2.1. The four classes of Persian metres

In speaking of the Persian metrical system, I refer to the productive system of intuitions possessed by participants, rather than the existing repertoire of attested metrical patterns. In this system, innovative metres are introduced occasionally and speakers agree on how metrical these unfamiliar patterns are to them.Footnote ³ In practice, however, I follow the lead of previous researchers in focusing only on the finite set of metres attested in corpora. As a relatively fixed source reflecting the metricality judgments of poets, they can serve as a reliable common reference point.

Hayes’s (Reference Hayes1979) account of Persian metres is arguably the most compelling among existing works. Relying on the data and initial analysis provided by Elwell-Sutton (Reference Elwell-Sutton1976), he identifies three classes of Persian metres. Published in 1979, his work does not explicitly mention moras, yet it effectively introduces three distinct classes of Persian metres with 5-, 6- and 7-mora constituents. For instance, HLH is a 5-mora constituent, as its syllables have 2, 1 and 2 moras, respectively. However, his account misses an entire class of Persian metres, that is, the relatively less common class of metres composed of 4-mora constituents. A more recent analysis by Deo & Kiparsky (Reference Deo and Kiparsky2011) covers this class, explicitly pointing out that it is based on 4-mora constituents. Overall, this results in four classes of Persian metres; I refer to them as 4-, 5-, 6- and 7-based metres. Other scholars such as Jali (Reference Jali1993) have already independently argued for such a 4-class division and – in line with what this paper is going to argue for – mapped the four classes to four musical time signatures (more on this in Section 3).

In addition to metre classes, it is useful to define another term to denote collections of metres. Following Khanlari (Reference Khanlari1948) and as a preliminary definition, I consider two metres $ {m}_1 $ and $ {m}_2 $ to belong to the same ‘metre family’ if one is an initial substring of the other. Thus, for instance, ‘HLLH HLLH’ and ‘HLLH HLLH H’ count as belonging to the same family since the former is an initial substring of the latter (this definition for metre families is revised in Section 3 after constituents are formally defined).

I take the metre families Hayes (Reference Hayes1979) accounts for as a starting point. To fill the gaps in his list, I add to it every metre family that appears more than twice in Parhizi’s (2002) corpus (his corpus contains nearly 45,000 poems; Elwell-Sutton’s contains around 20,000) and does not contain caesuras.Footnote ⁴ This combination, which constitutes the entire set of metre families I shall account for, is presented in Table 1. Metre families not directly accounted for in Hayes’s analysis have an underlined row id in the table. The rightmost column shows the frequency of each metre family in Elwell-Sutton’s corpus.

Table 1 The metre families covered.

The dashes reflect Hayes’s fragmentation of the metres into constituents, and in the case of those not discussed by Hayes, they are discussed by Parhizi. The fragmentations eventually proposed in this paper are different in many cases. In the table, no dashes are used for constituent boundaries that would not match a syllable boundary (i.e. those falling between the two moras of an H syllable), for example, between the first and second 6-mora halves of LLHLHLHH in row 22. These boundaries are discussed in detail in Section 5. For row 10, Hayes suggests a silent mora in the beginning of the first metron (see Section 5).

I do not attempt to account for frequency differences between these metre families, as usage frequency is affected by important factors beside metrical well-formedness, including genres and historical trends, practical concerns regarding the syllable structure of wordsFootnote ⁵ and most importantly, rhythmic concerns that do not match well-formedness preferences. Regarding the last point, note that for instance, 4-based metres are found perfectly well formed (perhaps even more than all 7-based metres), but the poetic tradition seems to often find them too ‘sing-songy’ to be suitable for serious poetry (on the deliberate use of metrical complexity as an aesthetic tool in poetry, see Fabb & Halle Reference Fabb and Halle2006). Thus, the ideal method of measuring degrees of metrical well formedness (in the narrow, rhythm-oriented, sense) in Persian seems to be conducting experiments involving participants rather than consulting corpus frequencies. In any case, existing theories of Persian metrics generally do not account for frequency differences between metre families either.Footnote ⁶

3.1. Hierarchy of accents

I use the standard method for the representation of metrical accents, that is, the metrical grid (Liberman Reference Liberman1975, Lerdahl & Jackendoff Reference Lerdahl and Jackendoff1983, Prince Reference Prince1983). Without further ado, let us look at an example. The accent pattern of a 4-based metre is presented in Example (3).

