From Unicode to Typography, a Case Study the Greek Script

Abstract

this paper we will try to synthesize, from a typographical point of view, the various instances of Greek script. Globally, one can say that the Greek script is used for the following cases :

Full text

From Unicode to Typography, a Case Study: the Greek Script
Yannis Haralambous
Atelier Fluxus Virus
187 rue Nationale
59800 Lille, France
yannis@fluxus-virus.com
Contents
1 The Greek Language 3
1.1
Classification of the Greek Language, Notations ................... 3
1.1.1
Ancient Greek: Α, τΑ, αΑ ........................... 3
1.1.2 “
Purified” Greek (kathare´vousa): Κ ...................... 4
1.1.3
Vernacular Greek (dimotikı´): ∆, π∆, µ∆, κ∆ ................. 4
1.2
Letters ......................................... 5
1.2.1
Archaic letters ................................. 5
1.2.2
The letter yod ................................. 7
1.2.3
Variant forms ................................. 7
1.2.4
The turned letters iota and upsilon with tilde ................. 9
1.2.5
The ου and κα ligatures ............................ 9
1.3
Accentuation and Diacritics .............................. 11
1.3.1
Accents and breathings ............................ 11
1.3.2
Diaeresis .................................... 12
1.3.3
Subscript and adscript iota ........................... 13
1.3.4
The monotonic system ............................. 14
1.3.5
The TONISMOS software ........................... 15
1.3.6
Other diacritics used in Greek ......................... 15
1.3.7
Other languages written in the Greek script .................. 15
1.4
The Greek Numbering Systems ............................ 16
1.4.1
The Acrophonic Numbering System ...................... 16
1.4.2
The Alphabetic Numerals ........................... 17
1.5
Hyphenation ...................................... 18
1.5.1
Hyphenation of Α and Κ ............................ 18
1.5.2
Hyphenation of ∆ ............................... 19
1.6
Punctuation and typographical conventions ...................... 19
1.6.1
Punctuation .................................. 19
1.6.2
Hanging diacritics ............................... 20
1.6.3
Letterspacing ................................. 20
1.7
Typefaces ....................................... 21
1

From Unicode to Typography, aCaseStudy: the Greek Script
1.7.1 The typefaces in the apla´ style. ........................ 22
1.7.2
The Times family typefaces........................... 22
1.7.3
The “scholarly” typefaces: Porson, Greek Sans 486, New Hellenic. ..... 22
1.7.4
The adaptations of Latin typefaces. ...................... 22
1.7.5
The original creations of the last few years................... 23
1.7.6
Samples .................................... 24
2
Mathematics 25
2.1
Greek Letters and Mathematical Typography ..................... 25
Introduction
LΟδοÊσσεου| ’χιεµνο| κϊ καπν¿ν
ποτρ¾οσκοντα νοεζαϊ χε|
γκϊεε| [Viz
, p. 135]
The Greek script has a long history and, although the Greek language is spoken only by about 20 million
people
, the Greek script is one of the most widely known in the world. In this paper we will try to syn-
thesize, from a typographical point of view, the various instances of Greek script. Globally, one can say
that the Greek script is used for the following cases
:
1.
Greek language ;
2.
Mathematics ;
3.
Universally used symbols (such as µ for “micro,” Ω for “Ohm,” etc.) ;
4.
International Phonetic Alphabet ;
5.
African languages.
The typographical behaviour of letters is quite different in each of these cases: not only the shape of let-
ters can be quite different, but they also behave differently with respect to standard typographical trans-
formations (change of case, italics, etc.). InthefollowingtablewesummarizethebehaviouroftheGreek
script vs
. the context in which it is used:
Example Uppercase Italics Bold Variants
Greek language νθρωπο Yes Yes Yes Yes
Mathematics α =sin(ω − 2π) SD Style dep. SD SD
Univ. symbols 10 µΩ No Yes Yes No
IPA fªR'ʃteən No Slanted Yes SD
African languages tɔxªtcxªwo Yes Yes Yes No
where “SD” stands for “semantically different.”
In the following sections we will investigate the first two cases:
1
the Greek language and Greek math-
ematical symbols. The purpose of this paper is to give directives for the proper use of the Greek script
for all kinds of Unicode users
: font designers, typesetters, authors, publishers, developers of Unicode-
compliant software.
1
Originally, the paper was intended to cover all five cases. Unfortunately because of lack of time (and space... the paper is
already almost
40 pages long) only the first two cases are covered.
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1 The Greek Language
1.1 Classification of the Greek Language, Notations
As for every language, Greek has evolved continually during its existence. Hence, any classification of it
into different types can only be artificial
; nevertheless we need to classify it from a typographical point
of view
, into three types and their sub-types: ancient Greek, which we will denote Α (with two subtypes:
τΑ and αΑ), kathare´vousa, for which we will write Κ and dimotikı´ written as ∆ (with three sub-types:
κ∆, π∆ and µ∆). Follows the rationale behind this classification:
1.1.1 Ancient Greek: Α, τΑ, αΑ
We will call Α the typographical representation of whatever dates from ancient times until the Renais
-
sance.
Some history: until the 3rd century a.d. only capital letters were used ; from the 4th century and
afterwards the capital letters were slowly transformed into lowercase
-only ; finally, in the 10th centu-
ry scribes started using both upper and lowercase letters [Mio, pp. 77-89]. Accents and breathings were
introduced by Aristophanes the Byzantine
(257-180 b.c.) but have been applied regularly only since
the
8th century a.d. [Mio, p.57].
Nowadays, when we represent texts of those periods typographically, we have three choices:
(
a) to use epigraphical typefaces ;
(
b) to reproduce accents and breathings, whenever they are used in the original, faithfully, but with
modern types
;
(
c) to follow modern rules of accentuation and complete the missing accents and breathings.
These three methods can all be applied to the same text, according to the targeted audience: solution (a)
will apply best for an audience of epigraphologists and paleographers, and may be completely unreadable
for the average Greek speaker or scholar
; solution (b) is a good compromise: in most of the times it will
be accurate enough for the paleographer
, and still comprehensible (although sometimes obscure) by the
common mortal
; solution (c) is the one applied in text- and schoolbooks: content is more important than
form and spelling is standardized by the editor of the text
.
In this paper we will not enter into solution (a): Unicode does not cover (yet) epigraphical charac-
ters, and this subject would lead us too far. We will give more details on the differences between solutions
(b) and (c) in §1.3.1, when we will describe the accent and breathing system. These two possible repre-
sentations of Α are our two “sub-types”: τΑ stands for “standardized typographical representation” and
αΑ for
“non-standardized typographical representation.” Here is an example: in Figure 1, the reader can
see the
“Nikandre” inscription (6th century b.c.). Here is the typographical representation of part of this
inscription
, given by [Fri, p. 274]:
h
¯
ορη ∆εινοδ¬κh
¯
οτ
¯
˜
οΝα
hσ¬
¯
ο, hσοχοv λ(λ)h
¯
ον.
In [Phi, ins0090.txt] we find an alternative typographical representation of the same inscription (some
words in
“rectified” forms):
κοËρη ∆εινοδ¬κ
˘
η
¯
οτb Ναχσ¬ου, χσοχοv λ(λ)
˘
´
η
¯
ον.
Both representations are αΑ ; here is a temptative representation in τΑ (standardized ancient Greek
spelling
), partly obtained by applying the Athenian spelling reform of 403 b.c. where long ε and ο were
replaced by
η and ω, and combinations χσ and φσ by ξ and ψ [Fri, p. 106]:
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Figure 1: “Nikandre” inscription,6th century b.c..
κ¾ρη ∆εινοδ¬κου τοÖ Ναξ¬ου, ξοχοv λλων.
This τΑ form can be understood by any Greek reader ; this is not the case of the first αΑ form, which
requires knowledge of paleography to be understood
.
The distinction between τΑ and αΑ is important to us, because not all characters necessary for the
latter are provided by Unicode
, nor can all of them be obtained by combining character sequences.
1.1.2 “Purified” Greek (kathare´vousa): Κ
In the early
19th century, as the modern Greek nation came to being, freeing itself from the Ottoman
empire
, a few Greek scholars, living in Europe, began a project whose goal was to “purify” the language
actually spoken in Greece
, by bringing it closer to ancient Greek. They aimed to replace words borrowed
from Latin
, Italian, Turkish, Slavic, Albanian, Armenian, Arabic, etc. by, either new words with Greek
etymology
, or original ancient Greek words. They also tried to establish a grammar of “purified” modern
Greek
. This project was taken over by scholars in Greece, and until the end of the 19th century was taken
to such an extent that the result
, the so called arkha
ú
ızousa kathare´vousa “ancient-like,” became totally
uncomprehensible to the common reader
. In the 20th century, under the pressure of supporters of the
spoken language
(dimotikı´, see §1.1.3), Κ became simpler. Its latest version, aplı´ kathare´vousa “simple,”
wasusedinGreeceuntilthe1970s, for official, technical and scientific documents, as well as for some
newspapers
.
This “purification” project could be compared to the project of revival of Hebrew language in post-
war Israel. The project in Israel succeeded, as Ivrit has become a living language, while the kathare´vousa
project was officially abandoned in
1982.
The spelling and hyphenation rules of Κ are the same as for τΑ.
1.1.3 Vernacular Greek (dimotikı´): ∆, π∆, µ∆, κ∆
Dimotikı´
, which could be the only form of contemporary Greek language if there had been no “purifica-
tion” project in the 19th century, is the continuation of medieval and Renaissance Greek, as it had been
spoken and written in Greece
, before, during Ottoman occupancy and afterwards.
The three subtypes κ∆, π∆ and µ∆ correspond to three stages in the (typographical) history of ∆.
First, at the late 19th and early 20th centuries, ∆ was still rarely printed. When this was the case, it was
considered to be an
“exotic,” deviated form of Κ, and spelled accordingly. This is a very interesting period,
because authors, in the absence of a standard ∆ grammar, didn’tknowhowtowrite∆ and invented weird
spellings only to give their writings pseudo
-grammatical foundations. In some sense, we can say that ∆
was not written
, but transcribed. It is this type of ∆ which we will call κ∆ (“dimotikı´ in a kathare´vousa
context
”).
