Take the frequency of middle C to be f0 = 262 Hz and compute the ratios fn/f0 fo

Question

Take the frequency of middle C to be f0 = 262 Hz and compute the ratios fn/f0 for the frequencies fn corresponding to a) D, b) E, c) F, d) G, e) A, and f) B and g) F#. By referring to Table 12-3, you will see that for D, n = 2. For the work that you will turn in, do the following additional steps. Convert the decimals that your calculator reports to the nearest fraction (e.g. 1.49 -> 3/2). This does not work very well for F#, but do you recognize the number that your calculator gives you for this value? (This interval is called the tritone. It's one of the "blue notes" that figure prominently in Blues, Jazz, and Rock and Roll. What interval is present in this (12 tone) scale that the Greeks found especially harmonious?

Explanation / Answer

ratios for all the notes

D=1.11=4/2

E=1.259=5/2

F=1.33=6/2

G=3/2

A=1.67=6/2

B=1.885=7/2

F#=1.41=5/2

The Greek found A note that is rtio 1.68 as more harmonious as this is the Golden section and the value is called phi

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