In this representation, each row of asterisks can be seen as an appropriate tapping pattern. Together, they show the accent structure. The syllable pattern is placed under the accent hierarchy, such that each asterisk in the lowest level corresponds to the beginning of a mora in the syllable sequence. A space is placed after every H syllable, representing the extra mora. The asterisks in the lowest row are our metrical positions. In each row, an asterisk means that a tap is expected at the beginning of the mora it represents in the corresponding tapping pattern. The lowest row, for instance, represents the fastest tapping pattern appropriate for this metrical form, where the beginning of each mora receives a tap. A position with more asterisks above it is said to have a stronger accent. It is worth noting that all of the metres we call 4-based have identical tapping patterns. The shared tapping pattern between different 4-based metres supports our decision to place them in the same class.

The correspondence between the accent structure observed here and metre in music is straightforward. A mora corresponds to the distance between two consecutive pulses (i.e. two consecutive asterisks at the lowest level) and syllable onsets (or the beginnings of syllable nuclei) correspond to musical events. The metre here corresponds to a simple metre in music, and if we take moras as equal to eighth notes, each 8-mora sequence starting with a maximally strong event can be taken to correspond to a musical measure in a $ \frac{4}{4} $ time signature. The measure-initial strong events count as ‘downbeats’.

We can use these accent patterns to devise a hierarchical constituent structure. Inspired by the way units, such as measures and beats, are generally identified in music, I propose that metrical structures are composed of hierarchies of constituents, such that in each metrical constituent, the first position has the strongest metrical accent.Footnote ¹⁰ Building upon this hypothesis, which we may call the ‘head-initiality hypothesis’, a unique tree with binary branching can be created for each metrical grid. The corresponding tree structure for the metre in Example (3) is shown in Example (4). I call the constituents at the lowest level of the hierarchy ‘feet’, and the ones above them ‘metra’ (singular: ‘metron’) and ‘cola’ (singular: ‘colon’), respectively. The tree and the grid express the same information regarding the accent hierarchy, although they have different theoretical implications that are not our concern here. In what follows, I generally use tree terminology to refer to different parts of a metrical form and use grids for showing actual accent patterns. It is worth noting that even though technically one may count single moras as constituents below the foot level, for simplicity, I use the term ‘constituent’ only to refer to feet and units above it in the metrical hierarchy.

3.2. Accents and metre classes

So far, we have shown that similarity of tapping patterns motivates classifying a group of Persian metres together, all of which can be viewed as having 4-mora metra. We refer to these metres as 4-based metres. A tendency towards repetition at the level of cola leads to all such metres having 8-mora repetition cycles.

In 6-based metres, the rhythm is compound: the asterisks are three moras apart in the second row from below, meaning that the feet have three moras each (instead of two). The tapping patterns associated with one such metre (based on alternations of HLLH and LHLH) is presented in Example (5). Compound (i.e. ternary) metre is far more popular than simple metre in Persian poetry. This fits well with the observation that Persian music is overwhelmingly dominated by rhythms with compound time signatures (Farhat Reference Farhat2004: p. 115).

The case of 5- and 7-based metres (henceforth ‘odd’ metres, as opposed to ‘even’ metres) is slightly more complicated. In these metres, the metron cannot be divided into two equal halves. The accent pattern of a 7-based metre based on repetitions of HHLH is shown in Example (6).