Later on, ∆ was standardized and slowly replaced Κ in all facets of life. ∆, like Κ started by being
written with three accents and two breathings
. In the early fifties one of the accents (varı´a) was abolished,
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but still two accents and two breathings remained. We will call π∆ (“polytonic” =multi-accent), ∆ written
with two or three accents and breathings
. In 1981, one accent and the two breathings were abolished,
so that only one accent remained (oxı´a). We will call ∆ written with only one accent µ∆ (“monotonic” =
one
-accent).
The 1981 and subsequent reforms have also simplified spelling and hyphenation rules. Here is an
example of a sentence
, first written in κ∆ [Per, p.30], then in π∆ (spelling as in [Wen]) and finally in µ∆
(spelling as in [Teg]):
κ∆: Χαρτε νεUα´v, χαρτε νεUο τ δροσερ σαv νεUτα
π∆: Χαρε´τε νειv, χαρε´τε νειο τ δροσερ σαv νειτα
µ∆: Χαρε¬τε νιεv, χαρε¬τε νιοι τα δροσερ σαv νιτα
Once again, the distinction between κ∆ and π∆ is important for us, because Unicode does not provide
all necessary characters to typeset in κ∆
. Also, the distinction between Κ and π∆ (and a fortiori µ∆) is
important because hyphenation rules are different
(see §1.5).
1.2 Letters
In this section we will describe the letters used by the Greek language, and the corresponding Unicode
characters
, and glyphs needed to typeset them. The basic Greek alphabet (common to Α, Κ and ∆) is:
αβγδεζη θικλµ νξοπρστυφχψω
ΑΒΓ∆ΕΖΗΘΙΚΛΜΝΞΟΠΡΣΤΥΦΧΨΩ
The letter sigma has a final form, written . Although this is a contextual property, there is a Unicode
character for this letter
: U+03C2 ; this is perfectly justified, because in some cases there is a semantical
difference between the medial and final form of
σ: for example, “φιλοσ.,” is necessarily the abreviation
of some word
(like φιλοσοφα) while “φλο.” is a single non-abbreviated word, followed by a sentence
period
. In cases like this the form of the σ cannot be determined by a simple algorithm.
There is a typographical curiosum, involving the final sigma: the Grammar of Pontiac Language by K. Topkha-
ras ([Top], reprinted in [Top
2
]), published in 1928, in the Soviet Union, for the (Pontiac) Greek speaking minori-
ties. This grammar completely abolishes accents, breathings, diphtongs, and uses only part of the alphabet. The 
is used for the sound ‘s’, and a double  for the English ‘sh’. Here is an excerpt of this book [Top, p.49]:
Σιν γλοανεµυν επεµνεν α αρχεον τιν γλοαν κε το ακλιτον το λεκοπον α πυ µεταχιρικυανατο ι πα-
λιεµυν, ονταν εθελναν να φανερονε πο καπιον ιδιοτιταν πυ ε εναν προοπον για πραµαν, λιφτακε-
τιατο καπιον αλο λ.χ. δινατο κε αδινατο.
1.2.1 Archaic letters
There are six additional letters
, used in Α and in numerals (see §1.4.2).
1.2.1.1 The digamma fg This letter represented the sound of Latin v (while β had rather the sound
of b
). It became an F in Latin. Its place in the alphabet is between ε and ζ.
In Figures 8a-e, the reader can see specially designed digammas in the various Monotype fonts (some
digammas and other archaic letters designed by Monotype itself
, others added by the author). It is inter-
esting to note that in Greece, although the specially designed digammas have always existed in Monotype
typefaces
, the real Latin F has been preferred in typesetting, maybe because in a Greek-only context, a
Latin letter is easier to distinguish than a specially designed letter whose goal is to be homogeneous with
the rest of the typeface
.
Here is an example, taken from [Oik, p. 180] (and below the same sentence, using the specially de-
signed digamma):
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πα¬ω (= χτυπ, θ. παF-, πF-j-ω = πα¬ω), πρτ. παιον, ...
πα¬ω (
= χτυπ, θ. παf-, πf-j-ω = πα¬ω), πρτ. παιον, ...
Indeed, in the first example the digamma can be more clearly distinguished ; the price to pay is a slight
loss of typographical quality
: a capital upright letter in the middle of a word typeset in lower case.
Digamma has not had the same typographical evolution as other Greek letters. Because of this, it
seems that a certain number of publishers and typographers wish to emphasize its epigraphical nature
and sometimes typeset it in upper case
(while not necessary) and even sometimes in a different font (for
example
, [Bai] uses a non-serif font while the Greek text is typeset in apla´). It is hard to say if this is
a stylistic choice
, or a technical necessity ; nevertheless the author considers it to be bad typographical
practice
.
In Unicode v2.1, letter digamma is encoded by characters U+03DD and U+03DC (lower and upper
case
).
1.2.1.2 The stigma  d This letter is used as a numeral only ; it represents number six (see §1.4.2).
There is a general confusion between stigma and digamma, in fact they have the same origin. Neverthe-
less, nowadays, digamma is used only in text and stigma only as a numeral. Some additional confusion
comes from the fact that early Greek typefaces use the stigma as a sigma
-tau ligature ; so that, for ex-
ample, τ στρεο στριγµα is written τ ρεο ριγµα. In modern Greek, in absence of a stigma, the
letters
στ are used for numeral 6.
The capital version of stigma has always been a problem for type designers. In Monotype fonts, one
finds glyphs similar to the lowercase stigma
, scaled to match the capital letters, as d (although this letter
resembles more a final sigma
 than a stigma ). The author has designed a capital stigma d for the apla´
typeface
, according to 19th and early 20th century originals: ν τει cΑΩid´. Another version of capital
stigma has been designed for use in ∆
: _ ; this is a ligature between a capital sigma and a lowercase tau:
according to the style of the surrounding text, one can choose between ´d´or στ´_´for number six.
In Unicode v2.1, letter stigma is encoded by characters U+03DB and U+03DA (lower and upper case).
1.2.1.3 The textual koppa hi This letter is the ancestor of the Latin q Q. In ancient Greece to
treat a person as illiterate or ignorant
, one would say: “οδ κππα γιγνσκων” (“he doesn’tevenknow
the koppa
”) [Ele, p.6]. The place of h in the alphabet is between π and ρ. It has been used widely in texts
before the Athenian reform of
403 b.c. (as in our example on page 3, in the word hρη, nowadays written
κρη). As in the case of the digamma, scholars sometimes use a Latin q instead of the specially designed
h, maybe because the latter can be mistakenly taken for a ρ(rho).
For the design of the capital textual koppa i, the author has followed [Boy].
This letter—both in upper- and lowercase form—is necessary for typesetting αΑ. Therefore the au-
thor considers that it should be included in Unicode.
1.2.1.4 The numeric koppa  This letter is used as a numeral only ; it represents number 90
(
see §1.4.2). It is a variant form of hi, nowadays semantically different: at some time the two forms
of koppa were used in parallel
, and progressively the “straight” shape was used for numerals only, and
the
“round” shape only in text. There seems to be no standard glyph for the capital version of ; often
(certainly because of its geometric, non-alphabetical nature) the same glyph is used for lowercase and
uppercase
. The author has designed two uppercase  candidates: p and q, the former being curly and
the second carrying serifs
; neither one of them is entirely satisfactory.
In Unicode v2.1, letter numeric koppa is encoded as characters U+03DF and U+03DE (lower and upper
case
).
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1.2.1.5 The sampi jk Thisletterisusedasanumeralonly; it represents number 900 (see §1.4.2).
For the design of the capital sampi k, the author has followed [Boy]. In some references, sampi is written
like an epigraphical
Μ(see [Lid, p. 1562] for a detailed explanation).
In Unicode v2.1, letter sampi is encoded as characters U+03E1 and U+03E0 (lower and upper case).
1.2.2
The letter yod
This letter is quite special
. It is included in Unicode as U+03F3. It represents a phoneme which has never
been written in ancient times
. Nevertheless that phoneme is necessary to explain certain grammatical
phenomena
, for example the fact that a root like ρπαγ- produces the noun ρπαγ and the verb ρπζω:
we say that the verb ending is -jω and that ρπαγ +jω = ρπζω [Oik, p.38].
In fact it is not a coincidence that the sound of letter yod is precisely the sound of ‘j’ in German: this
letter was introduced by German scholars and publishers
. It is very interesting to note that the yod is not
always written j
: in fact it depends on the background language of the document.
This may well be a unique case in the Unicode standard: a character whose glyph depends on the
background language
, i.e. not of the language in which it is used (ancient Greek) but of the main language
of the document
(English if it is an English translation or critical edition, French if it is a French one,
and so on). In France, the yod is often written y: [Fro, p. 114] and [Ver, p.11] use y throughout, [Rag, p.7]
mentions both j and y but afterwards uses j, while [Bai, for example p. 562, µθjoc] uses j.
According to [LeG], French scholars influenced by the German school first wrote the yod j. Later
on the use of y prevailed
. Finally, more recently, scholars have returned to j, considering it to be an IPA
symbol
.
This particular nature of yod justifies its presence in Unicode (taking a plain Latin j would not allow
French users to represent it by a y
). Nevertheless, the uppercase version of yod is missing: well under-
stood, yod will never appear at the beginning of a word, but the uppercase version is necessary for all-caps
titles
: for example in [Oik,32] we find the section title “Μετθεση του j (επνθεση).” If that title was to
be typeset in all
-caps, it would become “ΜΕΤΑΘΕΣΗ ΤΟΥ J (ΕΠΕΝΘΕΣΗ)” and the uppercase yod
would be necessary
.
1.2.3
Variant forms
Some of the letters have variant forms
. As we will see, they are all font-dependent, and are not seman-
tically different from the original letters, at least in the context of Greek text ; they can be semantically
different in mathematics
.
1.
