Once it is possible to discuss intervals between notes and understand their relationship to one another within a certain key, it becomes possible to combine notes in different ways. Combinations of notes are known as "chords." The progression between different chords is known as "chord progression" in music theory, or "harmony."

In the previous article, perfect fourths and perfect fifths were defined as the distance between the tonic, or first note in a key, and the fourth or fifth interval within that key, or the "sub-dominant" and "dominant" chords within that key. These two intervals are very instructive places to begin a discussion of a chord progression. "Dominant to tonic" for example, or the progression from the fifth chord in a major key to the tonic chord in a major key, is almost universally considered the strongest major chord progression in western music, and it is extraordinarily recognizable to the average listener.

In fact, after hearing a chord progression that stops on dominant, people will often hear tonic in their own mind even if it is not played. The same is true for the octave note in a scale. If a vocalist were to sing "do.. re.. mi.. fa.. so.. la.. ti........" everyone else in the room would hear "do" one octave higher than the first "do" and several of them would probably sing it out loud quietly. You can try this yourself. Imagine someone singing a major scale (progress up through the notes):

"do.. re.. mi.. fa.. so.. la.. ti........"

Did you hear the next note? Did you sing it? What you're doing is bringing the music back to tonic. If you start a progression on any note, it will naturally want to return to that note eventually. This is known as a "resolution" and it is one of the primary elements of diatonic music. The step between the "ti" and the higher octave "do" is the important tonal progression. In a major scale, it is an interval of a minor second, which is also known as a "half-step."

The reason dominant to tonic chord progression is so natural and so easy to hear is because dominant to tonic includes the progression of "ti" to "do," the same progression that everyone hears in their mind when a scale is played but not resolved. This is also why dominant to tonic is so strong. Here's how it works.

In order to construct a chord in the key of 'C,' you start with the tonic note, 'C.' We'll build a major chord. Add an interval of a major third, which would be the note of 'E.' Then add an interval of a perfect fifth, which would be the note of 'G.' Congratulations, you just built a chord known as "C major." This chord consists of the notes C, E and G played together at the same time. In the key of 'C,' "C major" or the "C major chord" is known as the "tonic" chord. Any music written in "C major" will want to go back to this chord eventually.

Now, we need to build a dominant chord. The dominant interval begins on the perfect fifth, which is the note of "G" in the key of "C major." You build the chord in exactly the same way. Start with dominant, add a major third, which would be the note of "B," and then add a perfect fifth, which would be the note of "D." Play G, B and D together, and you're playing the chord of "G major." The "G major" chord is the "dominant" chord in the key of "C major."

Here's where the "ti" to "do" progression happens. Notice something about the dominant chord? It has the note of "B" in it, which is one half step below the note of "C." That half step from "B" to "C" is "ti" to "do" in "C major." Even though it is surrounded by other notes, and could be surrounded by a choir and a symphony orchestra, almost any listener can still hear the simple progression from "ti" back to the tonic note, even subconsciously. This is the strongest tonal and chord progression in a diatonic harmony and it is so recognizable that it can be heard in literally thousands of musical compositions spanning many centuries.

Most musicians start to learn about tonal progression, intervals and chord progression when they learn to write music, because writing music correctly, i.e. the grammar of music, is nearly as well defined as the grammars of any written language. The difference is that music is also a mathematical construct, with well-defined and well understood relationships between sounds and combinations of sounds.

When studying music theory, musicians learn, for example, that "parallel fifths" are an undesirable voicing, as are "parallel octaves." What this means is that two voices, alto and tenor, for example, should not be a fifth apart from one chord to the next, nor should they be one octave apart. Many an hour has been spent by musicians puzzling over voicing in their original compositions to make sure there are no parallel fifths or octaves.

Art, like science, has something to offer to those who ask "why" in addition to those who ask "how?" Music is especially capable in this area, because it is possible to observe mathematical relationships in music that listeners consider pleasing.