0.0 Phonolo$ical typologies~ statistical counts and mathematical models 
The high structuring of phonology, the obvious classes of 
sounds, and the classes of their classes, have made phonological 
typologies a not too rare proposal. And even where typologies were 
not claimed as such, they were often implicit in the statements made. 
Both phonetic and phonemic, acoustic and articulatory, structural and 
non-structural, have all been proposed and have evoked discussions, 
critiques and applications. 
One can mention works by the Prague linguists culminating 
in the writings of, among others, Skali~ka, Kramsky, and no=ably 
Trubetzkoy and Jakobson. In America, we have work by Greenberg, 
Hockett, Saporta and Voegelin as well as numerous followers and 
critics. Among other European contributions the acoustic typologies 
by Menzerath and Meyer-Eppler. 
0.i Mathematical models and mathematlcal (more precisely sta- 
tistical) techniques of analysis have also been elaborated. Classi- 
fication, distribution and frequency characteristics of various sound 
patterns have been a particular concern and represent the bulk of 
numerical phonological typologies, especially in the U.S, I Often, 
again, the subject is classification of inventories and particular 
types (articulatory) of phonemeS. Such is, for instance, Pierce~s 
"A Statistical Study of New World Consonants", with counts of from the 
most to the least eo~on consonants and classes of consonants in 
a great number of Amerindian languager,, A critique end evaluation 
is found in Saporta 1957. We have probably the least structural 
end of the typological spectrum here. 
1.6 .... :~i c=_v,: fcauure typolo$ies 
There is another series of phonological typologies based 
on Jakobson's distinctive feature analysis and of course their 
Praguian and particularly their Trubetzkoyan background. 2 
2.0 The distinctive feature indices of Andre j Avram 
Typological indices derived from Jakobsonian featureswere 
proposed by Andrej Avram (1961). to study the distribution of 
distinctive features in the phonological system. 
well): 
Avram proposes the following indices (if I understand him 
P = number of phonemes 
T = number of features 
D = number of features with which each feature combines 
D m = average distribution of distinctive features 
R = coverage of each feature (how many phonemes it 
characterizes) 
Rm = coverage of the system as such (:R/T) 
C = complexity of a phoneme, i.e. how many features 
it is a bundle of 
C m - average complexity of the system (-EC/P) 
E = efficiency of a system; E-P/T 
2.1 
Avram also includes maxima and minima for Dm, Rm, Cm. 
His typology was a good first step for studying systems 
via their feature distribution. However, there are cases, such as 
the following two hypothetical systems, different (but of undecided 
distance), which Avram's typology fails to distinguish. 3 
Phonemes: PI P2 P3 
System A' 
Phonemes: PI' P2' P3' 
Distinctive features 
fl f2 
PI P2 P3 
pflI~p2 P3 
PI' P2' P3' 
fl 
f2 
PI' ~2' 
fl 
f2 
PI P2 P3 
+ 
o + 
PI' P2' P3' 
fl + + -- 
f2 + -- 0 
Indices: 
P = 3 P' = 3 
T - 4 T' = 4 
D m = 1 (Dm = D(f I) + D(-fl) + D(-f2) 4-D(-f2) D' - i m 
4 
Rm = 1 or 33.33% R' m = 1 or 33.33% 
E - P/T = 3/4 - .75 E' = P'/T' = 3/4 = 
.75 
Cm - (i ~ 2 + 2)/3 = 5/3 = 1.66 C'm = (2+2+1)/3 = 
5/3 - 1.66 
It is obvious after inspection of the indices, that the two 
systems are not distinguls~ed. Such aloss of information is character- 
istic of averaging. 
3.0 Postovalova's valence and probability indices 
More complicated yet much more adequate measures of distinctive 
feature distributions were proposed by the Soviet linguist Postovalova. 
Although they were first used for the study of Just one systems typological 
applications were also suggested by the author. 
Postovalova's paper in Problemy Lingulsti~eskogo Analiza 
examines the subject of feature distribution in a phonological system. 
Severa~ statistics are defined: 
3.1 
3.2 
simple probability, i.e. frequency of utilization of a 
feature by the system for phoneme composition; the three 
possibilities, +, --, 0 are considered separately. 
For feature a we have: 
i ! where m = number of rows with 
m 
Pa = ~ n = number of rows. 
conditional probabilities, indicating how frequently 
different pairs of features characterize phonemes in the 
system, which is to say, given feature a for a phoneme 
what are the chances that feature b will combine with a 