The beta without descender:.Sometimes the following rule is applied:βis used at the begin-
ning of words, and  otherwise, as in the words βλη, βιλο, βραρο. This rule seems to be
geographically very restricted
: the author has seen it applied in Greek books of the late 19th and
early
20th century (Α, Κ and κ∆); it seems to be applied, rigorously and continuously until today,
only in France: [Bai, p. 145], [Imp, p.95], [Ver, p.1], [Rag, p.2], all mention it and apply it ; the
monumental
[Ste] applies it strictly ; all Bude´ and Le Cerf editions of classical Greek texts apply it
as well
. On the other hand, this rule is unknown in the rest of the world: neither [Oik] (Greece),
nor [Ka¨g], [Fri], [Wen] (Germany), or [Lid], [Chi], [Bet] (England/US), or [Bol], [Sov] (Russia), or
[Nak] (Japan) mention it.
The form of β can be easily determined by an algorithm and hence this property is purely contextual
(like Arabic contextual forms, and not like the σ/ case where there can eventually be a semantic
layer
). The variant beta U+03d0 is called “Greek beta symbol” in Unicode, which implies that this
character is intended for mathematics
; nevertheless the author can hardly imagine this character
used in mathematics since it would be hard to distinguish from a
(more or less cursive) Latin b.
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Figure 2: Sample taken from a 1489 book, illustrating the random use of π and \ .
2. The “open” and “closed” letter pairs theta and phi:/θ, φ/(Unicode U+03D1, U+03B8, U+03C6,
U+03D5). These variant forms are mentionned in most grammars and dictionaries, but the author
was not able to detect any contextual rule involving them
. It is interesting to note that [Imp, p.95]
suggests that the open theta  be used at the beginning of words ; this rule is mentioned only by
[Imp] and the author has never seen it applied.
Nevertheless, open and closed versions of theta and phi can be semantically different (again with
certain restrictions
) in mathematics. Concerning the open and closed theta, [Caj, §631] writes: In
limit and remainder theorems Cauchy designated by θ an undetermined value [
...] Some writers
employ the form ϑ of the Greek letter
, and in [Caj, §657]: Harkness and Morley represent Jordan’s
θ, θ
1
,θ
2
,θ
2
by ϑ, ϑ
1
,ϑ
2
,ϑ
2
respectively. Goldberg, in [Gol], uses alternatively φ and ϕ whenever a
new object is defined and called phi
: this helps the reader switch between the different uses of the
same letter as mathematical symbol
.
This semantical difference between open and closed phi and theta in mathematics justifies their
presence in Unicode
.
3.
The “curly” capital Upsilon Υ(U+03D2) and lowercase kappa κ(U+03F0). These are purely stylistic ;
in fact they are the normal versions of uppercase upsilon and lowercase kappa in the apla´ font, while
the
“standard” versions Υκof the letters, in other words the glyphs shown in the Unicode book,
belong to the Times family of fonts (see Figure 8).
It is unfortunate that a glyph difference between two fonts has produced different Unicode char-
acters. Even in mathematics, the choice between κ and κ seemstobestylistic, and the difference
between Y
(Latin Y) and Υ is too small to be immediately recognizable.
4.
The “curly tail” rho 4 (U+03F1). The difference between ρ and 4 is simply that the latter is used
mainly in italic fonts
:τραvs.τÞρα. Again, in mathematics, the choice between ρ and % seems to
be purely stylistic
.
5.
The “round” pi \ (U+03D6). This letter has been a variant of π from the very first days of Greek
typography
: in Figure 2, thereadercanseeanexcerptof[Pol], a book printed in 1489 (!). In this
excerpt both versions of pi have been used
, apparently randomly.
Once again, [Imp, p.95] suggests that the round pi be used only at the beginning of word. Accord-
ing to [Tre], this rule has been applied in certain French journals (for example the Me´moires de la
Socie´te´ de Linguistique in the late
19th and early 20th century);[Tre] applies it in all of his writings ;
here is an extract of [Tre
2
, §43]:
γγων µοι \Aν τοπ’ πω εδω τ ε
Sophocle, Phil. 238 “il m’atoutre´ve´le´ pour que
je sache qui tu es
” ... \ολλG\λον γεγωνεE στι νκτωρ  µε’ µραν Antiphon 5,44
“
la voix porte beaucoup plus loin la nuit que le jour...”
[Imp] again, but in a different chapter (the one on typesetting of mathematics, p. 108) calls this
letter
“Doric pi.”
6.
The lunate sigma ]^. This letter looks like a Latin c, but without the bulb. It is the Byzantine form
of letter sigma
(which led to the Cyrillic C c). It is mainly used in Byzantine fonts: ÛˆÙÂÚ ÛˆÛÔÓ
ËÌ·˜
. [Bet] uses it as a remplacement for σ/, with the following argument: The [lunate] form of
sigma [
...]is, for reasons of convenience, the one increasingly used in modern editions. And indeed,
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From Unicode to Typography, aCaseStudy: the Greek Script
it is used by the Oxford Classical Editions.
One could say that the lunate sigma is again simply a stylistic variant of the regular sigma, without
contextuality
. Of course it would be interesting for the paleographer to mark up the different forms
of sigma in a text
, but this concerns also many other letters which have had variant forms. The only
argument that could justify the presence of this letter in Unicode is to encode texts in which the
contextual form of sigmas is not known
.
It should also be noted en passant, that if we consider the lunate sigma to be a useful Unicode
character
, then there should necessarily also be a capital version of it in Unicode.
1.2.4
The turned letters iota and upsilon with tilde
Letters
U and W are turned versions of letters iota and upsilon with tilde E,.Their capital versions V and
X, used a breve-like accent instead of the tilde. These letters are widely used in κ∆ to represent semi-
consonants (Uα is pronounced like the German ‘ja’ or the Russian ‘я’, while, inthesamecontext,ιαwould
be rather ‘i
-a’ in German or ‘иа’ in Russian).
It is interesting to note that the tilde of U and W has been used by typographers for reasons of con-
venience only (they simply turned around a type). In fact it should theoretically be a breve-like accent,
like the one of the uppercase versions. This accent is called ife´n or enotiko´n. In Unicode, there is already
the character U+203F which has the same name and shape
, but this character is a (spacing) punctuation
mark
, and not a combining mark, as needed in our case.
In Figure 3 the reader can see examples of the use of these letters, both in apla´ and in Times fonts.
These letters are not yet represented by Unicode characters. The author believes that they are necessary
for the encoding of κ∆ texts
, and considers that their insertion in Unicode would be very useful.
1.2.5
The ου and κα ligatures
In early Greek prints
, and until the early 19th century, a big numbers of esthetic ligatures was used in
Greek fonts
(the extreme case being the typeface Les grecs du roi by Claude Garamont, having thousands
of ligatures
). Some of these ligatures remained in titling or in the hand-written language and are still used
today
: the most important are the ου ligature and the κα ligature (“κα” meaning “and”). [Myl] has
included the former in his Euclid font
. Ligature κα is included in Unicode v2.1 U+03D7 and [wEve] pro-
poses the insertion of ligature ου. The author does not consider either of these ligatures to be necessary
because these ligatures are simply esthetic
(like the ff ligatures in Latin typefaces). Furthermore, they
do not appear in ordinary printed text
(the example given in [Myl, p.49] is purely experimental). [wEve]
argues that the Latin “et” has undergone a similar process and finally became the independent character
&
. This is of course true, but in Greece there is a tendancy of using the κα ligature in ordinary printed
text
, and, in the author’s opinion, it is not the role of Unicode to cause such an artificial evolution.
Of course, it would be marvelous to have fonts with the ligatures of the early Greek typefaces, as
one can find today Latin
, Fraktur and Arabic fonts with more and more esthetic ligatures. This issue is
independent of Unicode
. In Figure 4 the reader can see a sample from a book printed in Constantinople
in
1810 ([Pat], taken from [Kef, p. 117]), showing the ου and κα ligatures, as well as λλ, ει, αι, εν and στ
(
stigma-like) ligatures.
It should be noted, en passant, that in Greek titling, uppercase versions of the κα and ου ligatures
are used as well
.
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From Unicode to Typography, aCaseStudy: the Greek Script
Example in apla´ font [Per
2
, p.53]. Line 1 is in Κ, lines 2-9 in κ∆. Words
containing
U:γU(lines 3, 9), πεU(line 3), λUου (line 5), ’µµτUα(line 8),
µU(
line 9). The word δW on line 5 contains W.
Example in Times font [Kor, p.7]. Line 4 is in Κ, lines 1-3 and 5-9 in κ∆.
Words containing U:γU(lines 3, 6), γυU(line 3), γυUο (line 6), χλUα(line 7),
ΛU(
line 9). The spelling of  λπαι and ναι (both line 8) is typical of κ∆ ;
today these words would be written ο λπε and εναι.
Figure 3: Two examples of the use of turned iota and upsilon with tilde, in apla´ and
Times font
.
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From Unicode to Typography, aCaseStudy: the Greek Script
Figure 4: Sample from [Pat]: the ligature ου is used on lines 1 and 3 ; κα is used
on lines
1 and 4; λλon lines 2 and 3;ειon lines 2 and 5; αιon lines 3 and 5;ενon
line
4; στ()on line 5.
1.3 Accentuation and Diacritics
1.3.1 Accents and breathings
Greek vowels
(αεηιουω)can take the following three accents: acute oxı´a, grave varı´a, circumflex
perispome´ni
. While the glyphs of oxı´a and varı´a are simply those of acute and grave accent, the glyph
of perispome´ni can have many forms
: historically it started as a combination of acute and grave, but in
modern typographical representation we encounter either a tilde
(in apla´ and Times: C) or an inverted
breve
(in Porson and Greek Sans: ) or a macron (in Linotype Helvetica: , and other “modern” fonts).
2
When two vowels form a diphthong (two vowels pronounced as one, for example ου, pronounced ‘ou’),
then the accent is placed on the second vowel.
If the vowel is the first letter of the word, it must also take a breathing pne´vma. There are two breath-
ings: the rough one (dası´a, asper) H and the smooth one (psilı´, lenis) L. When combined with a breathing,
the accent is placed to the right of it when it is oxı´a or varı´a, or on top of it, when it is a perispome´ni; in
some typefaces
, the breathing is connected to the perispome´ni so that they seem to form a single accent:
qw(Linotype Helvetica), yt(Linotype New Century Schoolbook). If the word starts with a dipthong,
it is the second vowel that carries the breathing: οδν.
