Intervals and harmony

An interval is the distance between two pitches, usually measured as a number of steps on a scale.

A dyad is a pair of pitches sounding together (in other words, a two-note chord). Since a dyad is defined by the interval between the two pitches, dyads are often simply called intervals.

Thus, the term interval regularly refers both to the distance between two pitches on a scale and to a dyad whose pitches are separated by that distance.

Chromatic intervals

The simplest way to measure intervals, particularly at the keyboard, is to count the number of half-steps, or semitones, between two pitches. To determine the chromatic interval between C4 and E4, for example, start at C4 and ascend the chromatic scale to E4, counting steps along the way: C#4, D4, D#4, E4. E4 is four semitones higher than C4. Chromatic intervals are notated with a lower-case i followed by an Arabic numeral for the number of semitones. C4–E4 is four semitones, or i4.

Diatonic intervals

More commonly for tonal music, we are interested in the number of steps on the diatonic (major or minor) scale. This is a bit tricky—not because it's difficult, but because it's counterintuitive. Unfortunately, the system is too old and well engrained to change it now! But once you get past the initial strangeness, diatonic intervals are easy.

When identifying a diatonic interval, begin with the letter names only. That is, treat C, C-sharp, and C-flat all as C for the time being. Next, count the number of steps (different letters) between the two pitches in question,counting both pitches. This will give you the generic interval.

For example, from C4 to E4, counting both C and E, there are three diatonic steps (three letter names): C, D, E. Thus, the generic interval for C4–E4 is athird. The same is true for any C to any E: C#4 to E4, Cb4 to E#4, etc. They are all diatonic thirds.

Often more specificity is needed than generic intervals can provide. That specificity comes in the form of interval quality. And combining quality with a generic interval produces a specific interval.

There are five possible interval qualities:

• augmented (A)
• major (M)
• perfect (P)
• minor (m)
• diminished (d)

To obtain an interval's quality, find both the generic interval and the chromatic interval. Then consult the following table to find the specific interval.

For example, C4–E4 is a generic third, and has a chromatic interval of i4. A third that encompasses four semitones is a major third (M3). Note that both generic interval and chromatic interval are necessary to find the specific interval, since there are multiple specific diatonic intervals for each generic interval and for each chromatic interval.

Note that some generic intervals can be augmented, perfect, or diminished, and other intervals can be augmented, major, minor, or diminished. There is no generic interval that can be both major/minor and perfect; if it can be major or minor, it cannot be perfect, and if it can be perfect, it cannot be major or minor. An augmented version of an interval is always one semitone wider than major or perfect; diminished is always one semitone smaller than minor or perfect.

Solfège can also help to determine the specific interval. Each pair of solfège syllables will have the same interval, no matter what the key, as long as it is clear which syllable is the lower pitch and which is the upper pitch. Memorizing the intervals between solfège pairs can help speed along your analysis of dyads as they appear in music. For example, knowing that do–mi,fa–la, and sol–ti are always major thirds and knowing that re–fa, mi–sol,la–do, and ti–re are always minor thirds will allow for faster analysis of dyads in major keys.

Kazi Abdus Sobur