♫ Cantillizer ש֕ - Cantillation History & Interpretation

1. Introduction
2. Vocalization
   1. Aleppo Codex
3. Semiotics
4. Versification
5. Medieval Theory
6. Renaissance Theory
   1. Parsing Left & Right
      1. Recursive Bisection
      2. In-Rank Precedence
      3. Rules of Transformation
7. Modern Theory
   1. Constituent Structure Analysis
   2. Context-Free Grammar
   3. Distributional Analysis

Introduction

Three hypotheses pertain to the main or original purpose of cantillation marks, musical, rhetorical (diacritical and prosodic), and hermeneutic (syntactic and semantic). Cantillizer supports all without privileging any of the three. The goal of the Cantillizer software application project is to extract and process cantillation data from the Aleppo Codex of the Hebrew Bible for the purpose of studying both the linear and the hierarchical order (or environment) in which the signs occur. The database holds all cantillation information by book, chapter, and verse, allowing queries to provide display and distributional analysis of statistics that show the patterns or structure of the signs, independently of the linguistic data that they serve to punctuate. If the signs are musical notation, for example, then they might in fact bear little or no relation to the text, as is largely the case of Western musical notes. The same lyric may be sung to different melodies, and different lyrics may be sung to the same melody, both of which are indeed quite common occurrences. Psalm 18 and 2 Samuel 22 (as well as a couple of other texts) might seem to imply just such a phenomenon, one lyric, different melodies. Moreover, many verses (lyrics) can be found with exactly the same pattern of cantillation marks (melody). Cantillizer holds that the interest of any semiotic system of representation that consists of a fixed number of discrete elements, such as natural human languages, lies not in the signs themselves, which are arbitrary, unmotivated, and conventional, but in the complex relationships among the signs, which are logical and rule-based. Cantillizer hopes to derive the logical rules that govern cantillation marks.

Vocalization

Hebrew (like other Semitic languages) was originally and is still written without most vowels. Sometime between Jerome (c. 347-420), the Dalmatian theologian and author of the Latin translation of the Bible, and Saadia ben Joseph (892-942 CE), aka Gaon, the Jewish Egyptian philosopher and author of the Arabic translation, who testify respectively to the absence and presence of vowels, three rival schools of vocalization arose, the Babylonian, the Palestinian, and the Tiberian, with the last (and latest) eventually prevailing. As the Jerusalem Talmud (written in Tiberias, 4th century CE) and the Babylonian Talmud (written in Sura, 5th century CE) collected and organized different oral traditions of biblical commentary, the three pointing systems synthesized diverse local phonetic and musical phenomena.

Moreover, beginning in the second half of the eighth century amid political turmoil in the caliphate of Baghdad, the Karaites, a schismatic Jewish sect, posed a grave threat to rabbinical authority by opposing traditional biblical commentary in a back-to-the-text movement. The besieged Tiberian rabbis fought back by creating a textual standard that they called the Masorah or “tradition”. The Palestinian school under ben Naphtali (flourished c. 890-940 CE, given name either Jacob or Moses), the Jewish scribe and philologist, produced its own standard, but it has not survived, although many of its readings are known through secondary sources. The authors of the Masorah, who spoke medieval Aramaic, and learned to read Mishnaic (100-400 CE) and biblical Hebrew, have exerted more influence on the history of biblical scholarship than all of the Talmudists and exegetes put together, for they in large part determined what following generations of readers and philologists would understand as the words of the Bible. In adding vowels to the text, eliminating polysemy by suppressing homonymy, they essentially rewrote it.

Vocalization sparked a controversy that burned for more than five hundred years, until the advent of movable type allowed the advocates of the Masorah to impose its readings definitively. The tradition of printing the Bible with vowels, while almost all other Hebrew texts (including books and newspapers) lack them, is not a quaint usage benevolently conceived on behalf of Diaspora Jewish readers less skilled in the Hebrew language, but an ideological tactic to shrink the plethora of biblical variants down to one unique vision. Indeed this seemingly innocuous practice amounts to censorship. The actual Torah is manuscripted without vowels precisely because it is kept in the synagogue between the hands of the rabbis, and shown to the layman only under supervision. The following approximate chronology shows the steps that led to the establishment of the modern text of the Bible in the course of a thousand years of editorial, critical, linguistic, and musical thought:

• Canonization: 1st-2nd centuries CE

• Commentary: 2nd-5th centuries CE

• Punctuation: 2nd half first millennium
  

• Vocalization: 2nd half first millennium
  

• Cantillation: 2nd half first millennium
  

Motivation seems to have been on the one hand political, establishing and consolidating the power of the rabbinical Judaism of the synagogue in the face of the destruction of the second Temple (70 CE) and the subsequent rise of Christianity (canonization and commentary), on the other hand linguistic, theological, and ideological, normalizing and disambiguating the text of the Bible and its liturgical recitation in the face of the transition from Biblical Hebrew (BCE) and Mishnaic Hebrew (first half CE) to Aramaic (first millennium CE) as the spoken language of the Jews in Israel (punctuation, vocalization, cantillation).

Aleppo Codex

Isaiah 9:5b-6 (In 6a below variant reading retained in parentheses. Masorah circle לְםַ רְ֯בֵּ֨ה indicates variant in margin above right.)

וַיִּקְרָ֨א שְׁמ֜וֹ פֶּ֠לֶא יוֹעֵץ֙ אֵ֣ל גִּבּ֔וֹר אֲבִי־עַ֖ד שַׂר־שָׁלֽוֹם׃ [...]

לם רבה (לְמַרְבֵּ֨ה) הַמִּשְׂרָ֜ה וּלְשָׁל֣וֹם אֵֽין־קֵ֗ץ עַל־כִּסֵּ֤א דָוִד֙ וְעַל־מַמְלַכְתּ֔וֹ לְהָכִ֤ין אֹתָהּ֙ וּֽלְסַעֲדָ֔הּ בְּמִשְׁפָּ֖ט וּבִצְדָקָ֑ה מֵֽעַתָּה֙ וְעַד־עוֹלָ֔ם קִנְאַ֛ת יְהוָ֥ה צְבָא֖וֹת תַּֽעֲשֶׂה־זֹּֽאת׃

[...] Azla, Grsh, GtTl, Psta, Mnkh, LtZk, Tfka, Sluk

Azla, Grsh, Mnkh, Rvia, Mhpk, Psta, LtZk, Mhpk, Psta, LtZk, Tfka, Atnk, Psta, LtZk, Tvir, Mrka, Tfka, Sluk

[...] and his name shall be called Wonderful, Counsellor, The mighty God, The everlasting Father, The Prince of Peace.

