Psychoacoustic study of simple-tone dyads: frequency ratio and pitch

This study investigates how listeners perceive consonance and dissonance in dyads composed of simple (sine) tones, focusing on the effects of frequency ratio ($R$) and mean frequency ($F$). Seventy adult participants - categorized by musical training, gender, and age group - rated randomly ordered dyads using binary preference responses (like'' or dislike’’). Dyads represented standard Western intervals but were constructed with sine tones rather than musical notes, preserving interval ratios while varying absolute pitch. Statistical analyses reveal a consistent decrease in preference with increasing mean frequency, regardless of interval class or participant group. Octaves, fifths, fourths, and sixths showed a nearly linear decline in preference with increasing $F$. Major seconds were among the least preferred. Musicians rated octaves and certain consonant intervals more positively than non-musicians, while gender and age groups exhibited different sensitivity to high frequencies. The findings suggest that both interval structure and pitch range shape the perception of consonance in simple-tone dyads, with possible psychoacoustic explanations involving frequency sensitivity and auditory fatigue at higher frequencies.

💡 Research Summary

The paper investigates how listeners evaluate the consonance of dyads composed of pure sine tones, focusing on two acoustic parameters: the frequency ratio (R) that defines the musical interval, and the mean frequency (F) that determines the overall pitch height. Seventy adult participants from Greece were recruited, balanced across gender (39 women, 31 men), age (19–86 years), and musical training (23 musicians with ≥7 years of formal experience, 47 non‑musicians). Each participant heard 90 dyads in random order; the dyads covered standard Western intervals (octave, perfect fifth, perfect fourth, major/minor thirds, sixths, etc.) but were constructed from sine waves rather than instrument tones, preserving the exact rational ratios while allowing the absolute pitch to vary from 200 Hz to 5000 Hz in six discrete steps. Each stimulus lasted 2 seconds and was presented over calibrated headphones in a quiet laboratory. After each dyad, participants gave a binary judgment (“like” or “dislike”) via keyboard keys. Responses were coded as 1 (like) or 0 (dislike) and averaged across participants to obtain a preference score P for each (R, F) combination.

Statistical analysis began with a Shapiro‑Wilk test, which indicated that the preference distributions deviated from normality; consequently, non‑parametric Mann‑Whitney U tests were employed for all between‑group comparisons (musicians vs. non‑musicians, men vs. women, age brackets). The main findings are:

1. Mean‑frequency effect: Preference declines monotonically as the mean frequency increases, regardless of interval class. This trend is especially pronounced for higher pitch ranges (>3000 Hz) and suggests a psychoacoustic fatigue or reduced sensitivity at high frequencies.

2. Interval‑class effect: Consonant intervals (octave, perfect fifth, perfect fourth, major/minor sixths) retain relatively high preference scores across the entire frequency range, exhibiting an almost linear decrease with F. In contrast, the major second consistently receives the lowest preference, confirming its status as a strongly dissonant interval even when timbral cues are removed.

3. Musical training: Musicians rate consonant intervals more positively than non‑musicians, with differences of roughly 10–15 percentage points for octaves and perfect fifths. This aligns with prior literature indicating that long‑term exposure to tonal hierarchies sharpens perceptual biases toward culturally familiar consonances.

4. Gender and age: Women and younger participants show greater sensitivity to the high‑frequency decline, reporting lower preference scores in the upper F bands. This mirrors known gender‑related differences in high‑frequency hearing thresholds and age‑related auditory decline.

The authors interpret these results through a combined psychoacoustic and cognitive lens. The reduction in preference at high pitch is attributed to the ear’s decreasing sensitivity and increased auditory fatigue, while the persistence of consonant intervals is explained by the low “roughness” inherent in simple integer ratios, which minimizes beating and creates smoother waveforms. The binary response format proved advantageous: it reduced intra‑subject variability and highlighted robust group‑level patterns that might be obscured by finer Likert‑type scales.

In conclusion, the study demonstrates that both the relational structure of frequencies (the interval ratio) and the absolute pitch height jointly shape perceived consonance when timbral complexity is stripped away. Cultural familiarity (musical training) modulates these effects, but fundamental psychoacoustic mechanisms—frequency‑dependent sensitivity and roughness—remain dominant. The findings suggest that future research on consonance should control for pitch height and consider binary or categorical response designs to isolate the core acoustic determinants of musical pleasantness.