Uppercase letters do not take accents nor breathings, in all-caps typesetting: νθρωπο → ΑΝΘΡΩ-
ΠΟΣ.
In mixed lower/uppercase mode, accents and spirits are placed in front of the capital letter: ν-
θρωπο
→ MΑνθρωπο.
In Α (and some overzealous versions of Κ) there is also a consonant taking breathings: the rho HΡ.
Its behaviour is special: at the beginning of a word, the rho takes a dası´a: θυµο, inside a word it takes
no breathing
: ριον, but in the case of two consecutive rhos, the first takes psilı´ and the second dası´a:
Πο
[Ka¨g, p.3]. The latter rule seems not to be applied in France (neither [Bai] nor [Rag] mention or
apply it
).
Afewrules: let us count word syllables from the end ; accents can be placed only on syllables 1, 2
and 3. Syllable 3 can only take the oxı´a accent, syllable 2 can take oxı´a or perispome´ni, syllable 1 any
of the three accents
. On syllable 1, the choice between oxı´a and varı´a is contextual: when the word is
followed by a punctuation mark or an enclitic
(see [Bet, p. 252]) we use oxı´a, otherwise varı´a: σ κα
γ,  πατρ µου.
In the case of the enclitic, if the first word is accented on syllable 3, then a second
oxı´a accent is placed on syllable
1: νθρωπ τι.
In τΑ there are some accentuation restrictions: vowels ε and ο cannot take the perispome´ni accent ;
vowel υ cannot take the psilı´ breathing. These restrictions do not apply to αΑ. Other irregularities can
occur in αΑ
, for example accents and breathings written separately on diphthongs:Eον, Eναι, [Mio, p.58],
2
A typographer’s joke would be that “the circumflex accent has three forms, none of them being a circumflex.”
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th International Unicode Conference 11 Boston, MA, March 1999

From Unicode to Typography, aCaseStudy: the Greek Script
double accents on words µν and δ [idem], words accented on syllable 4, etc.
There are three grammatical phenomena of importance to typosetters: crasis kra´sis, elision e´kthlipsis
and suppresion afe´resis
.
• Crasis is the contraction of a vowel or diphthong at the end of a word, with the vowel or diphthong
of the following word
: τ νοµα → τονοµα. As we see in this example, the breathing appears to
be inside the word
. This breathing has the form of a psilı´ but is actually called koronı´s ; when the
second word is accented on that syllable
, then the accent is combined with the koronı´s. When the
first word takes a breathing then the resulting contracted word appears to have two breathings
: γ
οµαι
→ γµαι. When the first word is an aspirated monosyllabic (aone-syllable word with dası´a
breathing
) then instead of a koronı´s we write a dası´a:  νρ → νρ (in this case the breathing
seems to keep its name
: the author has found no trace of a different name for the “dası´a-shaped
koronı´s
.”
• Elision is the juxtaposition of a final vowel and an initial vowel: π οκα → πL οκα. The mark
that replaces the final vowel of the first word has again the shape of psilı´ and is called apostrophe
apo´strofos
.
• Suppresion (or inverse elision) is the opposite phenomenon: instead of removing the final vow-
el of the first word, we remove the initial vowel of the second word:  γ →  Lγ. Again, the
mark used is an apostrophe
, but this time it may happen that the initial syllable of the second word
already carries an accent
: in that case the accent is combined with the apostrophe and we obtain
constructions like
:  ναξ →  Mναξ (this is indeed strange because accents and breathings are
never placed upon
, or in front of, consonants).
• Elision and suppresion can be combined in the same word: πο στι  Πλοτο ; → πο LσθL  Πλο-
το ;  π σπδων
→  LπL σπδων [Rag, p.9].
It should be noted that, although the Greek apostrophe shares both the name and function of its
French counterpart
(de ombre → d’ombre) the fact that it can be combined with accents, in cases like
 Mναξ, makes the distinction between stand-alone diacritic and spacing punctuation mark unclear. And
the task of representing them in Unicode even harder
: indeed, in Unicode there is a combining mark
koronı´s U+0343
, but what about cases such as νρ, where the koronı´s is dası´a-shaped? In cases such as
 Mναξ should the koronı´s be combined with an acute accent and a space, or should U+1fce “Greek psilı´
and oxı´a
” be used, which is already a spacing character?
1.3.2 Diaeresis
Diaeresis dialitika´ is used when a diphthong is to be pronounced as two separate vowels
:ουis pronounced
‘ou
’, while οϋ is ‘o-i’. It can be combined with any one of the three accents:,but never with a breathing
since
, by definition, it can never be placed on the first letter of a word. Unlike other diacritics, dieresis
is also placed in all
-caps typesetting: Ροδη → ΡΟΪ∆ΗΣ. There is a variant form of capital iota with
vertically centered diaeresis
: [, in which case the same word looks like:ΡΟ[∆ΗΣ.
Diaeresis is not used whenever it is clear from the context that the diphthong is “broken.” For ex-
ample, when the word starts with a diphthong, the breathing is placed on the first vowel and diaeresis is
not written
: υτ instead of ϋτ. When the first vowel is accented, again the diaeresis is not written:
χιο
instead of χϊο. When a word is hyphenated between the two vowels of a broken diphthong, the
diaeresis is not written
: Μαου will be hyphenated Μα-ου.
There are other cases where diaeresis is used: one of them is to show that the letter iota is pronounced
(and not mute). Normally a mute iota is written as a subscript (see §1.3.3): τG ΘεG. But it can also be
written in normal size
. To show that this is not the case, and that the iota must indeed be pronounced, we
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From Unicode to Typography, aCaseStudy: the Greek Script
Figure 5: Four instances of capital letters with subscript iota: Mσωµεν on top left
figure
, line 4, Mδει on top right figure, line 3, Lδ on bottom left figure, line 3
[Pro, p. 489, 540, 770]. The bottom right figure is from [Roi, p. 150]: the three
letters
,  and  can be found in the same sentence.
use a diaeresis: for example, there is the word πρ (pronounced ‘pro’) which can be written πρι and
still pronounced the same way
; and there is another word, πρω, which is clearly and unambiguously
pronounced ‘pro
-i’.
The use of diaeresis goes even farther: a diaeresis is placed even if there is absolutely no grammatical
necessity to do so
, just to facilitate pronunciation: πιγκουνο, πιπλοποια, etc.
In µ∆ some of these spellings are unauthorized: [Teg] writes πρω (even in the etymological Α version
of the word
), επιπλοποια, but βουζω, κουζ, κουϊνττο, πιγκουνο, σουϊπστικ, τουστ (while, always
in
[Teg], other similar words again take no diaeresis: αλτρουισµ, ινδουισµ, καζουισµ, σντουιτ).
1.3.3
Subscript and adscript iota
The vowels
αηωcan be followed by a mute iota. In that case, the iota is written in smaller size, under
the letter
(in the middle of α or ω, and under the left stem of the η).
There is some confusion about the uppercase ΑΗΩwith mute iota. The glyphs displayed in the Uni-
code book show the subscript iota below these letters ; on the other hand, in the name of these characters
themuteiotaiscalledprosgegrame´ni
; this is a neologism meaning “written next to” (while ipogegrame´ni
means
“written under”). This does not agree with the glyphs, where the mute iota is indeed placed under,
and not next to the letter.
It seems that there have been many ways of typesetting these letter + mute iota combinations. In
Greece
, one of the traditional methods is to center the iota under the letter:,,.This seems to be
rather shocking for Western scholars
; Jeffrey Rusten [Rus], while reviewing the Palatino Unicode font,
writes: ...an oddity every classicist will notice right away, namely iota subscripts under capital letters.
This mistake is not the fault of the Palatino design team, but a longstanding error made already by Uni-
code and ISO before it, which it is too late to correct. In Figure 5 we show that this is indeed not an error,
but conforming to Greek typographical tradition.
Nevertheless, the usual spelling of capital vowels followed by mute iota is:ΑιΗιΩι,where the iota
is written at normal size
. In the case of Αι there is no risk of confusion with diphthong αι because of the
placement of the necessary breathing
: LΑι or HΑι in the case of the mute iota,Αor Α in the case of the
diphthong
. Examples: IΑιδη (mute iota), LΑϊδωνε (broken diphthong), Αδοµαι (diphthong).
Some typographers have tried other solutions: for example, in [Kal], a specially designed small iota is
placed next to the capital letter
, almost entirely under the baseline. Here are some examples using that
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From Unicode to Typography, aCaseStudy: the Greek Script
Figure 6: In the early days of the monotonic system, some books were printed with
a triangular accent
. This book, of political content, uses the form of the accent to
underline a cultural break with the past
. Notice that the triangular accent remains
upright
, even on italic letters.
convention: IΑmδη, KΗmτε, LΩmδ.
In all-caps typesetting, the mute iota is written as a small-caps iota (normal small-caps size, or even
smaller
): Αl∆ΗΣ, ΗlΤΕ, Ωl∆Η. There are also other conventions: sometimes the mute is written like a
normal uppercase iota
; in [Pro, p. 730] one finds lowercase iotas in an all-caps context: ΤΗι ΑΓΙΑι ΚΑΙ
ΜΕΓΑΛΗι ΠΕΜΠΤΗι.
See §1.3.7 for the case of iota with iota subscript n.
1.3.4 The monotonic system
In the early eighties
, the Greek Government reformed the language. This reform had many aspects: Κ
was officially abolished
, as were breathings and subscript iota, and the rules of the accentuation system
were modified so that only the oxı´a accent be used
, and only on words with more than one syllable (with
a few exceptions
: for example , πο, π, previously , πο, πF, to disinguish them from η, που, πω,
previously , πο, π). Furthermore, the spelling of several words has been simplified.
It is very important to note that the reform did not introduce a new accent, but rather removed two of
theexistingones
: the remaining accent is oxı´a. The Unicode table glyphs show a vertical accent, called
to´nos
. This word means “accent,” and is exact, since in that context there is only one accent. But this
accent has never been written as a vertical stroke
. Since the reform some publishers have experimented
with triangular and round accents
; see for example Figure 6 [Sai], a book from the very early days of the
monotonic system
(1983), a period where publishers and typographers were trying to find other solutions.
