[PD] making scales from frequency values

[Dudley Brooks]

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.
> 
> Andrew Faraday wrote:
>> 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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