Note that the asterisks at the second level in this metre are not equidistant. In each metron, the first foot has four moras, while the second one has three. This goes against the metrical well-formedness criteria introduced by Lerdahl & Jackend (Reference Lerdahl and Jackendoff1983: p. 69), according to which the distance between asterisks in level $ n $ must be two or three (not four) asterisks in level $ n-1 $ . However, as argued in GTTM (p. 97), and highlighted by London (Reference London2004: p. 103), this constraint only applies to classical Western tonal music and may be dropped in other traditions. The tapping patterns associated with 7-based metres such as this one show that the grid in Example (6) is indeed the correct grid (e.g. compare recordings 43 and 46 in the online database).

The same asymmetry is visible in 5-based metres. An example is shown in Example (7).

In this and other 5-based metres, the two feet in a metron are two and three moras long. We may argue that odd metres are generally less well formed because of their nonisochronous nature. This lower degree of well formedness seems to be responsible for the fact that repetition is typically observed more steadfastly (i.e. observed at the level of metra rather than cola) in these metres, resulting in the absence of metre families of cycle lengths 10 or 14 in the list of common Persian metres.

3.3. Anacrusis

So far, we have seen accent hierarchies that support a 4-class division of Persian metres and the idea of treating the metres as temporal patterns. Moreover, we used these accents to establish a constituent structure for the metres based on the head-initiality hypothesis. It is now time to see cases where the head-initiality hypothesis results in fragmentations completely different from those given in Table 1.

All major existing accounts of the Persian metre inventory divide a metre into constituents following a ‘left-to-right’ procedure. They start from the left side of the metre and count full constituents moving rightward. If necessary, they assume an incomplete constituent at the right edge. The typical fragmentation of a metre from the family ‘HHLLHH…’ under these theories is shown in Example (8).

However, in this metre, the first tap at the metron level falls at the beginning of the second syllable. Therefore, fragmenting the metre based on the head-initiality hypothesis yields a different result. The tapping pattern and the fragmentation induced by it are shown in Example (9).

Incomplete initial metra, such as the initial H in Example (9) correspond to pickup notes or anacruses (singular: anacrusis) in music. I use the latter term for them in this context too. I refer to incomplete metra at the end of metres (such as the final H in Example (9)) as ‘complements’.

To give a clearer picture of the structure of this metre, it is useful to present an annotated version of a performance of a poem in this metre (recording 10 in the online database). This performance involves singing and is therefore not an instance of the natural melody-free chanting style discussed earlier. However, its rhythmic structure is the same as that of the text-setting corresponding to the natural chanting style. In this and similar performances, which belong to Shia Muslim religious mourning ceremonies (known as ‘nowhe’), it is part of the tradition for the audience to beat on their chests along with the rhythm of the poem sung by the main performer. An asterisk above a syllable in Example (10) denotes a beating action at its onset. The duration of each metron is measured (in seconds) and shown on the third line of the gloss for each verse. The $ \mu $ signs indicate missing moras in the metre that are realised as pauses (more on this below).

The taps occur once per metron (for performances with foot-level and colon-level tapping on the same metre family, see recordings 34 and 35 in the online database). The total length of the metre (22 moras) is not a multiple of the length of a full metron (six moras). The pauses occur in such metres to make up for the missing morasFootnote ¹¹ and correspond to musical rests. A similar phenomenon is observed in Japanese (Asano Reference Asano2000, Cole & Miyashita Reference Cole and Miyashita2006) and Hausa (Kiparsky Reference Kiparsky, Gunkel and Hackstein2018) metrical poetry. The pause lengths measured in this recording confirm this; the lengths of the metra that include pauses are within the same range as the other ones (they are all between 1.33 and 1.49 seconds long), suggesting that the pauses are two moras long. Measurements for other recordings in the database show similar results.

We may now revise our definition of ‘metre family’. Let us call a set of metres composed of the same metra (under the present theory), starting with the same metron and having the same anacrustic syllables (if any) a ‘metre family’. Analysing metre structure based on the head-initiality hypothesis establishes interesting connections between metre families. The metre families in Table 2, for instance, are all based on the metron HLLH. The conventional left-to-right fragmentation method misses this generalisation, treating these metre families as composed of unrelated metra.

