Enigma 1185: Interval music
11 January 2016
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From New Scientist #2341, 4th May 2002 [link]
The relative frequencies of the notes of the diatonic music scale are:
C = 24, D = 27, E = 30, F = 32, G = 36, A = 40, B = 45, C’ = 48.
I recently built a series of oscillators so that I could hear how it sounded, but something went wrong with the wiring, so that I ended with an eight-note keyboard where only two were in the correct places.
However, when I played each key in order from the left, I noticed that the only intervals between adjacent notes were fourths (frequency ratio 4/3 or 3/4), fifths (3/2 or 2/3), or sixths (5/3 or 3/5).
Further, the interval (frequency ratio) between the two notes I did get right was one of these.
(a) If I played the left-hand key, what note letter did it sound?
(b) Could the notes have been arranged according to the same rules and have none in the right place?
(c) Could the notes have been arranged according to the same rules and have had more than two in the right place?