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From: Ron N. on 28 Jul 2010 18:40
On Jul 28, 8:52 am, Jerry Avins <j...(a)ieee.org> wrote:
> How can a sine and its second harmonic be in phase?

The solution to a particular differential equation may include
sinusoidal harmonics relation by phase to some initial
condition, or to the zero crossing of the fundamental mode.

If you find a harmonic of a different phase, it might not belong
to that particular resonator (instead being noise, or some other
string, some other instrument, etc.). Of course, you have to
compensate for the phase response of the data acquisition
mechanism, or just do pattern matching against a reference
spectrum (including phase) through the same system.


IMHO. YMMV.
--
rhn A.T nicholson d.0.t C-o-M
From: glen herrmannsfeldt on 28 Jul 2010 18:59
Ron N. <rhnlogic(a)yahoo.com> wrote:
> On Jul 28, 8:52�am, Jerry Avins <j...(a)ieee.org> wrote:
>> How can a sine and its second harmonic be in phase?

> The solution to a particular differential equation may include
> sinusoidal harmonics relation by phase to some initial
> condition, or to the zero crossing of the fundamental mode.

(snip)

I think it can make sense, but you do have to be careful.

One might say that different frequency sines are in phase
when they cross zero at the same time, and cosines in phase
when they have their maximal value at the same time.

If one says "sinusoid" instead of "sine" then that doesn't work.

But there are enough problems, such as boundary value
differential equations, where specific phases of different
sinusoids coincide, and that coincidence can be used as a
phase reference. Some such equations are said to have solutions
that are "sines" or "cosines" depending on the boundary
conditions. One result of such are the Fourier Sine
and Fourier Cosine transforms.

-- glen
From: Phil Martel on 31 Jul 2010 15:26


"Jerry Avins" <jya(a)ieee.org> wrote in message
news:nD04o.32556$o27.28215(a)newsfe08.iad...
).
<snip>
>
> Never mind morning coffee, I skipped lunch today. Arrgh! Never calculate
> on an empty stomach!
>
> Jerry
> --
> Engineering is the art of making what you want from things you can get.
> �����������������������������������������������������������������������
OTOH, never drink and derive.

From: fatalist on 2 Aug 2010 14:17
On Jul 26, 7:27 am, "Cirrus" <luigi.rosso(a)n_o_s_p_a_m.gmail.com>
wrote:
> Hi All,
>
> I'm a software engineer and musician who has always been keen on learning
> more about the meshing of these two fields.  I've been studying DSP for
> personal interest (I've created a couple fun software experiments like
> synthesizers, drum machines, tuners).  I just recently acquired one of
> these cool PolyTune tuners:http://www.tcelectronic.com/polytune.asp
>
> I've been so impressed by how well it works that I've tried my hand at
> figuring out the math to this myself.  I tried upgrading a simple FFT tuner
> I made to work like this.  
>
> I built a simple little test environment that is by no means robust but
> "kind of works".  I calculate the frequency spectrum with the FFT every 0.1
> seconds and examine certain ranges of interest for each string.  The
> biggest problem is that overtones from some of the lower frequencies
> collide with the area of interest of other strings.  For example, one
> overtone from the A string is right between the high E and its closest
> sharp semitone (F).  This creates two peaks in my area of interest for the
> high E string.  This makes it difficult to discern which peak is from the
> actual E string and which one is from the A string.  Furthermore the low E
> string has a pretty strong harmonic on the high E string.  Am I taking the
> wrong approach?
>
> I can provide some plots from my software if my explanation wasn't
> clear...
>
> Any ideas?

The fundamental frequencies of open strings on a tuned guitar form
some well defined ratios, like 4/3

The combined signal produced by all strings is thus supposed to be a
periodic signal if the guitar is well tuned

Can be done in time-domain, I believe, without any FFT but with some
trickery...

Also, read US Patent 7124075

http://www.google.com/patents/about?id=dB97AAAAEBAJ&dq=7124075

Might give you some insights

When you figure it all out be sure to let us know :-)

From: Richard Dobson on 2 Aug 2010 14:31
On 02/08/2010 19:17, fatalist wrote:
...
>
> The fundamental frequencies of open strings on a tuned guitar form
> some well defined ratios, like 4/3
>


For a guitar (with frets) they won't. The frets are placed according to
12-Tone Equal temperament, and hence the strings must be tuned
accordingly. The major third (G-B) especially is much wider than the
"just" harmonic ratio 5/4. The fourths (between the other strings) will
be close but not exact (a tad wider than harmonic).



Richard DObson

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