any fraction can be related to a ratio as follows:
Okay so i'm looking to create algebraic formula's specific ratio's. This relates to interval relationships in a musical scale for example:
An octave has ratio of 2:1 which is represented by the following formula:
where n = the number of octaves.
So if i wanted to find the value of the frequency 10 octaves above 20 hertz i would say:
So i'm wondering how you would formulate this for other frequency ratios. i.e:
3:2, 5:4 etc.
Any help would be great.
What does represent mathematically there in terms of an operation?
Say i wanted to find the frequency a fifth above 20 hertz. And a fifth has a relationship represented by the ration 3:2. How would i formulate that as i have done above with the octave?
For a fifth:
Please be careful using terms like 'fifth' on this forum as you are likely to be misinterpreted. try 'musical fifth'.
You want the following
f2 : 20 = 3:2
if you have had practice on ratios, you can rearrange as follows
0.5 * f2:10 = 1.5:1
0.5 * f2 = 1.5*10
f2 = 1.5 * 20
Otherwise, you can convert to fractions and solve like any other equation:
convert them both to fractions using the relationship
rearrange and solve for f2.
Sorry mate. Should have explained. A fifth is the term for an interval above a particular frequency that is a ratio of 3:2 with the original frequency.
Interval ratio - Wikipedia, the free encyclopedia
So just looking to create formula's for each interval ratio.