To meet this exigency, Zarlino proposed that for the lute the octave should be divided into twelve equal semitones; and after centuries of discussion this system of "equal temperament" has, within the last thirty-five years, been universally adopted as the best attainable for keyed instruments of every description.3 Again, Zarlino was in advance of his age in his classification of the ecclesiastical modes.
The key to making these beats sound decent is pitching them down several semitones - this gives them a trashy feel.
The chanter, based on the Highland pattern is longer and fitted with keywork to extend the compass and give semitones as required.
semitones as required.
Being a physicist, my first thought was merely to tabulate the required frequencies of the twelve semitones of the octave.