Giantpants wrote: ↑October 16th, 2019, 11:25 am(a) 113.2 Hzgz839918 wrote: ↑October 16th, 2019, 5:46 am Alice and Bob are playing a duet. Alice is supposed to play a note at 110.0 Hz and Bob is supposed to play a note at 164.8 Hz, but Bob accidentally plays his note 50 cents sharper than he is supposed to play it.
(a) What frequency does Bob actually play?
(b) If the interval between the notes is supposed to be a perfect fifth, Alice and Bob are playing most closely in what system of temperament? (A) Pythagorean (B) 12-tone equal (C) Just intonation (aka 5-prime) (D) All of these could be correct
(b) I’m not so sure, but I think it might be D. all of the above, since the frequency ratio is always 3:2?
For part (a), Bob wants to play a note at 164.8 hertz. If it were Alice who played 50 cents higher, then 113.2 Hz would be correct, but it is Bob whose note is too sharp. Maybe it was just misreading the question, but I'm guessing you have a pretty solid understanding of the math behind this.
For (b), if Bob had intended to play 165.0 Hz, then the ratio would be 3/2. But because the 8 in the tens place is a significant figure, we know that he really means to play 164.8 and not 165.0 Hz. Not every temperament has perfect fifths in ratio of 3/2, so try eliminating the ones that do require 3/2...