I stumbled on this question while checking a grade 7 mathematics book. It grabbed my eyes having been introduced to some of music's amazing topics.
I know that harmony ( or more accurately, consonance) occurs when two pitches vibrate at frequencies in small integer ratios e.g., 2:1, 3:2, 4:3, 5:4.
However this problem that you see in the screenshot claims a much simpler case. it states that if the ratio of the frequencies of two notes can be simplified, the two notes are harmonious. I am thinking about other possible numbers. Apart from the E and G in the example, imagine a 445 and 315 Hz notes. They make a ratio that can be simplified to 89:63. Would you call that harmony? 414 and 500 make up a 207:250 ratio. Would you consider the notes as harmonious?
I'd refute this claim according to my humble knowledge. However, I am not sure. it might just be true. Therefore, I'd like to ask your opinions about it.