Intervals

An interval is distance between two pitches. Intervals can be harmonic, with both pitches sounding at once, or melodic, when one pitch follows another.

General Intervals are based on scale degrees. The following chart diagrams all of the intervals within one octave:

However, within major and minor scales, some scale degrees are only one half-step apart (between scale degrees 3-4 and 7-1) while the others are a whole step apart. Specific intervals refer to the precise distance between pitches. Derived from the major scale, the following chart lists the Perfect and Major intervals (notated by an uppercase "P" or "M" plus the general interval) and the number of half steps they represent. When read out loud, they are read as "Major Second", "Perfect Fifth", etc.

Minor intervals are one-half step smaller than their major counterparts and are indicated by a lowercase "m". Most are found in the minor scale. Notice that the intervals of an octave, fifth and fourth are identical in both major and minor scales. These are also the intervals that are mathematically the most pure. This is why they are referred to as perfect intervals. They are neither major nor minor: they are perfect!

Combining the above specific intervals yields the following chart. There are two intervals that are missing: the single half-step (a minor second) and the interval of 6 half steps between the P4 and P5 which is called the tritone (because it consists of 3 (tri) whole steps (tones)).

When accidentals are added to pitches, they may expand or contract beyond the perfect, major or minor size. When a half-step is added to perfect or major intervals, they become augmented. When a half-step is subtracted from perfect or minor intervals, they become diminished. We add a plus sign "+" to the general interval for augmented intervals, and a small circle "o" to the general interval for diminished intervals.

The following chart shows how "augmenting" (enlarging) and diminishing (reducing) intervals by a half-step alters their specific interval size -- NOT the general interval. The general interval always remains the same regardless of how it it altered by accidentals. So a m2 reduced by a half-step becomes a o2. A P5 increased by a half-step becomes an +5 (NOT a m6).

Notice that the augmented fourth and the diminished fifth both contain 6 half steps. Also, an augmented second and a minor third both contain 3 half-steps. Just as the pitches are enharmonically related, intervals that contain the same number of half-steps are referred to as enharmonically equivalent intervals. It is important, however, just like with enharmonic pitches, not to change the general interval: a fourth always remains a fourth, whether perfect, augmented or diminished. Even though enharmonically equivalent intervals contain the same number of half-steps they may function differently in tonal music, and should never be referred to as their enharmonic equivalent.

Inversion of Intervals

Notice that if the lower note of an interval is raised one octave, the interval sounds similar to the original. This is called inverting the interval.

The following table lists all of the standard intervals and their inversions. Notice the pattern:

2nds invert into 7ths
3rds invert into 6ths
4ths invert into 5ths
Major intervals invert into minor intervals
Perfect intervals invert into Perfect intervals
Diminished intervals invert into augmented intervals.

Also notice that the chart only has to list up to the interval of a tritone: all intervals larger than that have already been listed.

Importance of Reading Intervals

Intervals are the building blocks of tonal harmony. It is vital to the understanding of music theory to be able to quickly and accurately recognize interval sizes. At first you may need to count the scale degrees to determine the general interval size and count the number of half-steps to determine the specific interval, but eventually, you should be able to recognize most intervals at sight. Just as one wouldn't be able to read very quickly if you needed to spell out each word ( c-a-t is "cat") one cannot read music effectively without being able to recognize intervals quickly. Here are some hints to make reading intervals easier at first:

Interval Identification Hints:

1. General intervals become easier when one learns to recognize the patterns of the intervals on the staff. Seconds are easy: they are right next to each other. Thirds both on adjacent lines or both on adjacent spaces. Notes a fifths apart are two lines or spaces apart. Sevenths are three. A fourth is between a third and fifth, and a sixth is between a fifth and seventh.
2. For perfect intervals: with the exception of the intervals between any B and F, (sharp, natural or flat) if the accidentals match (i.e. both are flats) it is a perfect interval. This is a helpful hint, since the identification of perfect fifths is basic to tonal music. Between B and F, one must memorize that B-flat to F is a perfect fifth and B to F-sharp is a perfect fifth.
3. Undoubtedly, you will begin to learn to recognize certain intervals before others. For instance, you may already recognize the interval C up to E as a M3, since the C scale is one of our most basic and common scales. Use these easily recognized intervals as points of reference to recognize close intervals. For instance, if C up to E is a M3, then we can quickly recognize that C up to E-flat is a half step lower, because of the flat, and so it must be a m3. Similarly, a m6 is one half step larger than a perfect fifth. A M7 is a half step smaller than a perfect octave, etc.
4. Practice reading and listening to them until you can easily recognize all intervals -- not just the easy ones. There are many software programs on the Internet and on the commercial market to help with this, but practice is still the best way to learn!

Links:

• Activities for Review of this section
• Next section: Tendency Tones and Minor Scales
• Table of Contents