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Five-Tone Tuning

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

name 12-tone 5-tone
A 440.0 440.0
A# 466.16
B 493.88
505.42

 
 
  Published under the terms of the Open Publication License Design by Interspire