Table 2 Metre families based on HLLH.

Interestingly, the relationship between these metre families emerges (although partially) in poetic practices too. They are considered so similar that they are sometimes used in different lines of the same work in less formal genres of poetry. The famous poem sung in recording 45 in the online database has lines starting with metre families of both rows 3 and 4. Similarly, in the genre known as bahr-e Tavīl (not a sung genre),Footnote ¹² using lines with metres of rows 2 and 3 together is relatively common.Footnote ¹³

This concludes our discussion of anacrusis. I end this section by repeating the list of the metre families this paper aims to account for in Table 3 (the same as the ones listed in Table 1), this time also presenting their (metron-level) tapping patterns and dividing them into metra based on the head-initiality hypothesis. This table contains the data that are to be accounted for through constraint interaction in the next section. In the case where a tap goes on the second mora in an H syllable (row 5), the two moras are shown as two ‘h’s. The three columns on the right indicate which of our three external sources confirm the tapping patterns reported by the author and the consultants. For syllable sequences that do not have one dominant metrical analysis (19 and 23), the competing forms are reported in separate rows.

Table 3 List of metre families, their metron-level tapping patterns and sources confirming their tapping patterns.

4.1. Assigning structure to syllable sequences

The third – and most important – factor determining the well formedness of a metrical form is the appropriateness of the assignment of the tree to the syllable sequence. The criteria governing this assignment can be modeled as the interaction of metrical constraints. The constraint interaction scheme I propose is different from classical Optimality Theory (Prince & Smolensky Reference Prince and Smolensky1993) in at least two ways. First, the constraints are weighted, with a clear ‘gang-up’ effect as in Harmonic Grammar (Legendre et al. Reference Legendre, Miyata and Smolensky1990, Prince & Smolensky Reference Prince and Smolensky1993). Second, the constraints are not meant to select an optimal output for a single input form. Instead, they assign well-formedness scores to independent metrical forms. This is similar to how MaxEnt grammars are used by Hayes & Wilson (Reference Hayes and Wilson2008) and Hayes et al. (Reference Hayes, Wilson and Shisko2012) to compare items in a lexicon and an inventory of metrical forms, respectively. Since we are interested only in the ranking of the metrical forms rather than their actual relative well-formedness scores, we can simply compare the sums of weighted constraint violation scores, doing away with logarithmic scaling and the rest of the MaxEnt machinery. I present a few relatively simple constraints with tentatively suggested weights and assume a simple summation function for calculating the cumulative effect of the violations, aiming to account for the metrical forms presented in Table 3 as the only forms meeting certain thresholds.

If Persian metre perception is a special case of general rhythm perception, we expect the constraints that determine metricality to be the same as the general constraints governing rhythm perception in humans. The diversity observed among different quantitative metrical traditions is then to be explained via different weight assignments to the same set of universal constraints, similar to how we may understand cross-cultural differences in musical preferences.

Theoretical works that have attempted to present formal accounts of musical preferences, for example, those of GTTM and London (Reference London2004), do not go into much detail regarding what constitutes a well-formed metrical form. GTTM, for instance, presents an almost comprehensive account of what makes an accent hierarchy well formed (loosely corresponding to our tree well-formedness rules) through what it calls ‘Metrical Well-Formedness Rules’, but their ‘Metrical Preference Rules’, which discuss the correspondence between a presented musical surface and the accent hierarchy assigned to it, are hardly adequate for our purposes. I take GTTM’s account as a starting point and look elsewhere for hints pointing to more subtle musical preferences.

Perhaps the most intuitive rule concerning metrical correspondence is what GTTM presents as a preference for the inception of musical events (corresponding to our syllable onsets) to be in metrically strong positions (p. 76). In GTTM, where these rules are supposed to decide which accent hierarchy to assign to a given musical surface (corresponding to a given syllable sequence), this rule is practically no different from its reverse formulation: a preference for strong metrical positions to align with musical events. For our purposes, however, since we wish to be able to compare well formedness among different metrical forms with different syllable sequences, the reverse formulation has different consequences and is indeed preferred.

