Harmonic Series

I'm looking for an extensive list or chart of the harmonic series that shows by how many cents each partial deviates from equal temperament. So far I've managed to find this out up to the 32nd partial but I'm struggling to find anything about the partials beyond that. Does anyone know anything about this or where I could find this information?

I'm basically looking for an expanded version of this: http://en.wikipedia.org/wiki/File:Harmonic_Series.png

k=12*log_2(n)

c= floor(100*k)-100*floor(k+.5)

n= harmonic # (1-fundamental, 2- 1st partial, etc)

c= deviation in cents

just worked it out off the top of my head, probably made a mistake, but should be something along those lines

now corrected.

Thank you for replying with an answer but do you have a version that doesn't require thought?

Seriously, I'm an amateur when it comes to mathematics. I have no idea how to use logarithms. If you could give me an example of the equation in action I may have a chance at figuring it out for myself but at the moment I'm stumped.

I've attached the first 100 notes of the harmonic series and their relation to the closest equal tempered note.

You can calculate cent values for the Nth harmonic using this equation:

CENT = 1200 x log N (base 2)

Máté

harmonics.xls

Excellent! Thank you, Máté; this is exactly the kind of thing I was looking for.

Why would you need anything more than the 7th partial? Just write a big dominant 7th chord and call it a day.

Why would you need anything more than the 7th partial? Just write a big dominant 7th chord and call it a day.

I'm writing a string quartet with the violins tuned a quarter tone flat and I'm going to round each partial to the nearest 50 cents so I can use a load of cool quarter tone harmonies that approximate the upper partials of the series. It may sound awful or who knows, it may actually work.

Check out String Quartet No. 2 by Georg Friedrich Haas (pretty sure there's a recording on YT): not very innovative as far as spectral music goes, but it's a good piece to study (and it's easy to hear that approximation is effective here). His 1st SQ is much more interesting but not as....didactic?

Btw, if 100 partials isn't extensive enough for you....I have a list of the first 130 partials ;)

I'm listening to it now and it is roughly what I had in mind but I don't like some of the runs up and down the series and the low fundamental drones he's used; it seems like an almost too obvious use of the series. I think I want to avoid that if I can. I like it though, definitely one for me to take a closer look at.

Oh and thanks for the offer but if I can't fashion something out of the first 100 partials then something is wrong, though I may very well come running back to take up that offer if I suffer a bout of writer's block!

http://wolfr.am/SRite3

That's right, i made this in case you want more. Just change the last number to get however many you want

Brilliant, thank you!

highly relevant