3.1.1 Formant analysis of monophthongs in Māori

The F1/F2 vowel spaces for the three speaker groups and for female and male speakers can be seen overlaid in Figure 1. Only the vowel centroids are plotted. Overall it can be seen that the shapes of the vowel spaces for all speaker groups, regardless of gender, are essentially triangular, with the point vowels being /iː aː oː/. There is also no noticeable difference in the overall extent of the vowel spaces between the three groups, for either gender, with the exception of the high vowels /i iː u uː/ for the young female speakers. These speakers’ high vowels are noticeably lower in the F1/F2 vowel space than the vowels of either of the elder groups. However this lowering is unlikely to be a sound change. Nor do we believe it an effect of age, as we would expect to see an increase for all F1 values if it were (Torre & Barlow Reference Torre III and Barlow2009, Reubold, Harrington & Kleber Reference Reubold, Harrington and Kleber2010). We can see no motivation for a lowering of /iː i/ and /uː u/, but since these speakers’ English fleece and goose vowels are also lower than those of the historical and present-day elders (see Figure 4), we consider that it is most likely to be a speaker effect.Footnote ¹⁰ This is further supported by the ANOVA which shows that, although there are significant differences between the vowels, there are no significant group effects for the women. However for the male speakers there were group effects (F(2,28) = 7.0, p < .01) with the F2 for the present-day elders being significantly lower (and the vowels farther back) than those for the young speakers (t(17.5) = –3.1, p < .05). There are also significant age by vowel interactions for all the data (female F1: F(7.5,101.3) = 7.0, p_GG < .001; female F2: F(6.4,86.5) = 9.2, p_GG < .001, male F1: F(7.3,102) = 5.7, p_GG < .001; male F2: F(6.5,91.6) = 11.7, p_GG < .001). The significant vowel movements identified from Bonferroni corrected t-tests are given in Table 3. For the male speakers the significant movements were the F1 of /e eː/ being significantly lower, and therefore the vowels phonetically more raised, for the Y speakers than the two elder groups and the F2 of /u uː/ being significantly higher, and therefore the vowels being fronter, for Y than PE. The F2 of /uː/ is also significantly higher for Y than HE. The fronting of /u uː/ over time was also significant for the female speakers, with the F2 of /u uː/ being significantly higher and the vowels again being fronter for the younger speakers than the present-day elders, F2 was also significantly higher for /u/ for Y compared to the historical elders. However there was no significant phonetic raising of /e eː/. Instead, for the women speakers, F1 for /i iː u uː/ was significantly higher (and the vowels lower) for the younger speakers than for the historical and the present-day elders.

Figure 1

The centroids of the Māori monophthongs in F1/F2 space for the historical elders (black), present-day elders (dark grey), youth (light grey) for female (left) and male (right) speakers.

Table 3

The values of the significant t-tests for the formants for Māori monophthongs for the female and male speakers.

*p ≤ .05, **p ≤ .01, ***p < .001

3.1.2 Distance measure analysis

The post-hoc analysis of the formant results indicated that a new method for measuring sound change was required. From Figure 1 we saw that the most obvious change over time was the fronting of the /u uː/ pair for both the female and male speakers. There was also a raising of the /e eː/ pair. This can clearly be seen for the male speakers, but it is also present for the female speakers, taking into account the change in the relative distance between /e eː/ and /iː/ over time. Post-hoc t-tests on the formant values revealed that there was a significant increase in F2 of /u uː/ over time for both genders. On the other hand, it was difficult to establish the extent of the front vowel raising over time, as the lowered /i iː/ and /u uː/ for the young female speakers created a problem when we were trying to establish the statistical significance of the vowel movements by using the traditional approach of analysing the first and second formant values of the vowels (e.g. Watson et al. Reference Watson, Maclagan and Harrington2000, Harlow et al. Reference Harlow, Keegan, King, Maclagan, Watson, Stanford and Preston2009). In comparison to the male speakers, the movement of /e eː/ was not significant for the female speakers, even though it was quite clear that a change had taken place over time as shown by the relative distances between /e eː/ and /iː/ in Figure 1. This led us to reflect on the efficacy of the entire approach of considering only the first and second formant values when looking at sound change in vowels. Visual comparisons of F1/F2 plots always involve taking the entire two dimensional vowel space into account when the extent of the vowel movements are considered, and we attempted to replicate this in the vowel space movement measure we adopted.

The vowel movements we have been looking at involve shifts of vowels either rising up the front edge of the vowel space, or moving along the top edge of the vowel space. Although these movements are primarily in F1 and F2 respectively (see Stevens Reference Stevens1998), there is always a noticeable movement on the other axis, particularly for the rising front vowels. Statistical analysis on the separate F1 and F2 measures is problematic, as vowel movements are never strictly in one dimension or the other, nor are F1 and F2 really independent. In terms of articulation there is rarely only one articulator that moves as a speaker goes from one vowel to the next. For example the raising of a front vowel involves changes to both the jaw opening and the tongue position, and both F1 and F2 are affected by these moves. Therefore to measure vowel movement, we decided to use Euclidean distance measures, which incorporate both F1 and F2 movements.Footnote ¹¹

In an F1 vs. F2 vowel space, when the first and second formants for vowel x are (x_F1,x_F2), and for vowel y are (y_F1,y_F2), then the Euclidean distance (EU (x, y)) between vowel x and y is calculated by the formula in (1):

1. (1) $EU( {x,\!y}) = \sqrt {{{( {{x_{F1}} - {y_{F1}}})}^2} + {{( {{x_{F2}} - {y_{F2}}})}^2}} $

