Introduction to Music Part II Classifying Intervals So far, the actual distance, in half-steps, between the two notes has not mattered. But a third made up of three half-steps sounds different from a third made up of four half-steps. And a fifth made up of seven half-steps sounds very different from one of only six half-steps. So in the second step of identifying an interval, clef, key signature, and accidentals become important. Figure 12: A to C natural and A to C sharp are both thirds, but A to C sharp is a larger interval, with a different sound. The difference between the intervals A to E natural and A to E flat is even more noticeable. Listen to the differences in the thirds and the fifths in Figure 12. So the second step to naming an interval is to classify it based on the number of half steps in the interval. Familiarity with the chromatic scale is necessary to do this accurately. Perfect Intervals Primes, octaves, fourths, and fifths can be perfect intervals. Note: These intervals are never classified as major or minor, although they can be augmented or diminished (discussed later). What makes these particular intervals perfect? The physics of sound waves (acoustics) shows us that the notes of a perfect interval are very closely related to each other. Because they are so closely related, they sound particularly good together, a fact that has been noticed since at least the times of classical Greece, and probably even longer. (Both the octave and the perfect fifth have prominent positions in most of the world's musical traditions.) Because they sound so closely related to each other, they have been given the name "perfect" intervals. A perfect prime is also called a unison. It is two notes that are the same pitch. A perfect octave is the "same" note an octave - 12 half-steps - higher or lower. A perfect 5th is 7 half-steps. A perfect fourth is 5 half-steps. Example Perfect Intervals Listen to the octave, perfect fourth, and perfect fifth. Major and Minor Intervals Seconds, thirds, sixths, and sevenths can be major intervals or minor intervals. The minor interval is always a half-step smaller than the major interval. Major and Minor Intervals * 1 half-step = minor second (m2) * 2 half-steps = major second (M2) * 3 half-steps = minor third (m3) * 4 half-steps = major third (M3) * 8 half-steps = minor sixth (m6) * 9 half-steps = major sixth (M6) * 10 half-steps = minor seventh (m7) * 11 half-steps = major seventh (M7) Example Major and Minor Intervals Listen to the minor second, major second, minor third, major third, minor sixth, major sixth, minor seventh, and major seventh. Exercises 6 and 7 Exercise 6 Give the complete name for each interval. Exercise 7 Fill in the second note of the interval given Exercises 6 and 7 - Solutions Augmented and Diminished Intervals If an interval is a half-step larger than a perfect or a major interval, it is called augmented. An interval that is a half-step smaller than a perfect or a minor interval is called diminished. A double sharp or double flat is sometimes needed to write an augmented or diminished interval correctly. Always remember, though, that it is the actual distance in half steps between the notes that determines the type of interval, not whether the notes are written as natural, sharp, or double-sharp. Example Some Diminished and Augmented Intervals Listen to the augmented prime, diminished second, augmented third, diminished sixth, augmented seventh, diminished octave, augmented fourth, and diminished fifth. Are you surprised that the augmented fourth and diminished fifth sound the same? Exercise 8 Write a note that will give the named interval. The solution is given on the following page. Exercise 8 - Solution Different Spellings of Intervals The diminished fifth and augmented fourth sound the same. Both are six half-steps, or three whole tones, so another term for this interval is a tritone. In Western Music, this unique interval, which cannot be spelled as a major, minor, or perfect interval, is considered unusually dissonant and unstable (tending to want to resolve to another interval). You have probably noticed by now that the tritone is not the only interval that can be "spelled" in more than one way. In fact, because of enharmonic spellings, the interval for any two pitches can be written in various ways. A major third could be written as a diminished fourth, for example, or a minor second as an augmented prime. Always classify the interval as it is written; the composer had a reason for writing it that way. That reason sometimes has to do with subtle differences in the way different written notes will be interpreted by performers, but it is mostly a matter of placing the notes correctly in the context of the key, the chord, and the evolving harmony. Figure 13: Any interval can be written in a variety of ways using enharmonic spelling. Always classify the interval as it is written. Inverting Intervals To invert any interval, simply imagine that one of the notes has moved one octave, so that the higher note has become the lower and vice-versa. Because inverting an interval only involves moving one note by an octave (it is still essentially the "same" note in the tonal system), intervals that are inversions of each other have a very close relationship in the tonal system. To find the inversion of an interval 1. To name the new interval, subtract the name of the old interval from 9. 2. The inversion of a perfect interval is still perfect. 3. The inversion of a major interval is minor, and of a minor interval is major. 4. The inversion of an augmented interval is diminished and of a diminished interval is augmented. Example Exercise 9 What are the inversions of the following intervals? 1. Augmented third 2. Perfect fifth 3. Diminished fifth 4. Major seventh 5. Minor sixth The solutions are given on the following page. Exercise 9 - Solution 1. Diminished sixth 2. Perfect fourth 3. Augmented fourth 4. Minor second 5. Major third Intervals - Summary Perfect Intervals * A perfect prime is often called a unison. It is two notes of the same pitch. * A perfect octave is often simply called an octave. It is the next "note with the same name". * Perfect intervals - unison, fourth, fifth, and octave - are never called major or minor Augmented and Diminished Intervals * An augmented interval is one half step larger than the perfect or major interval. * A diminished interval is one half step smaller than the perfect or minor interval. Inversions of Intervals * To find the inversion's number name, subtract the interval number name from 9. * Inversions of perfect intervals are perfect. * Inversions of major intervals are minor, and inversions of minor intervals are major. * Inversions of augmented intervals are diminished, and inversions of diminished intervals are augmented.