Of the increase of [his] government and peace [there shall be] no end, upon the throne of David, and upon his kingdom, to order it, and to establish it with judgment and with justice from henceforth even for ever. The zeal of the LORD of hosts will perform this. [Isaiah 9:6-7 in Christian numbering]

Wickes deems 5b mispunctuated (also note vowel variant פֵ/פֶ):

an abnormal accentuation,—the object being to mark not only the Name, but in a special and emphatic manner the separation of פֵּלֶא from יוֹעֶץ, ‘Wonder,—Counsellor.’ The regular accent for this purpose would have been פֵּ֤לֶא ׀.

The Aleppo Codex (c. 930), written in or around Tiberias (on the shores of the Sea of Galilee) by Solomon ben Buyaa under the direction of Aaron ben Asher (flourished first half of tenth century), the Jewish scribe and philologist, was the earliest extant complete vocalized Bible until 1947, when Syrian rioters burnt down the synagogue where it had been housed and diligently copied for five hundred years, since its removal from Jerusalem via Cairo. Jews managed to rescue about sixty percent of the manuscript and smuggle it back to Israel. The source text for virtually all subsequent editions, the Aleppo Codex is the single most important document in the three-thousand-year history of the Hebrew Bible.

In his guidelines for biblical scribes Moses ben Maimon (1135-1204), aka Maimonides, the Jewish Spanish physician and theologian, writes of this text:

The scroll on which I relied on for [clarification of] these matters was a scroll renowned in Egypt, which includes all the 24 books [of the Bible]. It was kept in Jerusalem for many years so that scrolls could be checked from it. Everyone relies upon it because it was corrected by ben Asher, who spent many years writing it precisely, and [afterward] checked it many times.

http://www.chabad.org/library/article_cdo/aid/925430/jewish/Chapter-Eight.htm

The spiritual leader may be prescribing more than describing, but his words carried enormous weight.

Cantillizer has obtained the best, most authoritative Unicode Aleppo Codex text currently published online, available from:

http://www.mechon-mamre.org/c/ct/c0.htm, where it may be freely and openly downloaded:

http://www.mechon-mamre.org/dlct.htm without any special permission, although a small donation is requested.

The raw data input consists in text files of the entire vocalized, punctuated, and cantillated Hebrew Bible, several million characters. Processing reduces this to cantillation data only, several hundred thousand characters. Cantillizer has not and will not publish anyone else’s data. Under the doctrine of fair usage we have extracted a small portion (approximately ten percent) of that data (cantillation marks only), emended the order of certain signs that are misencoded (despite being correctly rendered in graphical browser representation), processed it, analyzed it, and are publishing that emended and processed data, as well as the results of that analysis, in a format utterly incompatible with that of the original source text.

Semiotics

Cantillation refers to Jewish liturgical chant. In synagogue the lector chants from the unvocalized Torah and Hagiographa with the help of a prompter following in a cantillated text. He reads the entire Pentateuch and the five scrolls (Ruth, Song of Songs, Ecclesiastes, Lamentations, and Esther) in an annual rotation of weekly passages on the Sabbath and holidays. The precentor psalmodizes from a vocalized psalter. On the Sabbath and holidays he sings psalms and songs from the Bible, as well as other prayers and poems both ancient and modern. The cantor may double as lector or precentor in addition to his role as soloist and/or choirmaster, depending on the size, wealth, individual talents, and cultural traditions of the temple. Untold historical and geographical variations in synagogal custom and organization are attested. In the Middle Ages, and as late as the twentieth century in certain Jewish communities, such as those of Rome, Cairo, and Yemen, a signer cued the congregation to cantillation marks by means of hand signals.

These signs are attested in the Babylonian Talmud as early as the first half of the first millennium:

Why should one wipe with the left hand and not with the right? — Raba said: Because the Torah was given with the right hand, as it says, At His right hand was a fiery law unto them. Rabbah b. Hanah said: Because it is brought to the mouth. R. Simeon b. Lakish said: Because one binds the tefillin (on the left arm) with it. R. Nahman b. Isaac said: Because he points to the accents in the scroll with it.* A similar difference of opinion is found among Tannaim. R. Eliezer says, because one eats with it; R. Joshua says, because one writes with it; R. Akiba says, because one points with it to the accents in the scroll.

* Rashi explains: Because in chanting he makes corresponding movements with the right hand, this having been the custom of [Jewish] Palestinians in his day.

http://www.come-and-hear.com/berakoth/berakoth_62.html

Derenbourg’s late medieval source describes the chironomy:

Teras [geresh] is followed by legarmeh or revia, legarmeh by revia, revia by yetiv [pashta], yetiv by zakef, zakef by tevir or tifkha, tifkha by atnakh or sof pasuk [silluk]; then pazer is followed by telisha, and the latter by teras. “This order may change according to the words that enter the verse, one sees if the verse is long or short, if it presents a sequential narrative, or else if it contains invocations, letters marking surprise or determination. The meaning influences the pronunciation, and the latter influences the accentuation. The grammarians instruct, in addition to the sounds articulated by the mouth, for each accent a movement of the hand as well. Thus they say: for tsinorit (zarka), vigorously wave one finger; for segolta, curl three fingers forwards; for shofar [munakh], make a movement with two fingers; for pazer, a short, broad movement with two fingers; for karni para [great pazer], curl two fingers upwards; for telisha, wave fingers; for little zakef, an up-to-down movement of the fingers; teras [geresh] throws the word backwards, telisha drags it backwards; and so on for all the accents and servants [disjunctive & conjunctive signs respectively]” [quotation from source text].

