semi-tones
obviously make a “tone”). A scale that proceeds entirely by semi-tones is called a
“chromatic” scale because these notes can be used to “colour” other forms of scales. Major
scales however always use a mixture of tones and semi-tones in the same pattern –
TONE; TONE; SEMI-TONE (TONE) TONE; TONE; SEMI-TONE
NB: the pattern “tone; tone; semi-tone” is repeated with a joining tone in the middle. Each
half of a major scale is called a “tetrachord”.
This major scale pattern can start from any note. The starting (“tonic”, “home” or
“keynote”) note defines the name of the KEY. So, for example, a piece of music which uses
the major scale pattern starting from the note ‘C’ (as above and which, on the piano, only
involves the “white” notes), would be said to be in the key of C major; the same pattern
starting from D, which would need two “sharpened” (#), or “black” notes, the F and the C
(ie. each raised by a semi-tone in order to get the pattern right) would be said to be in the key
of D major, and so on.
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MAJOR AND MINOR TRIADS
Triads can be built on each note of the major scale (and also on all other scales). They are
always spelled as three alternate letter-names a “third” apart; for example C:E:G or D:F:A.
Using the keyboard above look at the gap, or “intervals”, between the notes of the triad built
on the first note of a major scale; it will be found to consist of a gap of four semi-tones,
followed by a gap of three semitones – eg: C: E: G. This is called a “major” triad – and
would be called the “chord” of C major, or often just “C”. Look now at the triad built on
the second note (D) of the scale. This time the pattern is a three semi-tone gap, followed by
a four-semi-tone one. This is called a “minor” triad and so the chord produced would be
called D minor (or Dm). On the third note (E) the triad is also minor. On the fourth (F) and
fifth (G) notes of the scale of C major, the triads formed by alternate letter-names are major;
on the sixth note (A: C: E) it’s minor again. Check it out
C
Dm
Em
F
G
Am
B dim (or Bº)
SEVENTH, DIMINISHED AND AUGMENTED TRIADS
What about the triad built on the seventh note (B) consisting of B: D: F?: This time both
gaps are three semi-tones (a minor third) apart and the triad is called “diminished”.
To recap: triads built on the first (I), fourth (IV) and fifth (V) notes of any major scale are
always “major” and consist of a major (four semi-tone) third followed by a “minor” (threesemi-tone) one. Triads built on the second (II), third (III) and sixth (VI) notes are always
“minor” and consist of a “minor” (three semi-tone) third followed by a “major” (four
semitone) one, and the triad built on the seventh (VII) note is always “diminished” ie. it
consists of two “minor” (three semi-tone) thirds.
There is one other form of triad; it is made up of two “major” (or four semi-tone) gaps and,
although it doesn’t appear naturally in the major scale (as it does in the minor), it’s often
used to “chromatically” add a note to “colour” the major scale. Examples of “augmented”
triads would be C: E: G# or G: B: D#. You should now be able to find any major, minor,
diminished or augmented triad based on any note simply by counting the semitones; 4:3 for
major, 3:4 for minor, 3:3 for diminished and 4:4 for augmented. Played together triads can
be called “chords” – chords can, of course, have more than three notes in them.
INVERSIONS
The strongest form of a triad is where the first note (or “root”) sounds at the bottom of the
chord; eg. C: E: G, but all triads and chords can also be “inverted” ie. played with the third
note at the bottom; eg. E; G; C, called a “first inversion” or 6:3 chord, or the fifth note at the
bottom; eg G: C: E, called a “second inversion” or 6:4 chord. Chords with more than three
notes can of course also be inverted with different notes as the bottom (or bass) note.
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EXTENDED TRIADS – chords of the 7th
Although the triad is the basis for classical harmony, “chords” in modern music are often
formed by adding another third on top; extending the triad to include the next alternate lettername, thus making a four-note chord.
This “extra” note can be a major, minor or
diminished third above the fifth note. NB: Not an augmented third because that would bring
you back to the starting note! Since this extra note is seven letter-names above the “tonic”
or “keynote”, chords so formed are called chords of the “seventh”.
The most commonly used seventh chord is the one build on the fifth note of the scale; the
additional note is a minor third (three semi-tones) above the fifth, so the interval from the
first (tonic) note to the additional seventh note is called a “minor seventh”. The chord is
also called a “dominant seventh” or “V7”. Adding a minor 7th to chord V makes the effect
of it moving to the tonic chord much stronger – the 7th (4th note of the scale) wanting to fall
down a tone, and the 3rd (7th note of the scale) wanting to rise a semi-tone to the tonic.
