# Best way to measure precise harmonics?

Discussion in 'Electronic Design' started by eromlignod, Oct 18, 2007.

1. ### eromlignodGuest

Hi guys:

I need to find the component harmonic frequencies of an AF wave and I
need for it to be pretty precise (+/- .001 Hz or so). I have access
to a spectrum analyzer, but it just doesn't seem to be precise enough
(or I'm using it wrong). It gives me peaks in a frequency domain, but
they are not pinpoint lines, ostensibly due to a limited-sample FFT.

Are there any other devices or methods to obtain accurate frequencies
of each harmonic to three decimal places? Thanks for any suggestions
you might have.

Don

2. ### Jan PanteltjeGuest

Tunabe filer - amplifier - frequency counter.
Something is strange in your setup, for sure
if the fundamental frequnecy is known, then the harmonics WILL be an exact
multiple of that.
If the fundamental frequency changes (is FM modulated), then you have a problem.
The question then comes up: What are you measuring, and why the accuracy?

3. ### Phil AllisonGuest

** Google Groper Alert !!!!!!

** That is DAMN precise !!!

You need to justify that or be considered a NUT case.

** Meaningless, to just drop that title with no explanation.

** Poor diddums.............

** Hang on, YOU just asked for 6 or 7 decimal places of accuracy.

Got a clue what the term means ????

** Don't tempt me.

........ Phil

4. ### John LarkinGuest

Measure the fundamental frequency with a counter. The harmonic
frequencies are precise integer multiples of that.

John

5. ### eromlignodGuest

Yeah, yeah...go **** yourself, asshole.

I'm dealing with the vibration of piano strings which go as low as
27.5 Hz. Pianos are routinely tuned to less than one "cent" of
deviation, which, at 27.5 Hz, amounts to about .016 Hz. That's just
to get it in tune for music. I need to be a little finer than that.

Currently I can measure the fundamental of the low note theoretically
to about 1/1000th of a cent. Actually I measure the period of the
wave by counting the vibrations of a 50 MHz oscillator compared to the
vibration of the string. But I have found that natural fluctuations
in the pitch of the string as it vibrates don't really allow you to
measure much better than a tenth of a cent or so.

I'm developing a method of string manufacture to control individual
harmonics relative to each other, so I need to be able to accurately
see their relative frequencies (or periods).

I was hoping there might be a common device or method for this.
Otherwise I'll just have to filter and use my present device.

Don

6. ### Ken S. TuckerGuest

Well you could generate a near sine wave oscillator,
with adjustable frequency, I'd use a computer to
generate that, then mix that with your output.
Filter out everything except +/- 1 hz, and measure
that amplitude relative to inputs.
I'm suggesting a very high Q notch filter, that uses
hetrodyning.
Sounds like fun.
Ken

7. ### John LarkinGuest

As you say, the frequency of a vibrating string varies with time, so
the exact frequency isn't a single value, and will also vary as a
function of initial amplitude.

I know a guy who makes handbell sets. He uses an n/c lathe, a striking
hammer, a microphone, and a computer that does fft's and things and
closes the machining loop to tune all the not-quite-integral harmonics
for best sound. He's learned a lot about this sort of thing. If you're
interested, I could put you into contact with him.

John

8. ### colinGuest

to get 0.001 hz resolution you need to sample it for something like 1000
seconds.

you can then do an an FFT, maybe with a soundcard or dsp micro etc.
or you can mix it with a known frequency and detect the beat,
but the beat frequency will be as low as 0.001 hz.

alternativly you can measure the period instead,
this would involve filtering out the frequency you want,
making it digital and feeding it into a period averaging meter
eg hp-5328b universal frequency counter.

this will give you 0.00001 % resolution or better averaged over 1
second but the acuracy will probably depend entirly upon how well you filter
the signal and the resultant snr.

Colin =^.^=

9. ### eromlignodGuest

Don

Thanks, John. Yeah, you might want to send me his info. Sounds like
he's doing something very similar.

I guess I should have posted a desired accuracy of "1/10 cent", which
is a logarithmic term that is relative to the frequency in question.
But I wasn't sure if everyone would be familiar with that
nomenclature, since it's primarily a musical term. Actually, 0.001 Hz
would be an absolute worst case for the lowest fundamental. Cents get
exponentially larger (in terms of Hz) as you go up in pitch.

Incidentally, I sustain the note with an "Ebow"-like magnetic
sustainer, so decay is not a factor, since the note vibrates
continuously at a steady amplitude. I still get variations of 1/10th
cent or more, though some of that might be the oscillator crystal.

Don

10. ### Ken S. TuckerGuest

That kind of accuracy requires very high quality
components. For example a 100 ohm resistor
with vary slightly with current, likewise a 100 uF
cap will vary depending on the stored voltage.
There are ways to compensate for that, but they
take time.
Better keep an eye on that bottom line, cost-
benefit ratio.
What's the application?
Ken

11. ### Jeff LiebermannGuest

Bad news. Piano harmonics are not exact integer multiples. See:
<http://en.wikipedia.org/wiki/Harmonic_series_(music)>
especially the section on "harmonics and tuning". If it were exact
integers, it would be easy.
<http://en.wikipedia.org/wiki/Piano_tuning>

In college, I attempted to tune an upright piano using an ancient HP
nixie tube counter to its limits of accuracy using exact harmonic
overtone series frequencies. It sounded "dead" and generally lousy. I
was later rescued by a professional piano tuner who explained how it
works. I've tuned 4 pianos since then, with varying degrees of effort
and success.