in the same phoneme. 
Given feature ~ the probability that ~ will combine with 
it for th~ same phoneme is: 
i °i Pa(b) = 
where m' - number of phonemes with a and b 
n' - number of phonemes with ~. 
3.3 Finally, Valence is defined by Postovalova to disclose 
information on a feature's combinability with the o~her 
features and also information on the system as a whole 
(by including total number of features). 
I Va(b) = Pa(b-----~) i where n = t°tal number °f distinctiVen -- 1 
features in the system. 
(The probability of a feature appearing combined with another 
feature would ben~ 1 if all features were equiprobable.) 
3.4 lllustracion from the hypothetical case of 2.1 (The Valence proposed 
by Postovalova is modified hy Afendras (1968), so that it appears as 
foature by feature matrix: this step is very important as it makes 
comparison across languages a matter of comparison of features drawn 
from the "Universal" system, rather than comparison between vowels 
and their features.) 
System A: 
fl f2 
~- -- 0 + -- 
fl -- 
0 
+ 
f2 - 
0 
0. 
O. 
i. 
O° 0, 
.5 .5 
0. O° 
i. O. 
i. 0. 
0. 0. 
Valences 
i. + 
0 fl -- 
0. 0 
+ 
f2- 
0 
+ 
System A': 
fl f2 
-- 0 • -- 0 
i. O. O. 
1. O. 0, 
0. l. O. 
.5 .5 O. 
0. O. i. 
0. 0. 0. 
Clearly, the two hypothetical systems are strongly dis- 
tinguished. 
4.0 Valence analysis of Balkan vocalic systems 
And now an application of this quantitative typology to a 
specific problem: the Balkan linguistic convergence area. Non-phonolog- 
Ica! aspects have been thoroughly investigated, in the classic treat- 
~ent by Sandfeld (1930) and most recently in some powerful typological 
4.1 
4.2 
studies (Kazazis, Civ'jan, Birnbaum in several articles, Klagstadt, 
etc.) Balkan phonology has prompted many comments by Jakobson, Ivid 
and others, but to my knowledge only one systematic study (Havr~nek, 
1933) which actually drew heavy criticism (Ma~ecki Stankiewicz). 
Interesting results were obtained by aPPlying the above method to the 
4 study of several Balkan idioms. 
But before discussing the results some of the basic problems 
encountered will be mentioned: 
The systems were compared against a maximal matrix which 
included all the features occurring in the population of the systems 
analyzed. 5 
Any of the actual systems include a subset of this maximal 
set of features. In the final correlation each system was considered 
as having O's throughout for the features which it did not utilize. 
But 0Ws were also indicative of impertinence of a feature for a given 
phoneme when the feature was distinctive for other phonemes in the 
system. Thus two kinds of concepts were collapsed as they both were 
represented by 0. However, this has probably been rectified by the 
fact that features not used in a system have a 0 throughout, 
Another actual handicap is the non-availability of distinctive 
feature descriptions for the vast majority of the systems compared. 
And even when available, they were often tinted by both the author's 
views and his preferences (e.g. Petrovici on Rumanian) or were out of 
different periods of theoretical development of distinctive features. 
8 
4.3 
in such cases, I took the liberty of normalizing the data by modifying 
the existing analyses (:the same method was followed throughout e.g. 
constructing branching-trees). In some other instances more than one 
solution were possible and for lack of data I kept the alternatives. 
Such systems appear in the figures as language X-l, 2, 3 etc. Other 
instances of numbered, multiple systems for one language refer to 
situations where such variety actually exists either stylistically or 
in social dialects (e.g. literary Makedonskl). 
Some features are very typical of vocalic systems either 
universally, or for the European languages, or, more specifically, for 
the Balkan languages. E.G. diffuseness, ~, flatness, stress 
(simDle occurrence is considered here, no____tttcombinations). Then, other 
features s.a. length, ton_.___~e, ~etc. are much less common. An 
ideal comparison should give different weights to such features. 
Sharing nasality, for instance, should be typologically very significant 
and two systems which do, should be classed as very similar. Converse- 
ly, if in a group of many languages which draw on 5-6 features to dis- 
tinguish their vowels, but usually have 3 or 4, only one uses nasality 
this should be significant enough to set this particular language quite 
