# the formula for 10 and 31 multi band eq frequency ranges

hi again nother quick one, I hope you guys can help, I know there is a formula to calculate the bands ranges of an eq on a mixer, the first few are each doubled i.e 20 25 31.5 40 50 63 80 100 125 160 200 250 315 400Hz etc I would like to know how it is calculated. For instance when does it change from double ranges to decade ranges?

Alternatively could some kind should give me a list of frequency ranges on a 10 band equalizer and then a 31 band equalizer and I can work it out?

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The standard ISO for a 31 band Eq is as follows HZ:20/25/31.5/40/50/63/80/100/125/160/200/250/315/400/500/630/800/1K/1.25K/1.6K/ 2K/ 2.5K/3.15K/4K/5K/6.3K/8K/10K/12.5K/16K/20K.

But I think that this wasn’t the question, the question was how to calculate it, right?

First, every octave doubles or divides per two a chosen frequency.

Let’s take as a reference 400 Hz, the upper octave of this frequency is 800, and the lower 200. Let’s assume that you want a 1/3 octave Eq: 800Hz-400Hz=400Hz;

Then 400Hz/3 = 133.33^Hz This means that the frequencies would be: 400/ 533.33^ (400+133.33^)/ 666.66^ (400+133.33^x2)/ 799.99^ (400+133.33^x3)

And for the lower octave 400-200=200; 200/3=66.66^; So: 200/ 266.66/333.3266/399.99

Notice that standard ISO has rounded those numbers 200/250/315/400

If you want an 1/12 octave for the frequencies among 400 and 800, then 400/12=33.33^ Then: 400/433.33^/466.66^/etc. and then rounded.

Notice also that the upper octave of 16K is 32K, so out of human range. I hope it helps. Regards.

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Yes, they double in frequency for each step. Seems like 10band eq's tend to start at 32hz and double through to 16k

Like this:

It's also nice to have a chart like this to put it in perspective:

If you can't make that out here is the link . So actually those frequencies are between B and C for most octaves.

If you do an image search for 31 band eq you will find a load of pictures of hardware eq's with the frequency bands marked on them.

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An octave is a 2:1 ratio between frequencies (doubling). I think you'll find that a 10-band EQ uses bands (frequencies) an octave apart. A 31-band EQ uses bands that are 1/3 of an octave apart. This is a standardized form that was specified by ISO (International Standards Organisation).

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for 1/3 octave steps, multiply the previous band by 2^(1/3) (that's 2 to the power of 1/3 = 1.259921049895). Starting with 20Hz, you'll get 20,25.198,31.748,40,50.397,etc, up to 20480. The 'standard' frequency bands for a 1/3 octave (20,25,31.5,40,50,63,etc) are essentially just for labelling - any practical application would use the calculated frequencies to ensure each band is spaced exactly 1/3 octave apart.

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I know it's an older question, but this site provides a guaranteed answer for those sorts of questions:

http://www.sengpielaudio.com/calculator-octave.htm

As its index is rather chaotic, the best I found way to actually find the information you're looking for is to google for the term you want to know more about, and add "sengpiel" to the search terms. So in this case, I googled for "sengpiel third octave" (without the quotes).

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The Serge modular has a 10 band EQ which has an irregular spacing between the bands. The idea is that it won't emphasize a particular note or key in the same way an octave or 1/3 octave eq would (although I suspect it may have also been to do with using easily available component values).

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