## 2 Materials and Methods
### Experimental Design
#### 2.6.2 Experimental Paradigm  
Participants completed a two-alternative forced choice (TAFC) [56] perceptual task in which they judged whether the \(f_{o}\) of two tokens was the'same' or 'different' for each trial. The average length of a usable task, hereafter called a run, for children was 5.16 min and the average length for adults was 4.17 min. Tokens presented during each trial were developed from a single /\(\alpha\)/ production described in the _Stimuli Development and Presentation_ section. During a single trial, participants heard a 500 ms, unmodified base token (average\(f_{o}\) of 216.2 Hz) and a 500 ms test token that was either (1) the same unmodified base token (216.2 Hz) or (2) a token with a modified \(f_{o}\). The timing between the two tokens in a single trial was 500 ms. Following the presentation of both tokens, the participant stated whether the two tokens were the same or different and the experimenter advanced to the next trial. Token order (i.e., whether the base token was presented first or second) was randomly determined for each trial. Approximately one-third of the trials had two tokens with the same \(f_{o}\), called 'catch' trials. These 'catch' trials were used to ensure data validity, attention to the task, and understanding of task instructions. The remaining trials were 'different' trials, in which the \(f_{o}\) value of the test token was adaptively altered based on the participant's performance, using the stair-step procedure outlined by [PERSON] [57]. All adults began with a test token that was 0.5 ST, that is, 6.34 Hz, higher than the base token. Based on the known developmental trends reported in the literature for pitch discrimination with pure tones (e.g., 34; 37; 38; 39; 40)), the test token was set between 0.5-3 ST (6.34-40.91 Hz) higher than the base token for the children. For each child, the experimenter determined the starting value of the test token according to the child's age as well as compliance during the training. Prior to implementing the flexible starting position, pilot testing indicated that using a variable starting place did not preclude an individual from reaching an estimate of their pitch discrimination abilities (Figure 1). Step-size magnitude was defined as the magnitude of change in \(f_{o}\) during the adaptive procedure. The first 10 trials had a step-size of 0.1 ST and the remaining trials had a smaller step-size of 0.06 ST, regardless of the direction of the change. The experimental paradigm began with a 1-down-1-up TAFC paradigm, wherein the \(f_{o}\) of the test token was moved closer to the \(f_{o}\) of the base token by a step-size after every correct answer. This was an effort to avoid an extensive number of trials in which the difference in \(f_{o}\) between the tokens was either too easy or too difficult for participants to discriminate. Following the first incorrect judgment, the procedure changed to a 2-down-1-up TAFC paradigm, in which two correct judgments in a row were required to elicit a reduction in the difference between the base and test token \(f_{o}\) values; a single incorrect judgment still resulted in an increase in the difference between the base and test token \(f_{o}\) values. The run ended after either 10 reversals (i.e., a change in direction of the test token, caused by two correct judgments followed by an incorrect  
Figure 1: Experimental runs from two participants. The first participant started both run #1 (solid black line) and run #2 at 1 semitone (ST, dotted black line). The second participant started run #1 at 1 ST (solid blue line) and started run #2 at 0.5 ST (dotted blue line). Red arrows indicate the last four reversals that were calculated for the just-noticeable-difference (JND) for participant #1, run #1.  
judgment, or an incorrect judgment followed by two correct judgments. See four reversals marked with the red arrows in Figure 1), or when 60 trials had been completed.