Golden Ratio Processor — User Guide

A modular Praat processor that uses the Golden Ratio (φ ≈ 1.618) to organize time, pitch, intensity, spectral shaping, modulation, and spatial motion.

Author: Shai Cohen Affiliation: Department of Music, Bar-Ilan University, Israel Version: 3.1.1 (2026) License: MIT License Repo: Praat AudioTools

Contents:

What this does Quick start Golden time structure Processing modules Controls and presets Channels and timing Output level Visualization Outputs Further reading

What this does

The processor uses φ = (1 + √5) / 2 ≈ 1.6180339887 as a common proportional rule across several independent audio transformations. Its central temporal landmark is the Golden Section:

T1 = T / φ ≈ 0.618T T2 = T - T1 ≈ 0.382T climax = T1

Enabled modules are applied sequentially. Pitch and intensity can develop toward T1; spectral modules derive frequency relationships from φ; micro-modulation uses φ-related rates; and the panning excursion blooms toward the same temporal point.

Important: φ is used here as a compositional and parameter-mapping framework. The processor does not assume that Golden-Ratio proportions are inherently or universally more pleasing.

Quick start

Select exactly one Sound object in Praat.
Run Golden_Ratio_Processor.praat.
Choose Subtle, Standard, or Pronounced.
Enable only the modules you want. The default combines pitch architecture, intensity structure, spectral-envelope warp, spectral filtering, and golden panning; micro-modulation is off by default.
For a stored output that must remain below full scale, choose Safety ceiling. Natural level deliberately leaves the result unscaled.

Unpitched material: Pitch architecture and micro-modulation depend on Praat pitch tracking. For percussion, noise, or other weakly pitched sources, consider disabling those two modules while retaining intensity, spectral, or spatial processing.

Golden time structure

The time architecture is calculated from the working duration. In normal spectral-envelope mode, this is the original duration. In Varispeed mode, varispeed is applied first and the Golden Section is then recalculated from the shortened result.

Point	Time	Role
Start	0	Beginning of the development section.
T1 / climax	T / φ ≈ 0.618T	Maximum pitch factor, intensity peak, and maximum pan excursion.
End	T	End of the resolution section.

Processing modules

Pitch architecture

Praat creates a Manipulation object for each audio channel, extracts its PitchTier, scales each voiced pitch target according to position in the Golden time structure, replaces the tier, and resynthesizes by overlap-add.

upper factor = 1 + strength × (φ − 1) lower factor = 1 − strength × (1 − 1/φ)

The factor starts at 1.0, rises linearly to the upper factor at T1, then falls linearly to the lower factor at the end. New F0 values are clamped to the selected pitch floor and ceiling.

Intensity structure

A global mean intensity and intensity standard deviation are measured from the analysis signal. The processor then applies a piecewise-linear dB envelope: soft at the beginning, strongest at T1, and soft again at the end.

Δ = 2 × intensity standard deviation peak = mean + Δ × (φ − 1) soft = mean − Δ / φ

This stage can create substantial gain on dynamically varied material. It does not normalize internally.

Spectral scaling

Off leaves the spectrum unchanged by this module.

Spectral formant warp is the default. FormantPath analysis supplies median F1–F5 landmarks only. Each valid landmark is mapped upward by the preset ratio, and the original complex FFT spectrum is multiplied by a smooth real-valued gain curve that removes energy around the old landmark and adds it around the mapped location. The same gain is applied to the real and imaginary spectrum rows, so complex-spectrum phase is preserved. This is a static whole-file spectral-envelope transformation, not LPC/FormantGrid resynthesis.

Varispeed changes both duration and pitch. The sampling frequency is temporarily overridden by the φ-derived ratio and the sound is resampled back to the original sample rate. The resulting duration is approximately the original duration divided by that ratio.

Preset	Strength	Spectral / varispeed ratio	Spectral-warp gain limit
Subtle	0.30	≈ 1.185	±9.5 dB
Standard	0.60	≈ 1.371	±14 dB
Pronounced	1.00	≈ 1.618	±20 dB

If fewer than two reliable spectral landmarks are found, the spectral-envelope warp is skipped and the Info window reports this.

Spectral filtering

The spectrum centre of gravity (cog) determines a φ-related Hann pass band:

exponent = 1 + strength lower = cog / φ^exponent upper = cog × φ^exponent

The limits are constrained to a usable frequency range. The filtered signal is then mixed back into the channel rather than replacing it completely: 15% filtered for Subtle, 30% for Standard, and 50% for Pronounced.

Praat's Hann-band filter is a zero-phase frequency-domain filter. Its smooth transitions reduce the ringing associated with abrupt rectangular filters, but it is still an acausal offline filter.

