 Hello again. In our first e-lecture about distinctive features, we examined the different approaches towards the definition of features from a historical perspective. In this follow-up e-lecture we will discuss today's system of distinctive features and we will show how distinctive features can be used to define natural classes, phonological rules and phonotactic statements. Let us start with a detailed look at today's most popular distinctive feature systems. Distinctive features constitute a limited set of phonological segments assumed to be part of universal grammar. The set of principles for language all humans are endowed with innately. Distinctive features are associated with a unary, that is a single valued, or a binary value, and are by convention enclosed in square brackets. By and large they are based on Jacobson's definition of acoustic features and on the sound pattern of English approach as defined by Chomsky and Halle. In order to develop a system of distinctive features for the existing vowels and consonants, we first of all have to find out the minimal number of features we need. So, how many features do we need? Well, there is a relatively simple formula to calculate the number of features for a given set of items. This formula says, take the square root of n, that is the number of items you want to define. Generate the integer value and add the number 1. Here are two examples. To find out the number of features we need to distinguish the 16 cardinal vowels, we have to take the square root of the number 16, which is of course 4. The integer value of 4 is also 4, and then we add 1, so the result will be 5. So to define the 16 cardinal vowels we need 5 distinctive features. Let's play the same game for the roughly 90 consonants we need. So, n would now be 90. The square root of 90 is roughly 9.5. The integer value of 9.5 is 9. We add 1, so we get the number 10. So to define the roughly 90 consonants that exist in the languages of the world, in terms of distinctive features, we would need 10 features at minimum. Okay, so much for our formula and for the calculation. To distinguish vowels and consonants from one another, the superordinary feature, consonantal, is normally used. So vowels or vocalic features are all minus-consonantal, and their five features refer to the articulatory definition of vowels. We know that from the definition of cardinal vowels, you will see that in a second. Consonantal features, by contrast, are marked with a feature plus-consonantal. As we've just calculated, we need 10 features at minimum to define consonants, and by and large, the consonantal features are grounded in the active articulator. Let us start with vocalic features. The parameters used for the phonetic classification of vowels, high, low, front, back, can be translated into phonological features on a direct one-to-one basis. Vowels, which involve a high tongue position, are defined by means of the feature plus-high. Vowels that do not have a high tongue position are associated with a feature minus-high, and the same applies to low. Low vowels receive the feature low, and all those vowels which are not low are defined as minus-low. The feature back is obviously associated with back vowels, and the feature minus-back is associated with all front vowels. And last but not least, we have the feature round, which defines all those vowels that are produced with rounded lips, and minus round defines all those vowels that are produced with spread lips. Let us look at some selected vowels. Cardinal number one would be defined as plus-high, minus-low, minus-back, and minus-round. Cardinal number five or would be defined as minus-high, plus-low, it is a back vowel, plus-back, and minus-round. And if we take all cardinal number seven, we would get a vowel which is minus-high and minus-low. It is a back vowel and it is produced with rounded lips. Now the same applies to all cardinal six, it's also minus-high, minus-low, plus-back, and plus-round. So how do we distinguish these two from one another? Well remember, we need five features. And here is the fifth. In order to obtain the four degrees of height, high, mid-high, mid-low, low, the feature which is encoded in the system of cardinal vowels, the additional binary feature, ATR, which stands for advanced tongue root, was introduced. Now we can draw a distinction between mid-high and mid-low vowels and we have added feature number five as calculated by our formula. So here is O once more, cardinal number seven, which is now plus ATR, and O, which is identical with O except that it is now minus-advanced tongue root. Since all vowels are minus-consonant, they automatically imply the major class feature plus sonorant and plus syllabic. These features were already introduced in the sound pattern of English approach in our first e-lectron distinctive features. Let us now look at the consonantal features that are used today. Consonantal features make reference to the active rather than the passive articulators. This grounding is not arbitrary since only active articulators such as the tongue, the lips, the uvula and the glottis are believed to be associated with cognitive substance. The passive articulators by contrast remain motionless. Modern consonantal feature systems are based on the sound pattern of English approach offered by Noam Chomsky and Morris Halley. However, whereas in the sound pattern of English system all features were binary, today's system of consonantal features include single-valued or unary articulation features. Depending on their function within the system, the consonantal features can be subdivided into two classes. You know them already. The first of them is the so-called major class or the major class features. And here the feature sonorant defines all those speech sounds that have a high amount of sonority as plus sonorant. That is the three highest, vowels, liquids and nasals are plus sonorant. The two lowest fricatives and plosives are minus sonorant. The feature plus continuant defines vowels, glides, trills and fricatives as plus continuant. Plosives and laterals are minus continuant. And then almost self-explanatory, the feature voice correlates with vocal chord action. A speech sound has the feature plus voice. If the vocal chords vibrate it has the feature minus voice if the glottis is open. And the last major class feature is nasal. Obviously it refers to nasal consonants sounds are produced by lowering the vealum and allowing air to pass outward through the nasal cavity. Non-nasal or oral sounds are produced with the vealum raised to prevent the passage of air through the nose. The second class of features are cavity features, typical articulatory features. One of them is lateral and obviously this feature refers to those consonants that are produced with a lateral manner of articulation. The most familiar of which is of course the alveolar lateral consonants. They are produced to allow the air to pass over one or both sides of the tongue. The feature labial is a unary feature. That is a feature with a single value only. It is associated with all those consonants that involve the lips as an active articulator. Thus bilabial and labial dental consonants are assigned the feature labial. Let us now look at the typical placement feature. The feature coronal was discussed at length in our first e-lecture on distinctive features. It was introduced by Chomsky and