far apart. Now, in the correlation some factors take this into account 
but indirectly and not sufficiently. On the other hand since in 
I 
reality (i.e. in the Balkan case) systems having "odd" features have 
also the "common" features, their typological distance is reflected 
in their having a higher number of features than the other languages, 
6 a fact reflected in the Valence matrix (:lower values for each cell). 
4.4 The introduction of a new feature usually results in a whole 
series of new phonemes, and actually the more numerous these phonemes 
the more important the new feature to the system. This is expressed 
by the product of number of distinctive features X number of phonemes = 
total # of cells in the feature by phoneme matrix. An index incorporat- 
ing this will reflect more qualities of the whole system. I propose 
therefor~tentativelysa modification of the valence formula to: 
V~(b) = Pa(b) where K - # of phonemes • (n -i) 
This weightinEmakes the index much more sensitive to varia- 
tions in the number of features. 
4.5 Higher order conditional probabilities can also be intro- 
duced, e.g. 1 \] Pab (c) = ~m 
where K = number of phonemes which have in common features a, b and ~, and 
m = number of phonemes with a and b in common. 
A Valence Vab(c) PaD(c) (n-l) can then be defined. 
And so on until we have the PI . . . (n-2) (n-l) and the resulting 
Valence. 
The results presented here are based on Postovalova's original formula. 
,,,, • , 0. • , , • • • • 222222d~,3~,eeodog~,dc,~dcdoddgeddcd~d~ddc~de333~3333- 
_ I _ I ...... I i .... 
o(.o 
~ O~ 
O0 • 
I I I I n ii * i 
10 
.... . .... .,,....,o°,.,,,,0,0,..°0,,..0~.,,,0.,,,0 
...... ¢cocc,eooccooeccooo?~$~?~ocoooc~ooo~TTTTT?TTT.,,, ~ , , , , , 
o 
© 
0,~ 
~m 
o~ 
o-- 
oo 
o • 
n ~ 
°~ 
~r 
I 
o c~ .i..I 
o o 
o 
~0 
z-4 
o c~ 
r-~ o 
o 
4o 
o 
co o 
o 
o 
,-4 
Q) 
~4 
c~ 
¢J 
~> 
40 
o 
40 
.r.4 
o 
G) 
t~ 
c~ ,o : 
ej 
40 
S. 
\" 
c.) 
~, ~,~ .~ .,~ 
c,I "(J 
gl ~l , 
~ ° 
e~ 
12 
5.0 Statistical correlation of Balkan Valence matrices 
51 vocalic System matrices were actually analyzed, their P , P (b) a a 
and V (b) matrices calculated~and these final matrices were correlated a 
and plotted using two different methods according to distance from 
each other. 7 
Gammon (1967) used a similar statistical technique for 
finding the similarity (conversely, the distance) between several 
Polynesian languages. In his case, the information was not in the 
form of matrices but in the farm of lists. 
6.0 Results 
in the final plotting (see figures I, 2, 3 and 4) several groupings 
can be discerned. 
First, in the multidimensionalsealin~ analysis, we can 
speak roughly of 3 groups: two form a sort of a nucleus in the center 
and the third (distributed in two subgroups also) surrounds it. 
On the external group we have Old Church Slavic, and close by Common 
Slavic. Then spread around mostly Serbo-croatlan dialects, with some 
other idioms (e.g. 7-vowel Mom~ilovci Bulgarian,(9#Nasal) vowels Barile 
Tosk Albanian, 8-vowel Meglenitie, 7-vowel E. Bosnia Serbo-croatian). 
This group seems to include only dialects with the feature of tenseness. 
Except for the Albanian dialect, all group members are dialects located 
~, 
~z 
q5 
..................... ~~~;~~ 
.................................... ~ ............ ~ 
........................................ ~~ 
.......... ~~~~~~ 
................................ ~2~~2~i~2 
............................... :::::::::::~~ 
o0°°,.,,, ...... *,*~~~~×~××~ 
gg~ggggooo~oo=Gggoo~ooo~eggo~ogo*~ggocg=oo;god~*~o 
G 
o 
o r-4 
e~ 
o 
{0 
o 
o 
o 
,-..4 ~.) 
~.> 
g4 
o 
o 
-r4 
(,,) 
G .,-4 
14 
Fig. 4. 
~ 34 35 
40 
15 
07 
1'/ 
7 
16 
21 
05 
10 
14 
19 
2'/ 
31 
3 
Diameter Cluster Analysis: 
Rearranged from Fig. 3. 
O 
S. CR (STANI~) 
S. CR (KOS-KAS.) 
s. CR (E. BOSE.) 
S. CR (Z- L, BAR) 
S. CR (Z-L, PIPERI\] 
ALB. T. (VACC.) 
GK. (PHARASSA) 
MAK. (SToJ~IT. 3) 
BG. (MON~IL.) 
S. CR (Z-L, IVIRKOV4 
BG. (ERKE~ 1) 
GK. (CONS.-SAR.) 
CK. (NORTH) 
ALB. G. (SCUT.) 
ALB. G. (DUSH.) 
BG. (BOBO~EVO) 
GK. (STAND.) 
MAK. (ST. LIT. I) 
RUM. (COMMON) 
22 
• 28 
--'-\[29 
--3 
@ 
BG (ST. LIT.) 
GK (BG. SAR. 2) 
BG (KOLAROV GR.) 
S-CR (Z-L, DOBROT) 
ALB. T. (BARILE) 
GK. (SILLI) 
O.C.S. 
COMMON SLAV. 
ALB. T. (BERAT) 
ALB. T. (MAND.) 
GK. MEDIEVAL 
BG. (RHODj) 
S-CR (I(RABOVA 1) 
GK (BG-SAR-2) 
RUM (AR-HRUP.) 
GK (THES. THRAC. ) 
BG (COL. STAND.) 
GK.(TSAK. PROP. ) 
