The system of tuning
"Musical temperament" refers to the system or method used to tune the intervals between the notes of a musical scale, ensuring that the instrument's pitches are in harmony across various keys and tonalities. Different temperaments address the inherent mathematical challenges of tuning in an attempt to strike a balance between pure harmonic ratios and practicality in playing various musical compositions.
The concept of musical temperament arises from the need to accommodate the mathematical relationships between musical intervals within the limitations of musical instruments. Because of the way frequencies interact, it's impossible to create a tuning system where every interval is perfectly in tune with one another across all keys. Therefore, temperaments involve a compromise between ideal harmonic purity and the practicality of playing in different keys.
Historically, various temperaments have been developed, each with its own set of rules for tuning. Some temperaments prioritize certain intervals, such as the pure fifth, while slightly altering other intervals. One common temperament is "equal temperament", where the octave is divided into twelve equal parts, resulting in each half-step being equidistant. This system enables modulation to any key, making it suitable for instruments like the piano that require versatility.
Other temperaments, like "just intonation", strive for pure harmonic ratios but can result in certain keys sounding more in tune than others due to the intricate relationships between intervals. Some historical compositions were tailored to specific temperaments, influencing the character of the music when played using historically accurate tuning.
Different historical periods, musical styles, and cultural preferences have led to the exploration and development of various temperaments. As technology advanced, especially in electronic instruments, musicians gained more flexibility in adopting and experimenting with different temperaments beyond the constraints of traditional acoustic instruments.