Due to the nonlinearity of the frequency scale, the range of frequencies for F2 is always considerably larger than that for F1. This means that the Euclidean distances calculated from raw F1 and F2 values would place more emphasis on F2 differences than F1 differences, on account of the larger frequency range in Hertz for F2. This is often addressed visually in vowel space plots, as although the plots are usually square in shape, the frequency range for F1 is typically only a third of the range used for F2 (see, for example, Figure 1 above). A better way is to explicitly account for how the signal is auditorily processed and use the perceptually motivated Bark scale (Traunmüller Reference Traunmüller1990) for the formant frequency values. This then counters the undue influence of F2 and ensures that F1 and F2 values have comparable impacts on the Euclidean distances. Calculating Euclidean distances from Bark-scaled formant values is a reasonably common approach (e.g. Harrington Reference Harrington2006, Löfqvist, Sahlén & Ibertsson Reference Löfqvist, Sahlén and Ibertsson2010, Neumeyer, Harrington & Draxler Reference Neumeyer, Harrington and Draxler2010).

Euclidean distances of formants are being used increasingly to measure the size of the vowel space (e.g. Ng, Chen & Sadaka Reference Ng, Chen and Sadaka2008, Löfqvist et al. Reference Löfqvist, Sahlén and Ibertsson2010, Neumeyer et al. Reference Neumeyer, Harrington and Draxler2010, Kaipa et al. Reference Kaipa, Robb, O'Beirne and Allison2012, Sasisekaran & Munson Reference Sasisekaran and Munson2012). However we wish to measure the extent of a vowel movement relative to a vowel space, not the actual vowel space itself. Harrington, Kleber & Reboul (Reference Harrington, Kleber and Reubold2008) use Euclidean distances to measure the fronting of /u/ over time, comparing the distances of /u/ to the point vowels /i/ and /a/ in order to determine how these change over time. This gives a good sense of vowel movement within a vowel space, and we will use a similar process. Although since we wish to measure the movement of more than one vowel, we take a slightly different approach.

Boë et al. (Reference Boë, Perrier, Guérin and Schwartz1989) proposed a maximal F1/F2 vowel space based on known articulatory constraints. Clearly any vowel shifts must occur within this space. In fact vowel shifts would be expected to occur within the vowel space of a particular language, and a vowel shift is described in terms of how the vowel position has changed over time relative to the entire vowel space, or more typically a side of the vowel space. It would be possible to use the model proposed by Boë et al. (Reference Boë, Perrier, Guérin and Schwartz1989) and calculate the extent of the vowel space in the F1/F2 plane for a given language. However a simpler approach is to define the vowel space by its point vowels, and calculate the Euclidean distance between the point vowels. This approach was also adopted by Kaipa et al. (Reference Kaipa, Robb, O'Beirne and Allison2012), although there they were investigating the speaker's recovery of a full vowel space after a glossectomy.

The Māori vowel space is essentially triangular, with the point vowels being /iː aː oː/. We propose to use the sides of the vowel space triangle as reference points to capture the formant movement.Footnote ¹² The choice of which side to use depends on the direction of the movement to be measured. For Māori there is no evidence that /aː/ or /oː/ have changed over time in this study, nor has /iː/ for the male speakers (see Table 3). In all these cases none of the post-hoc t-tests between groups were significant.Footnote ¹³ However the young female group do have /i iː/ and /u uː/ significantly lower in the vowel space than the elder groups even though their /oː/ is similar to the elders’ /oː/. As already noted, we consider that this is most likely to be an unexplained speaker effect rather than a sound change.

To calculate the vowel space movement (VSM) measures, we select the vowel to be investigated, x, identify the reference point vowel, y, and the reference side of the vowel triangle in F1/F2 space. The reference side of the vowel triangle goes between the reference point vowel y and another point vowel z. For each speaker we calculate the centroids of the three vowels (the two point vowels related to the reference side of the vowel triangle, and the vowel to be investigated). We then obtain the Euclidean distance between the reference point vowel and the vowel of interest, EU(y,x), and the Euclidean distance of the reference side of the vowel triangle, EU(y,z). The Euclidean distances are calculated from the first and second formants given in the Bark scale. Finally we take the ratio of the two Euclidean distances, thus yielding a VSM measure in (2)

1. (2) Equation 1

   $VSM = \frac{{EU( {y\hbox{\scriptsize\it,}x})}}{{EU( {y\hbox{\scriptsize\it,}z})}}$

Part (a) of Figure 2 illustrates the distances used to calculate a single VSM for a vowel in the front part of the vowel space that is involved in a fronting and raising movement. This VSM is calculated by:

1. (3) Equation 2

   $VSM_F(x) = \frac{{EU( {i\itscriptlengthmark \hbox{\scriptsize\it,}x})}}{{EU( {i\itscriptlengthmark \hbox{\scriptsize\it,}a\itscriptlengthmark})}}$ where VSM_F(x) is the vowel space measure for vowel x, with respect to the front side of the vowel triangle (i.e. the distance between the point vowels /iː/ and /aː/), the subscript F indicates the front of the vowel triangle, and /iː/ is the reference point vowel, y

Part (b) of Figure 2 illustrates the distances used to calculate a single VSM for a high vowel involved in a fronting movement. This VSM is calculated by:

1. (4) Equation 3

   $VSM_T(x) = \frac{{EU( {i\itscriptlengthmark\hbox{\scriptsize\it,}x})}}{{EU( {i\itscriptlengthmark\hbox{\scriptsize\it,}o\itscriptlengthmark})}}$ where VSM_T(x) is the vowel space measure for x, with respect to the top side of the vowel triangle (indicated by the subscript T) which is between point vowels /iː/ to /oː/, and the reference point vowel is /iː/