Micro-modulation

Optional dual-rate pitch modulation is applied with a second Manipulation/PitchTier resynthesis stage.

rate 1 = mean F0 / (φ × 40) rate 2 = rate 1 / φ depth = 20 × strength cents modulation = (sin(rate 1) + 0.5 × sin(rate 2)) / 1.5

Depths are 6 cents (Subtle), 12 cents (Standard), and 20 cents (Pronounced).

Golden panning

The pan excursion is zero at the start and end and reaches its preset maximum at T1. Oscillation speed rises from approximately 0.309 Hz to 0.5 Hz, a factor of φ, then falls again. Equal-power sine/cosine gains are stored in left and right IntensityTiers.

Mono input: the processed mono signal is duplicated and the two gain tiers create a stereo auto-pan. Maximum excursion is 30%, 60%, or 100% for Subtle, Standard, or Pronounced.

Two or more input channels: the original channel count is preserved. The left-tier gain is applied to channel 1 and the right-tier gain to channel 2; channels 3 and above pass through this panning stage unchanged. There is no crossfeed or decorrelation between existing channels, so this is gain-based spatial motion rather than stereo widening.

Controls and presets

Control	Default	Meaning
Preset	Subtle	Sets the common scaling strength: 0.30, 0.60, or 1.00.
Apply_pitch_architecture	On	Golden-section PitchTier scaling and overlap-add resynthesis.
Apply_intensity_structure	On	Golden-section amplitude envelope derived from measured intensity statistics.
Spectral_scaling_mode	Spectral formant warp	Off, duration-preserving spectral-envelope warp, or duration/pitch-changing varispeed.
Apply_spectral_filtering	On	Blends a φ-derived Hann pass-band into each channel.
Apply_golden_panning	On	Golden-section gain-based spatial motion.
Apply_micro_modulation	Off	Dual-rate φ-related vibrato.
Pitch_floor_Hz	75 Hz	Lower limit for pitch analysis and resynthesis.
Pitch_ceiling_Hz	600 Hz	Upper limit for pitch analysis and resynthesis.
Time_step_s	0.01 s	Time step used by pitch/formant analysis.
Output_level_mode	Natural level	No automatic gain change unless another mode is chosen.
Ceiling_peak	0.95	Target used by Safety ceiling and Peak normalize.
Draw_visualization	On	Draws the suite-standard diagnostic page.
Play_result	On	Plays the result. If stored peak exceeds 1.0, playback uses a temporary scaled copy; the stored output is unchanged.

True bypass: if all six processing components are disabled, the script copies the original Sound directly to _GoldenRatio_Bypass and exits before analysis or output-level processing.

Channels, analysis, and timing

Analysis: multichannel input is folded to mono for analysis only. If that fold nearly cancels because of anti-phase content, the script falls back to the loudest real channel.
Audio processing: every original channel is processed independently through the enabled pitch, intensity, spectral, filtering, and modulation modules.
Channel count: preserved unless panning is enabled on a mono input, in which case the result becomes stereo.
Sample rate: the final Sound uses the original sample rate, including after Varispeed.
Start time: processing is performed on a working copy shifted to time 0; the original xmin is restored to the final output.
Duration: preserved by all modules except Varispeed. Golden timing is calculated from the post-varispeed duration when Varispeed is selected.
Randomness: none. Given the same input and settings, processing is deterministic.

Output level

Mode	Behavior
Natural level	No final gain adjustment. Peaks may exceed 1.0; the script reports a warning when this occurs.
Safety ceiling	Attenuates only when the output peak exceeds `Ceiling_peak`.
Match input RMS	Scales the complete output so its RMS matches the original input RMS. No additional ceiling is applied afterward.
Peak normalize	Always scales any non-silent result so its peak equals `Ceiling_peak`.

Natural level can be much hotter than the input. The intensity structure intentionally creates a climax from the measured intensity spread, and spectral-envelope redistribution can also change instantaneous peaks. Choose Safety ceiling when you need a stored result guaranteed below the selected peak limit.

Visualization

When enabled, the Picture window uses the suite-standard 8-inch page and shows:

Input waveform with the Golden Section / climax marked at T1.
Pan architecture: actual pan position in blue inside the changing excursion envelope; if panning is off, the panel says so.
Output waveform on the same amplitude axis as the input. The original Golden-section time marker remains visible.
Summary strip with φ, T1/T2, input/output duration, spectral mode, pitch factors, filter band, panning state, input/output peak, and output-level action.

For multichannel Sound objects, Praat's waveform drawing can show multiple channels in the same panel. The visualization does not fold the stored output to mono.

Outputs

Normal output name: <original>_GoldenRatio_<PresetName>.
No-component bypass: <original>_GoldenRatio_Bypass.
Intermediate analysis and processing objects: removed before the script finishes.
Stored result: left selected in the Objects window.