For each pair of frequencies below, calculate the ratio of their frequencies as a simple fraction, then determine which pair has the higher dissonance.
a) 261.6 Hz and 392 Hz
b) 349.2 Hz and 392 Hz
I just don't know how to make these into simple fractions. Please help me
261.6:392=2616:3920
and
2616=2*2*2*109 (109 is prime number)
3920=2*2*2*2*5*7*7
261.6:392=109/490 - as simple as possible
Is it helpfull?
It helps a little bit but, it doesn't look like one of the examples he gave us.
eg. 600 Hz and 400 Hz
and the ratio that is given is 3:2
I'm not sure how but i think it can be simlified even more.
eg. 800 Hz and 700 Hz
ratio is 8:7.
109 is prime number, so it's impossible to simplify it more.
ok thanks :)
To determine the ratio of frequencies as a simple fraction, you need to divide the higher frequency by the lower frequency. Let's calculate the ratios for each pair of frequencies:
a) Ratio of frequencies: 392 Hz / 261.6 Hz = 1.4980...
b) Ratio of frequencies: 392 Hz / 349.2 Hz = 1.1224...
Now let's convert these ratios into simple fractions. One way to do this is by finding a common denominator and then simplifying the resulting fraction. In both cases, we can use 1000 as the common denominator to get whole numbers and make it easier to compare.
a) 1.4980... ≈ 1498/1000 = 749/500
b) 1.1224... ≈ 1122/1000 = 561/500
Therefore, the ratios as simple fractions are:
a) 749/500
b) 561/500
To determine which pair has the higher dissonance, we need to understand that dissonance occurs when the ratios of frequencies involve small integer fractions. In this case, the pair with the smaller, simpler fraction has a higher dissonance.
Comparing the fractions, we can see that 561/500 (pair b) is a simpler fraction than 749/500 (pair a). Therefore, pair b, with frequencies 349.2 Hz and 392 Hz, has a higher dissonance compared to pair a, with frequencies 261.6 Hz and 392 Hz.