Cantillation Chironomy

	Mehupakh	ש֤		Revia		ש֗
	Pashta	ש֙		Merekha	ש֥	Tifkha	ש֖
	Little Zakef	ש֔		Atnakh		ש֑
	Great Zakef	ש֕		Sof Pasuk [silluk]		שֽ׃

Cantillation marks belong to a complex system of punctuation or textual annotation (the dots, lines, and curves written above, below, within, and between Hebrew letters) that convey a enormous amount of information with breathtaking economy of means, as pertains to the following:

• Melody, modulation, and rhythm (cantillation)

• Tonic accent, intonation and pauses (cantillation)

• Metrical units (logical)

• Syntactic relationships (logical)

• Vowels (diacritical)

• Homographs and phonetic shifts (diacritical)

Cantillation marks perform the first four functions, but are only attested in conjunction with pointing, the vocalic and diacritical marks that perform the last two. All arose at the same time (evolving in three rival schools over a period of five hundred years, 500-1000 CE), and clear distinctions are seldom drawn among the characters (including digraphs and homographs), their names (including synonyms), and their intertwined roles. Since a thousand years of unrecorded harmonic and phonetic transformations separated the punctuators from the authors of the Bible, cantillation and diacritical marks do not accurately reflect historical phenomena of the biblical period, notes and vowels the rabbis had never heard. They may however reflect the Jewish culture, music, and dialects of the times and places in which they were written, medieval Sura (in Babylonia, modern-day Iraq) and Tiberias (on the shores of the Sea of Galilee). They may also accurately represent logical relationships (grammatical and metrical) actually present in the text.

In his notes to the publication of the anonymous Yemenite Hebrew grammar compilation Manuel du Lecteur (1870, source c. 1390 based on still older texts), Joseph Derenbourg, the Jewish Franco-German Orientalist and philologist, gives this colorful account of cantillation marks:

Accentuation is like the first stuttering of an unconscious grammar, and would perhaps never have undergone this development had it not been destined to compensate for science, which had not yet been formulated. This incomparable punctuation may only be understood as the expression of a tradition that had to materialize, for want of the ability to call to its aid the exact observation of the organism of language.

The author, a writer of great charm, shares with his fellow romantics an unhappily positivist view of the history of science. The sages who wrote the cantillation marks were scholars of the very highest order. That we still do not understand their meaning bears witness to our ignorance, not theirs. Whatever their original role may have been, musical, syntactic, prosodic, and/or phonological, cantillation marks constitute a series of data punctuating a linguistic text. The signs occur non-random in order, and their sequential patterns are easily discerned, if not so easily interpreted.

Versification

Almost every one of the several hundred thousand words in the Bible bears a cantillation mark, taking into account that some polysyllables bear two signs (frequently merekha tevir, and munakh little zakef), and considering makef (similar to a hyphen) as a word joiner. Hebrew is an oxytonic language, whose accent regularly falls on the last syllable of an utterance. Cantillation marks designate the first letter of this stressed syllable, with a few simple, rule-governed exceptions. Common occurrences include pretonic, prepositive, or postpositive signs, and the anticipation of the tonic accent (along with its sign), where permitted, in order to avoid the perceived cacophony of two consecutive stressed syllables. Two systems of cantillation marks occur in the Masorah, referred to as psalmody (Psalms, Proverbs, body of the book of Job) and prosody (prologue/epilogue of Job, and the rest of the books). Moreover Sephardi, Ashkenazi, and Yemenite cantors interpret cantillation marks differently in their trope (musical phrasing conventions).

Not enough is currently known about Ancient Hebrew versification to characterize the rhythm of the prosodic books of the Bible. Suffice to say that it feels quite irregular (or prosaic) to the modern reader, except for a few passages (Song of Deborah, Song of Hannah, Song of Moses, Song of Songs, Song of the Sea, Song of the Well) that feel more poetic, in content if not necessarily in form. The esthetics of prosody vary wildly according to the style of the text, from mythological narrative (Genesis) to liturgy and legislation (Deuteronomy), from epic history & family tragedy (Samuel) to ideological harangue (Jeremiah), from inspired hallucination (Ezekiel) to philosophical poem in prose (Ecclesiastes). On the contrary, the rhythm of the psalmodic books feels more regular, more poetic, than the rhythm of prosody. The typographical convention of leaving a blank space to mark the cæsura reinforces this impression. Parallelism and antithesis stand out more. The shorter stichs and verses vary less in length. The esthetics of psalmody embrace song and prayer (Psalms), theological thought (Job), and aphoristic wisdom (Proverbs). Cantillizer hopes to contribute to the research in this field.

Medieval Theory

Hebrew grammar has always tended towards the descriptive, as opposed to the more prescriptive Greek and Latin pedagogy, for the latter turned towards the future, teaching youth how to speak and write according to a normative ideal, while the former turns endlessly towards the past, deriving rules from the finite, heterogeneous, written data of the Bible with little or no care for the production of new utterances, since Aramaic had replaced Hebrew as the Jews’ vernacular language of spoken and written communication by the time of the Talmud. The institution of the yeshiva did not teach boys to speak Hebrew, except as a byproduct of teaching them to read and recite it. Jewish grammarians of the High Middle Ages wrote several treatises on cantillation, breaking the disjunctive signs (or lords) into three groups, variously defined according to musical criteria (conflated from Wickes and Yeivin):

I. highest-pitched (leadoff or exalted) melodies: shalshelet, geresh, pazer, telisha

II. high-pitched (or raised) melodies: segolta, revia, zarka, tevir, legarmeh

III. low (or sustained) melodies: silluk, atnakh, zakef, tifkha, pashta

Wickes would fain modify the organization:

The voice [in III] dropped and proceeded in measured tones, on approaching the two great pauses in the middle and at the end of the verse, and also the pauses next in magnitude to them marked by Zaqeph. (This last rule is indeed contrary to what we should have expected, for Zaqeph and its foretone Pashṭa seem from form and position high notes.*) When however the word, on which any of these accents falls, is Mil‘el [penultimate tonic accent], we are told that the melody changed and that they were chanted with a high note (the voice dropping however again, I presume, with the last syllable). The arsis in such cases explains the change in melody.

* If we were to transfer these accents to Class II, and bring T’bhir into Class III, we might suppose that all was in order. But we know too little of the musical value of the accents to be able to dogmatize.