The final plot in part (c) of Figure 2 illustrates the distances used to calculate a VSM for a back vowel that is involved in a vowel shift; this VSM is calculated by

1. (5) Equation 4

   $VSM_B(x) = \frac{{EU( {o\itscriptlengthmark\hbox{\scriptsize\it,}x})}}{{EU( {o\itscriptlengthmark\hbox{\scriptsize\it,}a\itscriptlengthmark})}}$ where VSM_B(x) is the vowel space measure for x, with respect to the back of the vowel triangle (indicated by subscript B) which is between the point vowels /oː/ and /aː/, and the reference point vowel is /aː/

Figure 2

The distances used to calculate a VSM in the (a) front (b) top and (c) back parts of the vowel space, as defined by the point vowels

To measure the extent of front vowel raising in Māori (i.e. the /e eː/ movement) the reference is the side of the triangle between the high front vowel and the low central vowel, that is the distance between /iː/ and /aː/, and we would calculate VSM_F(e) and VSM_F(eː) as per equation 2 (in (3) above) for each speaker. We then determined whether there were significant differences in the VSM for the three speaker groups (HE, PE, and Y). To measure the fronting of the high vowels in Māori (i.e. the /u uː/ movement), we calculated a similar ratio, but used as a reference distance the side of the vowel triangle between the high back vowel and the high front vowel, that is the distance between /iː/ and /oː/. We then calculated VSM_T(u) and VSM_T(uː) as per equation 3 for each speaker, and then investigated the overall speaker group differences as for /e eː/. The smaller the VSM value, the closer the vowel of interest (vowel x) is to the reference point vowel y, which is /iː/ for both the raising and fronting.

The VSM has the further advantage that it provides a method of speaker normalising vowel data based on each speaker's own vowel space. Firstly, using a perceptually based frequency scale has been shown to remove a certain amount of non-speaker-specific information from the signal (Bladon & Lindblom Reference Bladon and Lindblom1981). Secondly, by representing a vowel position as a relative measure made in comparison to an appropriate side of the vowel space, the VSM has the effect of speaker normalising the data.

3.1.3 Measures of vowel movement in Māori monophthongs

As discussed in the previous two sections, the vowels that showed most movement in the F1/F2 plots were /e eː/, and /u uː/, and it is those that we focus on in this section.

The vowel space movement (VSM) measures for these vowels are shown in box plots in Figure 3. The data for the female speakers are presented on the top and those for the male speakers are on the bottom. The far left plots are for the /eː/ analysis, and the centre left plots are for the /e/ analysis. To ensure the plots are clearly understood we will discuss in detail the top far left plot which shows the median VSM_F(eː) for the female speakers.

Figure 3

VSM_F(eː) (far left), VSM_F(e) (centre left), VSM_T(uː) (centre right), and VSM_T(u) (far right) in Māori for the three speaker groups, for the female speakers (top) and male speakers (bottom), where H = historical elders, P = present-day elders, Y = young group, and the y-axis shows the VSM ratios. The dots in the centres of the boxes represent the median VSM values, the boxes enclose from the upper to the lower quartiles and the whiskers represent the 95th and 5th percentiles.

The median for the historical elders is 0.227. Thus the Euclidean distance for /iː/ and /eː/ is 22.7% of the Euclidean distance between /iː/ and /aː/. The smaller the VSM_F value is, the closer the vowel of interest (/eː/ in this case) is to /iː/. The median VSM_F(eː) for the present-day elders is 0.185, which means the Euclidean distance between /iː eː/ is 18.5% of the Euclidean distance between /iː/ and /aː/. Therefore /eː/ is closer to /iː/ in the vowel space for the present-day elders, than for historical elders. This can also be clearly seen in the formant plots in Figure 1. The VSM_F(eː) for the young speakers is 0.065, which means the Euclidean distance between /iː eː/ is only 6.5% of the distance between /iː/ and /aː/: that is, for the young speakers, /eː/ is closer to /iː/ than for both the present-day elders and the historical elders. In summary the smaller the VSM_F(eː), the closer the vowel is to /iː/, i.e. the more it is raised and fronted.

It can be seen quite clearly in Figure 3 that the young speakers, regardless of gender, always have the lowest median VSM. That is, both / e / and /eː/ are closer to /iː/ for the younger speakers, compared to both elder groups. The VSM differences between the young and elder groups are all significant according to Bonferroni corrected t-tests (see Table 4). Although there is a trend for the median VSM_F of the historical elders all to be greater than those of the present-day elders, the differences are never significant. Overall it can therefore be seen that the raising of both /e eː/ over time in Māori for both female and male speakers, as observed in Figure 1, is significant.

Table 4

The values of the significant t-tests for VSM_F(eː), VSM_F(e), VSM_T(u), and VSM_T(uː).

*p ≤ .05, **p ≤ .01, ***p < .001

The fronting of /u uː/ can clearly be seen in the boxplots of the VSM_T , which are in the centre right and far right in Figure 3 (and observed in Figure 1). VSM differences between the young and elder groups are also significant for this vowel pair (see Table 4). Recall in this analysis the top of the vowel triangle was the reference side of the vowel space, and /iː/ remained the reference point vowel, that is we calculated VSM_T(x) using equation 3. The historical elders’ median VSMs for /u uː/ were between 0.64 and 0.78, whereas the median values for the young speakers were between 0.3 and 0.51. Consequently /u uː/ tokens for the younger speakers are considerably closer to the reference point vowel /iː/ than those from the elder speakers.

