Schwa variation in Tarifit CCəC words

Tarifit triconsonantal verbs in the simple imperative carry a prosodic-template schwa between the second and third root consonants, and Afkir and Zellou find two further phonetic variants: a shorter, coarticulating intrusive schwa inside the initial cluster ([Cə̆CəC], about a quarter of productions), and vowelless forms ([CCC], about five percent), neither of them sensitive to speaking style. The two schwas are independent processes, the template schwa a targeted segment whose deletion shortens the word and the intrusive schwa a targetless vocoid. Their distribution over the thirty-eight target words is tabulated by word. The words are the fragment's roots vocalized by the simple-imperative template CCəC (imperative, surface), and this file states the tables' generalizations over the pooled rows (root?, intrusion?, vowelless?), with each root's initial-cluster sonority profile read off its phones (Rising, Falling).

Two hypotheses about the intrusive schwa are set against each other: repair, on which insertion should be most frequent in the dispreferred falling-sonority clusters, and the syllable-planning account of Georgian, on which a vocoid is tolerated only where it boosts the planned sonority peak, hence in rising clusters. The data side with the second: every rising cluster shows intrusion at least variably unless its second consonant is voiceless (intrusion_of_rising), the words that never or rarely show intrusion are non-rising or have a voiceless second consonant (nonRising_or_voiceless_of_never_rarely), and the paper's three flagged exceptions are the only non-rising words with a voiceless second consonant that vary (variably_exceptions). The near-categorical class is exactly the words with medial /r/ (almostExclusively_iff_c2_r); it is not the rising class, since on the paper's scale the pharyngeal outranks the tap and /ʕrəm/ falls. Vowellessness tracks low sonority: the often-vowelless words have voiceless second and third consonants, except the flagged /ħkəm/ (voiceless_of_often_vowelless), and the never-vowelless words all carry a voiced consonant there (voiced_of_never_vowelless). The regression estimates, the acoustic measurements, and the perception result that an intrusive vowel aids discrimination only in falling clusters are reported in the paper without a formal counterpart here.

References

• [AZ25b]
• [Par02]
• [Hal06]

The simple imperative

def AfkirZellou2025.imperativeTemplate : Morphology.CVTemplate

The prosodic template CCəC of the simple imperative.

Equations

• AfkirZellou2025.imperativeTemplate = { slots := [Morphology.CVSlot.C, Morphology.CVSlot.C, Morphology.CVSlot.V, Morphology.CVSlot.C] }

def AfkirZellou2025.imperative (r : Morphology.ConsonantalRoot Phonology.Segment) : Morphology.TemplateMatch Phonology.Segment

In the simple imperative the consonants of a root fill the C-slots in order and the schwa the V-slot.

Equations

• One or more equations did not get rendered due to their size.

theorem AfkirZellou2025.spellout_imperative (a b c : Phonology.Segment) : (imperative { segments := [a, b, c] }).spellout = [a, b, Tarifit.schwa, c]

def AfkirZellou2025.surface (r : Morphology.ConsonantalRoot Phonology.Segment) : String

The transcription of a root's imperative.

Equations

• AfkirZellou2025.surface r = String.join (List.filterMap Tarifit.ipa? (AfkirZellou2025.imperative r).spellout)

def AfkirZellou2025.rank (x : Phonology.Segment) : ℕ

The Parker sonority rank of a phone.

Equations

• AfkirZellou2025.rank x = (Phonology.Sonority.Class.ofSegment x).parkerRank

def AfkirZellou2025.VoicelessAt (r : Morphology.ConsonantalRoot Phonology.Segment) (i : ℕ) : Prop

The phone at root position i is a voiceless obstruent.

Equations

• AfkirZellou2025.VoicelessAt r i = ∃ p ∈ r.segmentAt i, (Phonology.Sonority.Class.ofSegment p).Voiceless

def AfkirZellou2025.Rising (r : Morphology.ConsonantalRoot Phonology.Segment) : Prop

The initial cluster rises in sonority.

Equations

• AfkirZellou2025.Rising r = ∃ a ∈ r.segmentAt 0, ∃ b ∈ r.segmentAt 1, AfkirZellou2025.rank a < AfkirZellou2025.rank b

def AfkirZellou2025.Falling (r : Morphology.ConsonantalRoot Phonology.Segment) : Prop

The initial cluster falls in sonority.

Equations

• AfkirZellou2025.Falling r = ∃ a ∈ r.segmentAt 0, ∃ b ∈ r.segmentAt 1, AfkirZellou2025.rank b < AfkirZellou2025.rank a

@[instance_reducible]

instance AfkirZellou2025.instDecidableVoicelessAt (r : Morphology.ConsonantalRoot Phonology.Segment) (i : ℕ) : Decidable (VoicelessAt r i)

Equations

• AfkirZellou2025.instDecidableVoicelessAt r i = id inferInstance

@[instance_reducible]

instance AfkirZellou2025.instDecidableRising (r : Morphology.ConsonantalRoot Phonology.Segment) : Decidable (Rising r)

Equations

• AfkirZellou2025.instDecidableRising r = id inferInstance

@[instance_reducible]

instance AfkirZellou2025.instDecidableFalling (r : Morphology.ConsonantalRoot Phonology.Segment) : Decidable (Falling r)

Equations

• AfkirZellou2025.instDecidableFalling r = id inferInstance

The tables

inductive AfkirZellou2025.Intrusion : Type

Rate of the intrusive C1ə̆C2 schwa across a word's productions.

