# Alphabetical order

Alphabetical order is a system whereby

sequences of numbers or other ordered mathematical objects
.

When applied to strings or

lexicographical order
.

To determine which of two strings of characters comes first when arranging in alphabetical order, their first letters are compared. If they differ, then the string whose first letter comes earlier in the alphabet comes before the other string. If the first letters are the same, then the second letters are compared, and so on. If a position is reached where one string has no more letters to compare while the other does, then the first (shorter) string is deemed to come first in alphabetical order.

spaces, modified letters, such as those with diacritics, and non-letter characters such as marks of punctuation
.

The result of placing a set of words or strings in alphabetical order is that all of the strings beginning with the same letter are grouped together; within that grouping all words beginning with the same two-letter sequence are grouped together; and so on. The system thus tends to maximize the number of common initial letters between adjacent words.

## History

Alphabetical order was first used in the 1st millennium

hierarchical and by category, were preferred over alphabetical order for centuries.[2]

Parts of the Bible are dated to the 7th–6th centuries BCE. In the Book of Jeremiah, the prophet utilizes the Atbash substitution cipher, based on alphabetical order. Similarly, biblical authors used acrostics based on the (ordered) Hebrew alphabet.[3]

The first effective use of alphabetical order as a cataloging device among scholars may have been in ancient Alexandria,

Great Library of Alexandria, which was founded around 300 BCE. The poet and scholar Callimachus, who worked there, is thought to have created the world's first library catalog, known as the Pinakes, with scrolls shelved in alphabetical order of the first letter of authors' names.[2]

In the 1st century BC, Roman writer

De verborum significatu, with entries in alphabetic order.[6] In the 3rd century CE, Harpocration wrote a Homeric lexicon alphabetized by all letters.[7] In the 10th century, the author of the Suda
used alphabetic order with phonetic variations.

Alphabetical order as an aid to consultation started to enter the mainstream of

theologically – in the order of God's creation, starting with Deus (meaning God).[2]

In 1604

monolingual English dictionary, "Nowe if the word, which thou art desirous to finde, begin with (a) then looke in the beginning of this Table, but if with (v) looke towards the end".[9] Although as late as 1803 Samuel Taylor Coleridge condemned encyclopedias with "an arrangement determined by the accident of initial letters",[10]
many lists are today based on this principle.

## Ordering in the Latin script

### Basic order and examples

The standard order of the modern ISO basic Latin alphabet is:

A-B-C-D-E-F-G-H-I-J-K-L-M-N-O-P-Q-R-S-T-U-V-W-X-Y-Z

An example of straightforward alphabetical ordering follows:

• As; Aster; Astrolabe; Astronomy; Astrophysics; At; Ataman; Attack; Baa

Another example:

• Barnacle; Be; Been; Benefit; Bent

The above words are ordered alphabetically. As comes before Aster because they begin with the same two letters and As has no more letters after that whereas Aster does. The next three words come after Aster because their fourth letter (the first one that differs) is r, which comes after e (the fourth letter of Aster) in the alphabet. Those words themselves are ordered based on their sixth letters (l, n and p respectively). Then comes At, which differs from the preceding words in the second letter (t comes after s). Ataman comes after At for the same reason that Aster came after As. Attack follows Ataman based on comparison of their third letters, and Baa comes after all of the others because it has a different first letter.

### Treatment of multiword strings

When some of the strings being ordered consist of more than one word, i.e., they contain

spaces or other separators such as hyphens
, then two basic approaches may be taken. In the first approach, all strings are ordered initially according to their first word, as in the sequence:

• Oak; Oak Hill; Oak Ridge; Oakley Park; Oakley River
where all strings beginning with the separate word Oak precede all those beginning with Oakley, because Oak precedes Oakley in alphabetical order.

In the second approach, strings are alphabetized as if they had no spaces, giving the sequence:

• Oak; Oak Hill; Oakley Park; Oakley River; Oak Ridge
where Oak Ridge now comes after the Oakley strings, as it would if it were written "Oakridge".

The second approach is the one usually taken in dictionaries[citation needed], and it is thus often called dictionary order by publishers. The first approach has often been used in book indexes, although each publisher traditionally set its own standards for which approach to use therein; there was no ISO standard for book indexes (ISO 999) before 1975.

