Concord & Discord :: The distinction between what we would call music and what we would regard as noise is a matter of personal taste. We might use words like concordant and discordant to distinguish the acceptable from the unacceptable. Musical theorists have a particular technical use for the two words concord and discord when applied to 'harmony', the sound of three or more notes played simultaneously. We have always been aware of 'tunes' or 'melodies' but what distinguishes Western music from that of many other cultures, is the development of 'harmony' either through the interweaving of other musical lines around and about the 'melody line' (what we call 'counterpoint') or by supporting the 'melody line' with a progression of 'chords', groups of notes sounding simultaneously. Some harmonic intervals have a 'sweeter' sound than others - we call them concords. The perfect concords are the unison, the 5th, the inverse of the 5th (the 4th), and the octave. The imperfect concords are the major 3rd, minor 3rd and their respective inverses, the minor 6th and major 6th. All the remaining intervals as termed discords with one, the augmented 4th, having its own name, the tritone (meaning 'three tones'; the interval is six semitones wide - e.g. c to f#). Medieval theorists considered this interval so unpleasant that it was strictly forbidden and known as the diabolus in musica. At this point we should draw attention to what Descartes, the French philosopher, writing, on the 4th March 1630 to his friend Marin Mersenne, has to say about 'sweetness' in music: "... it is one thing to say that one consonance is sweeter than another, another thing to say it is more pleasing. Everyone knows that honey is sweeter than olives, yet many would prefer to eat olives, not honey. Thus, everyone knows that the fifth is sweeter than the fourth, the fourth sweeter than the major third, this in turn sweeter than the minor third. Yet there are places in which the minor third is more pleasing than the fifth; others indeed, where a dissonance is more pleasing than a consonance." We have already mentioned how the 'leading note' in a major scale 'pulls' the melodic line towards the tonic, one semitone higher. Chords too, give a sense of movement to a melody. When the intervals are concords the chord feels stable. Chords with discords call out to be 'resolved' as individual notes move up or down to form concords. For this reason we must understand that a chord may have both a form (what it is) and a function (where it is leading). We will consider this matter further when we discuss progressions. Triads :: We examined intervals in an earlier lesson. Intervals are always made up of two notes. We now want to discuss 'chords' and, particularly, chords made up of three notes chosen in a particular way. These 'chords' are called triads. The triad is made up of the root, which is the lowest note in the chord, together with the 3rd and 5th above it. If the root is one of the degrees of a major or minor scale then the triads are given Roman numerals or names identifying that degree, in the following way: I (tonic triad), II (supertonic triad), III (mediant triad), IV (subdominant triad), V (dominant triad), VI (submediant triad), VII (leading note triad) The tonic (I), subdominant (IV) and dominant (V) triads are called primary, the remainder are called secondary. In addition, the triads are classified according to the quality of the 3rd or 5th; i.e. whether diminished (for 3rd or 5th), major (for 3rd), minor (for 3rd) or augmented (for 3rd or 5th). triad quality how marked how constructed major triad unmarked or marked 'ma', with upper case Roman numerals major 3rd with a perfect 5th minor triad marked 'mi' or numbered with lower case Roman numerals minor 3rd with a perfect 5th augmented triad marked + or 'aug', with upper case Roman numerals major 3rd with an augmented 5th diminished triad marked ° or 'dim', with lower case Roman numerals minor 3rd and a diminished 5th The notes in a triad can be arranged so that the root is no longer the lowest note of the three. If the 3rd is the lowest note, the triad is said to be a 'first inversion' (using Roman notation, denoted by an additional 'b'; e.g. Vb) and when the 5th is the lowest note, the triad is said to be a 'second inversion' (using Roman notation, denoted by an additional c; e.g. Vc). For completeness, the root position may be denoted by an additional 'a'; e.g. Va. Triads where all the notes lie in positions closest to the other notes in the chord, are said to be in 'close' position, otherwise the triads are said to be in 'open' position. Let us now summarise the triad harmonisation of the major and natural minor scales using numbered chords: Notice the sign in front of III, VI and VII in the minor scale. The minor scale is named 'relative' to the major scale on the same key-note. The use of accidental signs in front of numbered chords should be understood to refer to 'raising' or 'lowering' notes in the chord and not necessarily the use of a 'sharp' or 'flat' sign to achieve this. So a 'sharpened' B flat becomes B natural, i.e. 