The subject of music is rich with cultural and political
overtones. We'll try to avoid delving too deeply into anything outside
the basic accoustic properties of pitches. One of the most popular
alternative scales divides the octave into five equally-spaced steps.
This tuning produces pitches that are distinct from those in the 12
pitches available in European music.
The original musical tradition behind the blues once used a five
step scale. You can revise the formula in Equation 39.1, “Musical Pitches” to use five steps instead of
twelve. This will provide a new table of frequencies. The intervals
should be called something distinctive like "V", "W", "X", "Y", "Z" and
"V" in the second octave.
Five-Tone Pitches. Develop a loop similar to the 12-tone Equal Temperament (the section called “Equal Temperament”) to create the 5-tone scale
pitches. Note that the 12-tone scale leads to 88 distinct pitches on a
piano; this 5-tone scale only needs 36.
Compare 12-Tone and 5-Tone Scales. Produce a three column table with the 12-tone pitch names and
frequencies aligned with the 5-tone frequencies. You will have to do
some clever sorting and matching. The frequencies for "V" will match
the frequencies for "A" precisely. The other pitches, however, will
fall into gaps.
The resulting table should look like the following