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Hi,<br>
<br>
A couple of thoughts.<br>
<br>
It might be useful to think in terms ratios instead of absolute
frequency values if you want to generalise your model so instead of
912, 2434, 4575 etc. 1, 2.66..., 5.01 and thus expressing all the
frequencies you found experimentally as ratios.<br>
<br>
This can help when dealing with scales and 'musical' (esp. tonal)
intervals because our perception of pitch is not linear (so for example
the interval between 110 Hz and 220 Hz is perceived as an octave
'difference', and so is the one between 220 and 440, yet their
mathematical difference is respectively 110 and 220).<br>
<br>
Just to complicate things :)... Also keep in mind that for 'realistic'
modelling of instruments you have to consider how partial presence and
quality changes with the changing of the fundamental pitch for many
various reasons some of which related to the intrinsic features of that
particular instrument (frequencies involved, meterials, shapes etc.) <br>
A good intuitive example of this is the piano where you can clearly
hear that lower the pitches (played keys) sound 'richer', than higher
ones.<br>
(I think this article might be interesting in this regard:
<a class="moz-txt-link-freetext" href="http://www.applied-acoustics.com/techtalk-physicalmodeling.htm">http://www.applied-acoustics.com/techtalk-physicalmodeling.htm</a>)<br>
<br>
Kind regards,<br>
Lorenzo.<br>
<br>
<br>
Andrew Turley wrote:
<blockquote
cite="mid:2e2d28010907202006j5cdb6b9v3379b2525bf276d6@mail.gmail.com"
type="cite">
<pre wrap="">The ratios are maintained because you're multiplying (I'm not quite
sure what you mean by "even out"). But yes, you could also convert to
MIDI and then use addition, and then convert back to set the
oscillator. Six of one, half-a-dozen of the other.
andy
On Mon, Jul 20, 2009 at 7:06 PM, Mike Moser-Booth<a class="moz-txt-link-rfc2396E" href="mailto:mmoserbooth@gmail.com"><mmoserbooth@gmail.com></a> wrote:
</pre>
<blockquote type="cite">
<pre wrap="">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] <a class="moz-txt-link-freetext" href="http://en.wikipedia.org/wiki/Harmonic_series_(music)">http://en.wikipedia.org/wiki/Harmonic_series_(music)</a>
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 <a class="moz-txt-link-rfc2396E" href="mailto:jbturgid@hotmail.com"><jbturgid@hotmail.com></a>
wrote:
</pre>
<blockquote type="cite">
<pre wrap="">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: <a class="moz-txt-link-abbreviated" href="mailto:jbeezez@googlemail.com">jbeezez@googlemail.com</a>
To: <a class="moz-txt-link-abbreviated" href="mailto:pd-list@iem.at">pd-list@iem.at</a>
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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