# [PD] making scales from frequency values

Derek Holzer derek at umatic.nl
Tue Jul 21 01:07:08 CEST 2009

```Hi Andrew,

it's really not so complicated, it's just simple math. If the root and
partial frequencies of his chimes don't fit any note in an existing
scale, then trying to squeeze them into one won't "sound good". It's
also a lot of list-searching and ear-guessing to see what the "closest
fit" might be. Using simple ratios like these will preserve the
intervals of the notes no matter what the original frequencies might be.

best,
D.

> I'll be honest, this sounds a bit advanced. It's logarithmic and thus
> beyond me.
>
> However...
>
> Perhaps try to find a list of just temperament or world music scales and
> their frequencies. See if any match up to the scale you're trying to
> achieve.
>
> Andrew
>
>  > Date: Tue, 21 Jul 2009 00:52:24 +0200
>  > From: derek at umatic.nl
>  > To: jbeezez at googlemail.com
>  > CC: pd-list at iem.at
>  > Subject: Re: [PD] making scales from frequency values
>  >
>  > Still not entirely sure I know what you're after, so at the risk of
>  > repeating myself, use the (just intoned) intervals here:
>  >
>  > 1, 1:1-unison;
>  > 2, 135:128-major_chroma;
>  > 3, 9:8-major_second;
>  > 4, 6:5-minor_third;
>  > 5, 5:4-major_third;
>  > 6, 4:3-perfect_fourth;
>  > 7, 45:32-diatonic_fourth;
>  > 8, 3:2-perfect_fifth;
>  > 9, 8:5-minor_sixth;
>  > 10, 27:16-pyth_major_sixth;
>  > 11, 9:5-minor_seventh;
>  > 12, 15:8-major_seventh;
>  > 13, 2:1-octave;
>  >
>  > I.e. major third = 6:5, and 6 divided by 5 is 1.2, so to transpose up a
>  > major third, multiply original frequency by 1.2.
>  >
>  > Or, 5 divided by 6 is 0.83333333, so multiply by that to transpose down
>  > a major third. Or cook up something with [expr] that does the job more
>  > precisely, like [expr f\$1 * (5/6)] etc etc...
>  >
>  > All of these should "sound good" across the whole musical spectrum so
>  > long as you don't plan on changing key ;-)
>  >
>  > D.
>  >
>  > J bz wrote:
>  >
>  > > If I'm saying that these frequencies are
>  > > 'good' to my ear, is there a way of creating equally 'good' sounding
>  > > notes to fill in the gaps in, say for example, a 12 note scale
> based on
>  > > these notes scaling from the lowest to the highest without doing the
>  > > whole thing 'by ear'?
>  >
>  > --
>  > ::: derek holzer ::: http://blog.myspace.com/macumbista :::
>  > http://www.vimeo.com/macumbista :::
>  > ---Oblique Strategy # 126:
>  > "Only one element of each kind"
>  >
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--
::: derek holzer ::: http://blog.myspace.com/macumbista :::
http://www.vimeo.com/macumbista :::
---Oblique Strategy # 3:
"A very small object
-Its centre"

```