These experiments have nowadays come to an end: today the oxı´a accent is used, as in the example in
Figure
18, p. 36. The official grammar states clearly that the accent of current [monotonic] Greek is the
oxı´a
[Tri, p. 22-23] ; there is no mention whatsoever of “symmetrical,”“vertical,”“triangular” or any other
form of accent
.
This means also that the distinction between “tonos” and “oxia” in Unicode character names (for ex-
ample, between U+03AC and U+1F71) is illusory. One could argue that this distinction allows a potential
spelling checker to distinguish between text written in the monotonic and polytonic systems
(for exam-
ple,µιλis correct in µ∆ but not in π∆,πιis correct in π∆ but not in µ∆) but this is a rather naı¨ve
argument
: texts are very rarely mixed monotonic and polytonic, and when this happens it is almost al-
ways for distinguishing µ∆ from Κ or Α, in which case there are far more differences in spelling than the
existence or not of more than one accent
; in such a case, linguistic markup is far more appropriate.
Thatsiswhy, the author considers that the glyphd ´Α ´Ε ´Η ´Ι ´Ο ´Υ ´Ω in the Unicode
Greek table should be redrawn and the corresponding characters in the Greek Extended table re
;oved,
so that there is only one character representing a Greek vowel with oxı´a, whether in the monotonic or
polytonic system
. It is very unfortunate, but because of the mistakenly vertical design of the oxı´a accent
in the
(monotonic) Greek Unicode table, some font companies have already designed fonts with vertical
oxı´a
; these fonts will soon be used in Greece and may, in the long term, alienate Greek typographical
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From Unicode to Typography, aCaseStudy: the Greek Script
conventions...
1.3.5
The TONISMOS software
Speaking of Greek accentuation, let us mention the TONISMOS software [wTon], which converts monotonic text
into polytonic text
, with or without grave accent and subscript iota. This program can be very useful for the input
of large quantities of text
(the text is typed in the monotonic system, the accents are added by TONISMOS, and
the result is compared with the original
), or as a complement to optical recognition of Greek text. Nevertheless the
program is not a spell checker/corrector
: when the monotonic input is not accurate, the resulting polytonic text will
be wrong as well
.
1.3.6 Other diacritics used in Greek
1.3.6.1 Macron and breve To indicate if a syllable is short or long, vowels can take the macron makro´n or
breve vrakhı´ diacritics
. If there is already an accent and/or a breathing on the vowel, the macron or breve is placed
between the existing diacritic and the letter
, as in the following example:
MΑνδρα µοι ννεπε ΜοÖσα πολËτροπον Äµλα πολλ
πλγχθηπε Τρο¬η ¯ερ¿νπτολ¬εθρον περσε·
To keep the same leading, the combinations of macron/breve and accent/breathing often have to be specially de-
signed.
1.3.6.2 Representing non-Greek phonemes There are cases where diacritics have been used to repre-
sent sounds not provided by the Greek alphabet itself. For example, [Geo] uses breve on letters ζ, σ, ξ and ψ—as
well as special constructions such as double consonants at beginning of word
—to represent the hard sounds of the
Cypriotic dialect
:
˘
Σ
˘
σλλα πο µαθεν τ
˘
ζα τρ πετ
˘
σι ντ
˘
ζε προκβκει, [...] τ
˘
ζι ο πστε τ
˘
ζι ο πατρδε ππφτουν τ
˘
ζα
γονατον,
[...] Ν φντ
˘
ζει ν παρατηρF που λα
˘
ξι τ
˘
ζα σπλιο, [...] τ
˘
ζι που γνετουν κλε
˘
ψι, 
µορα του ’ταν µορα·
It is interesting to note that in [Geo] the letters
˘
ζ and
˘
ξ with breve have been specially designed so that the letter
with diacritic fits in a normal line without changing the leading
.
In [Ele], the dotted letters β, γ, δ are used to represent the sounds ‘b’, ‘g’, ‘d’ in foreign words, as in
˙
Β
˙
γ
˙
δα
˙
δ for
‘Bagdad
’;in [Des] (mentionned in [Kal, p.44]) the translator uses the same dotted beta, gamma, delta, as well as
upsilon and epsilon with diaeresis
, zeta with (Latin-like) circumflex and sigma with tilde to represent the sounds of
French ‘b g d u e j ch
’. A different method for obtaining the same result: in [Mes] (also mentioned in [Kal, p.44])
the author uses Latin letters e u b g d ch in a Greek text context to represent certain Greek phonemes unavailable
in Greek
: bουφ, bαχτσδε, dλιε, gµια, etc.
1.3.7 Other languages written in the Greek script
The Greek script has been used for a certain number of minority languages [wMac]: Albanian (Tosk), South Slavic
(Macedonian), Aroumanian (Vlach), Gaguz, Surguchi, Urum (Greek Tatar), Turkish (Karamanli). These languages
often use diacritics to represent special sounds
, not present in Greek: [Fau, p. 182] gives a list of characters for
Elbassan Albanian in which we find dotted gamma
, nu, sigma and chi, sigma with diaeresis, Latin j and underlined
epsilon
. But, the same author in [Fau
2
, p. 539-541], gives samples with dotted lambda and pi, Latindandb,
overlined alpha and upsilon, epsilon with diaeresis, and even a digamma (!):
Γιτι νε
˙
κ γ µπ κε
˙
λκιφτε
¨
σε
ντερουρε µερι τ· [...]  δµ ν λε
¨
στζ νβετ ντ
ντον πιρα-
σµ, π
¨
σπε
τνα νβετ γκ  λιfου, σ γιτιγια 
¨
στε µπρετερα.  δ φουκα,  δ λεβδµι, ντ γτε τ
˙
πασσουρε βερττ.
[...]Λjαβdν bουκουρνε,α
¨
σκου νε κετ ζεµν.
[...]Ε dρ
¨
ετ ποσ κjιρνε, µερρ νουρ
˙
χλκουτ, ο jαdι
˙
γjρ !
14th International Unicode Conference 15 Boston, MA, March 1999

From Unicode to Typography, aCaseStudy: the Greek Script
Figure 7: Sample of acrophonic numerals. Greek text is in Porson.
On the other hand, [Gos, §5] uses a capital Cyrillic Б and an overlined iota, in a sample of the same language,
dated 1879. In [Gos, §512] we also find an interesting example of Osmanli Turkish, written in Greek script:
Ζρα LΑλλχ
˙
τ
˙
ουνγnαγn
˙
πο κα
˙
τρ σεβ
˙
τ, κ κεν
˙
τ MΙ
˙
πνι βαχι
˙
τιν βερ
˙
τ,τκινχρµν
˙
τν χελκ
λµαγnη
˙
πν
˙
τζακ 
˙
πε
˙
τ χαγnατ µαλκ λ.
where we find dotted pi and tau, as well as a iota with... subscript iota. The same sample is given in Arabic and
Armenian script
. By comparing them we see that the dotted pi corresponds to a non-standard pronunciation of
the Arabic script
: λµαγnη
˙
π is the transcription of adb , and hence
˙
π corresponds to a ‘p’ pronunciation of Arabic
letter
 (normally pronounced ‘b’) ; the
˙
τ corresponds to the sound of ‘d’, and finally the weird n is the transcription
of Arabic letter
c:
˙
τ
˙
ουνγnαγn is Ze .
[wMac] also mentions uses of dotted beta and delta, and underlined sigma.
1.4 The Greek Numbering Systems
There are two systems of Greek numbers: acrophonic and alphabetic ones.
1.4.1 The Acrophonic Numbering System
“Acrophonic” from a´kron (limit) and fonı´ (voice); what is meant is the first letter of a word, in this case
the first letter of the number
’sname. So we have a Pi for 5(= pe´nte), a Delta for 10 (= dhe´ka), aChi
for
1,000 (= khı´lia), aMufor10,000 (= miria´s). For one hundred, we have an Eta, because the eta at
that time was used also for the rough breathing
, and one hundred (κατ ekato´) indeed takes a rough
breathing
. Two exceptions : aIotaisusedfortheunit, and a Tau for 6,000. When fractions are needed,
then the Iota = 1 is written with an horizontal stroke to the right, the real Iota means
1
6
, aCmeans
1
12
, a
Tau
1
24
and a Chi
1
48
[Caj, §33-35]. And finally, when we want to multiply one of the numbers above by 5,
we include a smaller version of the corresponding letter in a normally sized Pi.
How do we represent these numbers typographically? There are two ways:
3
either we consider them
as abstract geometric shapes and represent them in an
“epigraphical style,” or we consider them as Greek
letters and represent them in the same typeface and style as the surrounding Greek text
. Here are these
numbers
, first in epigraphical style:
ABCDEFGHIJKLMN
and then in
“typographical style” [Ste]:
abcdefghijklmn
3
A similar choice is needed for the Berber alphabet Tifinagh, which, like acrophonic numerals, did not have the same typo-
graphical evolution as did the Latin or the Greek alphabet: one can represent it in an epigraphical, purely geometrical way, or
one can try to simulate what an hypothetical typographical evolution would be
, and adapt it to an existing Latin typeface. Such
an attempt has been made by the author
(see [Har, p. 145-146], [wHar, p.11]).
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th International Unicode Conference 16 Boston, MA, March 1999

From Unicode to Typography, aCaseStudy: the Greek Script
The reader can see in Figure 7 an example of printed text [Tod, p.73] using these characters. The text is
typeset in Porson
, and the acrophonic numerals in epigraphical style. Here is how the same text would
look typeset in Times with acrophonic numerals in typographical style
(to bring the result closer to Fig-
ure 7 we keep the numerals upright while the text is typeset in italics):
Λεωφéν ∆λιοv Îπρ Πιστοξ|νου ∆ηλ¬ου eeed,
Πατροκληv
[∆λ]ιοv Îπρ HΥψοκλουv ∆ηλ¬ου eee,
LΑρισ
|τε¬δηv Τνιοv Îπρ Ο®νδου Την¬ου eec,
[Κ]εφλαιον τ¾κου παρ τéν ®|[δ]ιωτéν heeeccb.
The acrophonic numerals are also called Herodianic
, after Herodianus, a Byzantine grammarian of
about
200 a.d. It would be useful to include them in Unicode, for the purpose of encoding scholarly Α
texts
, as the one in Figure 7.
