Phonological Mean Length of Utterance (PMLU)

PMLU_Target is calculated as the number of consonants in the target transcript. PMLU_Actual is calculated as the number of segments in the actual transcript plus the number of target-like consonants produced. In this case target-like will ignore diacritics between compared phones. PWP is defined as the ratio of PMLU_Actual to PMLU_Target.

$\begin{array}{rl}{\mathrm{PMLU}}_{\text{Target}}& =\sum _{t\in \mathrm{targetIPA}}\{\begin{array}{rl}0& t\text{ is a vowel}\\ 1& t\text{ is a consonant}\end{array}\\ {\mathrm{PMLU}}_{\text{Actual}}& =\left|\mathrm{actualIPA}\right|+\sum _{t,a\in \mathrm{targetIPA},\mathrm{actualIPA}}\{\begin{array}{rl}0& t\text{ is a vowel}\\ \left(\mathrm{stripdiacritics}\right(t)=\mathrm{stripdiacritics}(a\left)\right)& t\text{ is a consonant}\end{array}\\ \mathrm{PWP}& =\frac{{\mathrm{PMLU}}_{\text{Actual}}}{{\mathrm{PMLU}}_{\text{Target}}}\end{array}$

ePMLU_{TargetFeatures} is calculated as three times the number of consonants in the target transcript (one for each of 'manner', 'place' and 'voicing'.) ePMLU_{ActualFeatures} is calculated as the sum of the number of correctly produced place, manner, and voicing features for each target consonant. ePWP_Features is defined as the ratio of ePMLU_{ActualFeatures} to ePMLU_{TargetFeatures}.

$\begin{array}{rl}{\mathrm{ePMLU}}_{\text{Target Features}}& =\sum _{t\in \mathrm{targetIPA}}\{\begin{array}{rl}0& t\text{ is a vowel}\\ 3& t\text{ is a consonant}\end{array}\\ {\mathrm{ePMLU}}_{\text{Actual Features}}& =\sum _{t,a\in \mathrm{targetIPA},\mathrm{actualIPA}}\{\begin{array}{rl}0& t\text{ is a vowel}\\ \left(\mathrm{manner}\right(t)=\mathrm{manner}(a\left)\right)+\left(\mathrm{place}\right(t)=\mathrm{place}(a\left)\right)+\left(\mathrm{voicing}\right(t)=\mathrm{voicing}(a\left)\right)& t\text{ is a consonant}\end{array}\\ {\mathrm{ePWP}}_{\text{Features}}& =\frac{{\mathrm{ePMLU}}_{\text{Actual Features}}}{{\mathrm{ePMLU}}_{\text{Target Features}}}\end{array}$

ePMLU_{TargetSyllables} is calculated as two times the number of syllables in the target transcript plus the closed syllable bonus for each closed syllable. ePMLU_{ActualSyllables} is calculated in the same manner. ePWP_Syllables is defined as the ratio of ePMLU_{ActualSyllables} to ePMLU_{TargetSyllables}.

$\begin{array}{rl}{\mathrm{ePMLU}}_{\text{Target Syllables}}& =\sum _{\sigma \in \mathrm{targetIPA}}\{\begin{array}{rl}2& \sigma \text{ is open}\\ 2+\mathrm{closedSyllBonus}& \sigma \text{ is closed}\end{array}\\ {\mathrm{ePMLU}}_{\text{Actual Syllables}}& =\sum _{\sigma \in \mathrm{actualIPA}}\{\begin{array}{rl}2& \sigma \text{ is open}\\ 2+\mathrm{closedSyllBonus}& \sigma \text{ is closed}\end{array}\\ {\mathrm{ePWP}}_{\text{Syllables}}& =\frac{{\mathrm{ePMLU}}_{\text{Actual Syllables}}}{{\mathrm{ePMLU}}_{\text{Target Syllables}}}\end{array}$

ePMLU_Target is calculated as ePMLU_{TargetFeatures} plus ePMLU_{TargetSyllables}. ePMLU_Actual is calculated in the same manner. ePWP is defined as the ratio of ePMLU_Actual to ePMLU_Target.

$\begin{array}{rl}{\mathrm{ePMLU}}_{\text{Target}}& ={\mathrm{ePMLU}}_{\text{Target Features}}+{\mathrm{ePMLU}}_{\text{Target Syllables}}\\ {\mathrm{ePMLU}}_{\text{Actual}}& ={\mathrm{ePMLU}}_{\text{Actual Features}}+{\mathrm{ePMLU}}_{\text{Actual Syllables}}\\ \mathrm{ePWP}& =\frac{{\mathrm{ePMLU}}_{\text{Actual}}}{{\mathrm{ePMLU}}_{\text{Target}}}\end{array}$