equal temperament

Attributed to the Greek philosopher Aristoxenus (f. 350 BCE) equal temperament is today the most common system of tuning. It is used for the tuning of pianos, guitars, and other instruments that employ a fixed scale. The defining characteristic of equal temperament is that it divides the octave into equal parts.


Equal temperament's predecessors – such as just intonation and Pythagorean tuning – divide the tone based upon different ratios of the frequency. Just intonation, for example, fixes D on the frequency 9/8 times that of C. If the frequency of C is 262 Hz, then D, being 294.75 Hz, is 32.75 Hz higher than C. However, according to just intonation, F falls on the frequency 4/3 times that of C (349.33 Hz) and G falls on the frequency 3/2 times C (393 Hz). Thus the difference between F and G, an interval that is nominally the same as that between C and D, is approximately 44.6 Hz. This discrepancy between the size of intervals does not occur in equal temperament.


In equal temperament the frequency of each note is precisely 12√2 (approximately 1.05946) times higher than that of the preceding note. This ratio ensures that the interval between each note in the scale is exactly the same. The advantage of this is that compositions can be transposed between keys without having to substitute intervals in the original key with different-sized intervals in the new key. The only way to avoid this while using other temperaments is to retune the instruments. Despite its ancient origins, equal temperament has only recently entered into common usage following advancements in technology that have allowed us to accurately measure audio frequency.