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Equal Temperament

 

piano, key, inside

 

The archive contains posts discussing equal temperament.

 

Equal Temperament

What is equal temperament, and why do we use it to tune?

 

China

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.

 

Europe and The Western World

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.

 

Meantone

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.

 

Well Temperaments

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

Equal temperament could be thought of as a very regular well temperament. This gives it several advantages:

  1. It can play all of the scales.
  2. Though all the intervals besides the octave have tuning errors, the tuning errors remain spread evenly across the whole system. This means the temperament sounds very even.
  3. It limits the number of notes required to just twelve.
  4. Point three makes it practical for keyboard and fretted, stringed instruments.
  5. It can cycle around the circle of fifths.
  6. ET works well for chromatic styles, such as jazz and 21st century classical.
  7. It works fairly well with the tone color of the piano and guitar.

 

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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