3.1.4 New Zealand English monophthongs

The NZE F1/F2 vowel spaces for the three speaker groups for both genders can be seen in Figure 4. The distribution of the vowels is similar to those of other NZE speakers of a comparable age (e.g. Gordon et al. Reference Gordon, Campbell, Hay, Maclagan, Sudbury and Trudgill2004, Watson et al. Reference Watson, Maclagan and Harrington2000). There was a significant interaction for vowel and group (female F1: F(9.4,113.3) = 12.8, p_GG < .001; female F2: F(6.2,74.3) = 9.7, p_GG < .001, male F1: F(7.9,86.5) = 9.7, p_GG < .001; male F2: F(9.5,104.5) = 12.2, p_GG = 0). Also, as for the Māori vowels, there were speaker group effects for the F2 of the male speakers (F(2,22) = 5.2, p < .01), with the present-day elders having a significantly lower F2 (and phonetically farther back vowel) than both the young (t(15.1) = –2.9, p < .05) and the historical elders (t(12.2) = –2.9, p < .05).

Figure 4

Centroids for the NZE vowels of the three different speaker groups: historical elders (black), present-day elders (dark grey), and youth (light grey) for female and male speakers.

From Figure 4 it can be seen that, for both the genders over time, the trap and dress vowels are raising, the kit vowel is retracting and lowering, and the goose vowel is fronting. Trap raises from [ ] to [ɛ] for the men and from [ ] to [ ] for the women, dress raises from [ɛ] to [e] for the men and from [ ] to [e] for the women, kit moves from [ɪ] to [ ] for the men and from [ɪ] to [ ] for the women and goose moves from [ ] to [ ] for the men and from [ ] to [ ] for the women.

Post-hoc t-tests calculated from F1 and F2 (see Table 5) show these movements are all significant for the male speakers, and the kit and goose movements are significant for the female speakers. These are all well-known changes in NZE (e.g. Watson et al. Reference Watson, Maclagan and Harrington2000, Gordon et al. Reference Gordon, Campbell, Hay, Maclagan, Sudbury and Trudgill2004). However as with the Māori vowel space, the high vowels fleece and goose have considerably higher F1 values for the young female speakers than for either of the female elder groups, so that fleece is closer to start for the young females than for the older speakers. This reduced vowel height difference may give the visual impression that dress and trap have hardly risen for the young female speakers. Because fleece and dress are so close together for the young female speakers in Figure 4, we checked the tokens auditorily to see whether dress could now be confused with fleece but they were still clearly distinct.

Table 5

The values of the significant t-tests for the formants for New Zealand English monophthongs for the female and male speakers.

*p ≤ .05, **p ≤ .01, ***p < .001

The NZE vowel movements that potentially have some link with vowel movements in Māori are those involving dress, trap, and goose. These three NZE vowels have moved over time in a similar manner to the Māori vowels which are in a similar position in the F1/F2 vowel space. In contrast, while the NZE kit vowel was in a similar position to the Māori /i/ for the historical elders, its path after that point has diverged markedly. There has been considerable movement in the NZE kit vowel over time (retracting and lowering in F1/F2 space); in comparison, /i/ in Māori has not changed its position relative to /iː/ at all (see Figure 1 and Gordon et al. Reference Gordon, Campbell, Hay, Maclagan, Sudbury and Trudgill2004).

Therefore we will focus our attention on the movements of dress, trap, and goose using the VSM to analyse the extent of the movement (see Section 3.1.2). As the NZE vowel spaces are also triangular, we use an approach similar to the one used to measure Māori vowel movement. Post-hoc t-tests on F1 and F2 indicated that the point vowels start and thought have not changed over time for both men and women, and nor has fleece for the male speakers. Fleece has a significantly higher F1 for the young women compared to the female historical elders (see the comments just above). To measure front vowel raising (i.e. to calculate VSM_F( dress ) for dress and VSM_F( trap ) for trap) we adapted equation 2. We took the reference as the front side of the vowel space, and calculated the Euclidean distance between the point vowels fleece and start (with fleece being the reference point vowel y). The results of this analysis are shown in Figure 5, and the t-test results are presented in Table 6. The left most plot in Figure 5 is for the VSM_F( dress ) for the female (top row) and male (bottom row). Once again the youngest speakers have a lower VSM_F( dress ), compared to the two elder groups, which indicates that dress is closer to fleece for the young speakers than for the two elder groups, and these differences are significant (see Table 6). The two middle plots similarly show the VSM_F( trap ). The Y groups’ trap vowels are also significantly closer to fleece than for the two elder groups’ vowels (see Table 6). A consistent difference between the two elder groups can be observed in Figure 5, with the historical elder medians always greater than those for the present-day elders, however these differences are not significant except for goose for the female speakers (see Table 6).

Figure 5

VSM _F ( dress ) (left), VSM_F( trap ) (middle), and VSM_T( goose ) (right) for female (top) and male (bottom) speakers, where H = historical elders, P = present-day elders, Y = young group, and the y-axis shows the VSM ratios. The dots in the centres of the boxes represent the median VSM values, the boxes enclose from the upper to the lower quartiles and the whiskers represent the 95th and 5th percentiles.

Table 6

The values of the significant t-tests for VSM_F( dress ) _, VSM_F( trap ) and VSM_T( goose ).

