Understanding and Measuring Intervals Between Two Pitches
In Western music, the intervals between two pitches are a fundamental aspect of music theory. These intervals not only define the distances between notes but also dramatically influence the harmony and melody. This article explores the key components of intervals: their quality and quantity, and how they can be measured and invoked in music composition and analysis.
Quantity in Intervals
The quantity of an interval in music theory refers to its size—specifically, the number of notes that lie between the lower and higher pitch, rather than the number of step movements. For instance, in the interval C to E, if we have C-D-E, we count it as a third, as it covers three notes. If we switch the lower and higher pitch to E-C, we count E-F-G-A-B-C, making it a sixth. Note that the first and last notes in the interval are always included in the count.
Quality in Intervals
The quality of an interval describes its nature within the context of scales. For example, an interval from C to E, if both are based on the C major scale, is a major third. However, an interval from E to C would be a minor sixth, as it falls a half-step shorter than the expected sixth in the E major scale. Intervals are categorized into major, minor, diminished, and augmented based on their distance from a perfect interval.
Major, Minor, Diminished, and Augmented Intervals
Major and minor intervals are based on scale degrees. Major intervals are those found within a major scale. Minor intervals are those that are half-step smaller than a corresponding major interval. Diminished intervals are half-step smaller than minor intervals, and augmented intervals are half-step larger than major intervals. These classifications cover intervals within a single octave, with the following details:
Seconds, Thirds, Sixths, and Sevenths
Seconds: An interval from C to D is a second, from C to E is a major second, from C to Eb is a minor second, and from C to D# is an augmented second. Conversely, from D# to C is a diminished second. Thirds: An interval from C to E is a major third, from C to Eb is a minor third, from C to Ebb is a diminished third, and from C to E# is an augmented third. Conversely, from E# to C is a diminished third. Sixths: As mentioned, an interval from E to C is a minor sixth. From C to F is a perfect fourth, from C to F# is an augmented fourth, and from C to Fb is a diminished fourth. Conversely, from C to Gb is a diminished fifth, and from Gb to C is an augmented fourth. Sevenths: An interval from C to D is a minor seventh, from C to D# is an augmented seventh. Conversely, from E to D is a minor seventh.General Rules for Interval Inversion
Intervals invert such that the sum of their quantities equals 9. For example, a major third (C to E) inverted becomes a minor sixth (E to C). Perfect intervals (fourths, fifths, and octaves) invert to perfect intervals. Diminished intervals become augmented, and augmented intervals become diminished.
Special Cases
For intervals larger than a single octave, such as ninths, tenths, and higher, the same rules apply. For instance, an interval from B to F is a diminished fifth (if F is a half-step lower than F in the B major scale), and F to B is an augmented fourth. Doubly diminished and doubly augmented intervals are rarely used in practice but can be relevant in theoretical discussions.
Conclusion
Understanding and measuring intervals between two pitches is crucial for any musician or music theorist. This knowledge provides the foundation for creating harmonious music, analyzing existing compositions, and engaging with the rich traditions of Western art music. Mastery of interval theory can significantly enhance your skills in music composition, arrangement, and interpretation.