GK. (PONTIC) 
MAK (BOBO~. 1) 
MAK (SUCHO) 
RUM (AR. ALB. I) 
RUM (ST. LIT.) 
C,K-ATTIC ~.. 
MAK (BOBOS~. 2) ~ 
48 RUM (MOLD.) 
49 RUM (cRxs.) 
51 RUM (BANAT) 
42 RUM (Aa. FRAS. ) 
32 MAK (ST. LIT. 2) 
45RUM (AR. ALB. 2) 
46 RUM (ME GLEN. ) 
See Appendix A for list of idioms on this table. 
r 
in the Central Balkans, i.e. we have here an areal grouping. 
Four out of six Albanian systems 
(all of the dialects within the geographic area of the Balkans) fall 
in one group and are closer to Macedonian and Bulgarian than to 
Rumanlan. 
Greek dialects are quite diffused but stay within the two 
nuclear groups (this includes Classical Attic and Medieval Greek.) 
In the diz~eter method (figure 4), the most interesting 
grouping is that of all seven systems with the 5-vowel pattern 
(irrespective of additional features such as length - nasality - tone) 
on the same side of the initial bifurcation. 
Another subgrouplng includes only systems which use flatness 
to distinguish a second series of hack vowels (Rhodope Bulgarlan, 
Kra~ova I Serbo-croatian, Bulgarian Saraka~an Greekp and Hrupi~ta 
Arumenian). 
Among the other interesLing results are the following: con- 
trary to Old Church Slavic and Common Slavic, which in both analyses 
stand apart, Attic Greek is classed as very similar to the bulk of the 
systems analyzed: in the diameter method throug h early Joining of the 
branching tree, and in the multidimensional sealing by being located 
in the middle of the one of the two central constellations. This is 
all the mere intriguing in the light of the fact that in a similar 
statistical correlation (see figure 5) of some Balkan and other 
15 
16 
-, oo ~ ..... "oo .o°': .... . : ..... : ..... : ..... :.o... : ° .o :. - .,: -- 
~: 0 -~ . ~ .. ~- .:. ~ --~ 
: ",a \]r : 
"~. ~; 
• :~. o. --~ ~ ~ ~ 
: 
®~ E. : 
:' 
', # I;I / - , 
I/i • • ,4~ : o 
o 
:, 
:_o 
.. o 
--,~.-...: ..... : ..... : ..... : ..... : ..... : ..... : ..... : ..... :...'~- 
I IIIIIIIII IIIIIIIIIIIIIIIIII 
I 
~o 
o" . o: 
o" 
• ° 
" 2. 
17 
systems expressed in the Harary-Paper model for binary phoneme 
combinations. Attic was also in the center of the group and OCS (as 
well as Czech) quite distant from it. Is this not a strong indication 
of convergence of South Slavic towards a pattern characteristic of 
Greek since the time of Attic? If anythlng, one would intuitively 
class the old idioms (Common Slavic, OCS and Attic) as belonging to 
roughly the same ¢ype~: large systems, length, toner accent etc. as 
additional features. What "latent" structures are responsible for the 
outcome of the statistical analysis? 
7.0 Some Concluslons 
It is hoped that the advantages, possible uses and problems 
of this approach for typological classification as well as some uses 
of the latter, were sufficiently demonstrated, It is also hoped that 
criticism and suggesttovs on all aspects will further the ~ttlity and 
vigor of the approach. 9 Among the main objectives is a better anchor- 
leg of the model on mathematical theory and, parallel to this, better 
explanation of the linguistics behind the findings and in adapting the 
model. While thls last is obvious, the search for a model mathematic- 
ally well grounded is imperative if the approach is to profit more 
i0 As a from the power of a fully developed mathematical theory. 
concrete step in this direction, a Stochastic Process Model for the 
same problem is currently investigated, as well as other models 
applied to different ~speets of phonologle structure. 
l) 
2) 
18 
No t e_.._._~s 
See bibliography for particular works on typology. 
On mathematical models especially pertinent is the work 
of Spang-Hanssen, Harary and Paper, Ungeheuer, and more 
recently a series of studies by Soviet Linguists e.g. Revzin; 
V the work of other Soviet and East European linguists (Saum~an, 
Marcus, Kulagina etc.) is very interesting and could be 
applied to typological investigations. For an overview see 
Kiefer, 1968. 
On statistical techniques, Pierce (1957, 1962), Saporta (1957), 
Spang-Hanssen, Herdan; in Eastern Europe extensive work, of which 
one can mention Kr~msky who typifies some of the Prague research 
and Andreyev's group in the Soviet Union. 
For general discussions, see Birnbaum 1966, 1968, 1969, 
Edmundson 1967, Greenberg 1957, Horne 1966, Ku~era and Monroe 
1968, Plath 1963, Spang-Hanssen 1961-1964, Uspenskij 1966. 
For a historieal-phonetih typology see Grimes 1961. 