• never : Intrusion
• rarely : Intrusion
• variably : Intrusion
• almostExclusively : Intrusion

@[instance_reducible]

instance AfkirZellou2025.instDecidableEqIntrusion : DecidableEq Intrusion

Equations

• AfkirZellou2025.instDecidableEqIntrusion x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[instance_reducible]

instance AfkirZellou2025.instReprIntrusion : Repr Intrusion

Equations

• AfkirZellou2025.instReprIntrusion = { reprPrec := AfkirZellou2025.instReprIntrusion.repr }

def AfkirZellou2025.instReprIntrusion.repr : Intrusion → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

inductive AfkirZellou2025.Vowelless : Type

Rate of vowelless production of a word.

• never : Vowelless
• rarely : Vowelless
• often : Vowelless

@[instance_reducible]

instance AfkirZellou2025.instDecidableEqVowelless : DecidableEq Vowelless

Equations

• AfkirZellou2025.instDecidableEqVowelless x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def AfkirZellou2025.instReprVowelless.repr : Vowelless → ℕ → Std.Format

Equations

• One or more equations did not get rendered due to their size.

@[instance_reducible]

instance AfkirZellou2025.instReprVowelless : Repr Vowelless

Equations

• AfkirZellou2025.instReprVowelless = { reprPrec := AfkirZellou2025.instReprVowelless.repr }

def AfkirZellou2025.root? (e : Datum) : Option (Morphology.ConsonantalRoot Phonology.Segment)

The root a row reports, by the transcription of its imperative.

Equations

• AfkirZellou2025.root? e = List.find? (fun (x : Morphology.ConsonantalRoot Phonology.Segment) => AfkirZellou2025.surface x == e.primaryText) Tarifit.roots

def AfkirZellou2025.intrusion? (e : Datum) : Option Intrusion

The row's intrusion category.

Equations

• One or more equations did not get rendered due to their size.

def AfkirZellou2025.vowelless? (e : Datum) : Option Vowelless

The row's vowelless category.

Equations

• One or more equations did not get rendered due to their size.

theorem AfkirZellou2025.rows_complete (e : Datum) : e ∈ Examples.all → (root? e).isSome = true ∧ (intrusion? e).isSome = true ∧ (vowelless? e).isSome = true

Every row names a root and carries both categories.

The intrusive schwa

theorem AfkirZellou2025.almostExclusively_iff_c2_r (e : Datum) : e ∈ Examples.all → ∀ r ∈ root? e, intrusion? e = some Intrusion.almostExclusively ↔ r.segmentAt 1 = some Tarifit.r

Intrusion is near-categorical exactly in the words whose second consonant is /r/.

theorem AfkirZellou2025.intrusion_of_rising (e : Datum) : e ∈ Examples.all → ∀ r ∈ root? e, Rising r → intrusion? e = some Intrusion.variably ∨ intrusion? e = some Intrusion.almostExclusively ∨ VoicelessAt r 1

A rising cluster shows intrusion at least variably unless its second consonant is voiceless.

theorem AfkirZellou2025.nonRising_or_voiceless_of_never_rarely (e : Datum) : e ∈ Examples.all → intrusion? e = some Intrusion.never ∨ intrusion? e = some Intrusion.rarely → ∀ r ∈ root? e, ¬Rising r ∨ VoicelessAt r 1

Words that never or rarely show intrusion have a non-rising cluster or a voiceless second consonant.

theorem AfkirZellou2025.variably_exceptions (e : Datum) : e ∈ Examples.all → intrusion? e = some Intrusion.variably → ∀ r ∈ root? e, Rising r ∨ ¬VoicelessAt r 1 ∨ r ∈ [Tarifit.nqeb, Tarifit.nqer, Tarifit.qtes]

Variable intrusion goes with a rising cluster or a voiced second consonant, except for the three words the paper flags.

Vowelless production

theorem AfkirZellou2025.voiceless_of_often_vowelless (e : Datum) : e ∈ Examples.all → vowelless? e = some Vowelless.often → ∀ r ∈ root? e, VoicelessAt r 1 ∧ VoicelessAt r 2 ∨ r = Tarifit.hkem

Often-vowelless words have voiceless second and third consonants, except /ħkəm/.

theorem AfkirZellou2025.voiced_of_never_vowelless (e : Datum) : e ∈ Examples.all → vowelless? e = some Vowelless.never → ∀ r ∈ root? e, ¬VoicelessAt r 1 ∨ ¬VoicelessAt r 2

Never-vowelless words have a voiced second or third consonant.