Naming any tertial triad

We have introduced chord notation through the most basic chords of Western music: the tertial triads formed from the intervals of the major scale. But even tertial triads are not always limited to those intervals. They may be based on a different scale, and they may include extra-scalar pitches that don’t belong to the prevailing scale of the music.

For a truly “global” chord notation, we need to be able to specify any possible chord. A good place to start might be by naming all the tertial triads that are possible in the Western system.

Even within conventional Western music, the major scale is not the only scale available. There is also the minor scale, or rather scales, since some of the scale degrees in minor keys are variable in pitch, resulting in different scales according to which version of the degree is chosen in a given passage.

The most consistent difference from the major scale is that in a minor scale degree 3 is 300 cents above the tonic instead of 400. Degree 6 tends to vary between 800 and 900 cents above the tonic, and degree 7 between 1000 and 1100 cents.

In practice, degree 6 is more often 800 cents, while degree 7 must be 1100 cents at least some of the time for the music to be in a minor key rather than some other mode, so those are the values represented by the pitch lines for music in a minor key; but the alternative values are also too common to be considered extra-scalar pitches, and in the next two examples they are shown with dotted pitch lines.

The result is that minor keys offer a larger number of different tertial triads (without using extra-scalar pitches) than major keys do.

Examples of chords and tertial triads in global notation in a minor key.

As you can see, in a minor key the triad built on degree 4 can be either a minor chord or a major chord, depending which version of degree 6 it contains. We can notate either one easily enough, distinguishing them by the case of the Roman numerals: iv and IV respectively.

The problems begin when even the root of a chord doesn’t occur in the major scale, as with degree 3 and the lower versions of degrees 6 and 7 in a minor key. And things only get more complicated if we try to allow for other scales such as the “modes” of old church and folk music (dorian, phrygian etc).

We could continue to name each chord after the scale degree of its root in whatever scale the music uses. But that would result in a given symbol representing different chords in different contexts, which could be confusing. 

For instance, III would refer to two different chords depending whether scale degree 3 was 300 or 400 cents above the tonic. Moreover, this approach would require us to specify the scale before being able to specify the chords; and Global Notation aims to be able to specify one thing independently of another as far as possible.

Therefore, instead of making chord symbols dependent on the scale, Global Notation adopts the convention of treating the major scale as the “default” for all harmonic music.

That is, unmodified numbers, whether Arabic or Roman, refer to the scale degrees and chord roots as they appear in the major scale. Any other pitches are indicated by prefixes derived from staff notation: # (sharp) for a pitch 100 cents higher than that scale degree would be in the major scale, and b (flat) for a pitch 100 cents lower. For example, b3 would be a pitch 300 cents above the tonic, and bIII a major triad built on that pitch, regardless what scale the music uses.

This should not be taken to imply that the major scale is in any way more fundamental or “natural” than other scales; it is just that we need to adopt a single scale as a basis for describing all chords, and for historical reasons, the major scale is likely to be the one most familiar to the largest number of potential users of Global Notation. It’s a pragmatic choice.

Applying this principle, the tertial triads available within minor scales are named as below.

Chords in a minor key with their tertial triads written below.

Extending the principle, it’s easy to generate unique chord symbols for any kind of triad built on any of the twelve pitches available within the octave in the Western system of tuning. Of course, some of these chords will be far more common than others in actual music.

Note that each of the pitches outside of the major scale can be described or “spelled” in two different ways: for instance, the pitch between 4 and 5 is either #4 or b5, and a major triad with that pitch as root is either #IV or bV. The choice of spelling will depend on the musical context in ways that require a knowledge of harmony beyond what can be expounded here, but in the table below, the more common spelling is given in each case. The pitch lines in the table are set to the major scale as “default,” though in an actual score they would be set to whatever scale the music uses.

Examples of tertial triads written in different situations: Major Triads, Minor Triads, Augmented Triads and Diminished Triads. Each of these differ when notated.

The same principles would also enable us to indicate a triad with a major third and diminished fifth (e.g., V°), or one with a minor third and augmented fifth (e.g., biii+), although such triads are rare in practice. Even triads based on scales that use intervals other than multiples of 100 cents could be accommodated, for instance by adopting the quarter-tone sharp and flat symbols used for Middle Eastern music and devising a few additional symbols for specifying intervals such as a “neutral” third of 350 cents.

To name a chord in this notation system, we first have to decide which pitch is the tonic and which pitch is the root of the chord, and these decisions are not always straightforward. For instance, when music “modulates” (changes key), a single chord may have two different functions or identities: one in the old key and one in the new. In such cases, it is quite legitimate to give the same chord more than one name.

An example occurs in the first eight bars of Mozart’s famous “Turkish Rondo.” The A minor triad that occupies the first four bars is initially heard as chord i in the key of A minor, but then comes to function as chord iv in the key of E minor (keys are indicated in square brackets). Notice how some of the pitch lines change their position or thickness when the key changes to indicate the scale of the new key. A few notes have been left out from the middle of the texture to clarify the main harmony. For the ellipses indicating octave transposition and its cancellation, see Wide pitch range.

Mozart's "Turkish Rondo" with minor triads marked clearly below

If absolute pitch is being specified, it is also possible to name a chord without specifying its relationship to any tonic: the Roman numeral is simply replaced with a letter name, in upper or lower case and with any affix required, as in bB+ or #f°. And if we just want to refer to a type of chord without specifying its root in either relative or absolute terms, we can just use an X in place of the Roman numeral or letter name: for instance, x° would mean any diminished triad.

We now have a way of naming any tertial triad independently of the scale that the music uses. Our next challenge comes from the fact that not all chords are tertial triads.