Akan segments

This file lists the vowels of Akan as segments, together with the two consonants of its velar–palatal alternation. Akan has nine vowels, /i ɪ e ɛ a ɔ o ʊ u/, which Dolphyne groups into an advanced set /i e o u/ and an unadvanced set /ɪ ɛ a ɔ ʊ/ that do not mix within a word, the tongue-root harmony Stewart identified; in Casali's typology the inventory is a five-height system, with the low vowel the only one lacking a partner. In Akuapem and Asante a tenth quality, the advanced variant of /a/ before syllables with /i u/, joins the advanced set; it is not represented here. Velar stops become corono-dorsal palatal affricates before front vowels, the alternation McCarthy and Prince's account of Akan reduplication turns on.

The feature values come from the PHOIBLE chart. The chart codes the two vowel sets by [tense] and marks every plain vowel [−ATR], where the Akan literature has [ATR] carry the contrast, so a vowel is the segment of its chart entry's tongue-root reading, which takes the [tense] value as the [ATR] value and drops [tense]. The chart omits the palatal affricate, whose values are contours, and its segment is the velar stop's with the features McCarthy and Prince's corono-dorsal analysis adds.

Main definitions

• Akan.vowel: the segment of a vowel's chart entry, with [tense] read as [ATR].
• Akan.i, Akan.smallCapitalI and the like: the nine vowels, and Akan.vowels the set of them.
• Akan.k, Akan.tcCurl: the velar stop and its palatalized output.

Main results

• Akan.subset_aka: the vowels are those of PHOIBLE's Akan inventory.
• Akan.vowel_apply: a vowel has the chart's values off [ATR] and [tense].
• Akan.hasValue_atr_iff: the advanced vowels are /i e o u/.
• Akan.restrict_tcCurl_eq_k: the affricate has the stop's values off the four features palatalization writes.

References

• [Dol88]
• [Ste67]
• [Cas03]
• [McCP95]
• [Hay09]
• [MMcC19]

Vowels

def Akan.vowel (m : Data.PHOIBLE.FeatureMatrix) : Phonology.Segment

A vowel is the segment of its chart entry's tongue-root reading. The low vowel, which the chart leaves without [tense], keeps the chart's [−ATR].

Equations

• Akan.vowel m = Phonology.Segment.ofChart m.tenseAsATR

theorem Akan.vowel_apply (m : Data.PHOIBLE.FeatureMatrix) {f : Phonology.Feature} (ha : f ≠ Phonology.Feature.atr) (ht : f ≠ Phonology.Feature.tense) : vowel m f = m.toSegment f

A vowel has the chart's values off [ATR] and [tense].

def Akan.i : Phonology.Segment

The advanced high front vowel /i/.

Equations

• Akan.i = Akan.vowel Data.PHOIBLE.FeatureMatrix.i

def Akan.e : Phonology.Segment

The advanced mid front vowel /e/.

Equations

• Akan.e = Akan.vowel Data.PHOIBLE.FeatureMatrix.e

def Akan.o : Phonology.Segment

The advanced mid back vowel /o/.

Equations

• Akan.o = Akan.vowel Data.PHOIBLE.FeatureMatrix.o

def Akan.u : Phonology.Segment

The advanced high back vowel /u/.

Equations

• Akan.u = Akan.vowel Data.PHOIBLE.FeatureMatrix.u

def Akan.smallCapitalI : Phonology.Segment

The unadvanced high front vowel /ɪ/.

Equations

• Akan.smallCapitalI = Akan.vowel Data.PHOIBLE.FeatureMatrix.«ɪ»

def Akan.epsilon : Phonology.Segment

The unadvanced mid front vowel /ɛ/.

Equations

• Akan.epsilon = Akan.vowel Data.PHOIBLE.FeatureMatrix.«ɛ»

def Akan.a : Phonology.Segment

The low vowel /a/, which has no advanced partner.

Equations

• Akan.a = Akan.vowel Data.PHOIBLE.FeatureMatrix.a

def Akan.openO : Phonology.Segment

The unadvanced mid back vowel /ɔ/.

Equations

• Akan.openO = Akan.vowel Data.PHOIBLE.FeatureMatrix.«ɔ»

def Akan.upsilon : Phonology.Segment

The unadvanced high back vowel /ʊ/.

Equations

• Akan.upsilon = Akan.vowel Data.PHOIBLE.FeatureMatrix.«ʊ»

def Akan.vowels : Finset Phonology.Segment

The nine vowels, pairwise distinct.

Equations

• Akan.vowels = { val := ↑[Akan.i, Akan.e, Akan.o, Akan.u, Akan.smallCapitalI, Akan.epsilon, Akan.a, Akan.openO, Akan.upsilon], nodup := Akan.vowels._proof_1 }

theorem Akan.subset_aka : vowels ⊆ Finset.image vowel Data.PHOIBLE.Inventories.Akan.aka.featureMatrices

The vowels are those of PHOIBLE's Akan inventory.

theorem Akan.hasValue_atr_iff (x : Phonology.Segment) : x ∈ vowels → (x.HasValue Phonology.Feature.atr true ↔ x ∈ {i, e, o, u})

Dolphyne's advanced set is /i e o u/.

The velar–palatal alternation

def Akan.palatalized : Phonology.Segment

The features palatalization writes on the velar stop.

Equations

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

def Akan.k : Phonology.Segment

The voiceless velar stop /k/.

Equations

• Akan.k = Phonology.Segment.ofChart Data.PHOIBLE.FeatureMatrix.k

def Akan.tcCurl : Phonology.Segment

The voiceless palatal affricate /tɕ/ that the stop becomes before a front vowel, tcCurl being the name of the symbol tɕ. It keeps the stop's values, [+dorsal] among them, and adds [+coronal, −anterior, +distributed] with delayed release, so it is a corono-dorsal complex segment.

Equations

• Akan.tcCurl = Phonology.Segment.ofChart Data.PHOIBLE.FeatureMatrix.k Akan.palatalized

theorem Akan.restrict_tcCurl_eq_k : Phonology.Segment.restrict {Phonology.Feature.coronal, Phonology.Feature.anterior, Phonology.Feature.distributed, Phonology.Feature.delayedRelease}ᶜ tcCurl = Phonology.Segment.restrict {Phonology.Feature.coronal, Phonology.Feature.anterior, Phonology.Feature.distributed, Phonology.Feature.delayedRelease}ᶜ k

The affricate has the stop's values off the features palatalization writes.

theorem Akan.k_tcCurl_coronal : k.HasValue Phonology.Feature.coronal false ∧ tcCurl.HasValue Phonology.Feature.coronal true

Palatalization changes the value of [coronal].

theorem Akan.tcCurl_isComplex : tcCurl.IsComplex

The palatal affricate has two designated articulators.

theorem Akan.smallCapitalI_front_a_not_front : smallCapitalI.HasValue Phonology.Feature.front true ∧ a.HasValue Phonology.Feature.front false

The front vowel /ɪ/ triggers palatalization and the low vowel /a/ does not.