Of course Jekobson's work as well as that of Trubetzkoy is of a 
typological nature. Such is for instance Trubetzkoy's Gz~zuge 
der P;~nolo~e as well as his articles on vocalic or consonantal 
systems. For a discussion of the typological nature of 
I 
Jakobson, Fant and Halle's PPe~42ni~ies to Speech Analysis, see 
Voegelin 1956. 
3) 
4) 
5) 
Notes (cont.) 
It seems that no two "mirror" systems could be distinguished 
by this typology. A theoretical shortcoming in spite of the 
fact that not terribly many such cases exist. 
Much of the data analysis used for the present paper was done 
at the Johns Hopkins University, as part of my doctoral 
research which culminated in a thesis (May 1968). 
The idea of a maximal system thus defined can also be found 
in Voegelin 1963. Uspenskij (1965:63) defines it as follows, 
opposite to a minimal system: "Jazyk-~talon pervogo tipa 
(i.e. minimal) mo~zno ponlmat' kak teoretiko-mno~es tvennoj e 
proizvedenije %~sex xarakterlz\]&jemyx (v opredelennom aspekte) 
jazykov (modeleJ), t.e. kak invariantnuju dlja vsex ~tix 
jazykov model'; jazyk-~talon vtorogo tipa (i.e. maximal) 
V mozno ponimat' kak teoretlko-mnozestvennuju summu usex 
priznakov opisyvaemyx jazykov (modele~). Pri ~tom u ka~estve 
to~ki ot~eta pri tipologi~eskix sravnenijax dolmen 
ispol 'zovat 'sja j~zyk-6talon minimal 'nogo tipa; tem samym 
jazyk-6talon ~togo tipa mo~et ~" ' " cc~tat ssa osnovnym. Uspenskij 
points out that the minimal system in a sense "catches the 
essence" of the languages to be compared. See also the Ph.D. 
dissertation by Afendras, The Balkans as a Linguistic Area: 
19 
6) 
Note__..ss (cont.) 
A Study in Phonological Convergence. Baltimore, 1968, 
§ 3.4, 3.5 (i01-I12), 4.9-4.10 (139-140), and Ch. 5 (141-152) 
for establishing and discussion of the maximal and minimal 
vocalic and consonantal systems in the Balkans. 
Birnbaum (1966:20) in his discussion of Uspenskij above 
also expounds on the notions of maximal (:Boolean sum) and 
minimal (Boolean product) typological systems. 
Actually, much the same is implicit in some of the 
American typologies (of course Voegelin's, mentioned above) 
for instance. Pierce's, with its "omnipresent" consonants, 
the basic core : minlm~, and total collection of any conson- 
ants occurring in at least one language = maximum. 
See, for instance, in the statistical correlation (KRUSKAL 
Multidimensional Scaling) OCS, Common Slavic stand quite apart 
from almost all of the other languages. 
7) See appendix for a list of all the idioms analyzed. 
8) Reproduced from Afendras (1968:145) fig. 10. 
9) Parallel attempts, or rather converging a~tempts from other 
directions might also suggest improvements or better support 
20 
21 
lo) 
Note_~s (cont.) 
our findings. 
Grimes (1962), for instance, analyzes phonetic diverg- 
ence (: "scatter") within Romance and finds French and 
RumanXan display "high scatter" from expected innovations, 
therefore distances from the rest. "It is tempting to guess 
that the scatter In Rumanian could reflect the influence of 
non Romance speech communities that have interacted with the 
Rumanian community (or communities) '' . 
Now since in our analysis Rumanian is quite close to the 
other Balkan languages (unlike, for instance Serbocroatian) 
one could say that Grimes' study and this present complement- 
ary and mut~lly supportlng results. 
Edmundson's section on mathematical models In Borko 1967 prov- 
ides a starting point with the must and must nots of the 
researcher, the does and the does nots of the model. 
SUMMARY 
In this study, the vocalic systems of a large number of Balkan 
idioms (past and present) were analyzed in terms of Jakobsonian 
distinctive features. Various methods for comparison and scaling 
for similarity, as well as the problems encountered, are discussed 
and evaluated. Some questions of typology, such as distinctive 
feature weights, are revealed; suggestions are made for their 
future incorporation into typologies of this nature. 
It is a srtrprJusing fact in linguistic scholarship that no 
feasible, nor adequate manner for comparing phonological systems 
quantitatively has been devised. The notion of distinctive feature 
valenceproposed by the Russian linguist, V. I. Postovalova, 
answers the need for such a feature distribution measure. 
The valence matrices for the vocalic systems of flfty-one 
Balkan idioms, as well as simple and joint probabilities of distinctive 
