Very impressive William, but this would definitely cut into
my practice time which needs my complete concentration and free from outside
interference....................Laurent
----- Original Message -----
From: <[EMAIL PROTECTED]>
To: <[EMAIL PROTECTED]>
Sent: Wednesday, December 31, 2003 11:35 PM
Subject: [Hornlist] The math of partials and harmonics
> Well I'm running into many problems with the harmonics chart in Excel. The
> programming does work to a point, however it is not portable to the web in
any
> quick format.
>
> In addition, the entire chart itself is about 4 pages each with tables
that
> are 2000-3000 pixels wide to 4000 pixels tall and so forth. I covered all
the
> bases :)
>
> Therefore I'm learning SQL databases with some PHP. I'm going to try to
> produce an online chart customizeable to any horn or combinations of horns
(F/Bb
> double, F/Bb/High Eb triple, etc.). Also I'm going to try to get into
Maple soon
> and work up some nice formulaic proofs to accompany this.
>
> If this works out for PHP I should be able to produce an optional color
coded
> one as well.
>
> I'll post more about this later, however it will involve some neat tricks.
> I'm associating all note names with a number 1 through 12.
>
> 0 ---- Fundamental note name (say A for example since I'm using A=440 by
> example)
> 1 ---- half step above 0 (Bb)
> 2 ---- half step above 1 (B)
>
> and so forth. With this I can assign octaves by listing notes by half step
> from 0 (the fundamental, or rather A=440 divided by 16 which gives us the
second
> E below the Bass clef. This theoretical fundamental is 1 2 and 3 on the Eb
> horn. This is why this division is chosen because one can simply move up
by half
> steps on the Eb horn to reach the realm of the F horn, and one can keep
going
> up the horns to Bb, Eb Alto, F Alto, and Bb Alto.
>
> Now with this one can assign all the notes by half step from 1 to however
> high you wish to go. The frequency values are attained by the following
formula:
>
> 2^(1/12) * Fundamental.
>
> Going up note by note we will have:
>
> 2^(1/12) * (2^(1/12) * Fundamental) for the 2nd note
> 2^(1/12) * [2^(1/12) * (2^(1/12) * Fundamental)] for the 3rd note, and so
> forth.
>
> Therefore one finds that the equation for any note's frequency is the
> following:
>
> {[2^(1/12)] ^ x } * F0
>
> Where, x is the xth note above the Fundamental. Thus we can find that the
> octave is the following:
>
> {[2^(1/12)] ^ x } * F0
> --- x = 12 --- this means that we are looking for the 12th note above F0
> (fundamental).
> {[2^(1/12)] ^ 12 } * F0
> {[2^(12/12)]} * F0
> (2^1) * F0
> 2 * F0
>
> Which is the octave right above the fundamental. We can also determine the
> note name and the octave of any note in our arbitrary half note scale (F0
to any
> note you choose). All we have to do is divide the integer value of the
note
> in our list by 12 and correlate that with it's remainder. The 12th note
from
> the fundamental would be an even octave from our first note because if one
> divides it by 12, one has 1 with no remainder. Thus:
>
> int(Note_Number / 12) yields our octave number
> Note_Number - [int(Note_Number/12) * Octave_Number] yields the remainder
> (one could also use a floor function or even a remainder function to
> determine both)
>
> Now for the harmonics which are easy to determine. All one has to do is
> multiply the Note_Number frequencies by the harmonic. F0 on the 4th
Harmonic would
> be F0*4 for example. The 14th Harmonic of the 45th note would be that
> frequency times 14.
>
> Now after this one must determine where these harmonics lie with regards
to
> note values. One simply CANNOT use the closest frequency value to the note
> since the scale is logarhythmic. The quickest way is to find the closest
note
> frequency through programming is to find the closest value to the
frequency (a
> simple mathematical function can do this) and then going one step forward,
one
> step backward in note frequencies and determining which note has the
smallest
> intonation defficiency in cents and printing out the correllating note
value.
>
> Intonation in cents is determined by the following formula:
>
> { 1200*ln(T/V) } / ln(2)
> Where
> T = Testing value
> V = Value you are comparing T to (T is sharp or flat to V)
>
> With this you can determine the ideal pitch tendencies of every single
note.
>
> I hope this was informative. Soon I will be complete with these tables and
> all this programming...
>
> I wont spoil the surprises but there are some very fascinating things to
this
> math, and a lot of things that make it a lot simpler than you would think.
> For example, if the instrument is in tune then it will not matter what A
you
> tune to, even if its 200Hz or 2000Hz, the note names of every harmonic and
their
> pitch tendencies will always be the same. Do the math, you'll be surprised
:)
>
> -William
>
> _______________________________________________
> post: [EMAIL PROTECTED]
> set your options at
http://music.memphis.edu/mailman/options/horn/lesmis7%40fix.net
>
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