“Higher value, higher note” is only one design. We compare linear and
logarithmic scales, continuous and discrete pitch, loudness limits, stereo
position and tempo. The test is not whether a result sounds pleasant, but
whether its perceptual ordering matches the intended data relationship.
Scalar values → choose data domain → choose auditory range → define scale →
listen for discriminability → publish the rule. A mapping legend must let
another person reconstruct the operation without hearing the artefact.
The lab uses the same sequence for three mappings, creating a controlled
comparison rather than three unrelated compositions.
Observation guide 03
Mapping
Use this page before the slides, then return to the checkpoint after the lab.
After this week, you can
Match data relationships to perceptually distinguishable sound dimensions.
Compare linear, logarithmic and quantised scales with the same values.
Select a mapping from listening evidence rather than musical preference.
Inspectable teaching model
normalised value
0.100.120.200.240.480.500.820.90
A synthetic scalar sequence with one small and one large increase. Values are a teaching model, not an astronomical observation.
Worked notebook
Test the scale, not the melody
A synthetic scalar sequence with one small and one large increase.
Render the values with a linear 220 to 660 Hz mapping.
Render them again after logarithmic scaling.
Quantise a third version to five pitches while keeping duration fixed.
Ask listeners to locate the two largest changes without seeing the plot.
What the method supportsThe best mapping depends on the comparison task. Quantisation may clarify categories while erasing small differences; a logarithmic scale may expand low values and compress high ones.
CheckpointIf a listener can rank all values but cannot judge their differences, which data relationship did the mapping preserve?Reveal the reasoning
It preserved ordinal order, not interval size.
A ranking task only requires higher and lower to remain ordered. Claims about twice as much or equal differences require a mapping whose perceptual intervals support that stronger relationship.