*p ≤ .05, **p ≤ .01, ***p < .001

It is interesting to observe in Figure 5 that the median VSM_F( dress ) for the male HE is 0.36 and the median VSM_F( trap ) for the male Y group is 0.38. These values are very similar, and suggest the two vowels may occupy a similar position in the F1/F2 vowel space. It can be seen in Figure 4 that this is the case, with the centroid for the younger male speakers’ trap vowels in a very similar space to the centroid of older male speakers’ dress vowels. This emphasises the considerable extent of the trap raising in NZE with dress having raised similarly. A parallel pattern can be observed in the female data. However, because the female HE had raised dress relatively more than the male HE had, the young females’ trap vowels do not overlap with the female historical elders’ dress vowels.

The goose movement measures, VSM_T( goose ), were calculated using the VSM adapted from equation 3 in Section 3.1.2, but as the movement of goose is along the top of the vowel space the reference distance was taken to be between fleece and thought, with fleece remaining the reference point vowel. As is apparent in both Figures 4 and 5 NZE goose has fronted considerably. The median VSM_T( goose ) values for the historical elders are around 0.59, whereas for the young speakers they are around 0.20 (see Figure 5) and this difference is significant (see Table 6), as is the difference between the young speakers and the present-day elders. There is also a trend for the historical elders to have a backer goose than the present-day elders, but this is only significant for the female speakers.

3.1.5 Correlations between monophthong movements in Māori and NZE

There were substantial movements over time for both the Māori /e eː/ and the NZE dress and trap, which occupy a similar place in the vowel spaces for the respective speaker groups. The same observation can be made for /u uː/ in Māori and goose in NZE. It would therefore be of interest to see whether there are any correlations among these movements.

A Pearson's product–moment correlation analysis on the VSM _T values showed the Māori /uː/ and /u/ movements over time are highly correlated with the NZE goose fronting (female /uː/ r(24) = 0.88, /u/ r(24) = 0.86; male /uː/ r(23) = 0.8, /u/ r(23) = 0.76). All these correlations are highly significant, with p < .001. Figure 6 plots the VSM_T(uː) and VSM_T(u) for each speaker against their VSM_T( goose ). In the plots, each point represents a single speaker, with the label being the speaker group they belong to. It can clearly be seen that the young speakers (Y) are all clustered in the bottom left of the plots. The historical elders (H on the plots) tend to be in the top right section of the graphs, although a notable number of present-day elders (P on the plots) are also in this section. However from the plots it can be seen that as the VSM_T( goose ) or VSM_T(uː) and VSM_T(u) increase, (i.e. goose, /uː/, /u/ and are produced as more back vowels), the speakers change from the young group to the elder groups.

Figure 6

The correlations of the NZE goose movement with the Māori /uː/ and /u/ using the VSM, female data on the top row, male data on the bottom row (p < .001 in all cases), where Y = young speakers, P = present-day elders, and H = historical elders.

Similarly, the movements (measured with the VSM _F values) of the Māori /eː/ and /e/ are highly correlated with the NZE dress (male /eː/ r(23) = 0.92, /e/ r(23) = 0.90, female /eː/ r(24) = 0.91, /e/ r(24) = 0.88). The Māori /eː/ and /e/ are also highly correlated with NZE trap (male /eː/ r(23) = 0.83, /e/ r(23) = 0.78); female /eː/ r(23) = 0.83, /e/ r(23) = 0.78), although the correlation is somewhat lower.Footnote ¹⁴ Again all these correlations are highly significant, with p < .001. The correlations of the Māori /eː/ and /e/ data with NZE dress are plotted in Figure 7. As with the /uː/ data, there is a noticeable clustering of the young speakers in the lower left sections of the plots. However both the elder groups are more mixed together compared to the /uː/ data. Nonetheless, as the VSM_F(eː) or VSM_F(e) and VSM_F( dress ) increase (that is as dress becomes more open) the speakers change from the Y group to the elder groups. The correlations plots for trap look very similar to those for dress and will not be plotted.

Figure 7

The correlations of the NZE /e/ dress movement with the Māori /eː/ (left) and /e/ (right) using the VSM, female data on the top row, male data on the bottom row (p < .001 in all cases), where Y = young speakers, P = present-day elders, and H = historical elders.

3.1.6 Monophthong discussion

In this study we showed that the raising of /e, eː/ and fronting /u, uː/ over time is significant as was found in Harlow et al. (Reference Harlow, Keegan, King, Maclagan, Watson, Stanford and Preston2009), which analysed a subset of twenty of the male speakers analysed in the present study. However the extent of the movement shown here is less; the difference here is only between the young and the two elder groups combined. There was no significant difference between the elder groups, although there were usually (non-significant) trends suggesting that sound changes were already occurring between the historical and present-day elders. The less dramatic nature of the significant movements between this study and Harlow et al. (Reference Harlow, Keegan, King, Maclagan, Watson, Stanford and Preston2009) probably arose because the present study uses more stringent statistical tests. The larger speaker cohort in this study may also have played a part, with the larger data set used in the present calculations being more reliable. It is of note that the female and male speakers behave in fairly similar ways.

The significant movements in the analysis of the NZE data again agree with earlier studies that showed that dress and trap were raising, and goose was fronting (see e.g. Watson et al. Reference Watson, Maclagan and Harrington2000, Reference Watson, Maclagan, King and Harlow2008; Gordon et al. Reference Gordon, Campbell, Hay, Maclagan, Sudbury and Trudgill2004). The movement of kit was also revealed to be significant (see Figure 4) in the post-hoc t-test on the formant values. But since in this present study we are interested in vowels that may have influenced the movement of the Māori vowels, and the movement of kit over time is in the reverse direction to the movement of Māori /iː/ and /i/, no VSM values were calculated for kit.