Wickes calls the analyses: “brief and enigmatical”. Why could the rabbis not come up with a plausible theory, or at least an evocative creation myth, to account for the signs? Perhaps the punctuation sprang up spontaneously but gradually from musical sources themselves bereft of an explicit theoretical background, under the cross-pollination of similar contemporaneous systems of musical annotation (which lack grammatical significance) in Greek and Syriac liturgical texts, by the more or less unspoken conventions of many sages belonging to different schools, culturally, geographically, and chronologically confined, exchanging signs, song, and syntax through manuscripts, correspondence, and occasional travel, so that no one consciously understood what was happening, as allophones create pidgins and children learn creoles without necessarily being able to explain their structure. Wickes opts somewhat harshly for just such an hypothesis: “Jewish writers on the accents had no more idea of this law [dichotomy] than they had of many of the chief grammatical rules.” Yet these same scholars wrote beautifully and eloquently of complex questions of phonetics, morphology, and syntax. Judah Hayyuj (Cordova c. 940-1010) and David Kimhi (Narbonne c. 1160-1235) were brilliant philologists, while Aaron ben Asher (Tiberias † c. 960) traced his family of scribes (veritable co-authors of the Masorah) five generations back, when cantillation marks may still have been in their later developmental stages. However Wickes and Yeivin propose no general theory of the verse, and indeed almost never quote a full verse of text. This myopia leads to a forest-for-the-trees error. While counting the words and syllables of isolated clauses may allow one to account for the presence of a given allograph (or contextual variant): great shalshelet, segolta, little zakef, or great zakef, and the presence before it of an associated allograph: Ø, zarka, pashta/yetiv, or Ø respectively, it does not tell us how those contextual determinations came about in the first place.

In the history of ideas, for philosophical and technological reasons, a formal science such as mathematics (Euclid fl. 300 BCE) reached comparatively high levels of sophistication at a relatively early date, followed much later by a natural science such as physics (Galileo 1564-1642), while a social science such as linguistics (Saussure 1857-1913) took even longer to catch up. The beginnings of solfège (Guido of Arezzo c. 990-1050) roughly coincided with the Oriental innovation of cantillation marks, but Occidental harmonic theory would not develop in full until much later (Rameau 1683-1764). That the signs belong to two distinct fields of knowledge, language and music, could only contribute to confusion about their origins and meaning, not to mention some inevitable obfuscation due to their biblical context. Furthermore, the phoneme and the musical note are mental objects rather than physical phenomena (diverse analog and acoustic phonetic realizations or pitches) within digital systems of symbolic representation. Medieval authors could hardly have recognized cantillation marks as graphemes. It is therefore not at all surprising to find that so much controversy has surrounded the signs since their inception.

Renaissance Theory

Parsing Left & Right

Building on the previous theory, Samuel Bohl (1611-1639), the German Orientalist and philologist, divides cantillation marks into five organizational ranks or levels. The following tables, based on the Treatises (1881 and 1887) of William Wickes, the British mathematician and philologist, will be updated on the basis of data gleaned from the distributional analysis of Cantillizer. The examples in the following tables display the Ezra SIL SR font. The names and even the forms of the signs vary considerably in the literature, including but not limited to differences in the Ashkenazi and Sephardic traditions. Allographs are attested within the same font family:

Font / Sign	Zarka or Tsinor	Little Pazer	Darga
Ezra SIL SR	ש֮	ש֡	ש֧
Ezra SIL	ש֮	ש֡	ש֧

Transliteration is intended only to help readers of English recognize and pronounce the names of the cantillation marks, and does not mean to imply anything about Hebrew phonetics or orthography. The spelling kh represents the phoneme [x] as -ch, the German ach-laut in Bach.

Prosodic Hierarchy

Emperor		King		Duke		Earl		Footman
Silluk	דָּבָֽר׃	Segolta	דָּבָר֒	Revia	דָּבָ֗ר	Geresh	דָּבָ֜ר	Azla	דָּבָ֨ר	Mehupakh	דָּבָ֤ר
Atnakh	דָּבָ֑ר	Great Shalshelet	דָּבָ֓ר׀	Pashta	שֶּׁ֙מֶשׁ֙	Double Geresh	דָּבָ֞ר	Darga	דָּבָ֧ר	Merekha	דָּבָ֥ר
		Little Zakef	דָּבָ֔ר	Yetiv	מֶ֚לֶךְ	Munakh Legameh	דָּבָ֣ר׀	Double Merekha	דָּבָ֦ר	Munakh	דָּבָ֣ר
		Great Zakef	דָּבָ֕ר	Zarka	דָּבָר֮	Great Telisha	דָּ֠בָר	Galgal	דָּבָ֪ר
		Tifkha	דָּבָ֖ר	Tevir	דָּבָ֛ר	Little Pazer	דָּבָ֡ר	Little Telisha	דָּבָר֩
						Great Pazer	דָּבָ֟ר

The first four groups (emperor, king, duke, and earl) are disjunctive or pausal (indicating a musical, syntactic, and/or logical break after the word), with members listed in descending order of hierarchical or structural power, while the last (footman) is subordinate, conjunctive or non-pausal (indicating a musical, syntactic, and/or logical link to the following word), with members listed in English alphabetical order. An example of a full verse (Genesis 1:21, further analyzed below):

Munakh, Little Zakef, Tifkha, Atnakh, Munakh, Munakh, Munakh, Little Pazer, Little Telisha, Azla, Geresh, Revia, Azla, Mehupakh, Pashta, Little Zakef, Merekha, Tifkha, Silluk.

Psalmodic Hierarchy

Emperor		King		Duke		Earl		Footman
Silluk	דָּבָֽר׃	Ole Veyored	דָּ֫בָ֥ר	Revia Mugrash	דָּ֝בָ֗ר	Little Pazer	דָּבָ֡ר	Azla	דָּבָ֨ר	Mehupakh	דָּבָ֤ר
		Atnakh	דָּבָ֑ר	Revia	דָּבָ֗ר	Azla Legarmeh	דָּבָ֨ר׀	Galgal	דָּבָ֪ר	Merekha	דָּבָ֥ר
				Tsinor	דָּבָר֮	Mehupakh Legarmeh	דָּבָ֤ר׀	Illuy	דָּבָ֬ר	Munakh	דָּבָ֣ר
				Dekhi	דָּ֭בָר	Great Shalshelet	דָּבָ֓ר׀	Little Shalshelet	דָּבָ֓ר	Tarkha	דָּבָ֖ר
										Tsinorit	דָּ֘בָר

