# [PD] making scales from frequency values

Andrew Turley aturley at acm.org
Tue Jul 21 01:55:13 CEST 2009

```Just FYI, looking at BT2,BT3 and BT4 I see that the ratios of the
first partials is pretty close to a major second. Also, the ratio of
the first and second partials is just about 2.64 for each of the tones
you have given, which works out to something like 1 octave + a 4th
(between the major and diatonic).

The attached patch lets you set the first partial frequency (either
specifying the exact frequency or using the slider to select a MIDI
note), then sets the remaining partials as a ratio of the first
partial. I calculated the ratios using the ratios from BT2.  This
should give you an idea of how to maintain the spacing of the
partials. You can then use a chart like the one Derek included to
figure out which frequencies to use for the first partials, or you
could play around and find them by hand.

Does that help at all?

andy

On Mon, Jul 20, 2009 at 4:20 PM, Dudley
Brooks<dbrooks at runforyourlife.org> wrote:
> If he's trying to make a scale which sounds "good" with notes which have
> non-harmonic partials (I don't have the original post to see whether the
> listed frequencies are, indeed, non-harmonic), then he might be interested
> in this:
>
> http://ebook30.com/magazine/music/89538/tuning-timbre-spectrum-scale.html
>
> There's another site on which you can enter the partial frequencies and it
> will generate a "consonant" scale for that timbre.  Unfortunately, I have
> lost the URL, and haven't yet successfully figured out what to search on to
> find it!
>
> Surely someone on this list knows the site (and theory) I'm referring to.
>
> -- Dudley
>
> Derek Holzer wrote:
>>
>> 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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>>
>
>
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