The VSM analysis yielded results similar to the more traditional analysis carried out on the formant values alone. However it enabled us to compare the relative movements of the vowels in the vowel spaces between the speaker groups more easily, and exposed effects that could not be seen with formant analysis. For example, the VSM showed that the raising over time for the females for dress and for /e eː/ in their respective vowel spaces was significant, whereas the formant analysis did not. It was also very informative in the correlation analysis. It is possible to do a correlation analysis on the formant values, but for the raising of /e eː/ separate analyses would need to be done for F1 and F2 whereas the VSM reduced that information down to one measure.

This study has shown that the movements of Māori /e eː/ are highly correlated with the movements of the NZE dress and trap, as are the movements of the Māori /u uː/ with those of NZE goose. The latter result confirms earlier findings in Maclagan et al. (Reference Maclagan, Watson, Harlow, King and Keegan2009). This all strongly suggests that Māori has been influenced by the more dominant and prevalent NZE with the two major sound changes in the Māori monophthongs being linked to NZE influences.

3.2.1 Measures of diphthong movement

There are two different types of movements we wish to measure with the diphthong data. Firstly we wish to see whether the movements of the diphthong targets are significant, and secondly we wish to determine acoustically what is happening with the diphthong mergers.

As with the monophthong analysis, we used the VSM measures based on Euclidean distance ratios to ascertain the extent of the diphthong target movements. Here we only focused on /ae ai au ou/ as /ao/ is a stable vowel that has not changed over time. As there have been possible movement in both targets for the four diphthongs, we measured the movements for both. We measured the movement of the first targets with respect to the back of the vowel space. That is, using equation 4 we calculated VSM_B(x), with the distance between /oː/ and /aː/ as a reference side of the vowel space and /oː/ being the reference point vowel. For /au/ and /ou/ we also measured the degree of fronting of the first target, measuring the movement relative to the top of the vowel space: that is we calculated VSM_T(x), using equation 3. For the movement of the second target of /ae/ and /ai/, the front of the vowel space was the reference and we calculated VSM_F(x) using equation 2. For the second targets of /au/ and /ou/, we measured their movement with respect to the top of the vowel space and calculated VSM_T(x) (equation 3). For the second target movements /iː/ was the reference point vowel.

The significant target movements from the Bonferroni corrected t-tests on the VSM values are given in Table 7. The only significant movement for the first targets of /ae/ and /ai/ is their raising for the young male speakers. The centring and lowering of the second target of /ai/ observed in the young speakers (represented by a movement away from /iː/) is not significant for the men, and is only significant for the young female speakers compared to the elders. There is no difference between the elder groups. Since this is the more important target in terms of a potential merger between /ae/ and /ai/, it could indicate that the young women are ahead of the men in any merger.

Table 7

The values of the significant t-tests for the VSM analysis for Māori diphthongs for the female and male speakers.

*p ≤ .05, **p ≤ .01, ***p < .001

There is considerably more significant movement for the /au/ and /ou/ diphthong pair. The fronting of the second target of /au/ and /ou/ over time, clearly seen in Figure 8, is highly significant for both the female and the male speakers. However the movements of the first targets of these diphthongs are less clear. With respect to the /oː–aː/ side of the vowel space, the first target of /au/ is significantly further from /oː/ for the young speakers regardless of gender, although the behaviour of the two elder groups is inconsistent. There is also a trend for the first target of /ou/ to move away from /oː/, however this movement is only significant for the male speakers.

With respect to any fronting movement, the first target of /au/ is significantly closer to /iː/ for the Y compared to HE, for both genders. The first target of /ou/ is significantly closer to /iː/ (i.e. fronter) for the male young and present-day elders, compared to the historical elders, but for the female speakers there has been no significant movement.

A post-hoc t-test analysis of the formants provided similar results as to which movements were significant for the four diphthongs under analysis (see appendix Table A4). In addition, the post-hoc t-test showed /ao/ did not change with time.

To determine the extent of the mergers between /ae, ai/ and between /au, ou/, t-tests were performed on the first two formant values of both the first and second vowel targets. The significant results are presented in Table 8. For the male speakers, the first targets of /ae/ and /ai/ have merged for the young speakers, but this is not likely to contribute to the perception of a merger. The second target, more important for distinguishing between the diphthong pairs, is kept distinct for all male speaker groups. However, for the female speakers the young women do not distinguish the more important second targets at all and the less important first targets of /ae/ and /ai/ are distinguished only by first formant differences. This combination is likely to lead to the perception that /ae/ and /ai/ are merged for the young female speakers.

Table 8

The values of the t-tests where the F1 or F2 values for the diphthong pairs /ae, ai/ or /au, ou/ were significantly different at either the first (T1) or second (T2) target. The degrees of freedom for each speaker group are given in the appropriate column heading.

*p ≤ .05, **p ≤ .01, ***p < .001

The most pertinent target for the other diphthong pair, /au/ and /ou/, is the first target. From Table 8, it can be seen that all speaker groups except the young females keep the first targets of these diphthongs distinct in F1, which is the important dimension of relative vowel height. Only the male historical elders make a distinction between the less important second targets for the diphthong pair. There are no significant differences in F2 for either target. The young females therefore appear to have a merger between /au/ and /ou/ and the young males only just keep them distinct (p < .05).

3.2.2 Comparison with New Zealand English diphthongs

There are no direct correspondences between the Māori and the NZE diphthongs. However the most relevant NZE diphthongs to compare with the five Māori ones studied are the four NZE closing diphthongs face, price, goat, and mouth.Footnote ¹⁶ Figure 9 plots the centroids of the two targets for these four diphthongs for each of the three speaker groups, for both genders. The formant plots for the NZE diphthongs are superimposed on those for the Māori diphthongs, i.e. those from Figure 8, to enable easy comparison. This includes the ellipses for the short Māori vowels.

