November 25, 2002


Pursuing the Cascade Model



William Labov, University of Pennsylvania



Granted that language is a social fact, and not the property of any individual, it follows that a linguistic  change is equivalent to the diffusion of that change. An understanding of language change therefore demands an understanding of the mechanism of diffusion. It has long been observed that linguistic features spread outward from an originating center, but in a progressively weaker form as distance increases.[1]

 A major step towards the understanding of diffusion was made by Trudgill, in his studies of language change in the Brunlanes peninsula of Norway (1974). In Trudgillıs gravity model of diffusion, change spreads from the largest to the next largest city, in a predictable order, the influence of one city on another being proportional to the relative sizes of the city and inversely proportional to the distance between them. The model showed a good fit to the variable (ae) involving the progressive lowering and backing  of /ae/, and to the spread of London influence into Norfolk. Chambers and Trudgill 1980 develop the parallel palatalization of (sj) in Brunlanes with similar results.

In his study of 18 freshman girls at Northwestern University, Callary (1975) found that the raising of /ae/ in northern Illinois was correlated with the size of the speakersı home city. The efforts of Chambers and Trudgill to apply the gravity model to these data (1980: 201-2) met with partial success, in parallel with efforts of students in successive dialectology classes that I have taught. The more general pattern of the "cascade model" does appear to be supported:  that change proceeds from the largest city to the next largest city, and so progressively downward.  The problem of establishing the mechanism that produces this effect seems to be the same for the more specific gravity model and the more general cascade (or "hierarchical" ) model.

 It is not suggested all linguistic changes follow the same pattern of diffusion. Bailey, Wikle and Sand's investigation of Oklahoma located three distinct patterns (1993), showing that some changes spread geographically rather than hierarchically (the ³neighborhood² effect of Chambers and Trudgill).  The low back merger of /o/ and /oh/ is given as an example of the cascade model, though it is not demonstrated in the same detail as Trudgill's Norwegian studies. Boberg (2000) finds that this same feature does not follow the predictions of the cascade model across the U.S.-Canadian border, where the political (and structural boundary) is a categorical boundary., and  shows furthermore that the spread of American influence on foreign-(a) words is not governed by an urban hierarchy.

Other studies reflect the cascade model of diffusion with a smaller number of points of comparison. A clear example is Modaressiıs study of Tehran (1978), which was coupled with an auxiliary study of Ghazvin. Ghazvin is a city of considerable historical importance about150 km from the metropolis, but with a current population that is only a small fraction of Tehranıs half million.  Figure 1 shows the variable (an): the percent raising of standard /an/ to [un]. This is a well known characteristic of the Tehran dialect of Farsi, fairly stable in its age distribution. All age groups from Tehran show a high frequency of the vernacular variant in casual speech, but a reduction to vanishingly small levels for controlled speech. There is some suggestion of change in apparent time, with speakers over 50 somewhat behind the others. The speakers from Ghazvin follow the same pattern at a lower level, indicating that the variable may have diffused outward from the capital to the smaller city, and may still be continuing to do so.


Figure 1. Percent raising of (an) in the Farsi of Tehran and Ghazvin.



The Atlas of North American English has traced the progress of a number of linguistic changes in progress (Labov, Ash and Boberg. in press).  Of these, the Northern Cities Shift is the most likely candidate for a study of the cascade model, since it was first discovered in the major cities of Chicago, Detroit and Buffalo, and is now seen to cover a vast area involving many cities (71 cities with a population of 17,000,000 people in a territory of 33,000 square miles). This shift is a rotation of five vowels of English in the pattern of Figure 2.


Figure 2. The Northern Cities Shift


. The earliest and most extended elements of the change involve the raising and fronting of /ae/ and the fronting of /o/, followed by the lowering of /oh/ to low back position. The most recent changes are the lowering and backing of /e/ and the backing of /^/ to the position formerly occupied by /oh/.

