Digital Sound & Music: Concepts, Applications, & Science, Chapter 3, last updated 6/25/2013

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a fourth or fifth into a minor interval. This is because if you lower the higher note by one

semitone, you’ve change the interval to a smaller one because you’ve lost one of the lettered

notes in the interval. For example, in the key of C if you shorten a perfect fourth by one

semitone, the top note is an E rather than F, so the interval is no longer a fourth. There’s no

black key to use between E and F. A third, on the other hand, can be shortened so that instead of

being from C to E, it’s from C to E♭. There are still three lettered notes in the interval – c C,

D, and E – but now we have a minor third instead of a major third.

The intervals that cannot be made minor are called perfect. These are the perfect unison,

perfect fourth, perfect fifth, and perfect eighth.

Two other types of intervals exist: diminished and augmented. A diminished interval is

one semitone smaller than a perfect interval or two semitones smaller than a major interval. An

augmented interval is one semitone larger than a perfect or major interval. All the intervals for

the key of C are shown in Figure 3.28. The intervals for other keys could be illustrated similarly.

Figure 3.28 All intervals

You can create a compound interval by taking any of the interval types defined above

and moving the upper note up by one or more octaves. If you’re trying to identify intervals in a

score, you can count the number of lettered notes from the beginning to the end of the interval

and “mod” that number by 7. The result gives you the type of interval. For example, if the

remainder is 3, then the interval is a third. The mod operation divides by an integer and gives the

remainder. This is the same as repeatedly subtracting 7 (the number of notes in an octave, not

counting the repeat of the first note an octave higher) until you reach a number that is less than 7.

Figure 3.29 shows examples of two compound intervals. The first goes from C4 to G5, a span of

12 notes. 12 mod 7 = 5, so this is a compound perfect fifth. The second interval goes from E4