### Special cases

#### Modified letters

In French, modified letters (such as those with diacritics) are treated the same as the base letter for alphabetical ordering purposes. For example, rôle comes between rock and rose, as if it were written role. However, languages that use such letters systematically generally have their own ordering rules. See § Language-specific conventions below.

#### Ordering by surname

In most cultures where

family names are written after given names
, it is still desired to sort lists of names (as in telephone directories) by family name first. In this case, names need to be reordered to be sorted correctly. For example, Juan Hernandes and Brian O'Leary should be sorted as "Hernandes, Juan" and "O'Leary, Brian" even if they are not written this way. Capturing this rule in a computer collation algorithm is complex, and simple attempts will fail. For example, unless the algorithm has at its disposal an extensive list of family names, there is no way to decide if "Gillian Lucille van der Waal" is "van der Waal, Gillian Lucille", "Waal, Gillian Lucille van der", or even "Lucille van der Waal, Gillian".

Ordering by surname is frequently encountered in academic contexts. Within a single multi-author paper, ordering the authors alphabetically by surname, rather than by other methods such as reverse seniority or subjective degree of contribution to the paper, is seen as a way of "acknowledg[ing] similar contributions" or "avoid[ing] disharmony in collaborating groups".[11] The practice in certain fields of ordering citations in bibliographies by the surnames of their authors has been found to create bias in favour of authors with surnames which appear earlier in the alphabet, while this effect does not appear in fields in which bibliographies are ordered chronologically.[12]

#### The and other common words

If a phrase begins with a very common word (such as "the", "a" or "an", called articles in grammar), that word is sometimes ignored or moved to the end of the phrase, but this is not always the case. For example, the book "The Shining" might be treated as "Shining", or "Shining, The" and therefore before the book title "Summer of Sam". However, it may also be treated as simply "The Shining" and after "Summer of Sam". Similarly, "A Wrinkle in Time" might be treated as "Wrinkle in Time", "Wrinkle in Time, A", or "A Wrinkle in Time". All three alphabetization methods are fairly easy to create by algorithm, but many programs rely on simple lexicographic ordering instead.

#### Mac prefixes

The prefixes M and Mc in Irish and Scottish surnames are abbreviations for Mac and are sometimes alphabetized as if the spelling is Mac in full. Thus McKinley might be listed before Mackintosh (as it would be if it had been spelled out as "MacKinley"). Since the advent of computer-sorted lists, this type of alphabetization is less frequently encountered, though it is still used in British telephone directories.

#### St prefix

The prefix St or St. is an abbreviation of "Saint", and is traditionally alphabetized as if the spelling is Saint in full. Thus in a gazetteer St John's might be listed before Salem (as if it would be if it had been spelled out as "Saint John's"). Since the advent of computer-sorted lists, this type of alphabetization is less frequently encountered, though it is still sometimes used.

#### Ligatures

Ligatures (two or more letters merged into one symbol) which are not considered distinct letters, such as Æ and Œ in English, are typically collated as if the letters were separate—"æther" and "aether" would be ordered the same relative to all other words. This is true even when the ligature is not purely stylistic, such as in loanwords
and brand names.

Special rules may need to be adopted to sort strings which vary only by whether two letters are joined by a ligature.

### Treatment of numerals

When some of the strings contain

24 heures du Mans as if spelled "vingt-quatre..." (French for "twenty-four"). When numerals or other symbols are used as special graphical forms of letters, as 1337 for leet or the movie Seven (which was stylised as Se7en), they may be sorted as if they were those letters. Natural sort order
orders strings alphabetically, except that multi-digit numbers are treated as a single character and ordered by the value of the number encoded by the digits.

In the case of monarchs and popes, although their numbers are in Roman numerals and resemble letters, they are normally arranged in numerical order: so, for example, even though V comes after I, the Danish king Christian IX comes after his predecessor Christian VIII.

### Language-specific conventions

Languages which use an

extended Latin alphabet generally have their own conventions for treatment of the extra letters. Also in some languages certain digraphs are treated as single letters for collation purposes. For example, the Spanish alphabet treats ñ as a basic letter following n, and formerly treated the digraphs ch and ll as basic letters following c and l, respectively. Now сh and ll are alphabetized as two-letter combinations. The new alphabetization rule was issued by the Royal Spanish Academy
in 1994. These digraphs were still formally designated as letters but they are no longer so since 2010. On the other hand, the digraph rr follows rqu as expected (and did so even before the 1994 alphabetization rule), while vowels with acute accents (á, é, í, ó, ú) have always been ordered in parallel with their base letters, as has the letter ü.

