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 Pythagorean & equal-tempered scales

 

 

 

In the equal-tempered scale, the octave is divided into 12 equal intervals, or semitones. Each semitone is accorded a measure of 100 cents, so that the octave is 1200 cents and a tone interval of two semitones is 200 cents.

The seven intervals between successive notes of the Pythagorean octave consist of five Pythagorean tone intervals (T) of 9/8 and two leimmas (L) of 256/243:

T—T—L—T—T—T—L

The Pythagorean tone interval is about 204 cents, i.e., 2% higher in pitch than the modern tone interval, and the leimma is about 90 cents, i.e., about 10% smaller than a semitone. The Pythagorean musical scale may be heard here.

 

 

 

 

 

 

 
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