Parallel Encoding and Target Approximation (PENTA) model —An interactive demo

(updated from Xu & Prom-on, 2014)
Initial settings Starting pitch: Upper bound: Lower bound: Order:

Pitch target presets
Pitch Targets
   HRLFN
Slope
Height
Duration
ShortNormalLong
Strength
WeakNeutralStrong
Syllable sequence

Communicative function tiers

The Tone tier (above) sets each syllable's base pitch target -- exactly as before. Add extra tiers to layer other communicative functions (e.g. Focus, Boundary) on top of it. Each extra tier gets two independent rows in the table above: a height row (Higher/Lower, shifting the target by a fixed number of semitones) and a width row (Wider/Narrower, pushing the target further from, or pulling it toward, the centre of your pitch range, also measured in semitones) -- so a syllable can be both Higher and Wider on the same tier at once. The height row never touches the target's slope. The width row's Narrower option also compresses slope by the same factor, so a dynamic (sloped) tone's own excursion shrinks together with its position; Wider only repositions height and leaves slope at the tone's own default, rather than stretching it further. Neutral (the default) has no effect.

qTA delay settings Second stage duration: Weak lambda:

Instructions:

The page opens with a default F0 curve already plotted. Make changes in any of the editable boxes and then press "Replot" to see the effects on the underlying pitch targets and the Communicative Functions panel beneath the plot. The plot itself can be downloaded via the camera icon of the floating toolbar in the top right corner.

Initial settings:

Starting pitch: The starting point for the first syllable in your sequence, in Hz.
Upper bound: The upper limit on the pitch range, in Hz -- its semitone midpoint with the lower bound is the centre reference for the Wider/Narrower tier effect below. If a combined target ends up outside the current bounds, the bound is automatically widened to fit it (with a small margin), and the input above updates to show the new value.
Lower bound: The lower limit on the pitch range, in Hz. Also auto-widens the same way.
Order: Manipulates the number of derivatives included in the system.
The tiers' Higher/Lower/Wider/Narrower effects are specified and applied in semitones internally, but the F0 plot itself is displayed in Hz throughout, matching Starting pitch, bounds, and the Tone/Duration/Strength presets, which are also all in Hz.

Pitch target presets:

Specifications for the target height and slope of tone categories in Hz. Dynamic targets such as R or F have a positive or negative slope respectively. Static targets such as H or L have a slope of 0. Duration and articulatory strength presets work the same way, for each syllable's Duration/Strength category.

Communicative function tiers:

The Tone tier is the base communicative function: it sets each syllable's underlying pitch target, just as in the original demo. Any extra tier you add (e.g. Focus, Boundary, Sentence type) is a second function layered on top of that same target -- this is the core PENTA idea that a single surface pitch target sequence can simultaneously encode several communicative functions. Each extra tier has its own Δheight in semitones (for its Higher/Lower row) and range factor (for its Wider/Narrower row), both of which you can edit. The two rows are independent, so a syllable can be Higher and Wider on the same tier at the same time. The height row never changes the target's slope. On the width row, Narrower also compresses slope by the same factor it pulls height toward the pitch-range centre, so a dynamic tone's whole excursion shrinks; Wider only repositions height and leaves slope at the tone's own default. Marking a syllable Neutral on a row leaves that dimension unaffected.

Syllable sequence:

One column per syllable. Choose a Tone, Duration and Strength category, plus a category on every active function tier. Use "+ Add syllable" / the × button to grow or shrink the sequence.

qTA delay:

When there are syllables longer than 200ms, the delay implementation will kick in. This mean that the syllable will be split into two stages, with a weaker articulatory strength for the first stage (this stage will be highlighted in grey). The initial weak articulatory strength will need to be specified in the pop up window. The second stage is treated as carrying the syllable's real target (see Pitch targets below) -- the first stage is only the articulatory delay leading up to it.

Explanation:

Basic assumption: Production of tone and intonation is a process of successively approaching syllabic pitch targets at varying pitch ranges with different levels of strength.
Pitch targets: specified by: y = b + a * x, where b is height and a is slope. Height is defined at the syllable's own temporal midpoint (the second stage's midpoint, for a syllable split by qTA delay) rather than at either edge, so a dynamic (sloped) tone can drift at most half its total height range away from Height by either edge of the syllable, instead of the full range to one side.
Duration: Specifies duration of each syllable, which is the temporal domain of a target.
Strength: Determines the amount of strength used to approach a target. Greater strength leads to faster target approximation.
Multi-functional targets: Each syllable's final target height starts from its Tone-tier height, converted to semitones. Every extra tier is then applied in turn, in semitones: its Higher/Lower row adds or subtracts a fixed Δheight, and its Wider/Narrower row pushes the running height further from, or pulls it toward, the semitone centre of your pitch range. Narrower also scales the target's slope by that same factor, so a dynamic tone's own excursion shrinks along with its position; Wider leaves slope at the tone's own default rather than stretching it further. The qTA solver itself now runs natively in semitones this way, and only the final F0 curve, and the dashed target lines, are converted back to Hz for display. Several functions can jointly determine one target this way, as PENTA proposes.