The NCS is found in the North (the broken isogloss in Figure 3).a dialect region defined by the conditions that permit the NCS to occur . These are (1) the relatively back position of /ow/ (F2 of the nucleus < 1200 Hz) and a lax  front nucleus  for /ey/ (F2 of the nucleus < 2200 Hz).[2]


Figure 3. The Northern Cities Shift defining the Inland North dialect, and the larger region of the North. EOD: F2(e) ­ F2 (o) < 375 Hz. The North: F2(ow) < 1200 Hz and F2(ey) < 2200 Hz.




Within the North, the dialect area known as the Inland North is defined by active participation in the NCS.  Since this  complex phenomenon involves five different vowels, the progress of the shift is best defined by indices that involve the relative movement of several elements. One such index is based on the fact that in the course of the NCS, /e/ moves back to mid center position, while /o/ moves forward to low center position; two vowels that were originally defined as front vs. back become closely aligned in the front-back dimension. Thus the EOD index of the progress of the NCS is the difference between F2 of /e/ and  F2 of /o/. In Figure 3, the solid circles represent speakers for whom F2(e) - F2(o) is less than 375 Hz. The solid isogloss defined by these speakers also defines the Inland North dialect area, ranging from western New York State  to southeastern Wisconsin, and including a corridor running from Chicago to St. Louis.

 In pursuit of the cascade model of linguistic change, we can ask whether there is evidence that the progress of the NCS is related to city size.. 

Table 1 gives some evidence that it is. The table gives eight indices of the progress of the NCS, with signs adjusted so that positive values show effects correlated with the direction of change. The age coefficients show the expected effect of the change for an age difference of one generation, or 25 years; the city size figures register the expected effect of a difference of 1,000,000 in city size. The first five indices are simple measures of mean formant positions:  the raising of /ae/ is registered by the lowering of F1 and the fronting of /ae/ by the raising of F2;  the fronting of /o/ by the raising of F2;  the lowering of /e/ by the raising of F1, and the backing of /e/ by the lowering of F2.  The EAEQ index is the percent of speakers for whom the relative positions of /ae/ and /e/ have become reversed in the course of the change;  that is, that /ae/ is higher and fronter than /e/.. The EOD measure involves the backing of /e/ and the fronting of /o/, as defined in Figure 3.  The UHO measure also involves the relative position of two phonemes: it is the difference between the F2 of  wedge /^/ and /o/. As the NCS progresses, this figure becomes increasingly negative.

         Since the earliest stages of the change, the three at the left, are almost completed, there is no significant age effect, but these significant effects appear strongly for the rest of the measures.  City size is a significant and uniform determinant of each stage of the shift, although it is somewhat smaller for EOD than for the other measures. A complementary table for all other 314 Telsur speakers outside of the North shows only three significant relations to city size, all quite small, and two in the opposite direction of the sound change. We can therefore conclude that the NCS is an urban phenomenon and is more advanced in the larger cities than smaller ones..


Table 1. Regression coefficients for eight indices of the Northern Cities Shift in the Northern region [N=126]. : Coefficient for age shows the expected effect for age differences of 25 years; for city size, the expected effect for a population difference of 1,000,000. All figures are significant at p < .05 or better..


                 F1(ae)       F2(ae)     F2(o)      F1(e)      F2(e)     EAEQ      EOD       UHO

Age                                                         20.0        26.0        35.0        90.5        61.2

City Size    25.7        43.7        39.1        18.4        39.1        29.6          6.0        66.2



This is not quite the same as concluding that diffusion of the NCS follows the cascade model.  Table 3 shows that the distribution of city sizes concentrates the largest cities heavily in the Inland North. All eighteen of the cities of over half a million are in that area;  on the other hand, 23 of the smaller cities of less than 50,000 population are outside of the Inland North. It is possible that the Inland North can be viewed as a homogeneous urban area in which change is diffused geographically, spreading steadily across the terrain. Table 3 shows that the situation is intermediate in this respect. For each index, there are three degrees of ordering among the four city size units. In other words, it is not a simple dichotomy between the Inland North and elsewhere.