feature occurrence are calculated. Finally, the results are correlated 
and submitted to computerized factor analysis (various programs). 
22 
APPENDIX A 
A LIST OF ALL BALKAN IDIOMS ANALYZED 
ALBaNIaN 
i. Dushmani Geg 
2. Scutari Geg 
3. Berat Tosc 
4. Mandres Tosc 
5. Barile (Italy) Tosc 
6. Vaccarizzo (Italy) Tosc 
BULGARIAN 
7. Colloquial Standard 
8, Literary Standard 
9. Bobo~evo 
i0. Erke~ (2) 
ii° Kolarovgrad 
12. Mom~ilovci 
13, Rhodope 
CREEK 
14, Standard; also most JUDEO-SPANISH 
w 15, ConserVative Sarakacan 
16, North including $arakacan; some JUDEO-SPANISH 
17. Saraka~an of Bulgaria I 
23 
24 
A-'P i~X"~2X A (cont.) 
G~ESK (cont.) 
i$. Saraka~an of Bulgaria II 
19. Propontis Tsakonian 
20. Thessalian, Thracian 
21. >\[!crasiatic - PontUs 
22. Micrasiatic - Pharassa 
23. Micrasiatic - Silli, also TURKISH 
24. Early medieval 
25. Attic Classical 
>LkKEDONSKI 
26. Standard Literary I 
27. Standard Literary II (Regional-Styllstic variant) 
28. Standard Literary III (Regional-Stylistic variant) 
29. Sucho 
~v 30. Boboscica I 
31. vv Boboseica II (alternative phonemicization) 
32. OLD CHURCH SLAVONIC 
33. COY~ON SLAVIC j 
34. C O}.~iON RUMTuN IAN 
APPENDIX A (cont.) 
Rb~"~%NIAN 
35. Standard 
36. Banat 
37. Crimean 
38. Moldavian 
39. Fraseri Arumanian 
40. Other Arumanian of Albania 
41. Other Arumanian of Albania 
42. Hrupi§ta Arumanian 
43. Meglenitic 
SERBOCROATIAN 
44. Standard Literary 
45. E. Bosnia ~tokavian 
46. Kosovo-Resava (Kasidol) 
47. Zeta-Lov~en (Mrkovi~i) 
48. Zeta-Lov~en (Piperi) 
49. Zeta-Lov~en (Dobrota) 
50. Zeta-LoV~en (Bar) 
51~ E-dialects (Banat) Kra~ova 
I 
II (alternative phonemicization) 
25 
26 
APPENDIX B 
I) S~MPLE DISTINCTIVE FEATURE MATRICES 
(GREEK AND MAKEDONSKI DIALECTS) 
2) SAMPLE VALENCE MATRICES FOR TWO OF THE ABOVE 
(adapted from Afendras 1968) 
27 
ORIGINAL DISTINCTIVE FEATURE MATRIX OF GREEK (STANDARD) 
DIFFUSE/NON. DIFF. 
COMPACT/NON. COMP. 
GRAVE/ACUTE 
STRESSED/UNSTRES. 
IIIii ieaouieaou 
0=*-00-*-0 
-=0++--0+- 
Np ~ 10 
Nf-- 4 
ORIGINAL DISTINCTIVE FEATURE MATRIX OF N. GREEK (CONS. SAR. ) 
DIFFUSE/NON DIFF. 
COMPACT/NON. COMP. 
GRAVE/ACUTE 
STRESSED/UNSTRES. 
clll/l iueo~aiua 
00--++00~ 
~+000 .... 
Np= 9 
Nf =4 
ORIGINAL DISTINCTIVE FEATURE MATRIX OF N. GREEK (GENERAL) 
DIFFUSE/NON. DIFF. 
GRAVE/ACUTE 
COMPACT/NON. COMP. 
STRESSED/UNSTRES. 
• • /#1 
ieaouiua 
4--- ~ -- ~- 4- ÷-- 
0-~-000~ 
Np=8 
Nf =4 
28 
ORIGINAL DISTINCTIVE FEATURE MATRIX OF MAKEDONSKI (ST. LIT. I) 
DIFFUSE/NON. DIFF. 
COMPACT/NON. COMP. 
ieaou 
~---÷ 
0---0 
Np=6 
Nf~3 
GRAVE/ACUTE --0-- 
ORIGINAL DISTINCTIVE FEATURE MATRIX OF MAKEDONSKI (ST. LIT. II) 
iueo~a 
DIFFUSE/NON DIFF. ~ ..... Np = 5 
Nf=3 
GRAVE/ACUTE - * + - * + 
FLAT/PLAIN 0-~0-* 
ORIGINAL DISTINCTIVE FEATURE MATRIX OF MAKEDONSKI (ST. LIT. HI) 
DIFFUSE/NON .DIFF. 
GRAVE/ACUTE 
iueoaa 
Np --6 
Nf =3 
COMPACT/NON. COMP. 00 .... 
29 
VALENCE MATRIX, PAGE I. 
(I} DIFFUSE/NON. DIFF. 
(2) COMPACT/NON. COMP. 
(3) GRAVE/ACUTE 
(4) STRESSED/UNSTRES. 
GREEK (STANDARD) 
1 
+ 0 - 
0.00 0.00 0.00 0.00 
0 0.00 0.00 0.00 0.00 
- 0.00 0.00 0.00 33.33 
• 0.00 0.00 11.11 0.00 
0 33.33 0.00 0.00 0.00 
- 0.00 0.00 22.22 0.00 
+ 16.67 0.00 11.11 0.00 
0 0.00 0.00 11.11 33.33 
- 16.67 0.00 11.11 0.00 
+ 16.67 0.00 16.67 16.67 
0 0.00 0.00 0.00 0.00 
- 16.67 0.00 16.67 16.67 
2 
0 4" 
0.00 0.00 16.67 
0.00 0.00 0.00 
0.00 0.00 16.67 
0.00 0.00 0.00 
33.33 0.00 16.67 
0.00 33.33 16.67 
16.67 16.67 0.00 
0.00 0.00 0.00 
16.67 16.67 0.00 
16.67 16.67 16.67 
0.00 0.00 0.00 
16.67 16.67 16.67 
4 
0 
33.33 0.00 6.67 0.00 6.67 
0.00 16.67 13.33 0.00 13.33 
0.00 16.67 13.33 0.00 13.33 
0.00 0.00 13.33 0.00 13.33 
0.00 0.00 6.67 0.00 6.67 
0.00 0.00 13.33 0.00 13.33 
16.67 16.67 0.00 0.00 0.00 
0.00 0.00 0.00 0.00 0.00 
16.67 16.67 0.00 0.00 0.00 
0.00 16.67 13.33 0.00 13.33 
0.00 0.00 0.00 0.00 0.00 
33.33 16.67 20.00 0.00 20.00 
A 
v 
C~,IO 
I 
O00 OQO 000 
00~ 000 ~00 
OQ 
~Q 
0 ~O~ 
000 
C~00 
c~ c~ c~ 
-o 
• o o 
÷0 I 
QO0 
c~ c~ c~ 
0 
~QO 
QO~ 
31 
Not___._ee: Most (but not all) of the works listed in the Bibliography ware 
accessible to the author. Very complete bibliographies of 
Typological Studies, Mathematical Linguistics, or, the overlap, 
Mathematical Typologles will be found in: I, 4-6, 20, 25, 26 
29, 31, 32, 45, 51, 54, 55, 65. 
The bibliography of the primary sources used for the distinctive 
feature analysls as well as detailed discussion can be found 
in I. 

