on consonance perception, we designed a custom analysis in which the .... IBM (2012) IBM SPSS Statistics for Macintosh (IBM, Armonk, NY). 6. Law LNC ...
Supporting Information Bowling et al. 10.1073/pnas.1713206115 SI Methods Stimuli. The pitches of the piano tones played in Logic Pro-9 were shifted to the appropriate Hertz values for each chord using Logic’s built in pitch shifting function. Each tone was then played for 2.5 s at the same MIDI intensity value and recorded using WireTap Studio (v1.2.2) (1) as an uncompressed WAV file. These files were read into Matlab (v2009a) (2), where the left and right channels were collapsed onto a single track, and the amplitude was normalized to the same RMS value. All tones had a linear fade applied to the last 0.03 s to avoid speaker “pops.” Chords were synthesized by summing the relevant tones in Matlab, after which the results were saved as uncompressed stereo WAV files (sampling rate = 44,100 Hz, bit depth = 16). The waveform and spectrogram of one chord from the experiment is shown in Fig. S3. Procedure. The experiment consisted of six blocks, each lasting
∼8 min with an opportunity for a break between blocks. The first two blocks consisted of 60 trials each, with one dyad per trial (each of the 12 chromatic dyads was rated 10 times). The third block consisted of 66 trials, with one triad per trial (each of the 66 chromatic triads was rated one time only). The fourth, fifth, and sixth blocks consisted of 73, 73, and 74 trials, respectively, with one tetrad per trial (like triads, each of the 220 chromatic tetrads was rated one time only).
Statistics. For intrarater reliability, an ICC (two-way mixedeffects, absolute agreement, single-measures model) was calculated for each subject based on the repeated dyad ratings. For interrater reliability, ICCs (two-way random-effects, consistency, single- and average-measures models) were calculated across subjects for each chord type (3, 4). Correlation analyses used Spearman correlations because data were not normally distributed (as determined by Kolmogorox–Smirnov tests). ANOVAs, Tukey range tests, Kolmogorox–Smirnov tests and Spearman correlations were calculated in Matlab [vR2015a; Statistics and Machine Learning Toolbox functions: “anova1.m,” “multcompare.m” (“ctype” set to “hsd”), “corr.m” (“type” set to “Spearman”) and “kstest.m”] (2). ICC calculations were performed in SPSS (v24; function: “Reliability Analysis”) (5). Assessing Vocal Similarity. Using the LCM as a cut-off for the percentage calculation of the harmonic similarity score is justified by the fact that the pattern of harmonics for any chord repeats after this value; placing the cut-off lower or higher (e.g., by using a specific frequency cut-off or limiting the calculation to a certain number of harmonics) would thus truncate the harmonic pattern in an arbitrary way, resulting in an incomplete harmonic similarity score. Whether or not to apply the frequency intervals metric to a given comparison between two chords was determined by the following criteria: (i) if the minimum interval between F0s of one chord was 50 Hz, the latter chord was predicted to be more consonant; (ii) if the minimum interval in both chords was