According to this formulation, the 6-mora metron HLLH is superior to HHH. If we denote musical events with vertical lines and empty pulses with dots, the two correspond to ‘|.|||.’ and ‘|.|.|.’, respectively. The second foot in the metron starts with a vertical line in the latter but with a dot in the former, therefore making the former more well formed under our proposal. A parallel formulation is used by Povel & Essens (Reference Povel and Essens1985). In their account of metre assignment to temporal patterns, they punish the assignment of accents to empty pulses. A translation of this constraint in the language of syllables and metrical constituents is presented below.

AlignSyllable: Metrical constituent boundaries must fall on syllable boundaries.

Let us now move to more subtle constraints. According to GTTM (p. 84), strong metrical positions tend to be aligned with the inception of long notes. This translates to a preference for feet and metra beginning with H syllables and in fact matches linguists’ long-standing practice of associating H syllables with strong positions. However, this does not constitute the full picture, as explained below.

Povel and Essens present a more detailed formula, disfavouring accents that fall anywhere other than positions of the following three types:

1. 1. Isolated events (i.e. events preceded and followed by silent pulses)

2. 2. The first and last events in a cluster of more than two events.

3. 3. The second event in a cluster of two events.

In essence, this requires accents to be on events that are preceded or followed by silences, with the qualification that in clusters of two events, only the second one is favoured to have an accent. Putting the qualification regarding clusters of two consecutive musical events aside (this tendency seems to have a very weak role if any in Persian metrics), we may capture the essence of the first two conditions in our own terminology as follows. H syllables attract two types of metrical positions: the beginning of a metrical constituent and its end. The second part of this statement is where we diverge from GTTM’s account and the common practice of associating H syllables with strong metrical positions.

Given its importance for our analysis, it is worth mentioning that the tendency for long inter-onset intervals in temporal patterns (corresponding to heavy syllables in our analysis) to precede strong metrical positions (corresponding to the end of metrical constituents in our analysis), along with its mirroring tendency described above, is well known in the literature on the psychology of rhythm (see Povel & Okkerman Reference Povel and Okkerman1981, Parncutt Reference Parncutt1994 and references cited therein). As Grube & Griffiths (Reference Grube and Griffiths2009) put it, ‘the basis of existing theories of temporal accent induction is the repeatedly reported behavioural finding of perceptual accentuations of tones that are followed and/or preceded by relatively long (silent) inter-onset intervals’.

Finally, note must be taken of the fact that neither of the two tendencies discussed above are either analogous or in conflict with the iambic–trochaic law well known among linguists. The iambic–trochaic law (Hayes Reference Hayes1985) concerns how listeners group musical events together, stating that in a sequence of musical events with alternating short and long inter-onset intervals, listeners tend towards iambic grouping. This is distinct from where metrical accents are placed, as demonstrated in Hayes’s example 5 (for a detailed account of the distinction between grouping and metrical structure, see GTTM).

It is now time to formalise our constraints regarding H syllables. As before, since we are interested in comparing different metrical forms with different syllable sequences (rather than different trees for a given syllable sequence), the direction of the tendency makes a difference for us. Here again, I suggest that not only H syllables attract the aforementioned metrical positions, but those positions require H syllables as well. It is the latter tendency that is of interest to us and is captured by the following two constraints.

H-initial: The first syllable in a constituent must be H.

H-final: The last syllable in a constituent must be H.

My goal in the remainder of this section is to use these constraints (and a few less impactful ones to be presented later) to account for the Persian metre inventory. In the following subsections, I discuss the four classes of metres one by one, beginning with 4-based metres.

4.2. 4-based metres

The effect of the three constraints introduced above is stronger on higher-level constituents. This is not surprising given the fact that a colon boundary, for instance, is a metron boundary and a foot boundary too. In 4-based metres, the colon is the lowest level in the hierarchy where most constraints have a visible effect. The only exception is that the AlignSyllable constraint seems to affect metron boundaries too, although it is violable (see row 5 in Table 5 below).

