Abstract
This study examines three major musical scales - the Pythagorean Scale, Just Intonation, and Equal Temperament - to determine which provides the optimal balance of harmonic quality and practical utility. The analysis focuses on two key criteria: the ability to produce harmonious chords (evaluated through frequency ratios) and capacity for perfect transposition (assessed by consistency of adjacent note intervals). Through mathematical analysis and experimental validation via listener surveys, the research finds that while Just Intonation produces the most harmonious chords due to its simple frequency ratios, Equal Temperament emerges as the most practical scale overall due to its perfect transposition capabilities. The slight reduction in chord harmony in Equal Temperament proves negligible in practice, making it the most suitable choice particularly for fixed-pitch instruments like pianos. The findings help explain why Equal Temperament has become the dominant tuning system in modern Western music while acknowledging the situational benefits of other scales for specific applications.
Keywords：Music, Harmonious chords, Mathematical ratios, Harmony, Frequency
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