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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.<br>
<br>
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.<br>
<br>
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.<br>
<br>
Best of luck,<br>
.mmb<br>
<br>
[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><br>
<br>
J bz wrote:<br>
<blockquote
cite="mid:9a4bdd8c0907201539o38e49d63ne64f675fb5372a0c@mail.gmail.com"
type="cite">Dear Mike and Andrew,<br>
<br>
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'?<br>
<br>
Cheers for weighing in,<br>
<br>
Jbz<br>
<br>
<div class="gmail_quote">On Mon, Jul 20, 2009 at 11:16 PM, Andrew
Faraday <span dir="ltr"><<a moz-do-not-send="true"
href="mailto:jbturgid@hotmail.com">jbturgid@hotmail.com</a>></span>
wrote:<br>
<blockquote class="gmail_quote"
style="border-left: 1px solid rgb(204, 204, 204); margin: 0pt 0pt 0pt 0.8ex; padding-left: 1ex;">
<div>Hey Jbz
<div><br>
</div>
<div>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. </div>
<div><br>
</div>
<div>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.</div>
<div><br>
</div>
<div>God bless</div>
<div><br>
</div>
<div>Andrew</div>
<div><br>
</div>
<div><br>
<hr>Date: Mon, 20 Jul 2009 22:24:05 +0100<br>
From: <a moz-do-not-send="true" href="mailto:jbeezez@googlemail.com"
target="_blank">jbeezez@googlemail.com</a><br>
To: <a moz-do-not-send="true" href="mailto:pd-list@iem.at"
target="_blank">pd-list@iem.at</a><br>
Subject: [PD] making scales from frequency values
<div>
<div class="h5"><br>
<br>
Dear all,<br>
<br>
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'.<br>
<br>
Here's the list that I have already:<br>
BT1 <br>
912Hz<br>
2434Hz<br>
4575Hz<br>
7175Hz<br>
11584Hz<br>
<br>
BT2<br>
1081Hz<br>
2861Hz<br>
5339Hz<br>
8325Hz<br>
15209Hz<br>
<br>
BT3<br>
1211Hz<br>
3196Hz<br>
5935Hz<br>
9199Hz<br>
15206Hz<br>
<br>
BT4<br>
1347Hz<br>
3553Hz<br>
6569Hz<br>
10128Hz<br>
18139Hz<br>
<br>
BT5<br>
1812Hz<br>
4699Hz<br>
8525Hz <br>
13264Hz<br>
15469Hz<br>
<br>
Is there one piece of mathematrical wizardy that can sort this in Pd?<br>
<br>
Cheers,<br>
<br>
Jbz<br>
</div>
</div>
</div>
<br>
<hr>Windows Live Messenger: Happy 10-Year Anniversary—get free
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</blockquote>
</div>
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