Shepard-Risset Glissando

This example synthesizes a Shepard-Risset glissando using bellplay~. The Shepard tone is an auditory illusion where a continuously ascending (or descending) pitch scale appears to rise (or fall) endlessly. This illusion is achieved by overlapping tones separated by octaves and applying amplitude modulation to mask their entry and exit.

shepard-risset_glissando.bell

## Define the number of octaves and duration per glissando cycle
$numocts = 8;
## ms per cycle
$period = 10000;
## how many cycles to repeat
$reps = 2;
## total buffer duration
$totdur = $numocts * $period;
## base frequency in Hz (A1)
$fzero = 55.0;
## Generate glissando frequency envelope
$gliss = exp2(arithmser(0, $numocts - 1, null, 3000));
$frequency = $fzero * $gliss;
## Iterate over multiple frequency ratios to create overlapping partials
for $r in 1 3/2 5/2 10/3 do (
    ## Create and transcribe sawtooth wave sweeping in frequency
    saw(
        @frequency $frequency * $r @duration $totdur
    ).transcribe() 
);
## Define operations to apply windowing and repetition to resulting buffer
$op = window() repeat($reps);
## Render audio, apply processing operations, and reset/clear timeline
$b = render(@reset 1 @process $op);
## Calculate onsets for staggered entries (every octave)
$onsets = arithmser(0, $b.getkey('duration') / $reps, null, $numocts);
## Retranscribe each repetition with an offset to simulate infinite rise
for $onset in $onsets do $b.transcribe($onset);
## Final render with post-processing
render(
    @play 1 @process (
        ## Crop initial partials to preserve illusion
        crop(
            @start maximum($onsets) @end -1
        ) 
        ## Add fade-in/out to smooth cropping
        fade(100, 100) 
        ## Apply subtle reverb for spatial depth
        freeverb(@roomsize 0.9 @wet 0.1) 
        ## Normalize output to -3 dB
        normalize(-3) 
    ) 
)