'raised' or 'sharpened' by a semitone. Let us finish by listening to each of these types of triad. To hear them press the play button displayed below. All Triads Diatonic Triads :: One question that has been asked about triads is 'what is the strict meaning of diatonic triad?' When, earlier, we discussed the difference between chromatic and diatonic notes we pointed out that notes in the major and minor scales of a particular key note are diatonic while those that do not appear in these scales are 'chromatic' (see lesson 11 - The Diatonic Scale). So in the key of C, E natural (which appears in the C major scale) and E flat (which appears in the C minor scale) are diatonic but E sharp (which appears in none of the C scales) is chromatic. A triad is a chord with three notes and three intervals, i.e. if the notes are named X, Y and Z then the three intervals are (i) between X and Y, (ii) between X and Z and (iii) between Y and Z. When written in its close root position, this means that the lowest note is the root, the lowest and the middle notes are an interval of a third apart and the middle to the highest notes are an interval of a third apart. The interval between the lowest and the highest notes is a fifth. So, a triad, written in its close root position, is formed from two thirds placed within a fifth. The root functions as the key note when determining whether or not the other two notes in the triad are diatonic or chromatic and therefore whether the triad is diatonic or not. If the root is C and the triad is [C - E - G] or [C - E flat - G], then the triad is diatonic, because E, E flat and G all appear in scales on C. The triads [C - E - G sharp] and [C - E flat - G flat] are not diatonic because neither G sharp nor G flat appear in the major or minor scales on C. Chords :: Chords can exist in isolation but Western music uses them in progression. We need to understand how they relate to one another. This becomes increasingly important when our chords are made up of a larger number of notes. We need to distinguish 'close' and 'open' harmonies (as with triads), chords where notes are repeated at different pitches, and chords where 'extra' notes are included (i.e. 7th, 9th, etc.). As we increase the number of different notes we find that the same arrangement of notes can be 'named' in more than one way and there are also many more 'inversions' possible. Diatonic triads to which a seventh is added are called 'diatonic 7th' chords and are marked 7. For example, V7a, from which the 'a' is usually omitted, i.e. V7, is a dominant 7th in root position while V7d is a dominant 7th, fourth inversion. The 3rd above the root of the dominant chord in minor keys (which is the 7th degree or leading note of the scale) is always raised a semitone. Let us finish by summarising the harmonisation in sevenths of the major scale using numbered chords: Ima7   IImi7   IIImi7   IVma7   V7   VImi7   VIImi°(5) where °, as we saw above, is shorthand for 'diminished'; and the harmonisation in sevenths of the natural minor scale using numbered chords: Imi7   IImi7(5)   IIIma7   IVmi7   Vmi7   VIma7   VII7 These points are examined in greater detail in lesson 17. Chords in Jazz :: Practical chord notation can be much simpler than that used by musical theorists because far fewer chord patterns are met in real life than can be imagined by the fevered mind of an academic. In jazz, the root of the triad is named with a capital letter, with the addition of 'm' meaning minor (major being understood), '+' or 'aug' if augmented and 'o' or 'dim' if diminished. The 3rd and 5th of the triad can be easily deduced so that it is only necessary to identify additional notes with small numbers. Thus in Cmaj7 the major 7th has been added to the triad C, E and G, while in C7 it is the minor 7th that has been added to the triad C, E and G. The performer is free to indulge in melodic and harmonic extemporisation and for this reason jazz notation is not prescriptive - rather it is descriptive of general ideas that might arise from the shape of a melody or from a chord progression. We will return again to these points in lesson 17. Broken & Spread Chords :: Chords do not have to be played as solid 'blocks' of sound. The performer can spread the chords out into a succession of notes each of which forms the original chord but which are now turned into a 'harmonic' melody. This was a device used often in the seventheenth and eighteenth centuries. The excerpt below produces animation from a sequence of broken chords over a repeated D root in the bass. The bass D is placed high in the chord so that the chords are actually being heard successively in the tenor line in root position, as a first inversion, then a second inversion and finally in root position again an octave higher. This excerpt is from a work for recorders in The Dolmetsch Library. Vivaldi, arranged J.S. Bach - Excerpt