In a few cases, such as

Kiowa
, the alphabet has been completely reordered.

Alphabetization rules applied in various languages are listed below.

• In
Roman Numerals. When the abjadiyya is used in numbering, a unique abstracted way of writing the letters must be used in order to distinguish those letters from three first letter of the sentence as well as from numbers. For example, the Alef "ا" which looks identical to the Hindi numeral one "١", a small oval loop extends clockwise of the letter's bottom, followed by a short tail. Although these characters are rarely used digitally, they have been recognized under ASCII as Arabic Mathematical Alphabet, with ranges from 1EE00 TO 1EEFF. [13] There is a less common order, which is ordered phonetically Sawti Alphabet  [ar], starting from the deep throat sound haa to the lip most meem. This order was created by Al-faraheedi
.
• In Azerbaijani, there are eight additional letters to the standard Latin alphabet. Five of them are vowels: i, ı, ö, ü, ə and three are consonants: ç, ş, ğ. The alphabet is the same as the Turkish, with the same sounds written with the same letters, except for three additional letters: q, x and ə for sounds that do not exist in Turkish. Although all the "Turkish letters" are collated in their "normal" alphabetical order like in Turkish, the three extra letters are collated arbitrarily after letters whose sounds approach theirs. So, q is collated just after k, x (pronounced like a German ch) is collated just after h and ə (pronounced roughly like an English short a) is collated just after e.
• In Breton, there is no "c", "q", "x" but there are the digraphs "ch" and "c'h", which are collated between "b" and "d". For example: « buzhugenn, chug, c'hoar, daeraouenn » (earthworm, juice, sister, teardrop).
• In
DŽ are also considered separate letters and are positioned between Ď and E
.
• In the Danish and Norwegian alphabets, the same extra vowels as in Swedish (see below) are also present but in a different order and with different glyphs (..., X, Y, Z, Æ, Ø, Å). Also, "Aa" collates as an equivalent to "Å". The Danish alphabet has traditionally seen "W" as a variant of "V", but today "W" is considered a separate letter.
• In
Ĳ) was formerly to be collated as Y (or sometimes as a separate letter: Y < IJ < Z), but is currently mostly collated as 2 letters (II < IJ < IK). Exceptions are phone directories; IJ is always collated as Y here because in many Dutch family names Y is used where modern spelling would require IJ. Note that a word starting with ij that is written with a capital I is also written with a capital J, for example, the town IJmuiden, the river IJssel and the country IJsland (Iceland
).
• In
ŭ (u with breve
), are counted as separate letters and collated separately (c, ĉ, d, e, f, g, ĝ, h, ĥ, i, j, ĵ ... s, ŝ, t, u, ŭ, v, z).
• In
Estonian alphabet
, which otherwise does not differ from the basic Latin alphabet.
• The
Ð, and the last five are V, Y, Ý, Æ, Ø
• In Filipino (Tagalog) and other Philippine languages, the letter Ng is treated as a separate letter. It is pronounced as in sing, ping-pong, etc. By itself, it is pronounced nang, but in general Filipino orthography, it is spelled as if it were two separate letters (n and g). Also, letter derivatives (such as Ñ) immediately follow the base letter. Filipino also is written with diacritics, but their use is very rare (except the tilde).
• The
Finnish alphabet
and collating rules are the same as those of Swedish.
• For French, the last accent in a given word determines the order.[14] For example, in French, the following four words would be sorted this way: cote < côte < coté < côté.
• In
German letters with umlaut (Ä, Ö, Ü) are treated generally just like their non-umlauted versions; ß
is always sorted as ss. This makes the alphabetic order Arbeit, Arg, Ärgerlich, Argument, Arm, Assistant, Aßlar, Assoziation. For phone directories and similar lists of names, the umlauts are to be collated like the letter combinations "ae", "oe", "ue" because a number of German surnames appear both with umlaut and in the non-umlauted form with "e" (Müller/Mueller). This makes the alphabetic order Udet, Übelacker, Uell, Ülle, Ueve, Üxküll, Uffenbach.
• The Hungarian vowels have accents, umlauts, and double accents, while consonants are written with single, double (digraphs) or triple (trigraph) characters. In collating, accented vowels are equivalent with their non-accented counterparts and double and triple characters follow their single originals. Hungarian alphabetic order is: A=Á, B, C, Cs, D, Dz, Dzs, E=É, F, G, Gy, H, I=Í, J, K, L, Ly, M, N, Ny, O=Ó, Ö=Ő, P, Q, R, S, Sz, T, Ty, U=Ú, Ü=Ű, V, W, X, Y, Z, Zs. (Before 1984, dz and dzs were not considered single letters for collation, but two letters each, d+z and d+zs instead.) It means that e.g. nádcukor should precede nádcsomó (even though s normally precedes u), since c precedes cs in the collation. Difference in vowel length should only be taken into consideration if the two words are otherwise identical (e.g. egér, éger). Spaces and hyphens within phrases are ignored in collation. Ch also occurs as a digraph in certain words but it is not considered as a grapheme on its own right in terms of collation.