In his Cantillation of the Bible: Five Books of Moses (1957), Solomon Rosowsky, the Jewish Latvian cantor and composer, elaborates on the adulterous and incestuous relationships among these lords and ladies dancing round the table of King Arthur’s knights in hot pursuit of the Countess of Salisbury’s fallen garter. Dotted lines indicate the fealty of lords subject to emperors and kings. Horizontal arrows indicate the proxy of regents for exiled or usurped kings and dukes. Solid lines indicate the government of vassals by their lords:

The somewhat controversial principle of the aristocracy of the signs amuses and exasperates Derenbourg, but merely exasperates Wickes. The latter calls the extrapolated classification of cantillation marks: “fanciful and misleading”. The former once again waxes poetic:

But the worried and restless spirit of these doctors [rabbis], endlessly bent over the sacred text, divided and subdivided the words of each verse; the slightest nuances were spotted, not only breaks were noted, but also links, and despite the rule, “that a prince should not be demoted to the level of a servant, nor should the latter be promoted to the level of a lord,” [quotation from source text] a veritable hierarchy was established, a rather burlesque feudal system of accents, which entertained a few subtle savants of the fifteenth, sixteenth and seventeenth centuries. In this scale the lower nobility was confused with the lackeys, and accents such as telisha maintained their rank of master with difficulty. Throughout the ongoing creation of new dignitaries, the small stroke, straight or curved, placed above or below the line, tilted to the right or to the left, became the insignia of new ranks. Finally the denominations overflowed and overran, whether still more distinctions were made, or the punctuators invented new names for the same accents and afterwards new uses were sought for these innovations until then unknown.

In his Introduction to the Tiberian Mazorah (1980), Israel Yeivin proposes renaming the categories by means of Roman numerals:

Wickes opposes classification in this way (as did others before him), and indeed it does give a false impression of the accent systems. One cannot argue that the pause after one accent must be longer than the pause after another. The value of the accents is relative. In one verse a disjunctive accent might be used for a particular reason on a word closely related to the following, while in another the two words might be joined by a conjunctive (cf. the accentuation of the lists of nations in Ex 3:17 and Ex 13:5).

The division of the accents into four grades can, however, provide a useful guide. The general tendency of the accentuation is to divide a larger unit into two smaller units, and as a rule a unit ending with a disjunctive of one grade is divided by one of the grade below. Thus a unit ending with a disjunctive of grade I is divided by one of grade II, not by one of grade III, and so on.

The four grades of pausal accents are:-

I. Silluq, atnaḥ.

II. Segolta, shalshelet, zakef, ṭifḥa.

III. Zarqa, pashṭa, tevir, revia.

IV. Pazer, telisha, geresh, legarmeh.

The difference between the scheme proposed here and the earlier gradings into “emperors, kings, etc.”, is that the pausal value of the grades in this scheme is relative, not absolute. I.e. disjunctives of grade II are not characterized by a longer pausal value than those of grade III, but by the fact that their clause is normally divided by a disjunctive of grade III. For this reason, in a short verse, the real disjunctive value (in terms of ordinary syntax) of a disjunctive of grade II might be less than that of a disjunctive of grade IV in a long verse or in different circumstances. Furthermore, because of the requirements of the music of the chant, some major disjunctives must be preceded by particular minor disjunctives. For this reason, minor disjunctives (e.g. grade III) may come to fill a position in which, from the point of view of syntax, a disjunctive of a superior grade (e.g. grade II) might be expected.

Cantillizer supports the principle of relative hierarchy, while retaining the traditional titles of the ranks. Even Wickes allows: “We have considered a first group of accents—with similar rules—formed by Silluq and Athnach; and a second, consisting of Zaqeph, S’gôlta, and Tiphcha. We pass on now to the third group, embracing R’bhîa, Pashṭa, T’bhîr, and Zarqa.” The naming convention serves a useful mnemonic purpose, and the proposed association of a color scheme (emperor, king, duke, earl, footman) serves as a useful visual aid. They do no violence to the sign system, even if they may be considered anachronistic.

Recursive Bisection

The theory, widely accepted but hard to verify, suggests that the rabbis annotating the Hebrew Bible worked by means of a drill-down technique known as continuous dichotomy, or recursive bisection, under the influence of set theory geometry, a smattering of which had recently spread west from Hodu (India) through Persia (Iran) and Babylon (Iraq). To begin with the prosodic verse is split into stichs by the appointment of two emperors of unequal power, each governing an empire, the first his hemistich, the second the whole verse. The latter may seem superfluous, especially as it is already rendered more or less redundant by the presence of the metacantillation mark sof pasuk, but that is how it is written. The major dichotomy, initially represented by atnakh, falls in the following place: between elements of parallelism or antithesis (the characteristic rhetorical figures of biblical poetry), between logical units, or between syntactic units. Each clause is subsequently subdivided in the same way, so that the whole verse is divided into halves, then quarters, eighths, and sixteenths, to the extent that the heterogeneous linguistic text of each verse (written a thousand years before) allowed for such prosodic regularity.

Nesting Level 1: verse

The two hemistichs are then split into four realms by the appointment of two kings of equal power, each governing his own realm:

Nesting Level 2: stich

The next step is where the rabbis adhered to a particular logic of nesting principles. Moderns would most likely appoint four dukes of equal power to split the realms into eight duchies:

Nesting Level 3a: realm

The rabbis appointed a duke before a king, but a king before an emperor, in order to keep the linear hierarchy incrementally ascending, lest the Emperor bear the sight of an unwashed duke before (although not after) him. Each of the two kings thus appointed reigns over a dukedom (or duchy), not a kingdom (or realm):

Nesting Level 3b: realm

Finally the last step similarly diverges, where moderns would most likely appoint eight earls of equal power to split the duchies into sixteen earldoms:

Nesting Level 4a: duchy

The rabbis appointed an earl before a duke, but a duke before a king, and a king before an emperor. Each of the four dukes and two kings thus appointed reigns over an earldom:

Nesting Level 4b: duchy

The punctuators still held in their arsenal half a dozen signs of each rank below emperor to deploy, according to a dizzying galaxy of rules that pertain to length of clause (reckoned in number of words), applying mainly to contextual variants in complementary distribution. Nor were all of these subdivisions mandatory, and some may be repeated, as seen in an asymmetrical verse below. While almost every verse has two emperors, many abound in kings, dukes, and/or earls, with footmen scampering behind any of the lords, according to still more rules, in order to pick up stray metrical or lexical items left behind. Considerable latitude obtains here as well; as many as six conjunctive signs may follow in succession, according to predetermined patterns based on the following disjunctive sign. Cantillizer retains word breaks (space character) in order to take account of clause length, although a few rules pertaining to length of word (in syllables and depending on vowel length) are not supported. The latter rules do not appear to be necessary to the fundamental goal of determining the distribution of the signs.

