Phonological Mean Length of Utterance (PMLU)

PMLU_Target assigns one point to every target segment and one additional point to every target consonant. PMLU_Actual assigns one point when a target segment has an aligned actual segment. It adds another point when the aligned pair are consonants with the same base glyph; diacritics do not affect this comparison. Deletions and inserted actual segments receive no points. PWP is PMLU_Actual / PMLU_Target.

ePMLU_TargetFeatures assigns three points to every target consonant: one each for manner, place, and voicing. ePMLU_ActualFeatures assigns one point for each of those features that matches between an aligned target consonant and actual consonant. ePWP_Features is ePMLU_ActualFeatures / ePMLU_TargetFeatures; it is zero when the target score is zero.

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

ePMLU_TargetSyllables and ePMLU_ActualSyllables assign two points to every syllable in the corresponding transcript. A syllable whose phone pattern begins and ends with a consonant also receives the configured closed-syllable bonus. ePWP_Syllables is ePMLU_ActualSyllables / ePMLU_TargetSyllables; it is zero when the target score is zero.

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

ePMLU_Target is ePMLU_TargetFeatures + ePMLU_TargetSyllables. ePMLU_Actual is ePMLU_ActualFeatures + ePMLU_ActualSyllables. ePWP is ePMLU_Actual / ePMLU_Target; it is zero when the target score is zero.

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