1.4.2 The Alphabetic Numerals
The alphabetic numerals have suceeded the acrophonic numerals
; they allow a more compact represen-
tation of numbers, while demanding a higher mental effort. Here is the correspondence between Greek
alphabetic and Arabic numbers
:
α´ 1 ´ or στ´ 6 κ´ 20 ο´ 70 τ´ 300 ω´ 800
β´ 2
ζ´ 7 λ´ 30 π´ 80 υ´ 400 j´ 900
γ´ 3
η´ 8 µ´ 40 ´ 90 φ´ 500
δ´ 4 θ´ 9 ν´ 50 ρ´ 100 χ´ 600
ε´ 5 ι´ 10 ξ´ 60 σ´ 200 ψ´ 700
where ,  and j are the letters stigma, numeric koppa, sampi, described in §1.2.1.2, §1.2.1.4, §1.2.1.5.
The notation στ´ is used in Greece today, when the  character is absent from the font. The mark ´
(
U+0374) is not an apostrophe (as it is, unfortunately, often typeset in Greece) but a spacing acute accent,
called kere´a (=mast, protuberance, today: antenna). To represent thousands, an inverted kere´a is placed
in front of the letter
: cα is 1,000, cθ is 9,000. Units are combined with decades, hundreds, thousands to
form numbers
: ρκγ´ is 123, cαjθ´ is 1,999.
With the rules given above, the highest possible representable number is cθjθ´ = 9,999 ; up to this
number
, Greek alphabetical numbers have always been unique and non-ambiguous, until today. This is
not the case for numbers above
9,999.
According to [Ele], one can continue this way, placing the inverted kere´a in front of numbers ι,... j,
so that the highest representable number is cjθjθ´, that is 999,999. [Oik, p. 134] avoids the question
by not giving examples above
cκ (20,000). According to [Mio, p. 100], to represent ten-thousands, Greeks
either used the alphabetic number followed by the word
µυριδε (meaning “ten-thousands”), as in ε´
µυριδε,
or a diaeresis on the letter, like in
¨
ε.
[Caj, §36] states some additional conventions: sometimes
the number of ten
-thousands was written before a capital Μ, (the initial of miria´s, actually a remainder of
the acrophonic numbering system
) and the whole number was overlined: εΜcδτκα´ for 54,321 ; in some
cases a centered dot · is used instead of M
; finally, one encounters the alphabetic number placed upon
the capital M
, as in
ε
M, or the coefficient of the myriads written as an exponent to a lowercase µ, like in
µ
ε
cδτκα´.
One could ask: why not follow [Ele] and continue defining cι as 10,000 and so on? A probable answer
is the fact that then the system would be ambiguous
: is cρκγ´ 120,003 or 100,023?
It is obvious that the way of representing numbers beyond 9,999 has never been standardized and
notations have varied
. On the other hand, for numbers under 9,999 there has been no variation until
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From Unicode to Typography, aCaseStudy: the Greek Script
today ; indeed the alphabetic numbering system is still widely used in Greece today, for ordinals only.
Counting by α´,β´, ... is a very common form of enumeration in Greece (similarly to i, ii, iii, ... in the
West
) and everybody can instantly recognize these numbers, at least until κγ´ (29). Laws have also been
numbered in the Greek system
; in that case one can easily find numbers covering the whole range of
(standard) alphabetic Greek numerals.
Just like Roman enumeration, Greek alphabetic enumeration can be lowercase or uppercase ; in fact
one can easily have independent enumerations in the two cases
, lower and upper. Forthisreason, the
case distinction is essential for the three
“numerals-only” letters stigma, numeric koppa and sampi. This
distinction
, while present in ISO 10646 v.1,is absent from Unicode ; it should be re-introduced to allow
proper enumerations
.
To return to Α, there have been other interesting conventions [Caj, §§41-44]: for example, to express the frac-
tion
17
21
, Heron writes ιζ´ κα´´ κα´´ (the denominator written twice, with double kere´a), Archimedes and Eutocius
write
ιζ
κα´
or
κα
ιζ
(
note that the denominator is written on the top, and the nominator at the bottom). Diophantus, in expressing large
numbers writes
γ·cχκα
cβψδ
˜
for
36, 621
2, 704
.
Again
, note that nominator and denominator are inverted. Unit fractions were written with a double kere´a:ζ´´ for
1
7
,
ριβ´´
for
1
112
, etc. The Byzantines sometimes wrote the denominator of a fraction as an exponent:θ
ια
in this notation
means
9
11
[Caj, §271].
About the 2nd century a.d., the Babylonian sexadecimal numbers were used in Greek astronomy. The letter ο
(
omicron with a bar) or b, was used to designate a vacant space in the writing of numbers (there was no zero provid-
ed, in any Greek numbering system); the opposite notation has also been used: all letters representing numbers
have a bar
, and the “zero” omicron has none, so that it is distinguished from ο´ (70). Ptolemy believed that the
value of π is 3+
8
60
+
30
60×60
and he wrote this as γ η λ, or γη´ λ´´ (this notation is strangely close to the modern
notation
3° 8
0
30
00
).
1.5 Hyphenation
Greek hyphenation rules are very simple to one who knows the language, and can be very difficult other-
wise: they take into account etymology (Α, Κ) and pronunciation (∆). Furthermore there are important
deviations between the rules applied in Greece and these used in the West
.
The minimal number of letters that can be left on a line is 1(unlike in English where this number
is
3): one often sees hyphenations such as -εροπλανοφρο, which do not seem to shock anyone.
1.5.1
Hyphenation of Α and Κ
Let us start with the rules for Α
(and Κ), as formulated in Greece [Oik, p.16] and [Aca]. Let c
1
,c
2
,... be
consonants
, and v
1
,v
2
,... vowels ; then:
I v
1
c
1
v
2
is hyphenated v
1
−c
1
v
2
: κα-τ, πρF-το, -δωρ ;
II v
1
c
1
c
2
v
2
is hyphenated v
1
−c
1
c
2
v
2
if there is a (Α or Κ) Greek word starting with c
1
c
2
: κ-κνο
(κν
like κνισµ), -βδο (βδ like βδλλα), θε-σµ (σµ like σµCνο). Otherwise it is hyphenated
v
1
c
1
−c
2
v
2
: λ-λο, ορ-τ, λαν-θνω.
III v
1
c
1
c
2
...c
n
v
2
, for n ≥ 3 is hyphenated v
1
−c
1
c
2
...c
n
v
2
if there is a (Α or Κ) Greek word start-
ing with c
1
c
2
: κτο-πτρον (πτ like πτω), γ-στρα (στ like στρογγλο), -σχν (σχ like σχCµα).
Otherwise it is hyphenated v
1
c
1
−c
2
...c
n
v
2
: ν-θρωπο, µελγ-χρω, ρ-κτο.
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From Unicode to Typography, aCaseStudy: the Greek Script
IV Compound words are divided into their original parts, except if the final vowel of the first word
has been removed
: συν-οικα, ξ-οδο, µετα-γραφ, but πα-ρρχοµαι (from παρ[]andρχοµαι),
-πχω (
from π[]andχω), πρω-ταγωνιστ (from πρτ[ο-]andγωνιστ).
The Western rules are expressed in a different way [Chi, §9.130-135]:
II
0
v
1
c
1
c
2
v
2
is hyphenated v
1
c
1
−c
2
v
2
if either (a) the consonant is doubled c
1
= c
2
, or (b) if c
1
is a
mute consonant and c
2
its corresponding aspirate (γχ, κχ, πφ, τθ), or (c) if c
1
is λ, ρ, µ, or ν(with
the exception of c
1
c
2
= µν, which is not hyphenated).
III
0
v
1
c
1
c
2
...c
n
v
2
is hyphenated v
1
−c
1
c
2
...c
n
v
2
, unless one of the conditions of rule II
0
applies to
c
1
c
2
.
IV
0
Compound words are divided into their original parts.
These rules produce different hyphenations than II, III, IV:
• according to II, αχµ is hyphenated αχ-µ, because there is no Greek word starting with χµ ;
according to II
0
, it is hyphenated α-χµ.
• rule IV
0
does not take into account the exception of rule IV, namely the case where the first com-
ponent of a compound word has lost its final vowel. This makes an enormous difference: according
to IV
0
we have hyphenations φ-οδο (π + δ), π-χω (π + χω), κατ-χω (κατ + χω),
παρ-οξνω (παρ
+ ξνω), and there are hundreds (thousands?) other examples, all wrongly hy-
phenated for IV.
The author ignores the reasons for these deviations: intuitively, a combination of rules I, II, III, IV
0
,
would be the best (αχ-µ sounds more natural than α-χµ), and the purpose of hyphenation is, after
all
, to make reading of broken words easier, so that intuition is perhaps more important than universal
grammatical rules
.
1.5.2
Hyphenation of ∆
In ∆ new combinations of consonants appeared
(for example µπ, pronounced ‘mb’ or ‘b’) which made
new hyphenation rules a necessity
. The various grammatical reforms went even farther: rule IV was abol-
ished (compound words are now treated like non-compound ones);this is sometimes very counterintu-
itive. Here are the two new rules which have been added [Tri, p. 20-21]:
V the pairs of consonants µπ, ντ, γκ are hyphenated if, and only if, their pronunciation is nasal: µ-
πλι, µ-πορο, πν-τε
but µπα-µπ, ντα-ντεω, ξε-µπλκω.
VI vowel pairs αϊ, αη, οϊ, οη, and ι∗,υ∗,ει∗,οι∗, where ∗ is any vowel, are not hyphenated when they
are pronounced without glottal stop
: νεριδα, Γιννη, µυαλ, but βο-θητο, π-εση, π-ον. A
not so obvious case
: πινω (pronounced pia´no or like in Russian пяно) vs. µει-νω (pronounced
mi
-a´no, with a glottal stop, like in Russian миано).
Of course these rules are impossible to apply for somebody not speaking the language. Furthermore, both
rules are quite ambiguous because people do not always pronounce words the same way
, especially for-
eign ones. Rule VI is reminiscent of letters U and W of κ∆ (see §1.2.4): the words that are not hyphenated
are precisely those which would be written with those letters
: νερUδα, ΓUννη, µWαλ.