Figure 9

Centroid plots of the four English diphthongs face, price, goat, and mouth are plotted in black for the three speaker groups. The data for the five Māori diphthongs are plotted in grey. The diphthong symbol is at the first target. The arrow is a schematic representation of the movement and ends at the second target. The ellipses represent each speaker group's short Māori monophthongs. Male speakers are in the right column and female speakers in the left.

The ANOVAs on F1 and F2 values of the four NZE diphthongs revealed a number of significant relationships. There was a significant group effect for F1 of the second target of the female speakers (F(2,24) = 9.3, p < .01). Post-hoc t-test analysis revealed that the young females have a significantly greater F1 (and therefore phonetically lower vowels) than the present-day elders (t(18.4) = 2.6, p < .05), and the historical elders (t(13.5) = 4.3, p < .01). In addition there was a significant interaction between speaker group and vowel with the exception of F1 for the second target for both genders (female T1F1: F(3.5,41.8) = 4.2, p_GG < .01; female T1F2: F(4.6,55.5) = 3.9, p_GG < .01; female T2F2: F(3.0,36.3) = 11.8, p_GG < .001; male T1F1: F(2.9,31.6) = 7.5, p_GG < .001; male T1F2: F(4.1,45.6) = 8.6, p_GG < .001); male T2F2: F(3.0,33.5) = 6.7, p_GG = .001).

If we consider the female historical elders (top left hand plot in Figure 9), it is apparent that, for these speakers, the Māori and NZE diphthongs are relatively similar. Face has a phonetically higher T1 than /ai/, but price and /ae/ are very similar, with both targets for each vowel being in very similar positions in the vowel space. mouth and /au/ are also similar. Both start within or near to the ellipse for /a/, though T1 for mouth is more central than that for /au/. T1 for goat is more central in the vowel space than is T1 for /ou/, but both finish at the same point within the /u/ ellipse. By contrast, the differences between the historical elders’ Māori and NZE diphthong targets and the young speakers’ diphthong targets is quite striking. One notable change over time is the lowering of the second target for face and price. Post-hoc t-tests show that this movement is significant in F2 for the female speakers (see appendix Table A4). This movement is probably NZE glide weakening (see Gordon et al. Reference Gordon, Campbell, Hay, Maclagan, Sudbury and Trudgill2004) though it is possible that the lowering of the second target of price may also be linked to the /ai ae/ merger. However the most noticeable change over time for the NZE diphthongs is the fronting of the second target of goat, which is significant in post-hoc t-tests for both genders (see Table A5 in the appendix). It is this that appears to have the strongest parallel movement with any of the Māori diphthongs.

No VSM values will be given for the NZE diphthongs to investigate the significance of the vowel movements, although the values were calculated for the following correlation analysis.

3.2.3 Correlation investigation for the Māori diphthongs

The observed movements of the Māori diphthongs may well have been influenced by the monophthong movements in both Māori and English, as well as the NZE diphthong movements. All three categories will be considered in the following correlation analysis.

The strongest movement in the five Māori diphthongs investigated was the dramatic fronting of the second target of /au/ and /ou/. It was this movement that had the strongest correlation with any of the monophthongs studied, for either Māori or English. The VSM correlation results are given in Table 9. For both the female and the male speakers, the fronting movement of /au/ and /ou/ is very highly correlated with the fronting of Māori /u uː/, and NZE goose. It is also correlated with the second target of NZE goat, although the correlation is lower for the women than for the men.

Table 9

Significant correlations of VSM_T(T2au) and VSM_T(T2ou) with a number of different VSM values.

*p ≤ .05, **p ≤ .01, ***p < .001

Although the second targets of /au/ and /ou/ are less important to their distinction, it may well be that the dramatic movement of these second targets contributed to the merger between them (see Figure 8, and Table 8). A correlation analysis of the appropriate VSMs shows that fronting of the first target of /au/ is highly correlated with the fronting of the second target (female: r(27) = 0.88, male r(29) = 0.74, p < .001), and the fronting of the first target of /ou/ is also correlated with the fronting of its second target, but to a lesser degree (female r(27) = 0.53, male r(29) = 0.68 p < .01). The correlation plots are given in Figure 10. Here it can clearly be seen that as the second target of /au/ fronts in the vowel space (i.e. gets closer to /iː/), so too does the first target, regardless of gender. This also happens for the male /ou/. There are two young female speakers shown at the bottom right of the second plot whose first target of /ou/ is quite different from the other speakers. If their data is removed from the analysis the correlation between the two targets of /ou/ for the female speakers increases to r(25) = 0.88, p < .01. Finally, the young speakers are predominantly in the bottom left of the plots, indicating that the second targets of their diphthongs are relatively close to /iː/, and there is a tendency for the historical elders to be in the top right, indicating that the second targets of their diphthongs are relatively farther from /iː/.

Figure 10

The correlations of the T1 /au/ and T1 /ou/ movements with the T2 /au/ and T2 /ou/ movements, respectively, using the VSM, female data top row plots, male data bottom row plots (p < .001 in all cases), where Y = young group, P = present-day elders, and H = historical elders. The dotted line in the top right plot, VSM_T(T1ou)~VSM_T(T2ou), shows the correlation that is obtained when two outlier female Y speakers are removed from the analysis.

