Today we’ll complete our understanding of intervals with a technical look at them.
The quantitative name of an interval is determined by counting the number of letter names it contains, including the first and last. This number, which describes the size of an interval in terms of the scale steps it encompasses, is preceded by a qualitative term. We found that scales were constructed of major seconds, which contain two half steps, or minor seconds which contain one half step. While it is possible to define the larger intervals in terms of the number of half steps it contains, it is more convenient to describe them as they relate to the keynote, or tonic, of a major scale.
The diatonic intervals as they normally occur up from the tonic of the major scale are called either major or perfect. Some numerical intervals have three possible qualifying descriptive terms, and some have four. These must be memorized according to the following chart:
Fig. 1
(a) Intervals (left column) that are normally major become augmented if the distance between the notes is increased one half step. If it is decreased one half step the interval becomes minor. If it is further decreased one half step it becomes diminished.
(b) Intervals (right column) that are normally perfect become augmented if the distance between the notes is increased one half step. If it is decreased one half step the interval becomes diminished.
Intervals can become doubly augmented or doubly diminished.
Fig. 2
The names of the basic white-key intervals as they occur from the tonic of the C major scale must be memorized.
Fig. 3
Practice altering these basic intervals by the addition of accidentals according to the patterns shown in Figure 1.
Remember: Accidentals are placed on the staff immediately before the note they affect. They obtain for that note only for the duration of that particular measure, unless cancelled.
For example, name the following intervals:
Answers:
Measure 1 – Augmented 1st/prime/perfect
Measure 2 – Diminished 3rd
Measure 3 – Augmented 6th
Measure 4 – Diminished 7th
Measure 5 – Augmented 4th
Measure 6 – Diminished 4th
Measure 7 – Diminished 5th
Measure 8 – Augmented octave
Fig. 4
From this point on you may use the following abbreviations for the qualifying terms of intervals:
- M = major
- m = minor
- A = augmented
- d = diminished
- P = perfect
To correctly name the intervals larger than a second, you first count the letters to find the quantitative name. The qualitative name is then found according to one of the following methods:
1. Memorize the correct names of the white-key intervals given for the key of C major (Fig. 3). These may be altered, meaning, made larger or smaller by the use of accidentals, according to Figure 1.
For example: perfect intervals may be altered as follows:
Fig. 5
Imperfect intervals may be altered:
Fig. 6
2. When the lower note of an interval is not C, the key signature of the major scale of the lower note must be imagined.
Fig. 7
If the upper note then occurs as a normal scale degree in the major scale of the lower note, then the interval will be either major or perfect, according to which of the two groups of intervals given in Figure 68 it belongs to. If the note is larger or smaller than would normally occur, then the quality of the interval will be determined by the accidental used.
Sometimes it is helpful to check the quality of large intervals by imagining the quality of the complementary small intervals that are more easily seen.
For example: The quality of sixths and sevenths will be the opposite of the complementary thirds and seconds.
Fig. 8
To determine the quality of compound intervals, it is convenient to disregard the octave and to imagine the simple intervals.
Fig. 9
Finally, if the interval utilizes unusual combinations of accidentals, especially double sharps or double flats, it is sometimes convenient to determine the quality of the unaltered notes (letter names) and then make the necessary adjustments.
Fig. 10
Inversion of Intervals – If the lower tone of an interval is placed an octave higher, or if the upper tone of an interval is placed an octave lower, the interval is said to have been inverted.
Thus, seconds become sevenths, thirds become sixths, and fourths become fifths. (The original interval and its complementary one add up to the number nine).
As for the quality of the interval, perfect remains perfect when inverted, major becomes minor, minor becomes major, augmented becomes diminished, and diminished becomes augmented.
Fig. 11
Intervals no larger than an octave are called simple intervals. Those greater than an octave are called compound intervals. Thus any simple interval is made compound by the addition of an octave. (The numerical name of the simple interval is added to the number seven to produce the name of the compound interval.)
Fig. 12