The archive contains posts discussing equal temperament.
What is equal temperament, and why do we use it to tune?
Equal temperament (ET) is the standard for tuning pianos. ET first came into common use in Europe, but Zhu Zaiyu of China first worked out the math in the late 1500s. However, ET did not impact the everyday Chinese music of the time.
The Chinese had tuned bells, one for each month. Moreover, the bells required a special tuning. They needed to be tuned so that the pitches cycled back to their starting point at the new year.
ET solved this problem. The rest of Chinese music remained pentatonic based, which musicians tuned using concepts from the monochord.
ET in Europe came into use to solve a problem. Namely, the issues caused by the mismatch of vocal versus instrumental tuning.
In the Medieval period, the instruments were tuned using Pythagorean tuning. However, when singers harmonize, they approximate just intonation. This means that instruments tuned to Pythagorean tuning do not support vocal harmony very well.
Diverse compromise systems had gained popularity over the years. Keyboardists tuned up using meantone in Mozart’s day. Meantone does a good job of tuning the major thirds, but can function in only a limited number of keys.
J.S. Bach’s The Well-Tempered Clavier creates a showcase for Bach’s tuning. We do not know exactly how Bach tuned his keyboard. However, generally the well temperaments can use every key, but some keys remain better in tune than others. Plus, it also creates key coloration.
Equal temperament could be thought of as a very regular well temperament. This gives it several advantages:
However, ET does not work nearly so well with the organ’s tone color. Also, the equal tempered major third remains barely in tune. For this reason, I created Supplemented Equal Temperament (SET). SET is an enhanced version of ET. ET gets discussed in the archive posts mostly in relation to SET.
© 2021 Geoffrey Keith
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