Chords

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 scale degrees (with or without extra-scalar pitches) 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 a C, an E, and a 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 (of which there are at least seven of each) 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 indepedently 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 (and equivalent qualities for other chords) than to write out every detail of the accompaniment. On the other hand, 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 characterized 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 pitch 1 of the scale (the tonic) is called chord I, and so on up the scale using Roman numerals for the chords build on each scale degree. This enables us to represent not just “C-major-ness”—a quality that will have different effects in different keys—but “tonic-major-ness,” a quality that means the same in any key. And the same applies to chords build on other pitches of the scale.

To “build” a chord, you take any scale degree as the “root” of the chord, add the pitch two scale degrees above the root, then add the pitch two scale degrees above that. The added pitches are called the “third” and “fifth” (counting upwards from the root as “first” pitch). This gives a chord comprising three different scale degrees: a “triad.”

Triads are considered the norm in Western music, although the process of adding pitches two scale degrees higher can be continued to produce more complex chords. Any of the scale degrees 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 basic form of 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.

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, an interval of two scale degrees is either 300 or 400 cents. This results in four possible types of triad, distinguished in global notation as follows:

lower
interval
upper
interval
chord
type
numeral
case
suffix example
400 300 major upper   IV
300 400 minor lower   vi
400 400 augmented upper + III+
300 300 diminished lower ° vii°

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, a suffix is added: + for 800 cents, ° for 600.

The chords that commonly occur in major and minor keys are listed 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. In minor keys, scale degree 6 tends to vary between 800 and 900 cents above the tonic, and scale degree 7 between 1000 and 1100 cents, resulting in a larger total number of chords than for major keys. When the root itself falls between the “default” scale degrees represented by the pitch lines—when it is in effect an extra-scalar pitch—the chord symbol is preceded by a sign drawn from staff notation: # (sharp) for a root higher than the scale degree of the same number, b (flat) for lower (by 100 cents in either case).

The chord symbols are written below the layer for sounds of specified pitch on the basis that an accompaniment is most often lower in pitch than the melody and the chords are strongly related to the bass (see Relating melody to chords). As some chord symbols involve a number of characters, and thus a certain horizontal length, there might be ambiguity as to when exactly a new chord begins. To avoid that, we adopt the convention that the left-hand edge of any chord symbol specifies the moment when the chord begins.

Triads involving extra-scalar pitches that are not the root can be indicated by varying the case and suffix (if any) of the chord symbol. For instance, v° would be a diminished triad built on scale degree 5; VI+ an augmented triad built on scale degree 6.

Chords involving more than the standard three scale degrees can be indicated by adding numbers to the end of the chord symbol in the manner of guitar chord symbols. For instance, a chord including the sixth scale degree (counting upwards from the root) would have a number 6 at the end. Depending on the root and scale, the sixth scale degree from the root may be either a “minor sixth” of 800 cents or a “major sixth” of 900 cents; these are distinguished by writing b6 and #6 respectively. For example, a IV chord with an added major sixth would be IV#6. (This is a slight departure from usual music theory practice, aimed at making the intervals of each chord as explicit as possible.)

The same procedure is applied to chords with an added second or seventh scale degree (again counting from the root). For instance, a V chord with an added minor seventh would be Vb7.

As for an added fourth, the two possible intervals between a root and the fourth scale degree above it, 500 and 600 cents, are normally described as a “perfect fourth” and an “augmented fourth” rather than “minor” and “major” fourths, but for our purposes they can be distinguished in the same way, by writing b4 and #4 respectively.

A chord with an added fourth often doesn’t have a third, in which case we can write -3 (“minus third”) before the fourth. Thus, what guitarists call a “suspended fourth chord” would be written as (for instance) I-3b4. Similarly, a chord that lacks a fifth can be specified with -5 (“minus fifth”). “Minus” numbers are placed before “added” numbers, regardless of numerical sequence, so a IV chord with an added major second and no third would be IV-3#2.

Occasionally, we may need to specify added pitches that form a “diminished” interval (100 cents narrower than the “minor” version) or an “augmented” one (100 cents wider than the “major” version) above the root of the chord. This is done by writing bb (double flat) and ## (double sharp) respectively. For instance, the lush “augmented sixth” chord popular with Romantic composers would be written (in a major key) as bVI##6. (Music theory buffs will recognize that as the specifically “German” version of the augmented sixth chord. The Italian one would be bVI-5##6, and the French, bVI-5#4##6!)

All of this of course assumes that triads are the “normal” or “basic” type of chord, so these chord symbols should only be used for musical styles in which that is in fact the case. Music based on different types of chord will call for different types of chord symbol which can’t be covered on this already lengthy page.

However, we are now ready to apply our chord symbols to an example in which they do help to show what is going on. “When the Saints Go Marching In” is usually performed with a triadic accompaniment something like the one shown in the chord symbols below.

Melodies relate to chords rather like the way they relate to drones: by combining with them to create various forms of “consonance” and “dissonance.” To represent that in notation, it’s not enough to write the melody and chords separately using different kinds of symbol for each, as in the above example. We need to show what actual pitches each chord consists of and whether each melody note “harmonizes” with its accompanying chord or not. To do that, we’ll need to notate melody and chords in a way that makes them more “relatable” to each other, and preferably within the same space. That’s our next challenge.

Next: Relating melody to chords

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