A particular feature of Hungarian collation is that contracted forms of double di- and trigraphs (such as ggy from gy + gy or ddzs from dzs + dzs) should be collated as if they were written in full (independently of the fact of the contraction and the elements of the di- or trigraphs). For example, kaszinó should precede kassza (even though the fourth character z would normally come after s in the alphabet), because the fourth "character" (grapheme) of the word kassza is considered a second sz (decomposing ssz into sz + sz), which does follow i (in kaszinó).
• In
Þ, Æ
, Ö.
• voice-onset time
, then the affricates, fricatives, liquids, and nasals:
A, AU, E, I, O, U, B, F, P, V, D, J, T, TH, G, C, K, Q, CH, X, S, Z, L, Y, W, H, M, N
• In Lithuanian, specifically Lithuanian letters go after their Latin originals. Another change is that Y comes just before J: ... G, H, I, Į, Y, J, K...
• In Polish, specifically Polish letters derived from the Latin alphabet are collated after their originals: A, Ą, B, C, Ć, D, E, Ę, ..., L, Ł, M, N, Ń, O, Ó, P, ..., S, Ś, T, ..., Z, Ź, Ż. The digraphs for collation purposes are treated as if they were two separate letters.
• In
Portuguese
, the collating order is just like in English: A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z. Digraphs and letters with diacritics are not included in the alphabet.
• In Romanian, special characters derived from the Latin alphabet are collated after their originals: A, Ă, Â, ..., I, Î, ..., S, Ș, T, Ț, ..., Z.
• In Serbo-Croatian and other related South Slavic languages, the five accented characters and three conjoined characters are sorted after the originals: ..., C, Č, Ć, D, DŽ, Đ, E, ..., L, LJ, M, N, NJ, O, ..., S, Š, T, ..., Z, Ž.
• RAE adopted the more conventional usage, and now LL is collated between LK and LM, and CH between CG and CI. The six characters with diacritics Á, É, Í, Ó, Ú, Ü are treated as the original letters A, E, I, O, U, for example: radio, ráfaga, rana, rápido, rastrillo. The only Spanish-specific collating question is Ñ (eñe
) as a different letter collated after N.
• In the
(2006) "W" was considered a separate letter.
• In the Turkish alphabet there are six additional letters: ç, ğ, ı, ö, ş, and ü (but no q, w, and x). They are collated with ç after c, ğ after g, ı before i, ö after o, ş after s, and ü after u. Originally, when the alphabet was introduced in 1928, ı was collated after i, but the order was changed later so that letters having shapes containing dots, cedilles or other adorning marks always follow the letters with corresponding bare shapes. Note that in Turkish orthography the letter I is the majuscule of dotless ı, whereas İ is the majuscule of dotted i.
• In many
Azeri or the Jaꞑalif orthography for Tatar), there used to be the letter Gha (Ƣƣ), which came between G and H
. It is now in disuse.
• In
ô, ơ, ư while f, j, w, z
are absent, even though they are still in some use (like Internet address, foreign loan language). "f" is replaced by the combination "ph". The same as for "w" is "qu".
• In Volapük ä, ö and ü are counted as separate letters and collated separately (a, ä, b ... o, ö, p ... u, ü, v) while q and w are absent.[15]
• In Welsh the digraphs CH, DD, FF, NG, LL, PH, RH, and TH are treated as single letters, and each is listed after the first character of the pair (except for NG which is listed after G), producing the order A, B, C, CH, D, DD, E, F, FF, G, NG, H, and so on. It can sometimes happen, however, that word compounding results in the juxtaposition of two letters which do not form a digraph. An example is the word LLONGYFARCH (composed from LLON + GYFARCH). This results in such an ordering as, for example, LAWR, LWCUS, LLONG, LLOM, LLONGYFARCH (NG is a digraph in LLONG, but not in LLONGYFARCH). The letter combination R+H (as distinct from the digraph RH) may similarly arise by juxtaposition in compounds, although this tends not to produce any pairs in which misidentification could affect the ordering. For the other potentially confusing letter combinations that may occur – namely, D+D and L+L – a hyphen is used in the spelling (e.g. AD-DAL, CHWIL-LYS).
• In Pinyin alphabetical order, for two Chinese characters with the same pinyin basic letters, if there is a difference of basic letter "e" and modified letter "ê", or of basic letter "u" and modified letter "ü", then the pinyin with a modified letter comes after the pinyin without a modified letter. For example, "額 (è)欸(ê̄)","路(lù)驢(lǘ)","努(nǔ)女(nǚ)". Characters of the same pinyin letters (including modified letters ê and ü.) are arranged according to their tones in the order of "first tone (i.e., "flat tone"), second tone (rising tone), third tone (falling-rising tone), fourth tone (falling tone), fifth tone (neutral tone)", such as "媽(mā)麻(má)馬(mǎ)罵(mà)嗎(ma)".[a]

