# How To Divide the Frequency Spectrum Logarithmically?

Hello, I am trying to build a vocoder and was wondering how I might divide the frequency spectrum up according to its loudness as opposed to frequency? For instance, if I wanted 8 bands in my vocoder, is there an equation I can use to determine the best possible frequency spectrum for each band?

You could research "Bark" of "Mel" coefficients. They help slice the

spectrum in 24 bands. They are designed by taking into account the

sensibility of human ears. But I’m not sure that’s what you are looking for,

though.

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> Hello, I am trying to build a vocoder and was wondering how I might divide the

> frequency spectrum up according to its loudness as opposed to frequency? For

> instance, if I wanted 8 bands in my vocoder, is there an equation I can use to

> determine the best possible frequency spectrum for each band?

> –

> -k.

That’s exactly what I’m looking for. Since human hearing is logarithmic (lower frequencies are much louder and more distinct than higher frequencies), I am looking for a method to divide the frequencies so that each frequency range contains the same amount of energy. Though I’ve decided to just make the frequencies variables, as their manipulation mid-vocoding could most likely produce some cool effects :-D

Well that’s mostly true, but don’t confuse perceptual loudness and frequency resolution.

Check out the equal loudness curves http://en.wikipedia.org/wiki/Loudness – sensitivity does vary with frequency (as well as many other things) but the dependence is not simple (or logarithmic).

Frequency resolution is logarithmic however. The critical bandwidth of the human cochlea is something like a minor 3rd as far as I remember, and of course the number of Hz that a minor 3rd spans grows exponentially with frequency.

G’luck with the vocoding!

Aengus.

Quote: aengus wrote on Wed, 18 June 2008 21:08

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> Frequency resolution is logarithmic however. The critical bandwidth of the human cochlea is something like a minor 3rd as far as I remember, and of course the number of Hz that a minor 3rd spans grows exponentially with frequency.

>

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I guess that is the question, how do you calculate the position

of all these "minor 3rds". That would be a very useful thing to

know.

On Jun 19, 2008, at 8:28 AM, Anthony Palomba wrote:

> I guess that is the question, how do you calculate the position

> of all these "minor 3rds". That would be a very useful thing to

> know.

mtof or mtof~ are probably the most direct way in Max.

-C

Chris Muir

cbm@well.com

Kyle Kaplan schrieb:

> Hello, I am trying to build a vocoder and was wondering how I might

> divide the frequency spectrum up according to its loudness as opposed

> to frequency? For instance, if I wanted 8 bands in my vocoder, is

> there an equation I can use to determine the best possible frequency

> spectrum for each band?

In the end this is a matter of taste, but definitely look into mtof,

thinking of midi notes as range is more the way we hear. You probably

want equal intervals as bandwidth…

Stefan

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———-()——–www.ccmix.com

thanks for the advice, hadn’t thought of using mtof but now that you mention it, it makes perfect sense.

I’d also look at the frequency ranges traditionally used for vocoders

and other effects like the Moog MuRF. You probably don’t want to

divide the spectrum evenly if you’re going for a warm analog sound.

The high end probably matters less than the low end. You might also

consider a shelf filter on either the low or high ends.

The Moog MuRF uses:

200. 300. 450. 675. 1000. 1500. 2200. 3400.

(100 150 225 325 500 700 1200 Hz differences)

Peter McCulloch

A tempered minor third is the frequency ratio sqrt(sqrt(2)), ie pow(2, 0.25). A tempered major third is pow(2, 0.333333).

Analog vocoders only approximated third-octave divisions, and I don’t suppose for a moment that the cut-off frequencies on a Moog were cent-accurate.

You can either use some hard-coded numbers, or do the math. It’s not hard if you got past logarithms in high school.

– P.

The Moog ratios worked quite well. In the spirit of ‘sharing is fun’ here’s my super simple 8-band vocoder for anyone who’s interested. wasn’t really sure on the Q, so I set it to something that sounded OK and attached some flonum boxes for personal adjustment.