Segments Inventories and Syllable Inventories

Another hypothesis is that the size of the segment inventory is related to the phonotactics of the language in such a way as to limit the total number of possible syllables that can be constructed from the segments and suprasegmental properties that it has. Languages might then have approximately equal numbers of syllables even though they differ substantially in the number of segments. Rough maintenance of syllable inventory size is evisaged as the functional of cyclic historical processes by, for example, Matisoff (1973). He outlines an imaginary language in which, at some arbitrary stating point, "the number of possible syllables is very large since there is a rich system of syllable-initial and -final consonants". At a later stage of the language these initial and final consonantal systems are found to have simplified but "the number of vowels has increased and lexically contrastive tones have arisen" maintaining contrasting syllabic possibilities. If tone or vowel contrasts are lost, consonat clustering will increase at the syllable margins again.

A brief investigation of the relationship between segmental inventory size and syllable inventory size was carried out by calculating the number of possible syllables in 9 languages. The languages are Tsou (418), Quechua (819), Thai (400), Rotokas (625), Gã (117), Hawaiian (424), Vietnamese (303), Cantonese, Higi, and Yoruba (the last three are not in UPSID but detailed data on the phonotactics are available in convenient form for these languages). The 9 languages range from those with small segment inventories (Rotokas, Hawaiian) to those with relatively large inventories (Vietnamese, Higi, Quechua) and from those with relatively simple suprasegmental properties (Tsou, Hawaiian, Quechua) to those with complex suprasegmental phenomena (Yoruba, Thai, Cantonese, Vietnamese). In calculating the number of possible syllables, general co-occirrence restrictions were taken into account, but the failure of a particular combination of elements to be attested if parallel combinations were permited is taken only as evidence of an accidental gap, and such a combination is counted as a possible syllable. The calculations reveal very different numbers of possible syllables in these languages. The totals are given in Table 1.5.

Table 1.5 Syllable inventory size of 9 selected languages
Language	Total possible syllables
Hawaiian	162
Rotokas	350
Yoruba	582
Tsou	968
Gã	2,331
Cantonese	3,456
Quechua	4,068
Vietnamese	14,430
Thai	23,638

Even with the uncertainties involved in this kind of counting, the numbers differ markedly enough for the conclusion to be drawn that language are not strikingly similar in terms of the size of their syllable inventories.

In following up this study, several tests were done to see which of a number of possible predictors correlated best with syllable inventory size. The predictors used were the number of segments, the number of vowels, the number of consonants, the number of permitted syllable structures (CV, CVC, CCVC, etc.), the number of suprasegmental contrasts (e.g. number of stress levels time number of tone), and a number representing a maximal count of segmental differences in which the number of vowels was multiplied by the number of suprasegmentals. Of these, the best predictor is the number of permitted syllable types (r = .69), an indication that the phonotactic possibilities of the language are the most important factor contributing to the number of syllables. The next best predictor is the number of suprasegmentas (r = .59), with the correlation with the various segmental counts all being somewhat lower. Although all the predictors tested show a positive simple correlation with the number of syllables, in a multiple regression analysis only the number of vowels contributes a worthwhile improvement to the analysis (r^2 change = .19) beyond the number of syllable types. Thus we can say that syllable inventory size does not depend heavily on segment inventory size. Nonetheless, because the predictors do have positive correlations with syllable inventory size, the picture is once
again of a tendency for complexity of different types to go together.

(Patterns of Sounds, Ian Maddieson)

Segments and Suprasegmentals

Despite the failure to find any confirmation of a compensation hypothesis in several tests involving segmental subinventories, it is possible that the compensation exists at another level. One possibility was evidently in the minds of Firchow and Firchow (1969). In their paper on Rotokas (625), which has an inventory of only 11 segments, they remark that "as the Rotokas segmental phonemes are simple, the suprasegmentals are complicated". A similar view of a compensatory relationship between segmental and suprasegmental complexity seems implicit in much of the literature on the historical development of tone. For example, Hombert, Ohala and Ewan (1979) refer to "the development of contrastive tones on vowels because of the loss of a voicing distinction on obstruents". If this phenomenon is part of a pervasive relationship of compensation we would expect that, in general, languages with larger segmental inventories would tend to have more complex suprasegmental characteristics.

In order to test this predictions, the languages in UPSID which have less than 20 or more than 45 segments were examined to determine if the first group had obviously more complex patterns of stress and tone thatn the second. Both groups contain 28 languages. The findings on the suprasegmental properties of these languages, as far as they cam be ascertained, are summarized in Table 1.4.

Despite some considerable uncertainty of interpretation and the incompleteness of the data, the indications are quite clear that these suprasegmental properties are not more elaborate in the languages with simpler segmental inventories. If anything, they tend to be more elaborate in the languages with larger inventories.

There are more "large" languages with contrastive stress and with complex tone systems (more than 2 tones) that "small" languages. There are more "small" languages lacking stress and tone. The overall tendency appears once againn to be more that complexity of different kinds goes hand in hand, rather than for complexity of one sort to be balanced by simplicity elsewhere.

