Equal Tempered Tuning & Flaws in Just Tuning

Just tuning presents an interesting method of tuning the different notes of a scale based on specific frequency ratios, and ultimately ends up with twelve notes of unique frequency intervals that are perfectly harmonic. While this sounds like the best possible tuning system in theory, it runs into some substantial problems in practice. For example, when an instrument is tuned to C, the minor third of D-F ends up having a different frequency ratio than the normal minor third, C-Eb. There are many other cases in which these harmonic inconsistencies occur, such as changing the key of the song, and this leads to dissonance and a lack of flexibility in playing music.

Equal tempered tuning, also known as equal temperament tuning, aims to resolve the problems created by just tuning. It does so by making the twelve semitones of an octave equally spaced in terms of the relationship of their frequencies. This process adds consistency to the tuning process that just tuning lacks, but loses some of the harmonic purity of the fractional intervals. The relationship between the frequencies of notes in equal tempered tuning is given by the equation, frequency ratio = 2^(n/12), where n is the number of semitones (The Physics of Music and Color). To hear a comparison between equal temperament and just tuning, check out this video.

The general consensus is that the flexibility given by equal temperament tuning is essential and makes up for the lack of purity that is achieved through just tuning.

Works Cited:

1.  Gunther, Leon. The Physics of Music and Color. New York, New York: Springer, 2012.