Table 5 4-based cola ranked in order of well formedness.

We can use our constraints to determine the most well-formed 8-mora cola. In getting from the well-formed cola to the well-formed metres, two points must be kept in mind. First, due to a tendency towards repetition, there are no common 4-based metres (and in fact no common Persian metres in general) in which two different cola occur. Second, Persian metrics seems to generally disfavour anacrustic 4-based metres. These two facts together mean that there is a one-to-one mapping between cola and metre families in 4-based metres. Thus, Table 5 for well-formed 4-based cola corresponds to a list of well-formed 4-based Persian metre families.

Table 5 contains all possible 8-mora cola that do not induce the illegal LLL sequence and calculates violations of any of the three correspondence constraints, as well as the *HHH constraint on syllable sequences. Violations of the latter constraint are counted based on how many HHH sequences occur if the colon is repeated twice (this is to account for cases where HHH emerges only in repetition). The symbol ‘ $ c $ ’ indicates that constraint violations at the colon level are concerned, similarly, ‘ $ m $ ’ indicates the metron level. Each asterisk marks a violation.

The goal here is not to find the exact weights but to demonstrate how a fixed weight assignment for the constraints can account for all the Persian metres in Table 3. I propose the weights 4, 3 and 2 for the three correspondence constraints and 1 for *HHH, arguing that these weights can account for the distribution of metra not only in 4-based cola but throughout the entire metrical system.

The weighted sum of violations can be viewed as a negative well-formedness score. The metre families shaded in gray are not attested in Parhizi’s corpus and are not part of the set we wish to cover. It is clear from the table that the constraints successfully account for the desired metre families. Note, however, that the shaded metre families (except perhaps the last row) are also found at least marginally metrical by the author and the consultants.

4.3. Simple 6-based metres

We may now use the same set of constraints and weights to rank well-formed constituents in 6-based metres. In these metres (and in fact any metre class other than 4-based metres), the metron, rather than the colon, is the lowest level of the constituent hierarchy where most constraints have a strong effect. This is analogous to how measures in $ \frac{6}{8} $ and $ \frac{4}{4} $ time signatures correspond to different levels in the metrical grid if we take eighth notes as the lowest level of the grid in both.Footnote ¹⁴ Thus, I start by ranking 6-mora metra in terms of well formedness in Table 6, applying the same constraints and the same weights as before but shifting their scope of action one level down in the hierarchy. The letter $ m $ indicates that the constraint’s violations are examined at the metron level, and $ f $ indicates the foot level. Violations of *HHH are not considered here because unlike the 4-based case, the rows in this table do not correspond to individual metre families and unlike the other constraints, *HHH is sensitive to how metra are arranged in a metre. I examine the effect of this constraint below when discussing metre families.

Table 6 6-based metra ranked in order of well formedness.

In practice, the last three metra (i.e. those with violations scores greater than 5) never show up in our list of common metres. Of the remaining five, HHH is also absent from these metres in spite of being well formed for reasons discussed later in this section.

As the next step, we may discuss the circumstances under which two metra can cooccur in a colon. Persian metres have a general tendency towards repetition. This tendency, which is well known in poetry and exists in musical rhythm too (Lerdahl & Jackendoff Reference Lerdahl and Jackendoff1983), is inviolable at the colon level (as mentioned earlier) and relatively powerful at the metron level as well. It is therefore natural that concatenating two instances of the same metron generally results in a well-formed colon.

Given this tendency towards full resemblance between co-occurring metra, it is natural to expect that even in cases where nonidentical metra co-occur, they must be to some extent similar. We may use ‘edit distance’ (how many atomic edit operations are needed to get from one sequence to the other) as a measure of similarity. One of the atomic operations that can get us from any of the four well-formed 6-mora metra to another is swapping adjacent L and H syllables, which amounts to moving an event to an adjacent silent pulse. For instance, LLHH (‘|||.|.’) is only one swapping operation away from LHLH (‘||.||.’). If we take one swapping operation as the minimum edit distance allowed between co-occurring metra, the first three pairs in Example (13) would be the only well-formed 6-based pairs.Footnote ¹⁵ The other edit operation that may count as minimal is replacing a silent pulse by an evented pause (or vice versa). This would get us the last two rows in Example (13).

