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Chapter Twelve - Intervals
The distance between two notes is called an interval. There are two basic types of intervals in music: melodic and harmonic. A melodic interval occurs between consecutive notes of a melody. A harmonic interval occurs between two notes that are played at the same time.
There are two elements to the labelling of intervals in music. The first element is the interval number and the second element is the interval prefix. The most general measurement of an interval is the interval number. The interval number does not precisely measure an interval and the interval prefix is needed along with the interval number in order to provide an exact measurement of an interval.
Interval Number
The interval number is a measurement of the difference in the two notes in regard to their position on the staff. To determine the appropriate number for an interval, count (starting with the number 1) the line/space positions from the lower note to the higher note.
As an example, the interval from the note E up to the note A is a 4th (counting the E line position as one; 1- "E" line, 2- "F" space, 3- "G" line, 4- "A" space).
Likewise, the interval between D (space below the staff) and B (middle line) is a 6th (counting the "D" space as one; 1- "D" space, 2- "E" line, 3- "F" space, 4- "G" line, 5- "A" space, 6- "B" line).
The examples in this chapter use both the treble and bass clefs and the labelled interval is in both the treble and bass. The listed interval does not pertain to the distance between notes in the treble and bass.
Notice that both of the notes of odd numbered intervals (3rds, 5ths, 7ths, etc.) are on either lines or spaces.
Conversely, on the even numbered intervals (2nds, 4ths, 6ths, etc.) one note is on a line and the other is on a space. This visual guide can help you quickly identify intervals.
Counting Half Steps
In order to precisely measure and label intervals you must count the half step distance between the two notes. When counting the interval number you started your count with the number one, however when counting half step distances you should start your count by designating the first note of the interval with the number zero then count each additional half step from that note to the other note of the interval. As an example the distance in half steps between the notes C and D is two half steps (count C =0, C#= 1, D= 2), and the distance from E to A is five half steps (E=0, F=1, F#=2, G=3, G#=4, A=5)
Five different terms are used as the interval prefix: Perfect, Major, Minor, Diminished, and Augmented. These terms are used to describe what is known as the quality of an interval.
The major scale is used as a model to define the Perfect and Major intervals. Starting from the first note of a major scale and measuring to the other tones of the scale, the following intervals are defined.
Perfect Unison (two notes that are the same)
Major Second (First note to the second note of the scale)
Major Third (First note to the third note of the scale)
Perfect Fourth (First note to the fourth note of the scale)
Perfect Fifth (First note to the fifth note of the scale)
Major Sixth (First note to the sixth note of the scale)
Major Seventh (First note to the seventh note of the scale)
Perfect Octave (First note to the first note of the next octave)
When starting from the first note of a Major scale, there are no ascending intervals of minor, diminished or augmented quality.
Intervals of an unison, fourth, fifth, and octave are sometimes referred to as Perfect. In order to be a perfect interval there must be a precise distance, measured in half steps, between the two notes. As stated above, the intervals from the first note of major scale to the fourth, fifth, and octave are referred to as "Perfect" in regard to their interval prefix. These perfect intervals have a specific measurement in half steps as shown below.
Perfect Unisons have 0 half steps (i.e. C to C)
Perfect Fourths have 5 half steps (i.e. C to F)
Perfect Fifths have 7 half steps (i.e. C to G)
Perfect Octaves have 12 half steps. (i.e. C to the next C)
Any perfect interval made smaller by one half step becomes diminished. As an example the notes C to G comprise a Perfect Fifth (7 half steps), yet the notes C to Gb comprise a Diminished Fifth (6 half steps) because the distance is one half step smaller than the Perfect Fifth C to G. Similarly, the interval from C# to G is also a Diminished Fifth (6 half steps).
While Fourths, Fifths, and Octaves can be diminished intervals, the most common diminished interval is the Diminished Fifth. In more rare musical situations you might encounter a Diminished Fourth or Diminished Octave.
When measuring the fifths that are inherent in the major scale, you will notice that all are perfect except one. The fifth interval above the 7th scale degree is a diminished fifth while the fifth interval above all other scale degrees is a perfect fifth.
