TDRA-1 Scott-family p-centre models

Purpose

TDRA-1 is a switchable Scott-family slot with three alternatives: the original TGAplus Scott-inspired AM-rise midpoint model, the historical Scott/Villing FAIM model, and a broad vocalic-band FAIM-inspired continuous-speech adaptation.

Two-stage continuous-speech adaptation

The two FAIM modes have two distinct components. First, the retained AM-rise midpoint detector identifies candidate regions from broadband trough → rising slope → peak geometry. Second, the selected spectral front end tests the candidate with a band-energy envelope. Historical FAIM uses the narrow 578 Hz sub-band / 4 ERB channel; broad vocalic-band FAIM uses the user-adjustable broad band, default 300–2500 Hz. The candidate trough proposes the search region only and is not the FAIM event reference.

Scott-inspired AM-rise midpoint

The original TGAplus emulation is retained as a selectable model and as the fallback source for the two FAIM modes. A preceding broadband AM trough and following AM peak must satisfy the configured candidate minimum trough-to-peak difference and minimum spacing; the marker is placed at the trough-to-peak midpoint. Because this mode uses AM-rise geometry directly and does not require a valid spectral FAIM threshold crossing, it normally produces the largest number of direct markers.

Historical Scott/Villing FAIM

This mode keeps the literature-oriented spectral front end: a single 578 Hz sub-band auditory-band approximation with 4 ERB bandwidth, full-wave rectification, and a 25 Hz envelope low-pass. ERB means Equivalent Rectangular Bandwidth, a psychoacoustic auditory-filter bandwidth measure; 4 ERB means four auditory-filter bandwidth units at the selected centre frequency, not four Hertz. The 578 Hz channel is historically important in Scott/Villing FAIM but is not treated here as a universally privileged hearing frequency.

Broad vocalic-band FAIM

This is the default continuous-speech adaptation. It replaces the narrow 578 Hz channel with a broad user-adjustable vocalic/sonorant band, default 300–2500 Hz, intended to cover much of the F1–F2 energy region while reducing dependence on consonantal high-frequency cues and on one narrow F1-region channel. This mode is FAIM-inspired rather than a faithful Scott/Villing spectral front end.

FAIM timing feature

Within each candidate region, the selected spectral band is rectified and low-pass filtered at 25 Hz, then the estimator searches for a local band-rise onset before the band peak. The user-selected amplitude threshold, default 50% of the local band peak, is searched between that local onset and peak. The 25 Hz low-pass has a separate role from the spectral band limits: it smooths the rectified band-energy envelope after filtering.

Regression controls

Scott original preset: p-centre = -11.2 + 0.407 × threshold_time. Villing revised preset: p-centre = -65.6 + 1.07 × threshold_time. Intercept and slope are user-editable in Custom mode. Times are in milliseconds relative to the local band onset. In broad vocalic-band mode these coefficients are reference presets rather than guaranteed optimal mappings.

Parameters

Default TDRA-1 model: broad vocalic-band FAIM; broad band 300–2500 Hz; threshold 50%; Scott original regression preset; candidate minimum trough-to-peak difference 0.15; candidate minimum spacing 100 ms; post-peak candidate margin 50 ms; onset-to-peak window 20–300 ms; minimum band rise 10% of the local peak. The broad-band limits, threshold, regression coefficients and onset/fallback parameters are user-facing controls.

Fallback and hit counts

The broad vocalic-band mode does not simply increase the number of detected events. It applies the same FAIM-style validity tests to a broader 300–2500 Hz spectral envelope. Because this broader envelope can have different onset, peak and threshold-crossing behaviour from the historical 578 Hz channel, it may produce fewer valid FAIM hits and more AM-rise midpoint fallback markers. Fallback markers occur when the AM-rise candidate is retained but the selected spectral test does not yield a valid local rise, threshold crossing or regression result.

Fallback policy

If the selected band has too little energy, no valid local band onset is found, the onset is already above the selected threshold, the threshold crossing cannot be found, or the regression result would fall before the band onset or outside the event window, the candidate is not discarded and is not clamped to a trough. The retained AM-rise midpoint timing is used as explicit fallback and the event is flagged internally. Blue markers indicate fallback events in FAIM modes.

Output

The active TDRA-1 selector determines which Scott-family marker sequence is rendered and exported. TDRA interval metrics such as nPVI, rhythm frequency and mean beat interval are calculated from the selected TDRA-1 marker times.

TDRA-2 Cummins A: native AM contour + Cummins rise detector

Input contour

Cummins A applies the shared Cummins rising-slope beat-identification rule to the TGAplus-native AM contour. This contour is the same active-interval envelope used by the Scott-family and Gibbon envelope-based models, with the selected amplitude, squared, or RMS envelope method and the independent TDRA smoothing controls.

Shared Cummins detector

Cummins A and Cummins B use the same Cummins beat-identification rule. The detector computes the contour minimum and maximum over the active TDRA analysis interval, sets the effective threshold to threshold × (maximum − minimum), scans for monotonic rising slopes, keeps rises whose height exceeds the threshold, trims each accepted rise to its central 10%–90% amplitude region, and places the marker at the midpoint of those trimmed indices.