Moreover, thousands of Hebrew morphemes may be inflected with an alternate, so-called pausal form of vocalisation. More than ninety-five percent of these allomorphs carry the signs silluk, atnakh or ole veyored, with the only other significant number of cases falling on zakef, tifkha, or revia. James Price has written of this phenomenon.

In-Rank Precedence

Based on the work of Mordechai Breuer (1981), Helmut Richter (to whom a great debt is owed for the exposition above and below) formulates the rule of  in-rank precedence: “of any two [disjunctive] marks with equal rank with no intervening stronger mark, the earlier one is considered stronger,” which may be broken down thus:

1. A sign y (such as little zakef) preceding itself or another sign x of equal rank (such as tifkha) indicates higher value of y.

2. Signs of lower rank (such as pashta) intervening between y and x are disregarded in the application of provision 1.

3. A sign of higher rank (such as atnakh) intervening between y and x interrupts the application of provision 1.

4. This rule never applies to the dependency of atnakh upon silluk, where the converse always obtains, the sign that follows (silluk) retaining hierarchical superiority over the sign of equal rank that precedes it (atnakh).

So a given string:

may be represented in a tree diagram as follows:

Assuming the jurisdiction of in-rank precedence (in conjunction with other algorithms), Cantillizer might also perform verse parsing, yielding such trees as output. It should be noted that (contrary to the other signs) the placement of silluk is always mandatory, i.e. on the last accented syllable of the verse. The diagram is conceptual, taking into account (to some extent) sequential word order, titular rank, hierarchical promotions & demotions, and how the biblical verse is in fact broken down into nested levels. The application of provision 1 may be seen in the in-rank precedence of Little Zakef2-4 to Tifkha1-2 and of Revia1-2 to Pashta1-3. The application of provision 2 may be seen in the in-rank precedence Little Zakef1-3 to Little Zakef2-4. The application of provision 3 may be seen in the lack of precedence of Tifkha1 to Little Zakef3, of Pashta1-3 to Pashta2-4, and of Geresh1 to Geresh2. The application of provision 4 may be seen in the ubiquitous superiority of Silluk to Atnakh. For an example of this rule derived from the statistical analysis of sign order, see 2 Samuel 12. Thus tifkha, a king by nature, may in a given verse perform the function of a king (2 Samuel 12:1a), or of a duke (2 Samuel 12:11b), or of an earl (2 Samuel 12:4b), where a and b refer to successive stichs. Parallels are found in real civil or military hierarchies, where the scope of the theater of operations may dictate the effective rank of the officers in command, notwithstanding their nominal commission.

Esther 8:9, the longest verse of the Bible, counts thirty-five signs (Some authors deem the last azla to be metacantillation called metiga.) of which eighteen disjunctive:

וַיִּקָּֽרְא֣וּ סֹפְרֵֽי־הַמֶּ֣לֶךְ בָּֽעֵת־הַ֠הִיא בַּחֹ֨דֶשׁ הַשְּׁלִישִׁ֜י הוּא־חֹ֣דֶשׁ סִיוָ֗ן בִּשְׁלוֹשָׁ֣ה וְעֶשְׂרִים֮ בּוֹ֒ וַיִּכָּתֵ֣ב כְּֽכָל־אֲשֶׁר־צִוָּ֣ה מָרְדֳּכַ֣י אֶל־הַיְּהוּדִ֡ים וְאֶ֣ל הָאֲחַשְׁדַּרְפְּנִֽים־וְהַפַּחוֹת֩ וְשָׂרֵ֨י הַמְּדִינ֜וֹת אֲשֶׁ֣ר ׀ מֵהֹ֣דּוּ וְעַד־כּ֗וּשׁ שֶׁ֣בַע וְעֶשְׂרִ֤ים וּמֵאָה֙ מְדִינָ֔ה מְדִינָ֤ה וּמְדִינָה֙ כִּכְתָבָ֔הּ וְעַ֥ם וָעָ֖ם כִּלְשֹׁנ֑וֹ וְאֶ֨ל־הַיְּהוּדִ֔ים כִּכְתָבָ֖ם וְכִלְשׁוֹנָֽם׃

Mnkh Mnkh GtTl Azla Grsh Mnkh Rvia Mnkh Zrka Sgol Mnkh Mnkh Mnkh LtPz Mnkh LtTl Azla Grsh MnLg Mnkh Rvia Mnkh Mhpk Psta LtZk Mhpk Psta LtZk Mrka Tfka Atnk Azla LtZk Tfka Sluk

Then were the king’s scribes called at that time in the third month, that [is], the month Sivan, on the three and twentieth [day] thereof; and it was written according to all that Mordecai commanded unto the Jews, and to the lieutenants, and the deputies and rulers of the provinces which [are] from India unto Ethiopia, an hundred twenty and seven provinces, unto every province according to the writing thereof, and unto every people after their language, and to the Jews according to their writing, and according to their language.

Something of a curiosity, the verse contains a thirty-five-Unicode-character compound: הָאֲחַשְׁדַּרְפְּנִֽים־וְהַפַּחוֹת֩, Aramaic or foreign roots referring to the satraps and prefects of the Persian government. At ten letters the first component is already the longest word in the Bible by that measure when preceded by the proclitic -ו in Esther 9:3.

The following tree diagrams represent the complex nesting structure of this long, lopsided verse. This front-loaded verse differs greatly from the generic, symmetrical model above and from the much shorter, back-loaded example below.