Any perfect interval made larger by one half step becomes augmented. As an example, the notes C to F comprise a Perfect Fourth (5 half steps), yet the notes C to F# comprise an Augmented Fourth (6 half steps) because the distance is one half step larger than the Perfect Fourth C to F. Similarly, the interval from Cb to F is also an Augmented Fourth (6 half steps).
While Unisons, Fourths, Fifths, and Octaves can be Augmented intervals, the most common Augmented intervals are the Augmented Fourth and the Augmented Fifth interval (in addition to Augmented 2nds and Augmented 6th intervals mentioned below). In more rare musical situations you might encounter an Augmented Unison or Augmented Octave.
When measuring the fourths that are inherent in the major scale, you will notice that all are perfect except one. The fourth interval above the 4th scale degree is an augmented fourth while the fourth interval above all other scale degrees is a perfect fourth.
The terms Perfect, Diminished or Augmented are valid prefixes for the intervals of unisons, fourths, fifths, and octaves. The terms Major and Minor are never used as prefixes for unisons, fourths, fifths and octaves
The intervals of seconds, thirds, sixths and sevenths sometimes have a prefix of Major. In order to be a major interval there must be a specific distance in half steps between the two notes of the interval. As stated above, the intervals from the first note of major scale to the second, third, sixth and seventh are referred to as "Major" in regard to their interval prefix. These major intervals have a specific measurement in half steps as shown below.
Major Seconds have 2 half steps (i.e. C to D)
Major Thirds have 4 half steps (i.e. C to E)
Major Sixths have 9 half steps (i.e. C to A)
Major Sevenths have 11 half steps (i.e. C to B)
Each tone of a major and minor scale is an interval of a 2nd from its adjacent scale tone. All of the whole step intervals within a scale formula are "Major seconds". As an example, the major scale formula is W-W-H-W-W-W-H (W=whole step, H=half step), indicating that five major seconds are used.
Major intervals made larger by one half step become Augmented. For example, since the interval for F to G (2 half steps) is a major second , the interval from F to G# (3 half steps) is an augmented second. An augmented second interval exists between the sixth and seventh scale degrees of all harmonic minor scales.
Although any interval can have a prefix of Augmented, the more common augmented intervals in music are the Augmented 2nd (as stated above) and Augmented 6th (in addition to the Augmented 4th and Augmented 5th mentioned in the previous section on augmented intervals). On more rare occasions one may find other augmented intervals.
Major intervals made smaller by one half step become Minor. As an example, given that the interval from C to D is a major 2nd, the interval from C to Db is a minor 2nd (the interval from C# to D is also a minor 2nd). Likewise, since the interval from C to E is a major 3rd, the interval from C to Eb is a minor 3rd (the interval from C# to E is also a minor 3rd).
The half step intervals in the major scale formula are the location of minor seconds within the scale structure.
Notice that the Harmonic minor scale has three minor 2nds within the scale structure.
Both Major and Minor scales have several minor intervals within their structure. When considering the intervals of a 3rd inherent in the major scale, there are four different minor thirds: 1) from the second note to the fourth note of the scale. 2) from the third note to the fifth note of the scale. 3) from the sixth note up to the first note (first note, next octave) and 4) from the seventh note up to the second note of the scale (second note, next octave).
Minor intervals made smaller by one half step become Diminished. As an example, since the interval from G up to F is a minor 7th, the interval from G# up to F is a diminished 7th. All Harmonic minor scales contain a diminished 7th interval from the seventh note up to the sixth note of the scale (sixth note, next octave).
A harmonic minor
7 1 2 3 4 5 6 7 8
The terms Major, Minor, Diminished or Augmented are valid prefixes for the intervals of seconds, thirds, sixths and sevenths. The term Perfect is never used as a prefix for seconds, thirds, sixths and sevenths.
The interval prefix qualities can be summarized as follows:
1) Major intervals made smaller by one half step become Minor.
2) Minor and Perfect intervals made smaller by one half step become Diminished.
3) Major and Perfect intervals made larger by one half step become Augmented.
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