1.6 Punctuation and typographical conventions
1.6.1 Punctuation
Greek punctuation is similar to Western punctuation
, with a few exceptions: the semicolon is used as a
question mark
, and the role of the semicolon is played by the upper dot (·). A Κ and π∆ punctuation
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From Unicode to Typography, aCaseStudy: the Greek Script
mark which that is not found in Unicode is ipodiastolı´: it has the glyph of the comma and is used in a
single word
:,τιto distinguish it from τι:
Π µου τι σο επε (
confirm to me that he told you)
Π µου ,τι σο επε (
tell me everything he told you).
Typographically speaking, the distinction between comma and ipodiastolı´ is important, because, contrar-
ily to the former, the latter is not followed by blank space. Fortunately the case of ,τι is unique and
unambiguous
.
4
The ipodiastolı´ is also used as decimal separator: 3,14159...
For quoting, double guillemets are used ; in the apla´ typeface these guillemets are round: «ζτω !».
In 19th and early 20th century books the (French) convention of adding a double guillemet (often an
inverted one
) at the beginning of each line is often used.
The spacing of punctuation is very interesting: different amounts of white space are placed in front
of colon
, semicolon, exclamation: roughly 1 point before the colon, 1.5-2 points before the semicolon
(Greek question mark) and 2.5-3 points before the exclamation mark. The author has found no precise
reference for these values
, so they should be considered purely empirical. No spacing is applied to the
other punctuation marks
(including the guillemets).
Also interesting is the case of the second level quotes. Here, quotes of the size and shape of the En-
glish ones are used, but the opening quotes are inverted, similar in form to raised small round guillemets:
rεσαγωγικ”.
Fortunately these quotes are provided by the Unicode standard (U+201F and U+201D, the
latter being the same closing double quotes as in English
);the author knows no other language in which
this combination of double quotes might be used
.
1.6.2 Hanging diacritics
Another interesting typographical convention
: “hanging diacritics.” As in English one may have “hanging
punctuation
” [Knu, p. 394], in Greek poetry one uses hanging breathings and accents, in the sense that
these marks
, when in front of an uppercase vowel, are typeset on the left margin, and alignment is done
with respect to the letter
:
M
Ενοιωσεν τι
το σαν ο στχοι
χαρη τχη
κα µαταιτη.
(
The vertical line is inserted to show the left alignment of the paragraph.) This convention is not applied
in prose text
.
1.6.3 Letterspacing
Bold is never used inside Greek text
, but only for titles. TheroleofboldinEnglishisplayedbyletterspac-
ing, whichinGreek(and German, and Russian) is very common (and there is no reason to compare it
with the
... stealing of sheep
5
): κνω δ ι α σ τ η µ  τ ω σ η, λλ δ  ν κλβω π ρ  β α τ α. Note that, as in
German and Russian
, letterspacing is done between letters only, and not between letters and punctua-
tion, or, in the case of Greek, between diacritics and (uppercase) vowels. Also interword spacing must be
slightly increased to avoid confusion with interletter space
.
4
In some typographical traditions of Α, a blank space is used instead of the ipodiastolı´ to separate  from τι.
5
Quoting Frederic Goudy: “Anyone who would letterspace lowercase letters would steal sheep.” [Gou]
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From Unicode to Typography, aCaseStudy: the Greek Script
(a) Monotype Greek 90, 91, 92
(b) Monotype Greek Times, also called
“Elsevier”
(c) Monotype Porson
(d) Monotype New Hellenic (attika´)
(e) Monotype Greek Sans 486
Figure 8: The Monotype Greek typefaces.
1.7 Typefaces
A good reference on the history of Greek typefaces is [Sch] ; in this paper, we will restrict ourselves on
the most common typefaces
, used currently or in the last few years.
One century of Greek typography, whether in Greece, or in the Western world, and until the arrival
of computer DTP
, can be summarized in one word: “Monotype” [wMon]. In fact, most printed books
are typeset in one
, or more, of the following typefaces: apla´ (which Monotype calls “Greek 90, 91, 92”),
Times, Porson, New Hellenic, Greek Sans 486.
When the phototypesetting machines were replaced by computers, the situation changed rapidly: the
Times fonts were taken over by the computer
, bad quality imitations of the original Monotype Greek 90
were used for the aplα style, new fonts were designed and used: Linotype released Greek Baskerville and
New Century Schoolbook
, Greek companies (like Magenta) have adapted many of the Latin typefaces
to the Greek script
.
We can roughly divide Greek text typefaces into five categories: apla´ (Didot), the Times family (called
Elsevier in Greece
), “scholarly” fonts (Porson, New Hellenic, Sans 486), adaptations of Latin typefaces,
and, finally, original creations of the last few years.
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From Unicode to Typography, aCaseStudy: the Greek Script
1.7.1 The typefaces in the apla´style.
This has been the most common style of Greek typefaces. Its ancestors are 19th century Didot type-
faces. Apla´ means “plain,”“simple” in Greek, and this is what this typeface has been: the most common
typeface for ordinary text
. Many companies have released versions in this style: Monotype “Greek 90”
(
upright), “Greek 91” (italic), “Greek 92” (bold), Linotype “Greek No.2,” Magenta “Memories.” The
author considers the Monotype ones to be
, by far the best choice, in fact the most beautiful Greek types
he has ever seen
(this paper is written in Monotype apla´).
Apla´ seems to be omnipresent: before the arrival of the computer most books were typeset in this
typeface
; today, high quality typesetting is almost always done in apla´. See Figure 16, on page 34, for a
sample of a book entirely typeset in apla´
.
An intrinsic characteristic of the apla´ family is that the ratio of lowercase height to uppercase height is
smaller than the one of typical Latin typefaces
. This makes harmonization between apla´ and Latin type-
faces harder.
1.7.2 The Times family typefaces.
What we call the “Times family,” and in Greece is called the “Elsevier” typeface, is actually a style used
since
1878 as an alternative to apla´. Compared to the latter, it is more modern and pragmatical. This is
why it often has been chosen for technical books
, or books by authors who wanted to avoid a conservative
image
.
Many companies have released Greek Times fonts, unfortunately not all of good quality. The best
seems to be the original Monotype Greek Times
(Figure 8b), which has afterwards been cloned to pro-
duce the homonymous, lower quality, standard Microsoft Windows 95/NT font (see [Har
3
, Figure 4]).
1.7.3 The “scholarly” typefaces: Porson, Greek Sans 486, New Hellenic.
The Porson typeface (see [Mos]) is used in most Anglosaxon scholarly Greek editions, including the Ox-
ford Classical Texts (Figure 14, p. 32). This font has also been used in Greece, as a replacement for
Greek
91, or as a companion font to New Hellenic. The German-Greek Langesheidt dictionary [Wen]
also uses Porson only for the Greek text
. Only two Porson versions are known to the author: the one by
Monotype
(again, by far the best) and a recent one, by the Greek Font Society.
Greek Sans 486 is actually a bold font. It has been used for the entries of the Oxford Lexicon of Greek
Personal Names
; a font with strong resemblances to it is used by the Association Guillaume Bude´ (see
Figure
15, p. 33) and Le Cerf editions as well as the Bailly dictionary [Bai].
New Hellenic is a very special font (see [Bow] for its history); in Greece it is called attika´ ; it is used
both for scholarly editions outside Greece
, as well as in Greece, for children books or schoolbooks. On
Figure
17, p. 35, the reader can see a page from a typical children book of the late sixties, typeset in New
Hellenic
, with quotations and captions in Porson, and the copyright mention of the photo in apla´. There
are two versions of this typeface known to be released
: the one by Monotype (the best) and a recent one,
by the Greek Font Society.
These typefaces are classics for scholarly editions ; but they are also used outside this context and
one can say that they have a special charm
; when used adequately they can greatly contribute to the
typographical quality of a document
.
1.7.4 The adaptations of Latin typefaces.
As it very often happens that texts are mixed (Greek/Latin alphabet), many companies have tried to adapt
Latin typefaces to Greek
. To state only the most important, Monotype [wMon] has adapted Gill Sans and
14th International Unicode Conference 22 Boston, MA, March 1999

From Unicode to Typography, aCaseStudy: the Greek Script
(a) Linotype New Baskerville Greek
(b) Linotype New Century School-
book Greek
(c) Magenta Optima Greek
(d) Magenta Souvenir Greek
(e) Magenta Garamond Greek
(f) Magenta Bodoni Greek
Figure 9: Some Linotype and Magenta Greek typefaces.
Figure 10 : The infamous “gothic Greek” typeface.
Helvetica, Linotype [wLin] has adapted New Baskerville, New Caledonia, New Century Schoolbook, Op-
tima, Souvenir, and others (see Figure 9aandb). The Greek company Magenta [wMag] has also adapted
a wide range of Latin typefaces
, including Univers, Garamond, Bodoni, and others (see Figure 9c-f).
The process of adapting Latin typefaces to Greek is hard—much harder than Cyrillic, Armenian or
Georgian
—because lowercase Greek letters have different design principles than Latin ones. For exam-
ple, the notion of serif, very fundamental for Latin lowercase letters, is not very natural for Greek letters.
In Magenta Bodoni (Figure 9f) the χ is just a Latin x, and the ι adotlessi; as for the λ, it could very well
be a reflected Latin y
. In the Garamond font, by the same company, the η is simply a Latin n, and the
κ, a k with the ascender lowered. Many Greek magazines use these fonts and people get used to them.
Naturally, in Greece there is a great demand for adaptations of Latin typefaces ; more and more of them
are made
, often quickly and without artistic care. Sometimes one even encounters typographical mon-
struosities, like the “gothic” font shown on Figure 10.
1.7.5
The original creations of the last few years.
There have been a few interesting font Greek creations in the last years: the Greek Font Society has
created a font called
“GFS Bodoni” [wSPr], after original typefaces by the Italian master (Figure 11a).
This font is so refreshing that we can’t resist the temptation of showing a few lines typeset with it [Roi,
p. 150]:
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From Unicode to Typography, aCaseStudy: the Greek Script
(a) Greek Font Society Bodoni
(b) Katsoulidis’ Apollonia
Figure 11: Creations of the last few years: GFS Bodoni and Katsoulidis’ Apollonia.