Esther 8:9 - Conceptual Verse Diagram

In the figure above the following types of node are defined:

• parent, e.g. segolta of revia (Sivan) & little zakef (provinces)

• grandparent, e.g. segolta of great telisha, zarka, revia (Ethiopia) & little zakef (writing)

• younger child (preceding parent in linear order), e.g. revia (Sivan) of segolta

• elder child (following parent in linear order), e.g. little zakef (provinces) of segolta

• only child, e.g. geresh (third) of great telisha

• childless, e.g. zarka

In the figure below the eighteen segments of text (corresponding to the eighteen disjunctives) are assigned as follows:

Parents (except silluk) of an only child govern their own clause, e.g. great telisha, or the following clause if preceded by their offspring. Childless nodes govern two clauses, their own and that of their ascendant (parent, grandparent etc.) following immediately in linear order, e.g. zarka & segolta, since zarka divides the two clauses. In other words parents of two children do not govern their clause directly, but through the tutelage of their immediately preceding descendant (child, grandchild etc.), e.g. segolta & zarka.

Esther 8:9 - Textual Verse Diagram (Click to enlarge & open image in new window.)

The following rules of primogeniture may be derived from the above:

• Younger children hold a rank one below their parent’s, e.g. duke < king.
  

• Elder children (except for those of atnakh) hold a rank equal to their parent’s, e.g. duke = duke.
  

• Only children’s behavior depends on whether they precede or follow their parent.
  

The same rules apply to psalmody, slightly adjusted for the fact that the verse has but one emperor (silluk) and one or two kings (ole veyored and/or atnakh). The short stichs of Psalms, Job and Proverbs do not develop the hierarchy to its fullest extent, as Psalms 17:14 (among the longest of psalmodic verses) shows.

Given their level high of abstraction, cantillation marks (independent, as they are, of sentence function, types of phrase, parts of speech, and even of language, as the Aramaic passages of Daniel and Ezra are cantillated according to the same system) may form the basis of a medieval macro-grammar that allows for the classification of all utterances in the Bible. The data collected from Cantillizer could help to formalize such rules.

Rules of Transformation

Wickes adapts a few rules, derived by the Jewish Italian philologist Samuel Luzzatto (1800-1865) apparently from musical esthetics, according to which certain disjunctive signs may under certain conditions be transformed into other disjunctive or conjunctive signs. While these transformations seem especially common (and far more complex) in the psalmodic books, they may also occur in the prosody. For example, revia may be transformed into pashta in order to avoid excessive repetition (pashta1 in 2 Samuel 12:1b), and geresh may be syncopated in favor of a string of conjunctive signs (preceding pashta in 2 Samuel 12:3a and 11a). Cantillizer supports these exceptions, which show up in the distribution or environment of the signs, i.e. in the first example pashta anomalously preceding revia, in the second little telisha and azla somewhat redundantly preceding mehupakh before pashta, where geresh might have been called for. Under various circumstances (concerning repetition, placement of tonic accent, length of vowel, word and clause, proximity to other signs, etc.) the following additional transformations may take place: revia > pashta > tevir/zarka (prosody), atnakh > revia mugrash, dekhi/little pazer > conjunctive,  azla/mehupakh legarmeh > conjunctive, revia > tsinor/conjunctive, revia mugrash > great shalshelet/conjunctive.

Modern Theory

Constituent Structure Analysis

In The Masoretes and the Punctuation of Biblical Hebrew (2002), David Robinson and Elisabeth Levy show great sensitivity to the semantic aspects of cantillation in this beautiful commentary:

Silluq is the strongest disjunctive accent, the equivalent of a modern full stop. It is written as a vertical bar under the tone syllable of the last word in a sentence (Gen 1.1 הָאָֽרֶץ׃ where אֽ is the accented letter). In appearance it is exactly the same as meteg. In the vast majority of cases, silluq is written under the word immediately before sof passuq (:) so it is usually redundant as a punctuation mark. But the Masoretes made good use of it in a few cases where they disagreed with the sentence divisions they had inherited from earlier rabbis. In Gen 35.22, for example, the end of the verse is doubly accented. The earlier rabbis had not placed a sof passuq between “and Israel heard it” and “the sons of Jacob were twelve”, although the structure of the narrative clearly requires one – it seems likely that this was a rather delicate means of passing over an unpleasant subject by minimising its emphasis. The Masoretes were not free to insert a sof passuq, and they obediently pointed the text in the form they had received it, but also inserted silluq at the end of “and Israel heard it” to indicate that there should have been a verse division at that point. Similar emendations of the traditional verse structure are to be found in Ex 20.2ff and Deut 5.6ff. With these exceptions silluq is always the last accent on a word. Any mark which appears before it is to be ignored for the purposes of punctuation.

Cantillizer’s source text for the Aleppo Codex reads atnakh (יִשְׂרָאֵ֑ל), giving silluk and sof pasuk (יִשְׂרָאֵֽל׃) as a variant (not retained in database), thus splitting one verse into two (hence the verse count of 154 in the weekly Torah pericope) and sending a cascade of corresponding transformations backwards:

וַיְהִ֗י בִּשְׁכֹּ֤ן יִשְׂרָאֵל֙ בָּאָ֣רֶץ הַהִ֔וא וַיֵּ֣לֶךְ רְאוּבֵ֗ן וַיִּשְׁכַּב֙ אֶת־בִּלְהָה֙ פִּילֶ֣גֶשׁ אָבִ֔יו וַיִּשְׁמַ֖ע יִשְׂרָאֵ֑ל וַיִּֽהְי֥וּ בְנֵֽי־יַעֲקֹ֖ב שְׁנֵ֥ים עָשָֽׂר׃

וַיְהִ֗י בִּשְׁכֹּ֤ן יִשְׂרָאֵל֙ בָּאָ֣רֶץ הַהִ֔וא וַיֵּ֣לֶךְ רְאוּבֵ֔ן וַיִּשְׁכַּ֕ב אֶת־בִּלְהָ֖ה פִּילֶ֣גֶשׁ אָבִ֑יו וַיִּשְׁמַ֖ע יִשְׂרָאֵֽל׃

וַיִּֽהְי֥וּ בְנֵֽי־יַעֲקֹ֖ב שְׁנֵ֥ים עָשָֽׂר׃

And it came to pass, when Israel dwelt in that land, that Reuben went and lay with Bilhah his father’s concubine: and Israel heard [it]. Now the sons of Jacob were twelve:

Generative grammar sees in cantillation marks evidence of constituent structure analysis. Tree diagrams, which in this respect disregard conjunctive signs and silluk, represent the syntactic relationships of sentences, as in the following figure illustrating Genesis 1:21.