The movements of the second targets of /ae/ and /ai/ are difficult to attribute to any particular vowel movement, as can be seen in Table 10. The raising of /e eː/ is correlated with the movement of the T2 target of /ae/ for the male speakers, but for the female speakers it is, by contrast, inversely correlated with the T2 target of /ai/. However it is difficult to see how the raising of /e eː/ can have any bearing on the lowering of the second target of /ai/. The second target of price has lowered and backed over time which follows a similar pattern to the second target of Māori /ai/ (see Figure 9). However although these movements are highly correlated for the female speakers, there is no significant correlation at all for the male speakers. This lack of consistent results in the correlation analysis strengthens the hypothesis that the merger is more likely to be due to glide weakening in /ai/ rather than to mirroring the movements of the associated monophthongs.

Table 10

Significant correlations of VSM_T(T2ae) and VSM_T(T2ai) with a variety of different VSM values.

*p ≤ .05, **p ≤ .01, ***p < .001

3.2.4 Diphthong discussion

There is strong evidence that there are changes in the Māori diphthongs, and this study has provided acoustic evidence of the merging of both /ou/ with /au/, and /ae/ with /ai/. However the motivation for the mergers is quite different for the two pairs.

Our data suggests that /ou/ and /au/ have always been fairly similar in the second target; the differences between them are only marked in the first formant of the first target, and these have been lost for the young female speakers (see Figure 8 and Table 8). The largest change over time for /au/ and /ou/ has been the fronting of the second target (see Figure 8) which is highly correlated with the movement in the Māori vowel space of /u uː/ but it is also correlated with the movement of goose and the second target of goat in the NZE vowel space. The first targets of /au/ and /ou/ have also fronted, and this fronting is correlated with the fronting of the second targets (Figure 10). It is possible that fronting of the entire diphthongs which can be seen in Figure 9 has caused the differences between the first targets of /au/ and /ou/ to be lost for the young female speakers, and to be very weak for the young male speakers (see Table 8).

Another factor in the loss of the distinction between /au/ and /ou/ may be because /ou/ has become unrounded over time. The closest NZE diphthong to /ou/ is goat, and the first target of this vowel has been unrounded in NZE since at least the early 1900s (Gordon et al. Reference Gordon, Campbell, Hay, Maclagan, Sudbury and Trudgill2004: 158). This may well have had some influence on Māori /ou/. There is anecdotal evidence to suggest that Māori /ou/ was originally lip rounded. The increase of F2 over time for the T1 of /ou/ may be partly due to the unrounding of the first target (lip unrounding means the vocal tract length shortens, causing the formants to raise; Lindblom & Sundberg Reference Lindblom and Sundberg1971). In support for this suggestion, we note that the HE speakers have a lower average F3 for /ou/ than either the PE or Y speakers, indicating that their T1 for /ou/ was more rounded than the first targets of the other speaker groups.

In Māori, the most fronted versions of both targets of /ou/ occur after /t/ in the plural pronouns mātou ‘we (exclusive)’, tātou ‘we (inclusive)’, koutou ‘you’, rātou ‘they’. In Maclagan et al. (Reference Maclagan, Watson, Harlow, King and Keegan2009) we noted that Māori /u uː/ which follow /t/ are more fronted than tokens that follow other consonants. The /ou/ phonemes in pronouns appear to follow a pattern similar to the tokens of /u/ that follow /t/ so that most tokens of /ou/ occur in a fronting context. The first element of the diphthong, /ou/, appears to have moved forward and lowered within the vowel space until it has moved from its initial position nearer the /o/ region (within the /o/ ellipse for the historical male speakers) so that it is now very central within in the vowel space, and closest to /a/. This means that the first targets of both /ou/ and /au/ are now closest to the same monophthong, /a/. This will have added perceptually to the merger.

It is difficult to attribute the merging of /ae/ and /ai/ to any one factor. It is quite clear that whereas these two diphthongs were distinct for the historical elders, this distinction has reduced over time (see Figure 8). But it is not clear precisely which factors caused the merger. Because of the prevalence of glide weakening over time in NZE, we suggest that the process of glide weakening has reduced the length of the glide in /ai/. Historically, NZE diphthongs have been subject to both diphthong shift and glide weakening (see Wells Reference Wells1982, Gordon et al. Reference Gordon, Campbell, Hay, Maclagan, Sudbury and Trudgill2004). Diphthong shift affected the first targets of the NZE vowels, resulting in more extensive diphthongisation with greater formant shifts. Glide weakening then reduced the lengths of the glides. The second targets of the Māori vowels appear to be more strongly affected by NZE than do the first targets, with /ai/ seeming to parallel the lowering of the second target of both face and price, a result that can be attributed to glide weakening.

These mergers have little effect on intelligibility because most or possibly all potential minimal pairs of words are different parts of speech so there is little possibility of misinterpretation. For /ai/ and /ae/, compare, for example, tae ‘to arrive (verb)’ and tai ‘sea, tide (noun)’, and for /au/ and /ou/ pau ‘to be used up (verb)’ and pou ‘post (noun)’. Because the most common contexts for /ou/ are the plural pronouns, this removes potential misinterpretations with /au/. In addition, Ngāti Porou, one of the largest tribes in the North Island of New Zealand, along with other groups speaking ‘Eastern’ dialects (Harlow Reference Harlow2007: 45–47), has traditionally pronounced and written the plural pronouns with /au/ thus potentially reinforcing the merger between /ou/ and /au/. The authors were not able to think of any plausible misinterpretations that could occur because of the diphthong mergers studied here.

Finally, though, in the midst of all this change, it is important to note that /ao/ has not changed at all over time. This is possibly a reflection on the stability of both the /a aː/ and /o oː/ vowels, which have essentially remained the same for all our speakers, regardless of the passage of time.