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Hi,

I have a question which answer I haven't been able to find in most technical books.

I understand the ratio of a P5 is 3:2; P4 is 4:3; M3 is 5:4; m3 is 6:5; M6 is 5:3 and m6 is 8:5. However, beyond an octave such as M10 which is a P8 + M3, and M17 which is 2 x P8 + M3, how do you calculate the ratio ?

Thank you in advance.

Faz.

You multiply the intervals

So for example P8 + M3 = 2/1 * 5/4 = 5/2


P8+P8 = 2/1 * 2/1 = 4/1

I would recommend splitting octaves first, assuming octaves are pure.
So , eg P8+M2 is NOT P5 + P5 in general (it might be in some combinations)

Multiply by 2 for each octave difference.

Could you illustrate ?

Thanks so much

So a M17 is :

2/1 x 2/1 x 5/4 = 20/4 = 5/1

A fifth is 3/2 the fundamental frequency. An octave and a fifth is two times that, or 3 times the fundamental. Two octaves and a fifth is 6 times the fundamental.

I'm sorry. I still don't understand what you are trying to say except the first sentence "a fifth is 3/2 the fundamental frequency".

"An octave and a fifth is two times that" ... what is "that" ? Can you express "that" in numerical figures ?

Oh, I get what you mean.

Thank you BDB.

It is helpful to think of the pattern of the overtone series in working through this.

The pattern, using C1 as the fundamental:

First Partial: The Fundamental -- C1
Second partial: one octave above the fundamental -- C2
Third Partial: one octave plus a perfect fifth above the fundamental -- G2
Fourth Partial: two octaves above the fundamental -- C3
Fifth Partial: two octaves and a major third above the fundamental -- E3
Sixth Partial: two octaves and a perfict fifth above the fundemantal -- G3
Seventh Partial: about two octaves and a minor seventh above the fundamental -- A#3
Eighth Partial: three octaves above the fundamental -- C4

The interval numbers you reference above point to coincident partials that exist between the notes of an interval. So:

Perfect 5th -- C1 and G1

These two notes have partials in common. The lowest partial they have in common sounds at the pitch of G2. The third partial of C1 sounds at the pitch of G2, and the second partial of G1 also sounds at the pitch of G2 (again, the second partial is an octave above the fundamental of G1). Because the third partial of C1 and the second partial of G1 both sound at about the same pitch, we have a 3:2 perfect fifth -- at least we do if that is the coincident partial we're paying attention to.

But this pair of notes has other coincident partials as well. For instance, the sixth partial of C1 sounds at G3 and the fourth partial of G1 also sounds at G3, so if this is the pitch we are listening for, we're attending to a 6:4 perfect fifth. Same interval, different reference point.

For the Major 17th C1 - E3, your lowest coincident partial is sounding at E3. That represents the fifth partial of C1 and the first partial (fundamental) of E3. Therefore, you are attending to a 5:1 M17.

Good post Floyd.

Great appreciate your post, Floyd.