Within the North, the Spearman rank correlation of city population with the NCS variables ranges from 1.9 to 2.44. This is considerably lower than the match of observation to prediction in Trudgillıs original study of Brunlanes, which show a correlation of 6.00, but it is a significant effect. On the other hand, Spearman rank correlations within the Inland North are vanishsingly small.. The obverse of this is sthat  the difference between the Inland North and the other areas is a very strong effect in the regression calculations.  When membership in the Inland North is added to the regression equations, the effect of city size loses significance except in the case of F2 of /e/.  Diffusion from city to city within the Inland North may have been the basic mechanism in the earlier stages of the shift, but now the area is remarkably uniform across the entire territory. The concentration of large cities in the Inland North is so great that their mutual influences may add up to a ceiling effect, producing the relatively uniform areas of the ANAE maps.


Table 2. City sizes in the Inland North and the North as a whole..

Size (100ıs)      Inland North        Other North        Total North

<50                              8                       23                       31

50-100                      20                         8                       28   

100-50                      25                       24                       49

>500                          18                         0                       18


Table 3. Mean values and standard deviations of three systematic indices of the progress of the NCS in the North.

      EOD                       EAEQ                            UHO. 

Size (1000ıs)                Mean    SD             Mean        SD                Mean      SD

<50                                 377      152            2.03        0.706               -78        263

50-200                            300      135            2.32        0.611               -74        117

200-500                          348      163            2.12        0.633               -41        133

> 500                              245      125            2.67        0.594               -19        126



The mechanism of the cascade model


The cascade model is well established as a mechanism of linguistic diffusion for some, but not all linguistic changes. Trudgillıs original examples from Norway have been supplemented by a number of examples of the diffusion of London English in England, and supported by Callary, Bailey et al. and Modaressiıs study of linguistic diffusion in Iran, The data from ANAE adds some large scale data to support the view that some linguistic changes.  spread across the larger speech community by the cascade model. It is therefore reasonable to ask what social mechanism is responsible for this effect.

In his original discussion on explanation, Trudgill suggests that attitudes and linguistic structure also have to be taken into account. Although there is no overt recognition of the NCS in the community, Eckertıs studies of social distribution in Detroit high schools (1999) show that the development of the NCS is tied to social category membership and gender, and the larger scale patterns of ANAE confirm these patterns. The importance of structural considerations is the central finding of the Atlas, The tight bundle of isoglosses that defines the southern limit of the NCS coincides with the North/Midland settlement line, and cuts across high concentrations of population density and high levels of communication. It can only be explained by the structural incompatibility of the vowel systems in the Northern and Midland regions (Labov in press).

The explanation of the cascade model itself must rest upon different considerations. Trudgillıs account focuses on ways of calculating distance;  the gravity model assumes that all influence weakens with increasing distance. It seems most likely that this weakening of influence is not due to psychological or social factors so much as the frequency of contact among speakers of the two cities. The assumption underlying this is Bloomfieldıs principle of density (1933:476), that people automatically and inevitably influence each otherıs language each time they speak to each other. The question remains, what mechanism produces the given frequency of contact among speakers from different cities?

There are two quite different mechanisms that might produce this result. One is that people from the smaller city come to the larger city. The attractions of the larger city are obvious:  employment, shopping, entertainment, education, and so on. To trace the linguistic consequences of such movements, we would have to know which members of the community travel for which purpose, and in each case how much linguistic contact they would have with speakers of the larger cityıs dialect. On the other hand, these representatives of the larger city may travel outwards to the smaller city, and bring with them the dialect features being diffused. The reasons for such outward movement are not so obvious. The most systematic travel is connected with the distribution of goods:  salesmen, truckers, and other representatives of the manufacturing firms of the larger city.

