Chords: the basics
We’ve so far been treating sounds of specified pitch as individual elements that are notated one by one even when several of them happen simultaneously. But as we’ve already seen in the case of a melody with drone, the relationships between simultaneously sounding pitches give rise to effects that transcend those of individual pitches and voices, such as effects of “consonance” and “dissonance.” A particular combination of pitch classes takes on an identity that is something more than the sum of its parts. The word for that “something” is a “chord.”
When you hear the pitch classes C, E, and G together, you are hearing a C major chord. The proof that the chord is more than the sum of its parts is that it doesn’t have to be formed of any particular C, E, and G: it can use any combination of Cs, Es, and Gs on the keyboard and so long as it uses all three of those pitch classes and no others, it will still be a C major chord. Its C-major-ness is something that transcends the exact pitches of which any particular C major chord in an actual piece of music will be formed.
Sometimes we may want to specify this C-major-ness in our notation independently of the particular pitches that comprise the chord. If we want to bring out the harmonic structure of a piece, it may be more efficient to represent the chords by their C-major-ness (or D-minor-ness, or whatever the “something” may be) than to write out every detail of the accompaniment. On the other hand, even if we are interested in the details as well, we may still want to specify the chords as a way of showing the “wood” as well as the “trees.”
In effect, this is what popular song lead sheets do when they show the melody in staff notation accompanied by guitar chord symbols such as “E” or “Asus4.” That leaves the guitarist free to choose exactly which form of each chord to use and how to render it into notes with an appropriate strumming or picking pattern.
There is nothing to prevent such chord symbols being written into Global Notation, with or without guitar “tab” (tablature) diagrams for each chord, provided the absolute pitch or key of the music is fixed. If the key were to be changed, however, all the chord symbols would have to be re-written.
That kind of inconvenience is one reason why Global Notation prefers to rely on relative pitch. Another reason is that, just as a chord is characterised by the relationships among its constituent pitches, a chord itself has relationships with other chords, and these work the same way in any key.
Using guitar chord symbols, it might not be obvious that the relationship between E and A in A major is the same as the relationship between A and D in D major, but this fact is completely obvious to listeners (even if they can’t explain it in words), and what Global Notation requires, as usual, is a way of specifying the relationship without having to specify the key or absolute pitch.
For this, we turn to a system used by music theorists in which a chord built on degree 1 of the scale (the tonic) is called chord I, and so on up the scale using Roman numerals for the chords built on each scale degree. We’ll see how chords are “built on” scale degrees in a moment.
By specifying only relative pitch, the Roman numerals enable us to represent not just “C-major-ness” - a quality that will have different effects in different keys - but things like “tonic-major-ness,” a quality that means the same in any key. By naming chords after the scale degree they are built on, we can describe the harmonic structure of a song in a way that remains true regardless what key the song is sung in.
To “build” the most common type of chord, you take any scale degree as the “root” of the chord, add the next-but-one scale degree above the root, then add the next-but-one scale degree above that.
Counting the starting point as “one,” the next-but-one note up the scale is the third note that you come to, so the interval between any pitch and the next-but-one scale degree is called a “third.” When the lower pitch of that interval is the root of a chord, the upper pitch is called the “third” of the chord.
The interval between the third of a chord and the next-but-one scale degree above that is also a third; so the upper pitch of this interval is two thirds above the root.
However, two thirds do not add up to a sixth. Counting upward from the root, the uppermost pitch here is the fifth note that you come to, so the interval between it and the root is a “fifth,” and this top pitch is called the “fifth” of the chord. Whenever you add two intervals together, you have to subtract 1 to allow for the fact that the starting point of each interval is counted as 1 when it should logically be zero.
A root, third, and fifth together form a chord comprising three different pitch classes: a “triad.” Any chord comprising three different pitch classes is a triad, but when the constituent pitches are selected in this particular way - by stacking up thirds - the triad is called a “tertial” triad.
Tertial triads are considered the norm in Western music theory, although most harmonic music uses at least some chords other than these. As already mentioned, any of the pitch classes comprising a chord can be used at any octave level without changing the identity of the chord, but for now we’ll illustrate triads in their most basic form: a root with a third and fifth directly above it.
As the intervals between adjacent scale degrees are usually not all equal, the intervals between the constituent pitches of a chord will vary depending which scale degree is taken as the root. For instance, when each degree of a major scale is taken as a chord root, we get three different “shapes” of triad: one with a small interval on top of a larger interval, one with the opposite, and one with both intervals the same size.
These varying intervals strongly affect the character of a chord, even after octave transpositions, and they need to be reflected in our chord notation.
In the Western major/minor scale system using modern keyboard tuning, an interval of two scale-steps is either 300 or 400 cents. This results in four possible types of triad, distinguished in Global Notation as follows:
The augmented triad doesn’t actually occur within the intervals of a major scale, but can occur when minor keys or extra-scalar pitches are used; see Naming any tertial triad.
To explain it another way: the interval between the root and the third of the triad is expressed by the case of the Roman numeral: upper case for 400 cents, lower case for 300. The interval between the root and the fifth is assumed to be 700 cents by default (as it usually is in practice). If it isn’t, an affix is added: + for 800 cents, ° for 600. (Although these affixes come after the thing that they modify, like suffixes, we are calling them “affixes” to distinguish them from the chord suffixes discussed on another page.)
The tertial triads that occur within the major scale are named using this system below. A “serif” font is used for the Roman numerals so that the upper-case “I” doesn’t just look like a vertical line.
Absolute pitch can be specified, as usual, by marking the pitch of the tonic pitch line. If you want to specify absolute pitch for each chord, as in conventional guitar chord notation, you can simply replace the Roman numerals with letters identifying each chord root, keeping the case and affixes as above. For example, in the key of C major, the chords would be C, d, e, F, G, a, b°.
We can now specify the basic tertial triads in any major key, and for some music this is enough. Indeed, a great deal of harmonic music can be performed using only a small selection from these tertial triads - most often, chords I, IV, and V.
The chord symbols are written below the layer for sounds of specified pitch on the basis that an accompaniment is often lower in pitch than the melody and the chords are strongly related to the bass (see Chord suffixes).
However, there is much more to harmony than these simple triads, and in many cases we will want to specify chords that are more complex in one way or another.