Having identified well-formed 6-based metron pairs, we may now compare different potentially well-formed 6-based cola, as shown in Example (7). Violations are calculated as we did for 4-based cola, only moving the relevant level of the hierarchy from cola to metra. A violation occurring in both metra is counted twice. To save room, wherever the violation scores happen to be the same irrespective of the order of the metra, only one of the two possible cola is presented, with the $ \rightleftarrows $ symbol next to it. Violation counts above two are written in digits. It must be noted that this table only gives a rough view of well formedness in 6-based cola. There are most likely other, less important, factors affecting well formedness of cola that are being ignored here (e.g. the effect of H-final and H-initial constraints at the colon level).

As Table 7 shows, all cola containing HHH metra are relatively ill formed chiefly because of inducing too many *HHH violations. This explains their absence from our list of common metres. However, there is an additional reason for their unpopularity. In general, using H in place of LL is allowed in Persian poetry (Shamisa Reference Shamisa2004). This means that colon 7 in Table 7, for instance, does show up in many poems, but only as a noncanonical form of ‘HLLH-HLLH’. This interchangeability causes such a colon to be rarely used as part of the ‘canonical form’ of a metre; any poem starting with lines based on this colon is likely to drift towards the more well-formed ‘HLLH-HLLH’ and allow the poem to be counted as based on ‘HLLH-HLLH’.

Table 7 6-based cola ranked in order of well formedness.

Having identified well-formed 6-based cola, we may now begin examining how they produce the common 6-based Persian metre families (as listed in Table 3). First, let us consider metres that contain only a single type of metron. I call such metres ‘simple’ and metres that contain more than one type of metron ‘complex’.

Interestingly, the sets of syllable sequences for some such simple metres overlap. For instance, the anacrustic metre family ‘H - LHLH - …’ has the same syllable sequence as ‘HLHL - HLHL - …’. Therefore, for this syllable sequence, both scansions seem plausible. However, upon hearing this syllable sequence, listeners strongly prefer the latter metrical analysis. This can be explained by a general preference for nonanacrustic forms. GTTM supports this, viewing anacrusis as a manifestation of group structure being out of phase with metrical structure and punishing it through a Metrical Preference Rule (p. 76). In such cases, we say that the less well-formed analysis for the syllable sequence ‘HLHLHLH…’ was hijacked by the more well-formed one. The relationship between HLLH and LLHH is even more interesting; in this case, HLLH is so well formed that anything based on repetitions of LLHH is always hijacked by a reading based on HLLH. Even the nonanacrustic form ‘LLHH-LLHH-…’ is hijacked by ‘LLH-HLLH-…’.

A list of all simple 6-based metre families is shown in Table 8. Hijacked forms (i.e. all forms based on repetitions of LLHH and all anacrustic forms based on repetition of LHLH and HLHL) are omitted. What remains is exactly the set of simple 6-based metre families we set out to account for, as seen in Table 3.

Table 8 Simple 6-based metres.

Even though frequencies are generally ignored in this paper, a word about frequency differences among the metre families based on HLLH (Table 8) seems pertinent here. Metres belonging to row 3 are particularly rare; their overall frequency is less than 0.1%, while the other three have frequencies 1.2%, 7.3% and 11.2%, as we saw earlier in Table 1. This reflects a general tendency that is seen in other parts of the Persian metre inventory too. I tentatively present this tendency as a constraint here, even though, unfortunately, no motivation outside of the data in Persian metrics can be seen for it at this point.Footnote ¹⁶

Omission: The moraic length of the omitted portion of an anacrustic constituent must be even.