We can get some insight into this process by comparing the social distribution of a linguistic variable in the larger and smaller city, Figure 4 shows the relation of education to the variable (an) in Tehran and Ghazvin, originally presented in Figure 1. It is apparent that in the original pattern of Tehran, (an) is negatively correlated with education:  those with the least education show the highest values. In Ghazvin, it is the opposite. More importantly, the value of (an) for those with some college match the values in Tehran quite closely.   The inference can be drawn that it is the group with higher education in Ghazvin who have direct contact with speakers of the Tehran dialect, and that this feature is then diffused from them downward in the educational scale. Contact has led to diffusion, but the source and direction of the contact leads to a reversal of the sociolinguistic norms in Ghazvin.


Figure 4. Relation of education to raising of (an) in Tehran and Ghazvin. (source: Modaressi 1978)



So far, we are making inferences from data that reflects a process already accomplished. In what follows, I will draw upon the real time studies of the diffusion of a variable that reveals in some detail the originating mechanism of the cascade model. The data here concerns the unique lexical item, the name for the sandwich now generally known as a Œsubmarineı or Œsubı sandwich throughout the United States. In 1967, two Cornell sociologists published a study of these terms based upon an examination of the listings and advertisements in the telephone directories across the United States.  At that time, the submarine sandwich culture had only recently been established as a cultural item, and the majority of cities did not show any advertisement at all.  In the years that followed, this item has been so widely developed that advertisements listing them can be found for every city under a number of headings:  restaurant, sandwich, pizza, delicatessen, caterers. Following Eames and Robboy, I have traced the development of this vocabulary in real time studies of telephone directories, with the help of the collection in the Library of Congress.

The submarine is a sandwich on a long roll, split in half. In its basic form it is filled with cold a variety of cold cuts, cheese, shredded lettuce, peppers, onions, salt, pepper, oil and vinegar. In addition to the general term submarine or sub, local terms in current use are grinder (New England outside of Boston), wedge (Westchester County), hero (New York City), torpedo or torp (Albany and Troy), hoagie  (Philadelphia), zeppelin or zep (Norristown, PA), poor boy (New Orleans). Here I will be concerned with the spread of hoagie from Philadelphia to the next largest city in Pennsylvania, Pittsburgh. Figure 5 shows the use of hoagie in Philadelphia and Pittsburgh, with the intervening and surrounding areas dominated by submarine. It is based upon responses to a questionnaire gathered by students in Philadelphia: these were the first terms used by subjects in identifying a long sandwich of this kind. One can see the zone of influence of Philadelphia which is evidently the result of contagious diffusion, and the concentration of hoagie in the city of Pittsburgh.


Figure 5. Distribution of terms for Œsubmarine sandwichı in Pennsylvania.


The sandwich called hoagie originated in Philadelphia in sandwich and ice cream shops, along with the Philadelphia steak sandwich or cheesesteak. Early telephone listings show that it became generalized in Philadelphia shortly after World War I, as shown in Table 4. The various spellings have been cited many times by those searching for the etymology of this term, but it is evident that by 1955, it had become focused on hoagie or hoagy. The growth of advertisements with this form demonstrate a clear consolidation by the mid 1950ıs.


Table 4. Lexical stem of Œhoagieı in Philadelphia telephone listings.


                 hogg-      hoog-     hog-       hoag-  submarine

1945              3            1            1

1950            10                         2            1

1955              4                         6          47            1


At the same time, another feature of popular cuisine was being established in Philadelphia and elsewhere. In the 1930ıs, the ancestor of the pizza was commonly known as a tomato pie or some equivalent. Advertisements referring to this item began to appear in the same post-war period, as shown in Table 5.  The now universal term pizza did not eliminate tomato pie until well after 1960, but it is apparent that its growth and establishment as an important cuisine elemenete dates from the mid 1950ıs. In the year 1960, the telephone directory established a separate section for pzza.