וַיִּבְרָ֣א אֱלֹהִ֔ים אֶת־הַתַּנִּינִ֖ם הַגְּדֹלִ֑ים וְאֵ֣ת כָּל־נֶ֣פֶשׁ הַֽחַיָּ֣ה ׀ הָֽרֹמֶ֡שֶׂת אֲשֶׁר֩ שָֽׁרְצ֨וּ הַמַּ֜יִם לְמִֽינֵהֶ֗ם וְאֵ֨ת כָּל־ע֤וֹף כָּנָף֙ לְמִינֵ֔הוּ וַיַּ֥רְא אֱלֹהִ֖ים כִּי־טֽוֹב׃

Both tifkha and pashta (but neither geresh nor little pazer) seem to be be demoted according to the rule of  in-rank precedence. This inconsistency, as well as the possible misinterpretation of munakh pasek as munakh legarmeh, might suggest the following emendation:

Citing the authority of Solomon bar Isaac (1040‑1105), aka Rashi, the Jewish French vintner and philologist (note dagesh variant נ/נּ):

The great fish in the sea, and in the words of the Aggadah (B.B. 74b), this refers to the Leviathan and its mate, for He created them male and female, and He slew the female and salted her away for the righteous in the future, for if they would propagate, the world could not exist because of them. הַתַּנִינִם is written. (i.e., the final “yud,” which denotes the plural, is missing, hence the implication that the Leviathan did not remain two, but that its number was reduced to one.)

http://www.chabad.org/library/bible_cdo/aid/8165/showrashi/true#v121

Wickes deems this verse mispunctuated:

Occasionally (it must be allowed) the accentuators have been led into fanciful extremes by the Midrash-teaching of the Schools. Thus in Gen. i.21 the Athnach is with הַתַּנִּינִ֖ם הַגְּדֹלִ֑ים, instead of at its proper place before וַיַּרְא אֱלֹהִים כִּי־טוֹב. And why? Because these wonderful creatures, about which Jewish fable has so much to relate, were counted to have nothing in common with the other creatures named. They were beings per se, and are put by themselves at the beginning of the verse!

In the emended version the cæsura would break the verse into its two main clauses: “and God created,” “and God saw,” but Wickes admits the received reading as emphasis or poetic license. In the silluk clause the major dichotomy falls on atnakh, then the remaining silluk (or B) clause’s major dichotomy falls on little zakef, with the minor dichotomy (or foretone) falling on tifkha, then in the little zakef B clause the major dichotomy falls on revia, with the minor dichotomy (or foretone) falling on pashta, and finally (or until no clause of three or more words remains) in the revia clause the major dichotomy falls on little pazer, with the minor dichotomy falling on geresh. In the atnakh (or A) clause the major dichotomy falls on little zakef, with the minor dichotomy (or foretone) falling on tifkha. Conjunctive signs appoint the remaining words.

The similar verse Genesis 1:24 (cf. also Genesis 1:12 and 1:25, which are more regularly appointed) confirms Wickes’ hypothesis but seems to defy most of the hierarchical rules above. Only children (geresh, pashta, little zakef, and tevir) abound, with atnakh postponed and revia anticipated:

וַיֹּ֣אמֶר אֱלֹהִ֗ים תּוֹצֵ֨א הָאָ֜רֶץ נֶ֤פֶשׁ חַיָּה֙ לְמִינָ֔הּ בְּהֵמָ֥ה וָרֶ֛מֶשׂ וְחַֽיְתוֹ־אֶ֖רֶץ לְמִינָ֑הּ וַֽיְהִי־כֵֽן׃

Mnkh Rvia Azla Grsh Mhpk Psta LtZk Mrka Tvir Tfka Atnk Sluk

The data collected from Cantillizer (for example, all verses in which atnakh immediately precedes silluk) may shed light on such exceptions.

Context-Free Grammar

Alain Verboomen’s online parsing machine analyzes the structure of Genesis 1:21 in nested tables based on the work of Richard Goerwitz (2004), applying the rule of in-rank precedence to little pazer and geresh, further demoting unmarked words joined by makef. He reads munakh rather than legarmeh with pasek interpreted as a mark of punctuation. Similarly Wickes gives this verse in his pasek list. Analysis does not appear to support two signs (other than recognized digraphs) falling on the same word, e.g. 2 Samuel 12:25a (compare: munakh, atnakh).

Gaya (הָֽרֹמֶ֡שֶׂת), pasek (הַֽחַיָּ֣ה׀), and makef (כָּל־נֶ֣פֶשׁ) are not interpreted as cantillation marks in traditional, rabbinical parsing, but rather as auxiliary interpunction (or metacantillation) that interacts with the signs, exerting and reflecting cross-influences among such other factors as letters, vowels, diacritical marks, and tonic accent. Gaya or meteg, a vowel qualifier, occurs in pretonic syllables that may otherwise, under certain conditions, carry a conjunctive sign; pasek performs a disjunctive function, separating words or converting a conjunctive sign into the corresponding disjunctive digraph; makef performs a conjunctive function, joining words, the first of which generally does not carry a sign.

Distributional Analysis

Musical, rhetorical, or hermeneutic, Cantillation marks once held meaning, tonal, syntactic, prosodic, and phonological, if only by the exquisite logic of a learned game played by idle scholars in those fields. However, as Derenbourg shrewdly recognizes, by the Renaissance that meaning had already broken down and been crushed under the burden of ever-growing expectations and the overweening zeal of analysis. The signs had become, and remain to this day, a semiotic system, with all the complex combinatory rules, exceptions, homonymy, synonymy, polysemy, and ambiguity common to such systems, but emptied of all semantic content. Today they constitute half a sign, signifier bereft of signified.

Cantillizer sees cantillation marks as a coherent, self-contained, digital system of symbolic representation. In a context-free model of grammar, the application will therefore perform distributional analysis on the whole corpus of signs in isolation from the Hebrew text. Distributional analysis defines the role of each discrete element in a system (e.g. phonemes in complementary/contrastive distribution or free variation) as a function of its environment, i.e. its position relative to (preceding and following, given sequential data) the other elements of the system. In studying this structure, these patterns and relationships by means of database technology, Cantillizer hopes to find the lost meaning of the signs.

Abbreviations

Cantillizer