By Hal Leonard Corp.
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Additional resources for 25 Essential Rock Bass Classics (Bass Recorded Versions)
In the case of Note, it takes two arguments, whose types are Dur and Pitch, respectively, whereas Rest takes one argument, a value of type Dur. In other words, the types of Note and Rest are: Note :: Dur → Pitch → Primitive Rest :: Dur → Primitive CHAPTER 2. SIMPLE MUSIC 31 For example, Note qn a440 is concert A played as a quarter note, and Rest 1 is a whole-note rest. This deﬁnition is not completely satisfactory, however, because we may wish to attach other information to a note, such as its loudness, or some other annotation or articulation.
These number systems possess many useful properties, such as the fact that multiplication and addition are commutative, and that multiplication distributes over addition. You have undoubtedly learned many of these properties in your studies, and have used them often in algebra, geometry, trigonometry, physics, and so on. Unfortunately, each of these number systems places great demands on computer systems. In particular, a number can in general require an arbitrary amount of memory to represent it.
Thus: hList d (p : ps) = hNote d p :+: hList d ps Note that this part of the deﬁnition of hList is recursive—it refers to itself! But the original problem—the harmonization of p : ps—has been reduced to the harmonization of p (previously captured in the function hNote) and the harmonization of ps (a slightly smaller problem than the original one). CHAPTER 1. COMPUTER MUSIC, EUTERPEA, AND HASKELL 21 Combining these two equations with the type signature yields the complete deﬁnition of the function hList: hList :: Dur → [Pitch ] → Music Pitch hList d [ ] = rest 0 hList d (p : ps) = hNote d p :+: hList d ps Recursion is a powerful technique that will be used many times in this textbook.