(Patterns of Sounds, Ian Maddieson)

Relationship between Size and Structure

"The data in UPSID have been used to address the question of the relationship between the size of an inventory and its membership. The total number of consonants in an inventory varies between 6 and 95 with a mean of 22.8. The total number of vowels varies between 3 and 46 with a mean of 8.7. The balance between consonants and vowels within an inventory was calculated by dividing the number of vowels by the number of consonants. The resulting ratio varies between 0.065 and 1.308 with a mean of 0.402. The median value of this vowel ratio is about 0.36; in other words, the typical language has less than half as many vowels as it has consonants. There are two important trends to observe; larger inventories tend to be more consonant-dominated, but there is also a tendency for the absolute number of vowels to be larger in the languages with larger inventories. The first is shown by the fact that the vowel ratio is inversely correlated with the number of consonants in an inventory (r=-0.4, p=0.0001) and the second by the fact that the total of vowels is positively correlated with the consonant total (r=0.38, p=0.0001). However, a large consonant inventory with a small vowel inventory is certainly possible, as, for example, in Haida (700: 46C, 3V), Jaqaru (820: 38C, 3V) or Burushaski (915: 38C, 5V). Small consonant inventories with a large number of vowels seem the least likely to occur (cf. the findings of Hockett 1955), although there is something of an areal/genetic tendency in this direction in New Guinea languages such as Pawaian (612: 10C, 12V), Daribi (616: 13C, 10V) and Fasu (617: 11C, 10V). In these cases a small number of consonants is combined with a contrast of vowel nasality. Despite some aberrant cases, however, there is a general though weak association between overall inventory size and consonant/vowel balance: larger inventories tend to have a greater proportion of consonants."
(Patterns of Sounds, Ian Maddieson)


I made a graphic to show the relation between the number of vowels and consonants in a speech inventory. Each language in the UPSID is represented as a cross in the plot and the gray shading is the density of languages in the vowel-consonant plan.

Speech Inventories

"Such an association suggests that inventory size and structure may be related in other ways as well. A simple form of such a hypothesis would propose that segment inventories are structured so that the smallest inventories contain the most frequent segments, and as the size of the inventory increases, segments are added in descending order of their overall frequency of occurrence. If this were so, all segments could be arranged in a single hierarchy. Such an extreme formulation is not correct, since no single segment is found in all languages. But if we add a corollary, that larger inventories tend to exclude some of the most common segments, then there is an interesting set of predictions to investigate. We may formulate these more cautiously in the following way: a smaller inventory has a greater probability of including a given common segment than a larger one, and a larger inventory has a greater probability of including an unusual segment type than a smaller one."
(Patterns of Sounds, Ian Maddieson)

I would say that there is a convergence towards a inventory size with a number of segments between 20 and 40 and using a restricted set o segments that tends to be common among languages those languages. As the language gets further away from this zone, we cannot say much about what would be its inventory.

Universality of Language

Edwar Sapir wrote in 1921: "There is no more striking general fact about language than its universality. One may argue as to whether a particular tribe engages in activities that are worthy of the name of religion or of art, but we know of no people that is not possessed of a fully developed language. The lowliest South African Bushman speaks in the forms of a rich symbolic system that is in essence perfectly comparable to the speech of the cultivated Frenchman."

Shepard Tone

Roger Shepard created an amusing auditory paradox, which is after him named: Shepard tone. It is based on a self-similar sequence of notes that consist on a superposition of 12 tones, each an octave higher then the lower neighbor. The 12 tones extend from the lower frequency limit of auditory perception to the upper frequency limit of hearing. In the present approach it goes from 10 Hz to 20,480 Hz, with all octave tones interleaved. The set of frequencies composing our Shepard tone is 10, 20, 40, 80, 160, 320, 640, 1280, 2560, 5120, 10,240, and 20,480 Hz. In order to create a paradoxal sound of a continouos ingreasing frequency sound, we create a sweep, an exponential chirp for each composing tone, going from its initial frequency to its following octave.

The instantaneous frequency of each tone is given by
$f(t) = f_0 k^t$.
As we want the final frequency after $T$ seconds to be $2 f_0$,
$f(T) = 2 f_0 = f_0 k^T$
That leads to
$k = e^{\frac{\ln 2}{T}}$
and the instantaneous frequency may be written as
$f(t) = f_0 e^{\frac{\ln 2}{T} t}$
An exponential chirp tone $x(t)$ is given by
$x(t) = \sin \left( 2 \pi \int_{0}^{t} f(\tau) d\tau \right)$
$x(t) = \sin \left( 2 \pi f_0 \frac{e^{\frac{\ln 2}{T}t}-1}{\ln 2 / T} \right)$

To acchieve a better result I have weighted the tones using a gaussian window, and I created the chirp tone with the double sampling frequency and in the end I made a resample to the desired sampling frequency, to attenuate the aliasing caused by the higher chirping tones.

fs = 44100;
fs2 = 2*fs;
ts = 1/fs2;
F = [10 20 40 80 160 320 640 1280 2560 5120 10240 20480];
w = gausswin(length(F));
x = [];
T = 10;
t = [0:1/fs2:T-1/fs2]';
x = zeros(size(t));
w(end+1)=0;
for i = 1 : length(F),
    x += linspace(w(i),w(i+1),length(t))' .* sin(2*pi*F(i)*(exp(log(2)/T * t)-1)/(log(2)/T));
end;
x = resample(x,1,2);

I used the function bellow to concatenate several chirping tones:

function y = concatenate(varargin)
y = varargin{1};
for i = 2 : nargin,
    x = varargin{i};
    o1 = linspace(1,0,11025)';
    o2 = linspace(0,1,11025)';
    y = [y(1:end-11025); o1.*y(end-11025+1:end)+o2.*x(1:11025); x(11025+1:end)];
end;

And the result is plotted in a Spectogram (see figure bellow) and might also be heard.

y = concatenate(x,x,x);
specgram(y,[],fs,[],[]);
soundsc(y,fs);