Parameters

Default Cummins A/B rise threshold 0.20. A threshold of 0 is valid. The threshold is interval-local because TDRA beat detection is applied to the active analysis interval.

Interpretation

Cummins A is not the original Praat–Perl pipeline. It replaces the Praat intensity contour with the TGAplus-native AM contour while retaining the Cummins rising-slope beat detector. This makes Cummins A directly comparable with the other AM-envelope TDRA displays.

Output

Absolute signal-time beat markers with fractional detector indices, rise slope, peak time and previous inter-beat interval.

TDRA-3 Cummins B: Praat–Perl filtered intensity + Cummins rise detector

Input contour

Cummins B applies the same Cummins rising-slope detector to a Praat-style filtered intensity contour. For Cummins B fidelity, the contour is computed over the full loaded sound first and only then cropped to the active TDRA analysis interval.

Praat-style preprocessing

Scale the full loaded signal to the configured average intensity, default 70 dB. Apply a Hann-band pass filter in the frequency domain with default pass band 500–2500 Hz and 100 Hz transition. If subtract mean is enabled, remove the mean from the full filtered signal. The resulting full-sound filtered signal is then used for intensity calculation before interval cropping.

Intensity contour

Emulate Praat To Intensity... 25 0 yes. The default pitch floor is 25 Hz. With automatic time step, dx = 0.8 / pitchFloor, giving 0.032 s at 25 Hz. The effective Gaussian-style window duration is 3.2 / pitchFloor, giving 0.128 s at 25 Hz. For each full-sound contour frame, compute a Gaussian-weighted local mean square, divide by the reference pressure squared, and convert to dB with 10 log10(meanSquare / reference²). The full intensity contour is then cropped to the active TDRA interval.

Contour generation vs beat detection

Cummins B uses the full loaded signal for contour generation, but beat detection remains interval-based. After cropping, the detector computes the max–min intensity range, threshold, rising slopes and beat markers only within the active TDRA analysis interval. Thus the full signal avoids filtering/intensity edge artefacts, while the selected or zoomed TDRA interval remains the actual analysis domain.

Shared Cummins detector

The detector is the same Cummins rising-slope rule used by Cummins A. It finds the contour minimum and maximum over the active interval, sets the effective threshold to threshold × (maximum − minimum), scans for monotonic rising slopes, keeps rises whose height exceeds the threshold, trims each accepted rise to the central 10%–90% amplitude region, and sets the beat index to the arithmetic midpoint of those two trimmed indices.

Timing rule

Preserve the fractional beat index. The cropped Cummins B contour keeps absolute full-sound frame timing, so x1 + dx × beatIndex is evaluated relative to the first retained full-sound contour frame rather than to a newly filtered local selection. Do not round the beat index for timing.

Interpretation

Cummins A and Cummins B may produce different marker counts, timings and contour shapes because they apply the same beat detector to different input contours: TGAplus-native AM for Cummins A, Praat-style filtered intensity for Cummins B.

Output

Absolute signal-time beat markers, raw dB values, display-normalised contour values, fractional beat indices, rise slopes and Praat-emulation metadata.

TDRA-4 Gibbon A: AM rise / maximum-slope beat timing

Gibbon A places beat markers on the rising part of the shared TDRA AM contour. In standard mode, candidate AM peaks are detected first, then the marker is placed at the point of maximum positive slope before the accepted peak.

The optional trough-to-peak rise anchor refines this localisation step. For each already detected Gibbon A peak, the algorithm searches for a preceding trough within the configured minimum and maximum trough–peak distance limits. If the trough is valid and the trough-to-peak rise is large enough, the rise interval is defined as:

preceding trough → accepted peak

The red Gibbon A marker is then placed at the maximum positive slope within this trough-to-peak interval.

If no valid trough is found, or if the trough-to-peak rise is below the selected threshold, the candidate is not rejected. Instead, it falls back to standard Gibbon A placement. In trough-to-peak mode, blue markers indicate fallback standard placements.

This option changes Gibbon A marker localisation only. It does not change Gibbon A peak admission, does not affect Gibbon B or the other TDRA models, and does not include pitch/F0 cues.

TDRA-5 Gibbon B: Peak beats

Input

The active analysis interval and TGAplus signal-only AM envelope.

Contour

The same normalised TGAplus AM-envelope contour used by the Scott, Cummins A and Gibbon A signal-only models.

Parameters

Default peak prominence 0.015; default minimum peak distance 50 ms.

Detection rule

Find local envelope peaks where the current value is at least the previous value and greater than the following value. Estimate local prominence from the larger of the left and right local bases. Keep candidates meeting the prominence threshold, sort by peak value and prominence, suppress peaks closer than the minimum distance, then return the retained peaks in chronological order.

Current scope

This is the signal-only implementation. Annotation-assisted Gibbon interval-peak variants and Segment nPVI are reserved for a future version and are not active here.

Output

Absolute signal-time peak markers with prominence-derived scores and previous inter-peak intervals.

Prominence note

The 0.015 default is a pragmatic lower default to reduce missed Gibbon A/B events in shallow-dip cases. It is not a principled replacement for a future hybrid criterion combining absolute height, local prominence, dip separation and spacing.