Supplementary material

Audio used for the listening tests

Listening test results

Listening test results are provided on a per-sample basis as Matlab .mat files. Each file contains a structure named answers, whose length equals the number of listeners who participated in the test.

For each listener, the structure contains the following fields:

• raw_answer: a cell array describing the pitches reported by the listener;
• frequencies: a numeric array containing the frequencies (in Hz) corresponding to the reported pitches;
• certainties: a numeric array containing the listener’s certainty ratings for each reported pitch.

Each element of raw_answer is a three-element cell array of the form {pitch_label, certainty, deviation}, where pitch_label is a pitch name in scientific notation (e.g., B2, F#4), certainty is a scalar between 0 and 1 indicating the listener’s confidence, and deviation indicates whether the perceived pitch was judged to be slightly lower (-1), in tune (0), or slightly higher (+1) than the piano reference.

For example:

{{'B2' '.5' '1'} {'F#4' '1' '-1'}}

indicates that the listener reported two pitches: B2, with a certainty of 0.5 and perceived as slightly higher than the piano reference, and F#4, with a certainty of 1 and perceived as slightly lower than the piano reference.

The entries in frequencies correspond to the reported pitches converted from MIDI note numbers to frequencies, incorporating the correction specified by the deviation field (+1 → +40 cent, −1 → −40 cent).

Evaluation of the number of perceived pitches

For each sample, the number of perceived pitches is evaluated as follows.

For each listener’s response for a given sample, the certainty values associated with the reported pitches are summed. For example, if a listener reports:

{{'E2' '1' '0'} {'E3' '1' '0'} {'G#3' '.2' '0'} {'E5' '.6' '0'}}

then the number of perceived pitches for that listener is 1 + 1 + 0.2 + 0.6 = 2.8.

The number of perceived pitches for the sample is defined as the mean of these listener-level values across all listeners.

Listener profiles and listening conditions