The Just Chromatic Scale

The western musical scale consists of twelve notes, each a semitone (half step) apart, and the scale consisting of all twelve notes is called the chromatic scale. Tuning an instrument to be able to play all twelve half steps of the chromatic scale adds a bit more difficulty to the process of tuning a pentatonic or diatonic scale.

Starting with the eight frequencies of a just diatonic scale, major third intervals are used to calculate the needed sharp/flat notes to complete the chromatic scale. Both descending and ascending major thirds can be used to find the ratios of the new notes, and the process of reducing the octave, as mentioned in my previous post, can be used to ultimately end up with the twelve ascending ratios of a chromatic scale. The following graphic is very useful in understanding the just chromatic tuning process:

(The Physics of Music and Color)

Works Cited:

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