## Automation

Unicode Collation Algorithm, which can be used to put strings containing any Unicode symbols into (an extension of) alphabetical order.[14] It can be made to conform to most of the language-specific conventions described above by tailoring its default collation table. Several such tailorings are collected in Common Locale Data Repository
.

## Similar orderings

The principle behind alphabetical ordering can still be applied in languages that do not strictly speaking use an alphabet – for example, they may be written using a syllabary or abugida – provided the symbols used have an established ordering.

For

radical-and-stroke sorting is frequently used as a way of defining an ordering on the symbols. Japanese sometimes uses pronunciation order, most commonly with the Gojūon order but sometimes with the older Iroha
ordering.

In mathematics,

lexicographical order is a means of ordering sequences in a manner analogous to that used to produce alphabetical order.[16]

Some computer applications use a version of alphabetical order that can be achieved using a very simple

ASCIIbetical order
.

A rhyming dictionary is based on sorting words in alphabetical order starting from the last to the first letter of the word.

## Notes

1. ^ There is an exception: In ABC Chinese–English Dictionary the tone order is "zero tone (neutral tone), first tone (flat tone), second tone (rising tone), third tone (falling-rising tone) and fourth tone (falling tone)".

## References

1. ^ Reinhard G. Lehmann: "27-30-22-26. How Many Letters Needs an Alphabet? The Case of Semitic", in: The idea of writing: Writing across borders, edited by Alex de Voogt and Joachim Friedrich Quack, Leiden: Brill 2012, pp. 11–52.
2. ^ a b c d Street, Julie (10 June 2020). "From A to Z - the surprising history of alphabetical order" (text and audio). ABC News (ABC Radio National). Australian Broadcasting Corporation. Archived from the original on 2 July 2020. Retrieved 6 July 2020.
3. ^ e.g. Psalms 25, 34, 37, 111, 112, 119 and 145 of the Hebrew Bible
4. ^ Daly, Lloyd. Contributions to the History of Alphabetization in Antiquity and the Middle Ages. Brussels, 1967. p. 25.
5. JSTOR 1088539
.
6. ^ LIVRE XI – texte latin – traduction + commentaires. Archived from the original on 9 June 2012. Retrieved 8 May 2012.
7. ^ Gibson, Craig (2002). Interpreting a classic: Demosthenes and his ancient commentators.
8. ^ Cawdrey, Robert (1604). A Table Alphabeticall. London. p. [A4]v.
9. ^
10. PMID 17227141
.
11. (PDF) from the original on 10 November 2018. Retrieved 10 November 2018.
12. ^ "Arabic Mathematical Alphabetic Symbols" (PDF). THE Unicode Standard. Archived (PDF) from the original on 30 October 2022. Retrieved 26 November 2022.
13. ^ a b "Unicode Technical Standard #10: Unicode collation algorithm". Unicode, Inc. (unicode.org). 20 March 2008. Archived from the original on 27 August 2008. Retrieved 27 August 2008.
14. ^ Midgley, Ralph. "Volapük to English dictionary" (PDF). Archived from the original (PDF) on 1 September 2012. Retrieved 24 September 2019.
15. .