Table 5. Lexical form of Œpizzaı in Philadelphia telephone listings

                         Tomato Pie    Pizza        Pizza/          Pizzeria     Pizza Pie

          Section                                      Tomato Pie

1931 Restaurant

1944      ³              1

1945      ³              1

1950      ³              6                5                1                4

1955      ³              6                1                6                7                4

1960  Pizza            6                1                5                4                1



For the past several decades, the heaviest concentration of advertisements for submarine sandwiches is to be found in the pizza section of the directories. But this association was not so strong in the formative period of the mid 1950ıs in Philadelphia. Table 6 lists the various combinations of items to be found in small advertisements in the Philadelphia Restaurant section in 1955. The combination of pizza and hoagie was a minority pattern at that time:  separate advertisements were in the majority.


Table 6. Small advertisements in Philadelphia Restaurant section: 1955.

Pizza       16          Pizza & Hoagie      1

Hoagie       5          Pizza & Sub          1          Pizza & Hoagie & Sub    8

Sub           6          Hoagie & Sub      27



With the help of the year telephone directories, it is possible to identify the exact year in which hoagie spread to Pittsburgh, and the mechanism by which this happened. . Table 7 shows the information gleaned from the Restaurant section of the Pittsburgh yellow pages from 1961 to 1966. The story begins with Grabını Go Pizza, who introduced a small ad in 1961-2 for hoagies. The next year, they were simply listed, but in the three years following they ran an ad for a submarine sandwich. Grab Œnı Go was unique in switching back to submarine after initiating a practice followed by everyone else. The other pizza listing in 1961-2 made no mention of a submarine sandwich.

In the following year, Village Pizza introduced an ad that included Hoagies, and maintained this practice consistently in the following years. In the following directory for 1964, Frank & Bettyıs Pizza Shop followed along and Patıs Pizzeria added a mention of hoagies in their ad.. The next year, 1965, showed a row of 7 hoagie ads, with only Grab Œnı Go advertising submarines. In 1966, three additional stores added their ads for hoagies.

It is also noteworthy that in 1965, Aspinwall Piza added as a second title for their ad, Augieıs Hoagies, and the following year, Andyıs Pizza added the label, Famous Hoagie.  It is evident that hoagies had become quite p;opular in Pittsburgh. Although the total listings in the restaurant section grew by 50% during this period, the expansion of hoagie is an independent and larger phenomenon.

The expansion of hoagie in Pittsburgh is entirely contained within the growing pizza complex:  no ads for hoagies appeared in any stores that did not feature pizzas. This is quite different from Pennsylvania, as Table 6 showed. It is not accidental that the term hoagie spread to Philadelphia in conjunction with the expansion of the pizza complex.  This is common throughout the United States, and is a cultural phenomenon of some interest.  However, the submarine sandwich has recently expanded independently, through such enterprises as the Subway chain.


Table 7. Diffusion of hoagie to Pittsburgh from 1961 to 1966.

H = hoagie; S = sub(marine). * = listing, no ad; # = ad, no mention of H or S.


                                                         1961-2       1962-3       1964          1965          1966

Grab Œnı Go Pizza                              H               *                S                S                S

Patıs Pizzeria                                      #                #                H               H               *

Village Pizza                                                          H               H               H               H

Campitiıs Don Pizzeria                                         #                #                H               *

Luigiıs Pizza                                                         *                *                H

Frank & Bettyıs Pizza Shop                                                   H               H               H

Aspinwall Pizza/Augieıs Hoagies                                                             H               H

Mac Tonyıs Nationwide                                                                           H               H

Luaraıs Restsaurant & Pizza                                                                                       H

Brookline Pizza                                                                                                           H

Arudyıs Pizza/Famous Hoagie                                                                                   H


Total listings in Restaurant section     68              75              75              91              93



The trend started by Village Pizza suggests that this particular merchant had a certain influence in the community. This suggestion is strongly reinforced by the fact that Village Pizza had a separate ad for pizza ovens. At the same time that they were competing with other pizza stores for the retail business, Village Pizza was supplying their competitors with the basic equipment needed to start and stay in business. It seems reasonable to suggest that these ovens were manufactured in Philadelphia, and that Village Pizza had a special connection with that city.

