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 Brooksdbrooks@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.
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@umatic.nl > To: jbeezez@googlemail.com > CC: pd-list@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" > > _______________________________________________ > Pd-list@iem.at mailing list > UNSUBSCRIBE and account-management -> http://lists.puredata.info/listinfo/pd-list
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