A Greek artist, Takis Katsoulidis, has created two interesting typefaces: “Katsoulidis” and “Apollonia”
(
Figure 11b), which he describes in [Kat] ; recently a Greek version of Palatino has been designed for
Microsoft
[wRus]. Let us hope that creative innovations like these will continue, for the sake of Greek
typography
.
This concludes our short description of the fonts available for typesetting Greek text. It should be
noted
, though, that when it comes to high quality typography of Α, Κ or π∆, there is no simple solution:
the Monotype fonts are excellent in design, but they are incomplete and have no kerning pairs, so that
the professional typesetter has a lot of work to do after purchasing them to really make them work
(this
is what the author has done
, see [Har
3
]); on the other hand, there are many freeware or commercial
“scholarly” fonts around, which have a more-or-less complete set of glyphs, but rather poor design (and,
unfortunately, there are many scholarly editions using precisely those fonts...).
1.7.6 Samples
At the end of this paper
, we present five sample pages:
• on Figure 14 the reader can see a page from the Oxford Classical Editions. It is typeset in Porson.
Only the lunate sigma (§1.2.3 (6)) is used.
• Figure 15 is a page from a Belles Lettres edition [He´r]. The Greek text is typeset in the special
font of the Association Guillaume Bude´
. This font is closely related to Monotype Greek Sans 486
(
Figure 8e). The critical apparatus uses the apla´ typeface (indeed, the font of the main body text
wouldbehardtoreadatlowersizes
).
• Figure 16: this page, in π∆, is from a book [Nte] printed in Greece in 1990. It has been typeset by
one of the only remaining traditional Monotype typesetting offices in Greece
, the one of Palivo-
giannis Bros. The typeface used is apla´ ; the Latin insertions are typeset in Didot.
• in Figure 17 we see a typical children book [Var] of the middle sixties, written in π∆. We have
chosen to show this page
, because it uses two “scholarly” fonts: New Hellenic for the main text,
and Porson for the quoted verses, and captions of figures. Underneath, and on the right of the
figure caption
, we see the photograph copyright, typeset in apla´.
• finally, in Figure 18 we see a page from a contemporary, computer-typeset magazine, in µ∆:ΗΥ-
ΦΕΝ
[Mas]. The typeface used is Helvetica.
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From Unicode to Typography, aCaseStudy: the Greek Script
2 Mathematics
The Greek alphabet is part of the standard mathematical notation. Perhaps the best known Greek let-
ter is π, precisely because of that magic number 3.14... The letter π was first used as a symbol for the
ratio
, for example He´rigone [Caj, §254] writes: hg π ga 2|2 hb π bd, meaning
hg
ga
=
hb
bd
(where 2|2 signi-
fies equality). The first occurence of π for 3.14... [Caj, §396] was in 1706, by William Jones (before that
William Oughtred wrote often
π
δ
, where π stood for periphery, and δ for diameter).
The letter
P
for “sum,” was first used by Euler [Caj, §438], in 1755: summam indicabimus signo Σ ; it
wasalsousedbyLagrange
, but otherwise received little attention during the 18th century. It reappeared
in
1822, in Fourier’s Theory of Heat and has remained ever since a standard mathematical symbol.
The letter
Q
for “product” was introduced by another great mathematician, Gauß, in 1812. It was
first used as a function
: Π(k,z)=
1·2·3···k
(z+1)(z+2)(z+3)···(z+k)
k
z
and later as Πz =1· 2 · 3 ···z (the factorial
of z
). Jacobi used
Q
as it is used today, in 1881.
The symbol ∆ for finite differences was first used by Euler [Caj, §640], in 1755, together with letter
P
. Lagrange had already used it in 1772. In 1808, acertainKramp[Caj, §641] proposed the Fraktur
letters D and S as substitutes for ∆ and
P
(in a book written in French !) ; this proposal did not meet
with wide acceptance
.
The symbol ∇ was first used by Hamilton in 1853. Heaviside called it “nabla” (for reasons unknown
to the author
) while at the same time others were calling it “atled” (the word “delta,” reversed).
In this century almost all Greek letters have been used as mathematical symbols (except omicron,
which is indistinguishable with Latin o ; and upsilon, which, depending on the typeface, is often confused
with Latin v
). As we will see, even the digamma is provided for mathematical typesetting !
2.1 Greek Letters and Mathematical Typography
Let us start with three examples. Figure 12a is an excerpt from a British book [Hrd], typeset in Cambridge
in
1908. We have chosen that particular excerpt because in it we see letters a and α in the same formula:
the lower limit of the first integral on line 6 is (a−β)/α (“a minus beta, divided by alpha”). Greek letters
are slanted
, in Porson style. Latin letters as mathematical symbols are typeset in italics.
The second example (Figure 12b) is a case of traditional French typography: it is from a book printed
by Hermann
(the publisher of Bourbaki), in 1959. Only lowercase Latin letters are in italics. Greek letters
are typeset in an upright apla´ typeface
. It is astonishing how small they are, compared to the surrounding
Latin letters
(typeset in Baskerville): see, for example, the expression Sθ(M ) in the displayed equation,
or the last words on the last line: “applications ϕ et θ,” or the upper limit of the sum: i = π where the
upper part of letter pi seems to be lower than the upper stroke of the equality sign
! This anomaly comes
from the fact that the ratio between the heights of lower
- and uppercase letters is much smaller in the
apla´ typeface than in most Latin ones
. On the other hand, the summation symbol
P
is very big. The
global result is quite pleasant
, both for the eye of the typographer and of the mathematician.
The third example (Figure 12c) is taken from a Russian book, printed by publisher Mir, in the Soviet
days
(in 1971). The text is typeset in the beautiful Russian “Antiqua” font. Latin letters, as mathematical
symbols
, are typeset in italics, whether they are in lower- or upper case. Greek letters are typeset in an
adaptation of the Greek Times font
, in upright style. Contrarily to normal size Greek letters, the symbols
P
and
Q
(sum and product) are in apla´ style (very thin strokes, completely flat serifs). Note that in
Russian mathematics
, Cyrillic letters are never used as mathematical symbols.
6
To be used in a mathematical context, Greek letters have to respect two, often contradictory, rules:
6
The only Cyrillic letter the author has ever seen in mathematics, was letter л, found in an American book dedicated to the
great Russian mathematician Lobachevskii
.
14
th International Unicode Conference 25 Boston, MA, March 1999

From Unicode to Typography, aCaseStudy: the Greek Script
(a) From a British book, 1908 [Hrd].
(b) From a French book, 1959 [Ser].
(c) From a Russian book, 1971 [Arn].
Figure 12: Samples of British, French and Russian mathematical typography
(scaled to 80%oforiginalsize).
14th International Unicode Conference 26 Boston, MA, March 1999

From Unicode to Typography, aCaseStudy: the Greek Script
(a) Computer Modern Math Italic
(b) MathTimes
(c) Adobe Mathematical Pi
(d) SMF Baskerville
Figure 13 : Greek symbols in some mathematical typefaces.
1. they have to be immediately identifiable as Greek letters. In a Greek text context, if you write αγω-
ναv,
even without the accents and breathings it is clear that the first and fifth letter is an alpha, and
not a Latin italic a
. This is not the case in mathematics, where Latin and Greek letters can be ar-
bitrarily mixed. The letter alpha must have a special design, distinguishing it from Latin a, so that
an expression like aαa
0
α
0
(a, alpha, a prime, alpha prime) is immediately clear ;
2.
their design must fit with the surrounding Latin letters and other mathematical symbols.
In Figure 13 the reader can see three very common mathematical Greek typefaces: Computer Mod-
ernMathItalic, Y&Y MathTimes and Adobe Mathematical Pi, as well as a typeface designed by the au-
thor for the Socie´te´Mathe´matique de France to fit with the Baskerville text style. These fonts (with the
exception of Adobe Mathematical Pi
) have been designed for T
E
X, therefore their spacing is not the one
of textual Greek fonts
(see for example the pair Γ∆ in any of these fonts).
The differences between these fonts are less obvious than those between the different textual type-
faces. In Figure 13(a,b,d) the letters A, B, E, F, Z, H, I, K, M, N, O, P, T, X, Y, Z and o have been taken
from the corresponding Latin typeface
: Computer Modern Roman, Times, ITC New Baskerville. Once
again
, Adobe Mathematical Pi is an exception: it already contains the complete Greek alphabet.
Computer Modern Math Italic [Knu
2
] has the following characteristics: the lowercase alpha is larger
than in other fonts
, the lowercase gamma is very asymmetric, the lambda has a junction between the two
strokes lower than the height of lowercase letters without ascenders
, the zeta has a very small upper curly
stroke
, the kappa is quite curly. The delta has the smallest upper stroke. The digamma and variant kappa
(which is too large) do not belong to the original font designed by Donald Knuth: they have been added
by the American Mathematical Society in the MS[AB]M fonts
; the author has never seen the digamma
used in mathematics
.
7
The uppercase phi has a round part smaller than in other fonts, almost the same
size as the one of the lowercase phi
. There are two epsilons, two thetas, two kappas, two pis, two rhos,
two sigmas, two phis: the complete set of variants. This font has been used by hundreds of thousands of
mathematicians throughout the world
; it looks very nice when in a text typeset in Computer Modern ;
on the other hand, it is hard to fit with other fonts (like Times) because it has thinner strokes.
MathTimes [wY&Y] was designed by Michael Spivak. Its design has some flaws (the lower stroke of ζ
ξ
and  is not very succesful, nor is the upper part of the open theta, etc.) but it fits very well with Latin
7
Following a logic similar to the one that proves the existence of extraterrestrial life by the large number of possible planets
that may have climatic conditions similar to Earth
, we can say that, given the large number of mathematicians using T
E
Xand
hence having the digamma symbol at their disposal
, theremustbeatleastone, that has already used that symbol. The author
would be very interested to hear about it
.
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th International Unicode Conference 27 Boston, MA, March 1999

From Unicode to Typography, aCaseStudy: the Greek Script
text typeset in Times. Unfortunately it does not fit very well with text typeset in Monotype Greek Times:
the ratio between thin (