How do these objects even out your ratios (or, I guess, what do you mean by that)? Finding the difference between two frequencies after converting them to a MIDI value allows you to work linearly instead of logarithmically, which is just easier--well, for me anyway. For example, after converting 912Hz and 1081Hz to MIDI and getting the difference, you come up with 2.9431. Now you can just think of them as 2.9431 half-steps apart, and that one number will work starting from any pitch. If you stick to the frequency realm, you'll have to consider them a ratio of 912:1081, which is fine, but a little ugly and not as easy.

As far as filling in the gaps, I don't know if this will help at all or not, but it might be something to think about. When you look at how the major scale is constructed, it can be seen as taking advantage of the first few harmonics in the harmonic series. I'll use the C major scale to (try to) illustrate. Going up from C in the harmonic series, you get an octave, a fifth (G), another octave, a major third (E), and another fifth [1]. Those last three notes are a C major triad (C-E-G). Now, stepping back a bit, the first note other than C in the series is G, the fifth, or dominant, in the scale. If you go the other way, down a fifth, you get F, the subdominant. Now, taking the intervals from the C major chord and applying them to G and F, you get G-B-D and F-A-C, respectively. The notes in those chords are what is used to fill in the gaps, and now you have all of the notes of a C major scale: C-D-E-F-G-A-B.

I mention all of that because you're already working with partials. So perhaps working with an interval or ratio between two of your partials and applying that to another of your partials to generate new frequencies might get you somewhere. Or it might suck, who the fuck knows :-). Either way, this sounds like an interesting project, and I'd be interested in seeing where you go with all of this.

Best of luck,
.mmb

[1] http://en.wikipedia.org/wiki/Harmonic_series_(music)

J bz wrote:
Dear Mike and Andrew,

Thank you for your speedy responses, though I think I am not explaining myself very well.  I don't want to use mtof or ftom as these objects even out my ratios.  What I'm looking to do is create a scale (say 12 notes for example) out of these ratio's with the possibility of filling in the consonant gaps whilst preserving the original frequencies and ratio's.  The 1st number in each group is the strongest partial so: 912Hz, 1081Hz, 1211Hz etc.  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'?

Cheers for weighing in,

Jbz

On Mon, Jul 20, 2009 at 11:16 PM, Andrew Faraday <jbturgid@hotmail.com> wrote:
Hey Jbz

I'm not sure if this is what you want, but if you convert a midi note to frequency [mtof] then multiply by integers, you get the natural partials. 

So if you multiply the outlet of [mtof] by 2 3 4 5 and 6. then you can change the multiplication figure, etc. I think that's the effect you're after.

God bless

Andrew


Date: Mon, 20 Jul 2009 22:24:05 +0100
From: jbeezez@googlemail.com
To: pd-list@iem.at
Subject: [PD] making scales from frequency values


Dear all,

I have five chimes.  I've worked out the frequencies (using Audacity) of the 5 strongest partials of each chime.  I now want to be able to work out how to change the octaves of the various partials?  My original intention was to find the nearest midinote and just use those but after listening to the results I would much prefer to keep the original ratio's whilst being able to alter the 'inversions'.

Here's the list that I have already:
BT1
    912Hz
  2434Hz
  4575Hz
  7175Hz
11584Hz

BT2
  1081Hz
  2861Hz
  5339Hz
  8325Hz
15209Hz

BT3
  1211Hz
  3196Hz
  5935Hz
  9199Hz
15206Hz

BT4
  1347Hz
  3553Hz
  6569Hz
10128Hz
18139Hz

BT5
  1812Hz
  4699Hz
  8525Hz
13264Hz
15469Hz

Is there one piece of mathematrical wizardy that can sort this in Pd?

Cheers,

Jbz

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