Re: Harmonics of different tunings
By: Khelair to All on Wed Oct 22 2014 06:30 pm
I've stumbled across a little bit of research that proves I went off half cocked. Xeper's post, I believe (I'm really sorry if I spelled that wrong), led me to look further.
I've got some of the right mathematical understanding, but I believe, in accordance with the different types of musical scales, that I didn't really know enough about the musical overtones, and any different scales that might apply. I'm gonna look a little bit deeper before I go off more half-cocked. ;)
If anybody has better knowledge of these things I'd totally love to be sho a lesson about what I'm missing, btw. I've been interested in these things a very long time, but not had a good primer nor any personal instruction in Grateful for anything that might be offered, I am. :)
Well, ok, I'm not gonna say I've got these things memorized in my head but I always remember A is 440 and E is 330Hz, and if I wanted to I could backtrack and get all the notes from that. Let's say we're going from E 330Hz to A 440Hz, we've got an interval called a perfect 4th, and it resonates at 4:3 ratio. If we move that E up an octave doubling its frequency to 660Hz, and we move from A440 to E660 we have a ratio that's called a perfect fifth, and that comes in at 3:2 and those are the only ratios we need to be aware of if we want to figure out the rest. Hopefully you're familiar with the terminology, but you can use the circle of 5ths to figure things out.
Let's say we were trying to figure out the frequency of B, well that's a perfect fifth up from E. So we've got an equation that looks like x:330 = 3:2, which we could figure B equals 165 x 3 or 495Hz (I just checked my work online and it said 494Hz on some site, but that's a pretty close approximation.
Anyhow, using the circle of 5th's you can figure out the base frequencies of the 12 notes. From B, you can find F# or E (but we already know E, because that's where we came from - 4th's and 5th's have inverse relationships).
So if A is normally 440Hz, -1 octave is 220, -2 = 110 and -3 = 55. I forget whether Dre tries to get his Bb or his A in tune with the hum, but I think it's the Bb. At the standard tuning, Bb comes out as 58.57 (I just looked that up, didn't do math), which seems like you would want to tune it up so it's 60Hz. B comes in at 61.74 Hz in standard tuning, which maybe means that there's a tuning down effect that would also have the similar consequenes for blending with ground noise
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