NAMES OF NOTES
The reason for the name “dominant” is that the notes of a major scale are all given names as
well as Roman numerals. The first note (I) (also known as the “home” or “keynote”) is, as
mentioned above, called the “tonic”. The second (II) is called the super-tonic (because it’s
“above” the tonic); the fifth (V) note is called the “dominant” (because after chord I it’s the
most important note in the scale); the third (III) note is called the “mediant” (because it’s
midway between the two most important notes of the scale I & V); the fourth (IV) is called
the “sub-dominant”; the sixth (VI) the “sub-mediant (because it’s the same distance below
the tonic as the mediant is above it); and the seventh note (VII) has the name “leading note”
because it leads on to the tonic.
Sevenths can also be added to any other triad. The seventh based on the tonic note is major
(because it’s in the major scale) so, for example, a seventh added to the triad on the note C;
(C: E: G: B) would be called “Cmaj7” (G to B is a 4 semi-tone or major third).
The
seventh note above the second note of the scale, for example D (D: F: A: C) however, is
minor (A to C is a 3 semi-tone or minor third) and so it is called “D minor 7th” or “Dm7”.
Check out other major or minor seventh chords.
Diminished seventh chords are formed by adding a minor third above diminished triad – eg:
B: D : F: Ab or C: Eb: G: Bbb (ie. “B double flat” = “A” but spelled this way to keep to
alternate letter-names). The interesting thing about this chord is that adding another minor
third brings you back to where you started; there are therefore only three possible diminished
7th chords (although the spelling of them may vary). NB: Similarly there can’t be a 7 th
augmented chord because adding another major third brings you back to the starting note; so
only four versions of an augmented chord are possible.
Many other chord sequence patterns can be invented and it’s worth experimenting with
chords changed from major to minor (lower the middle note a semi-tone) and vice versa or
with “fill in” chords which move both by tones and semi-tones. Because of its ambiguity the
diminished 7th chord is often used as a joining chord, or to move to another key (modulate);
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ADDING MORE THIRDS – 9ths, 11ths and 13ths (6ths)
The process of adding extra thirds can continue. Another major or minor third above a
seventh chord would be nine notes above the tonic and so it’s called a chord of the ninth
(9th); another third on top of that produces a chord of the eleventh (11th); and another; a
thirteenth (13th) chord (usually however called a 6th - work out why). After that we’re back
to the original starting point – but note that adding all these “extra” notes ends up by using
all the notes of the scale!
Obviously playing all the notes of the scale together would not be harmonious, so some notes
have to be missed out. This leads to many ambiguities as one chord begins to sound like
(and can therefore be substituted for) another. For example the chord of Dm7 (D: F: A: C)
contains the same notes as F6 (or F13) ie. F: A: C: D. Similarly the chord of C9 (which
would be C: E: G: Bflat: D) with the root missed out and in its second inversion contains the
same notes as Gm6, whilst flattening the ninth produces a diminished seventh chord. This
ambiguity of chords is one of the most fascinating things about harmony and the placing, or
arrangement, of the notes in a chord is of paramount importance to their effect.
MOVING AROUND
Relationships between chords are very important. The strongest relationship is always
between chords I and V (or V7) and many songs and pieces are based simply on these two
chords. Note that chords I & V7 contain all the notes of the scale but one). A good chord to
play before chord V is chord IV (remember it’s also major) and again many songs and pieces
are based simply on these three chords I, IV and V or (V7) – sometimes known as the “three
chord trick”. Another good approach to chord V is chord II (which is minor) because chord
II is five notes above, or four notes below, chord V and the II to V relationship therefore has
the same strength as the V to I relationship. The same is true between chord VI and chord
II; chord VI is five notes above (or four notes below) chord II. This gives another useful
chord sequence pattern which is used extensively in popular songs – I: VI: II: V (or V7).
The ambiguity of chords and relationships also makes it easier to move from one key (scale
pattern) to another (ie. to “modulate”). Diminished 7th chords are particularly useful as a
substitute for V7 chords. You can also approach a chord in one key, modify it if necessary,
and then leave it as a member of another key. A common use of this principle is in the
“cycle of fifths” where chord I is modified simply by adding a minor seventh which then
makes it a dominant seventh (ie. V7) in the key which is four notes above, or five notes
below. For example: C (chord 1 in the key of C major) with an added minor 7th become C7;
ie. chord V7 in the key of F major. In this way you can cycle around all twelve keys.
C7-F7-Bb7-Eb7-Ab7-Db7(ie.C#7)-F#7-B7-E7-A7-D7-G7-C.
The above is a very basic explanation of music harmony and chord structures which itself is
only a part of music as a whole. There are an almost infinite number of combinations
possible, including extra notes suspended from one chord to another (the “suspended fourth”
is quite common), and some chords can be very difficult to categorise but nevertheless sound
perfectly satisfactory in context - at least to the modern ear.
I hope the above helps in
understanding the basics, after that it’s up to you to experiment and apply.
© 2007 Tony Crimlisk