If this is the case, it is an example of how commercial contacts can activate the cascade model. Without knowing more about the owners of Village Pizza, we cannot say whether this is an example of a local Pittsburgh people going to Philadelphia and acquiring the use of the term there, or whether they or other people originally came from Philadelphia. In one case I was able to pursue this question, when I noted that a shop in Boulder, Colorado featured a hero sandwich.  I got the owner on the phone, and asked him if he had come from New York.  He was indeed a New Yorker..  When I asked him why he had used hero instead of sub he said, ³Well I figure that if they donıt know what it is, they can ask.²  At the end of the conversation he added, ³To tell the truth, I knew when I started up that I should put sub on the sign.  But I just couldnıt.²

This maintenance of metropolitan terminology is the obverse of a local personıs admiration for the practices of the big city. A certain part of the mechanism of diffusion can be accounted for by attitudes of this kind, as Trudgill originally maintained.  But numbers count. In the years since the Eames and Robboy study, many local terms for submarine sandwich have been extinguished by the spread of sub.  The big city competitors have held their ground:  hero in New York City, hoagie in Philadelphia, while zep and torp have become associated with the speech of the elderly. [3]

There can be no doubt that linguistic change and the acquisition of new forms is most vigorous and active in the adolescent years, and that language learning is slower in the years that follow (in press). Most of the processes discussed above reflect influences among adults, and reflect a slower and more erratic process by which language forms diffuse outward from their originating center. To understand the cascade model more deeply, we will have to know more about who travels where in what kind of enterprise. More importantly, we need to know how adults can influence the speech of others and shift their own practices, long after the critical period of language learning is over.




Bailey, Guy, Tom Wikle, Jan Tillery and Lori Sand. 1993. Some patterns of linguistic diffusion.. Language Variation and Change 5:359-390.

Bloomfield, Leonard. 1933. Language.. New York: Henry Holt.

Boberg, Charles 2000. Geolinguistic diffusion and the U.S.--Canada border. Language Variation and Change 12:1-24.

Callary, R. E. 1975. Phonological change and the development of an urban dialect in Illinois.  Language in Society 4:155-170.

Chambers, J.K. & Peter Trudgill. 1980. Dialectology.  Cambridge:  Cambridge U. Press.

Eames, Edwin and Howard Robboy. 1967. The sociocultural context of an  American dietary item.. The Cornell Journal of Social Relations 2:63-75. Reprinted in H. Robboy et al. (eds.), Social Interaction. New York: St. Martin's Press, 1979. Pp. 521-530.

Eckert, Penelope. 1999. Linguistic Variation as Social Practice. Oxford: Blackwell.

Labov, William. In press.  Driving forces.  In B. Laks and D. Simeoni (eds), Proceedings of the Conference on Origin and Evolution of Human Language. Paris, 202.

Labov, William, Sharon Ash and Charles Bobeg.  In press. Atlas of North American English.  Berlin:  Mouton/de Gruyter.

Trudgill, Peter.. 1974. Linguistic change and diffusion: description and explanation in sociolinguistic dialect geography. Language in Society 3:215-246.


[1] It is not obvious that it should be so; in fact, it has been proposed that rules or constraints tend to generalize as they diffuse, and affect a wider range of linguistic forms (19??).

[2]It appears that the full raising of /ae/ to upper mid position is inconsistent with a  fronted near-monophthongal form of /ey/, and the backing of /^/ is inconsistent with the fronting of /ow/.

[3] In 1997, I visited Troy, NY, to see if the term torpedo was surviving Torpedos was featured in a small delicatessen owned by an elder Italian man. But in a fast food chain called Mr Subbıs, neither of the two young women behind the counter used the term or thought their customers did.  One said that her grandfather said torpedo.