This constraint works against using LH as anacrusis here as it omits three moras from the full metron (HLLH), explaining the low frequency of row 3. In fact, simple metres based on the highest ranking 6-based metron (HLLH) are the only metres that can afford having LH as anacrusis (although as a rare form). In other cases, Omission is never violated (as seen in the following sections).

4.4. Complex 6-based metres

The well-formed 6-based cola of Table 7 produce the complex metre families shown in Table 9. Potential metre families that violate Omission are not listed. This yields the set of complex 6-based metre families that we wished to account for (see Table 3). Similar to the case of simple metres, some of these metre families share their syllable sequences. In front of each row’s id, the id of the row with which it shares its syllable sequence is written in square brackets. In all cases, both readings are available for the syllable sequence (although in most cases one is dominant). For instance, the participants in the experiment conducted by Mirzaee et al. (Reference Mirzaee, Naqshbandi, Meysami and Shokri2019) prefer 14 over 8, but in recording 19 in the database, the taps are based on the analysis of row 8.Footnote ¹⁷

Table 9 Complex 6-based metre families.

4.5. Odd metres

A new constraint is required in addition to the ones introduced previously to account for well-formed odd metra:

Long-first: In odd metra, the extra mora must be on the first foot.

Recall that one of the feet in an odd metron is longer than the other one. This constraint favours metra in which the longer foot comes first. If we view odd metrical structures as altered versions of even structures, the foot with the augmented mora can be seen as more complex. This is reminiscent of the ‘closure’ principle, which, under Hanson and Kiparsky’s (Reference Hanson and Kiparsky1996) account, states that metrical structures can be more ‘strict’ in a noninitial position or foot and more ‘relaxed’ in an initial position or foot. If we allow ourselves to extend the concept to a unit as small as the metron, the augmented mora can be seen as an extra source of complexity which is preferred to occur in its initial foot.

The ranking for 7-mora metra is shown in Table 10. I propose the weight 2 for the ‘long-first’ constraint. Foot boundaries are shown with dots. In each row, the foot boundary is placed in the position that would be least costly in terms of constraint violation. Since there are no common complex odd metres, the rows of this table correspond to entire metre families. Therefore, we may include *HHH violation calculations in this table as we did in the case of 4-based metres.

Table 10 7-based metra ranked in order of well formedness.

Only the first two metra have a visible presence among common Persian metres. A list of 7-based metre families based on the most well-formed 7-based metron (HHLH) is shown in Table 11. As always, the family violating Omission (‘H-HHLH-…’) is not included.

Table 11 Metre families based on HHLH.

Of the potential metre families based on the second 7-based metron (LLHLH), only the nonanacrustic ones are common in Persian poetry (see Table 1). The third 7-based metron (HLHH) is not entirely ill formed either. The nonanacrustic family based on this metron shares its syllable sequence with that of row 2 in Example (11). This allows acceptable alternative readings for metres with this syllable sequence. Recordings 2 and 3 in the online database show readings of this metre family based on anacrustic HHLH, and recording 4 shows a reading based on repetitions of HLHH.

The case of 5-based metres is quite similar to that of 7-based metres. The ranking table for 5-based metra is presented in Table 12.

Table 12 5-based metra ranked in order of well-formedness.

The metre families based on the most well-formed 5-based metron (HLH) are presented in Table 13. The family ‘H-HLH-…’ is not included since it violates Omission.

Table 13 Metre families based on HLH.

Here again, similar to the 7-based case, a nonanacrustic repetition of the marginally well-formed metron LHH (the second most well-formed 5-based metron) is available as a secondary reading for row 2, but the reading based on HLH prevails.

This concludes our coverage of the Persian metre inventory. To cover these metre families, I used two constraints on the syllable sequence (*LLL and *HHH), four constraints on constituent structure (H-final, H-initial, Long-First and Align-Syllable) and three tendencies in the arrangement of constituents next to each other (the Omission constraint, a tendency to avoid dissimilar constituents in a line and a preference for nonanacrustic forms).