References

i. Afendras, Evangelos A. 1968. The Balkans as a Linguistic Area: 
A Study in Phonological Convergence. Unpublished Ph.D. 
Dissertation, The Johns Hopkins University, Baltimore• 

2. Andreyev, N.D. (ed.) 1965. S!atistiko-Komblnatorno~e modelirovanlJe 
Jazykov. Moscow. 

3. Avram, AndreJ. 1964. Sur la typologie phonologique quantitative. 
Revue Roumaine de Linsulstlque. IX. ,131-134. 

4. Birnbaum, Henrik. 1966. On Typology, Affinity, and Balkan Linguistics. 
Zb. za filologlJu i lin~vlstlku. IX. 17-30. Novl Sad. 

5. • 1968• RekonstrukcJa wewn~trzna, kolejno~6 synchonicznych 
regu~ gramatykl syntetyczneJ i zagadnienie naJdawnieJszych stosunko~w 
mi~dzy J~zykaml Ba~tycklml a SEowa~sklml. IJOSLAP XI. 1-24. 

6. • 1969. Deep Structure and Typologlcal Linguistics. Un- 
published manuscript. 

7. Borko, H. 1967. (Ed.) Automated Language Processln~: The State of the 
Ar_._tt. New York, Wiley. 

8. Civ Jan, T.F. 1966. Im~a suscestrltel no~e v balkanskix Jazykax (:k 
strukturno-ti~olg~iceski j xarakteristike balkanskogo Jazykovogo 
sojuza). Moscow, AkademiJa Nauk. 

9. Edmundson, A.P. 1967. Mathematical Models in Linguistics and Language 
Processing. In Borko, (ed.). 

I0. Gammon, E. 1967. Quantitative Linguistic Typologles. ~OICL. Bucharest. 
(Preprlnt). 

ii. Greenberg, J. 1957. The Nature and Use of Linguistic Typologles. IJA__~L. 
Vol. 23. 68-77. 

12. Grimes, J. 1962. Measures of Linguistic Divergence. P91CL The 
llague, Mouton. 44-50 

13. Hamp, Eri . 1962. On the Interconnection of Sound Production, Per- 
ception and Phonemic Typology. P41CPS. Mouton. 639-642. 

14. Harary, F. and H. Paper. 1957. Toward a General Calculus of Phonemic 
Distribution. Lg. 33. 143-169. 

15. Haugen, Einar. 1957. Language Contact. P81CL. 771-785. 

16. Havr~nek, B. 1933. Zur phonologische Geographie. (Das Vokalsystem 
des balkanischen Sprachbundes.) PIICPS. 

17. Herdan, G. 1960. Ty2e-TokenMathematies. A Textbook of Mathematical 
Linbuistics. (See also 7.5 which reviews Harary-Paper's Model.) 

18. Hockett, G.F. 1958. A Manual of Phonology. Baltimore. 

19. . 1967. Lansuage t Mathematics and Linguistics. The 
Hague, Mouton. 

20. Home, K.M. 1966. Language Typology. 19th and 20th Century Views. 
Georgetown University 10LAL. 

21. Isacenko, A.F. 1939. Versuch einer Typolosie der Slawlsehen Sprachenj 
LS1, 64 ff. 

22. Ivi6, P. 1962. On the Structure of Dialect Differentiation. Word. 
18. 53 ff. and numerous other works on Serbocroation, interference 
and general dialectology. 

23. Jakobson, R. 1962. Sur la th~orie des affinit~s phonologiques 
entre les langues. S.W. I. 234-246. Mouton. 

24. . 1962. Uber die phonologischen Sprachb~nde. S.W.I. 137-143. 

25. . 1962. K xarakteristike JevraziJskogo Jazykovogo 
soJuza. Reprinted in: Selected writin~ 9 I. 117-136. Mouton. 

26. , C.G. Fant and M. Halle. 1967. Preliminaries to Speech 
~. 7th Printing. Cambridge. M.I.T. Press. 

27. Kazaris, Kostas. 1964. Some Balkan Constructions Corresponding to 
W. European Infinitives. Unpublished 'Ph.D. Thesis, Indiana 
University, Bloomington. 

28. . 1967. On a Generative Grammar of the Balkan Languages, 
Foundations of Language. 3. 117-123. Dordrecht. 

29. Kiefer, F. 1968. Mathematical Linguistics in Eastern Europe. 
American Elsevier, New York. 

30. Kramsky, J. 1959. Quantitative Typology of Languages. Lan_~ 
and Speech. II, no. 2. 

31. Kueera, H. and G.K. Monroe. 1968. A Comparative ~uantitative Phono- 
logy of Russian~ Czech and German. New York. (A rather exten- 
sive bibliography with references to Ku~era's other works is 
appended.) 

32, Lehmann, W.P. 1962. Historical Linguistics. New York. 

33. Lekomceva, M.I. 1963. TipologiJa fonologiceskix slstem. In: 
Issledovani~a po StrukturnoJ Tipologii. Moscow. 

34, Lyons, John. 1962. Phonemic and non-Phonemic Phonology; Typological 
Reflections. IJAL. 28. 127-133. 

35, Mackey, W.F. 1953. Billnguallsm and Linguistic Structure. Culture 
XIV. 143-149. 

36. Makajev, E. A. (Ed.) 1966. Problemy Lin~visti~eskogo Analiza. 
Moscow. Nauka. 

37. Ma~ecki, M. 1933. Systemy wokalne j@zykow ba~kanskich. Sprswozdania 
Posiedze~ Polska Akademia UmieJ@tnos'ci. 38. No. 8. p. 3 ff. 

38. Marcus, S. 1963a. Typologie des langues et modules ioglques. Acta 
Mathematica Academiae Scientiarum Hunsaricae. XVI. No. 3-4. 

39. . 1963b. Un model matematic al fonemului. Studii ~i eercet~ri 
matematlce, vol. 14, 405-421. 

40, . 1966. Le modelage math~matique en phonologle. Cahiers de 
Lingulstique th~orlque et appllqu~e, 109-116. 

