Clean playback can imply certainty that the data does not have. We compare
three strategies: a second voice for confidence bounds, timbral roughness for
uncertainty magnitude, and explicit silence for missing samples.
Value plus error and quality flag → keep each field separate → map value to
pitch, error to a bounded timbral cue, quality flag to an announcement →
provide the same fields as a table. Interpolation is never silent.
Students run a small recognition test to learn whether the uncertainty channel
clarifies or masks the primary pattern.
Observation guide 09
Uncertainty
Use this page before the slides, then return to the checkpoint after the lab.
After this week, you can
Distinguish a measured zero, a missing sample and a low-confidence value.
Give uncertainty its own bounded auditory channel.
Test whether that channel clarifies or masks the primary pattern.
Inspectable teaching model
relative brightness
10.980.950.900.860.890.960.99
Synthetic brightness values with one missing sample and unequal errors. Values are a teaching model, not an astronomical observation.
Worked notebook
Do not interpolate silently
Synthetic brightness values with one missing sample and unequal errors.
Map the measured value to pitch.
Represent error magnitude with a quiet, bounded roughness cue.
Replace the missing fifth sample with an explicit gap, not a zero.
Let listeners switch the uncertainty channel off for comparison.
What the method supportsThe gap states that no value was available. A zero tone would falsely report a measurement; interpolation would invent one unless it was separately labelled.
CheckpointWhich is more misleading for a missing sample: silence with an announced gap or a pitch calculated from interpolation?Reveal the reasoning
Unlabelled interpolation is more misleading.
A declared gap preserves the absence of evidence. Interpolation may be useful, but it becomes a modelled value and must remain distinguishable from observations in audio, tables and methods.