The Development of the Equal Temperament Scale
Evolution or Radical Change?
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The Development of the Equal Temperament ScaleEvolution or Radical Change?
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Well Temperament
The most common well temperament tuning was published by Andreas Werckmeister (1645 – 1706 CE) and referred to as “Werckmeister III”. As the name implies, Werckmeister created multiple versions of the well-tempered scale. His first two tunings were actually versions of Just Intonation.[i] At the same time these scales were being published, composers were experimenting with modulations between keys signatures. Contrary to popular belief, J.S. Bach’s Well Tempered Clavier was not written because the scale allowed for even sounding key signatures (equal temperament is needed for this); Bach’s work actually highlighted unique characteristics for each key signature when fixed pitch instruments were tuned using well temperament. However, it is unknown which version Bach used. Like mean-tone temperament, portions of a comma are used to
alter fifths in Well-Tempered scales. However,
the Pythagorean comma replaces the Syntonic.
This comma is calculated by dividing the ratio of twelve consecutive
perfect fifths by the ratio of seven consecutive octaves
Werckmeister
III Well-Temperament
Click here to listen to this scale. An advantage to this tuning is having one value for each chromatic. The spiral of fifths becomes a circle since four of the fifths tuned are lowered by one-fourth of a comma. All of the well-tempered scales share this quality. The disadvantage is the unevenness of semitones. The consonance of commonly used intervals is compromised for certain keys more than others. The way in which the Pythagorean comma is spread throughout the circle of fifths is what makes each well temperament unique. Analyzing their harmonic strengths would most likely correlate with the commonly used harmonies and key signatures of the time and place of their invention. With composers expanding the possibilities for key modulations and harmony, it became increasingly difficult to create a tempered scale for fixed pitch instruments. The scale used today was the compromise reached to accommodate the developments in Western music. Click here to listen to this scale applied to Mozart's Sonata no. 11 in A major. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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