41. -- , and E. Vasillu. 1960. Math~matiques et phonologic, Th~orie 
des graphes et le consonantisme de la langue roumaine. Revue de 
math~matique s pur es et appliqu~es, vol. 5, 519-540, 681-703. 

42, Menzerath, P. 1950. Typology of Languages, JAS____AA22. 698-701. 

43. and W. Meyer-Eppler. 1950. Sprachtypologlsche Unter- 
Suchungen I. Lund. 

44. Meyer-Eppler, W. Anwendungs der Kommunikatlonsforschung auf 
lautsprachliche und typographische Probleme. Sprachforum, i: 
70-77. 

45, Papp, F. 1966, Mathematical Linguistics in the Soviet Union. 
Mouton, The Hague. (An extensive bibliography appended.) 

46. Peterson, G. and F. Harary. 1961. Foundations of Phonemic Theory. 
ProceedinBs of the Symposia in Applied Mathematics. 12. R. 
Jakobson (ed.), Rhode Island.AmericanMathematical Society. 

47, Petrovici, E. 1962. Les traits distinctlfs des phonemes roumalns. 
P41CPS. 723-728. Mouton, The Hague. 

48, Piercep J. E. 1957. A Statistical Study of Consonants in New World 
Languages. 1JAL. 23. 36-45, 94-108. 

49. . 1962. Possible Electronic Computation of Typological 
Indices for Linguistic Structures. IJAL. 28:215-226. 

50. PJotrovsklJ, R. G. 1969. InformacionnyJe izmereniJa Jazyka. 
Leningrad. (Several earlier works can be found in his biblio- 
graphies as well as that in Papp (1966); some of his later 
work is also very pertinent to the statistical study of phono- 
logy.) 

51. Plath, W. 1963. Mathematical Linguistics. In: Trends in European 
and American Linguistics 1930-1960. Mohrmann, Sommerfelt and 
Whatmough (Eds.). Spectrum, Utrecht-Antwerp. 

52. Postovalova, V.I. 1966. 0 8o~eta~emostl differenclalWnyx prlznakov 
soglasnyx fonem sovremennogo russkogo Jazyka. In Problem~ 
Lin~vlsti~eskogo Anallza. Moscow. 

53. Reichenkron, G. 1962-3. Der Typus der Balkansprachen. Zeitschrlft 
for Balkanologie. E. 91-122. Wiesbaden. 

54. Revzin, I.I. 1962. Modell Jazyka. Moscow. 

55. . 1967. Method modellrqvanlJa i tipolo~i~a slav~ansklx az~. 
Moscow. 

56. Sandfeld, K. 1932. LinEuistique Balkanique. Paris. • 

57. Saporta, S. 1957. Methodological Considerations Regarding a Statis- 
tical Approach to Typologies. IJAL. 23:109-113. 

58. Skali~ka, V. 1958. Typologie slovanskg"ch Jazyk~, svl~st~ ru~tinyo ~R, 
78 ff. 

59. Spang-Hanssen, H. 1962. Mathematical Linguistics - Trend in Name 
or in Fact?PglCL. The Hague, Mouton. 61-71 (incl. discussion). 
35 

60. Stankiewicz, E. 1958. Toward a Phonemic Typology of the Slavic 
Languages. AC41CS The Hague, Mouton. 

61. Trnka, B. 1936. General Laws of Phonemic Combinations. TCLP. 6. 
57-62. 

62. Trubetzkoy, N.S. 1929. Zur allgemeinen Theorie der phonologischen 
Vokalsysteme. TCLP. 1 39-67. 

63. . Principes de phonologie. (French translation of J. 
Cantineau). Paris. 

64. Ungeheuer, G. 1959. Das loglstische Fundament bln~rer phonem- 
klassifikationen. Studia Lingulstica. XIII: 69-97. 

65. Uspenskij, B.A. 1962. Principy Strukturnoj Tipolo~ii. Hoscow. 

66. Voegelin, C.F. 1956. The@Scope of whole System (Distinctive Feature) 
and Subsystem Typologies. Word. XII. 444 ff. 

67. , F.M. Voegelin, S. Wurm, O'Grady and T. Matsuda. 1963. 
Obtaining an Index of Phonological differentiation from the 
construction of non-existent Minimax systems. IJAL. 29. No. i 5-28. 

68. Weinreich~ U. 1953. Languages in Contact. New York. 

69. , 1957. Research Frontiers in Bilinguallsm Studies. 
PSICL. 786-810 (including discussion). 

70. Weils, R. 1954. Archlvlng and Language Typology. IJAL. 20 101-107. 

71. Wolff, H. 1959. Subsystem Typologles and Area Linguistics. AL i, 
No. 7, 1-88. 

72. Birnbau~% Henrlk. 1968. SlavJanskije Jazyki na Balkanax i ponJ atiJe 
tak nazyvajemyx jazykovyx sojuzov. Glossa. vol. 2-1. 70-92. "~ 

73. ~irokov, O.S. 1964 Voprosy balkanskogo vtorlcnogo Jazykovogo rodstva 
(primenenije Statlstiki v diaxroni~eskoJ fonologii). In:Proble~v 
sravnitel'noj ~rammatiki indo2evropejskix jazykov. Nau~na--~a sessi~. 
Tezisy dokladov. Moscow. 68-69 

74. UspenskiJ, B.A. 1965. StrukturnaJa TipoloEiJa Jazykov. Moscow. 
