# Finding Natural Classes

I have a question regarding exercise 1, chapter 4, Introductory Phonology by Bruce Hayes.

Suppose we have the features high, low, back, round. We are given the table below, representing the vowels of a hypothetical language.

``````Vowels:           Front                       Back
Unrounded     Rounded         Unrounded    Rounded
high        i           y                ɯ            u
mid         e           ø                ˠ            o
low         æ           Œ                ɑ            ɒ
``````

My problem is about this question: Find as many natural classes as you can that have five members.

For natural classes that have four members, for example, I could think of the class [+high] or [+low]. But how about a five-member class?

• Classes that have 6 members are at the same time classes that have 5 members, aren't they? If so, then classes [+back] or [-back] or [+round] or [-round] are what you're looking for. There are other classes with 6 members there, you can find them yourself. Jun 17, 2019 at 15:39
• Oh, yes, if you we think of it like that, it's possible to find five-member classes. I read the question as "exactly five member". And I was just wondering if there are such classes. Any ideas about "exactly" five member classes? Jun 17, 2019 at 15:43
• Can you give more details about the book you took this exercise fom? Its author(s)? Date? Jun 17, 2019 at 16:24

Now when I have found the book and read the complete task of the exercise, I would say the answer is "In that hypothetical language, there are no natural classes that have five members".

Let's have a look at all the tasks of the exercise, not only at the one (d.) you quoted:

``````a. Find as many natural classes as you can
that have FOUR members.
List them, and define the natural class using features.

b. Find as many natural classes as you can
that have SIX members.
List them, and define the natural class using features.

c. Find as many natural classes as you can
that have EIGHT members.
List them, and define the natural class using features.

d. Find as many natural classes as you can
that have FIVE members.

e. Explain why [y, e] is not a natural class.
``````

It's not too difficult to answer questions a., b., and c., since natural classes with 4, 6, and 8 members respectfully are easy to find in the given chart, unlike classes with 5 members in our question d. Also note that questions a., b., and c. have the task "List them, and define the natural class using features" which is not found in question d.

The difficulty of question d. and the difference of its structure suggest the negative answer to d., "In that hypothetical language, there are no natural classes that have five members"

• Thanks a lot! I'd suspected that but couldn't trust my instincts. Thanks a lot! Jun 17, 2019 at 18:12

You can't find natural classes unless you have a theory of them. Usually the theory is based on a set of features and a theory of expressions. For example, [+hi,-rd] is a possible expression referring to two vowels in your set. With the labels you have, there is no way to refer to non-low ([-lo]) if these are privative features, or unless you have disjunctive expressions available for defining classes. So first you have to know what the features are, do they have plus and minus values, and can you tack together classes with braces ("or").

I advise against interpreting the instructions as meaning "at least", without instructor approval. When we say "3" we mean "3, no more and no less.

• Features get +/-. They are binary. Jun 17, 2019 at 16:51
• But, I do not have any idea about the disjunction thing you said. There was no such thing in the book, So it did not even enter my mind. How would we define naturall classes that way? Could you explain or give me a reference to check, please? Jun 17, 2019 at 16:51