Harmony - Intervals

Intervals

An interval is the relationship between two separate musical pitches. For example, in the melody "Twinkle Twinkle Little Star", the first two notes (the first "twinkle") and the second two notes (the second "twinkle") are at the interval of one fifth. What this means is that if the first two notes were the pitch "C", the second two notes would be the pitch "G"—four scale notes, or seven chromatic notes (a perfect fifth), above it.

The following are common intervals:

Therefore, the combination of notes with their specific intervals —a chord— creates harmony. For example, in a C chord, there are three notes: C, E, and G. The note "C" is the root, with the notes "E" and "G" providing harmony, and in a G7 (G dominant 7th) chord, the root G with each subsequent note (in this case B, D and F) provide the harmony.

In the musical scale, there are twelve pitches. Each pitch is referred to as a "degree" of the scale. The names A, B, C, D, E, F, and G are insignificant. The intervals, however, are not. Here is an example:

As can be seen, no note always corresponds to a certain degree of the scale. The "tonic", or 1st-degree note, can be any of the 12 notes (pitch classes) of the chromatic scale. All the other notes fall into place. So, when C is the tonic, the fourth degree, subdominant, is F. But when D is the tonic, the fourth degree is G. So while the note names are intransigent, the intervals are not. In layman's terms: the subdominant, "fourth" (four-step interval) is always a fourth, no matter what the tonic is. The great power of this fact is that any musical work can be played or sung in any key—it will be the same piece of music, as long as the intervals are kept the same, thus transposing the melody into the corresponding key. When the intervals surpass the perfect Octave (12 semitones), these intervals are named as "Compound intervals", which include particularly the 9th, 11th, and 13th Intervals, widely used in Jazz and Blues Music.

Compound Intervals are formed and named as following:

• 2nd + Octave = 9th
• 3rd + octave = 10th
• 4th + Octave = 11th
• 5th + octave = 12th
• 6th + Octave = 13th
• 7th + octave = 14th

The reason the two numbers don't "add" correctly is that one note is counted twice. Apart from this categorization, intervals can also be divided into consonant and dissonant. As explained in the following paragraphs, consonant intervals produce a sensation of relaxation and dissonant intervals a sensation of tension. In tonal music, the term consonant also means "brings resolution" (to some degree at least, whereas dissonance "requires resolution").

The consonant intervals are considered to be the perfect unison, octave, fifth, fourth and major and minor third and sixth, and their compound forms. An interval is referred to as "perfect" when the harmonic relationship is found in the natural overtone series (namely, the unison 1:1, octave 2:1, fifth 3:2, and fourth 4:3). The other basic intervals (second, third, sixth, and seventh) are called "imperfect" because the harmonic relationships are not found mathematically exact in the overtone series. In classical music the perfect fourth above the bass may be considered to be dissonant when its function is contrapuntal. Other intervals, the second and the seventh (and their compound forms) are considered Dissonant and require resolution (of the produced tension) and usually preparation (depending on the music style used). It should be noted that the effect of dissonance is perceived relatively within musical context: for example, a major seventh interval alone (i.e. C up to B) may be perceived as dissonant, but the same interval as part of a major seventh chord may sound relatively consonant. A tritone (the interval of the fourth step to the seventh step of the major scale, i.e. F to B) sounds very dissonant alone, but less so within the context of a dominant seventh chord (G7 or D♭7 in that example).