Halle in the sound pattern of English approach and refers to the activity of the blade of the tongue. This involves all those sounds that are produced between the dental and the palatial alveolar region. The feature anterior is associated with all those coronal consonants which are produced with a primary constriction located at or in front of the alveolar ridge. That is with labial, dental or alveolar consonants. And the feature distributed well that's the other side of the coronal area. It refers to all coronal consonants that are produced with a constriction that extends for a considerable distance along the mid sagittal axis of the vocal tract. In other words, the feature distributed refers to the distribution of the tongue over the passive articulator typical for dental and post alveolar consonants. And finally we need a feature to define velar consonants and the feature that has been chosen here is referred to as dorsal. It defines sounds articulated with the body of the tongue against the velum. The use of the term dorsal rather than velar follows the principle to refer to the active articulator rather than the definition of features on the basis of passive articulators. Let us finally discuss the question why we need distinctive features. Well distinctive features can be motivated in several ways. On the one hand we can discuss the efficiency and scientific adequacy with which phonological phenomena can be described. On the other we may find psychological support for distinctive features a question which we will neglect in this particular e-lecture. So let's look at natural classes first. A natural class is formally defined as a family of segments that share the same set of properties. Well here is an example. Here we have three consonants. Obviously we all know these are voiced plosive consonants and with phonemes the maximum generalization for these consonants is exactly that. It is a class of voiced plosive consonants. Compare this definition with the far more informative class of distinctive features plus voice minus sonorant minus continuant. Such a class statement is required for example to state the process of spironization between vowels found in many languages. The process where a plosive consonant changes into a fricative while maintaining its place of articulation. For example classes like a da may become a da and eventually a za a da a za a za. Here is a second example. Now the voiced consonant shown here are required to state the process of final devoicing in German. With phonemes no further generalization than just listing them is possible. Sometimes phonologists refer to this set as the set of voiced obstrants. Using features however these segments constitute a highly simple and informative natural class namely the class of voiced and minus sonorant consonants. In these and many other cases the use of distinctive features allows a much more adequate class definition than the use of phonemes. Well and the formulation of phonological rules even though it may be of some use in pedagogical grammar if we use phonemes can be shown to be much more informative and much simpler if we use distinctive features. And even more so the linguistic value of such statements is in terms of phonemes often not helpful when we want to find particular sound patterns. Consider the following example in English plural formation. We have examples such as cat and cats dog and dogs and then bus buses rows roses church churches and judge judges. A proper statement requires that we specify the phonological context for the respective alomorphs. Using phonemes the morphophonemic rule that defines the context for the alomorphs would have to list the phonemes in each case. For example the use of the alomorph is requires the listing of the phonemes that can occur prior to the word boundary and are followed by the plural morpheme and this morpheme would then be realized as is with distinctive features. This is relatively simple. We only define a natural class for the most specific context that is the class of continual minus sonorant and plus coronal consonants. So if any consonant shares these three features it qualifies for the context that needs is as the plural alomorph. Well and the remaining two contexts are relatively simple. We only have to specify the feature plus or minus voice to define the particular alomorphs. Here is another example. The example of coalescent assimilation in received pronunciation. The examples are well known. We bet you becomes bet you we fed you might be realized as fed you miss you may become miss you please you may be realized as please you. With phonemes we have to list the particular elements that occur prior to the palatal approximate. T, D, S and Z may become Ch, J, Sh and J if a palatal approximate follows. Now compare this with a statement of distinctive features. Using features we can once more state a natural class that changes one feature. The feature anterior from plus anterior to minus anterior in the context prior to a palatal approximate. In these and many other cases the statement of the respective rule in terms of features allows a more adequate representation than a formulation based on phonemes. And the same applies to phonotactic statements. Phonotactic statements are concerned with restrictions on the patterning of sound segments in the syllables of any given language. Syllables in English for example impose constraints on their onset structure. That is we want to find out what can occur in the onset that is in the position prior to the peak. Here are some examples we have syllables with nothing in the onset. Syllables such as in. We may have one consonant in the onset. Ring is an appropriate example. We may have two consonants in the onset bring or even three spring. Now especially if we have more than one consonant but even with one consonant we have to postulate particular restrictions or constraints about what can occur in the syllable onset. Here is a special case. A consonant plus a labia vela approximate. Twin would be an example. Now if we list all possibilities of consonant clusters that involve a labia vela approximate we find this pattern. Dwell, queen, gwen, swell and thwart are possible and the remaining consonant plus approximate combinations are impossible. But what distinguishes this set that is possible from that which is impossible. In terms of phonemes we would have to list those combinations that are impossible. With features this is relatively simple. Consonants that have the feature labial cannot occur in succession in the syllable onset. Again phonological generalizations are much simpler with features than with phonemes. Well let us summarize. Our two e-lectures on distinctive features should have achieved the following main goals. First they should have given you an idea what distinctive features are, how they were introduced to phonology from a historical point of view and how they are used today. Secondly and this has been a major focus of this particular e-lecture I hope to have illustrated that especially in theoretical phonology distinctive features are more useful than phonemes. Classes and rules can be defined more efficiently and phonotactic statements can be made with ease. This does not mean that the phoneme is out as a fundamental segment in phonology. However from a theoretical point of view there are numerous arguments in favor of the distinctive feature.