What he's apparently (not sure) trying to do is mimick the art of the
piano or string instrument tuner. That's going to be rough because
the very best piano tuners adjust their tuning for the type of music
to be played, the acoustics of the concert hall, and the expected
length of time between tuning and the actual concert. Basic guides,
such as:
<http://piano.detwiler.us/index.html>
are a great start. However, using a modified guitar tuner directly is
not going to result in the correct harmonic partials. Note the above
instructions say to ignore the piano tuner and rely on the beat notes.

My best guess(tm) is that it's going to take filters (to remove the
fundamental) and a period counter to do this.

12. ### John E. PerryGuest

The FFT sample length just determines the bin width of the FFT output
array. There are more fundamental problems with your idea (one aspect
of it addressed by Colin): any disturbance will broaden the _ACTUAL_
signal width to beyond most common FFT bin widths. Acoustic noise,
atmospheric pressure variations, electric interference, all contribute
to this signal broadening. As do ambient temperature and other things I
can't think of at the moment...

You're asking to do something that can't be done.

Now, this is more nearly feasible, and was addressed by Colin...
Actually, I think the figure is more like 4000 seconds...

And here is the only possibility of doing what you want; get the broad
signal peaks using a high-resolution spectrum analyzer, and find the
peak bin of each harmonic within its (probably many bin-width) hump. If
you're lucky, and in a very quiet acoustical environment, and there's
very little electrical noise, and the moon is in exactly the right
place, and you've sacrificed the right set of chickens, you may be able
to see a single bin that's a tiny bit higher than the others.

As to whether this will really mean anything, I couldn't say. I really
doubt it.
Personally, I doubt that this will give anything useful, even if you can
overcome the instrumentation setup issues.

John Perry

13. ### Paul Hovnanian P.E.Guest

Measure the fundamental. And good luck with that. With piano (or other
stringed instrument) the decay of the harmonics and possibly some phase
shifts over time will introduce errors at the .001 Hz level.

14. ### Don LancasterGuest

Not even wrong.

Piano string overtones are NOT exact multiples of the fundamental, due
to the lateral stiffness of strings.

An "exactly tuned" piano will thus sound awful.

Instead, the piano keyboard is "stretched", going something like 38
cents or so low on the low end and 12 cents or so high on the high end.

Since the enharmonic overtone relation of a string is well known, the
overtone frequencies are strictly locked to the fundamental. And thus
precisely defined.

Constult any standard piano tuning book for details.

--
Many thanks,

Don Lancaster voice phone: (928)428-4073
Synergetics 3860 West First Street Box 809 Thatcher, AZ 85552
rss: http://www.tinaja.com/whtnu.xml email:

Please visit my GURU's LAIR web site at http://www.tinaja.com

15. ### Tom BruhnsGuest

One of the problems you'll have is the length of time over which you
can make your measurement. To nail a frequency as accurately as you
want, if you don't know something a priori about it, you need to
observe it for a long time. Will the strings vibrate for 1000
seconds? If not, then realize that you are not dealing with a single
frequency but a spectral density. The attack and decay envelopes
modulate the string's natural frequency.

I can pretty easily measure frequencies in the audio range to 0.001Hz
resolution, IF they stick around long enough. FFT-based spectrum
analyzers worth having should have "zoom" capability, allowing you to
set essentially any center frequency you want and then set the span
very low. _IF_ you have a priori knowledge that the signal you are
looking at is a pure sinewave (that is, will maintain the same
amplitude for a long time and is not polluted by other signals at
other frequencies), you can very accurately determine its frequency in
a much shorter time. That's because you can measure the period of a
relatively small number of cycles. But any other signals, especially
ones not harmonically related to the tone you're looking at, will mess
up the waveform so that the period from zero crossing to zero crossing
is not constant from one cycle to the next. Ultimately, you'll be
limited by inevitable noise that will cause the same problem.

I have a frequency counter that finds low frequencies by the method of
inverting the waveform's period (or the period of multiple cycles),
but I can still get better accuracy in a given time using an FFT-based
spectrum analyzer, and have the added benefit of being able to observe
the shape of the FFT'd input spectrum, which gives confidence that the
signal is (or isn't) clean enough to use for accurate frequency
measurement. With an Agilent 89410 analyzer, I can get a 3200 point
FFT with 1Hz span centered down to 1 millihertz resolution, but at
that span and than number of points, it takes llllooooong time to
make a measurement. On the other hand, with that a priori knowledge
about the signal, I can resolve easily a tenth of the spacing between
FFT points, knowing the details of the windowing function (which
determines the filter shape that each FFT point represents).

Cheers,
Tom

16. ### Tom BruhnsGuest

One of the problems you'll have is the length of time over which you
can make your measurement. To nail a frequency as accurately as you
want, if you don't know something a priori about it, you need to
observe it for a long time. Will the strings vibrate for 1000
seconds? If not, then realize that you are not dealing with a single
frequency but a spectral density. The attack and decay envelopes
modulate the string's natural frequency.

I can pretty easily measure frequencies in the audio range to 0.001Hz
resolution, IF they stick around long enough. FFT-based spectrum
analyzers worth having should have "zoom" capability, allowing you to
set essentially any center frequency you want and then set the span
very low. _IF_ you have a priori knowledge that the signal you are
looking at is a pure sinewave (that is, will maintain the same
amplitude for a long time and is not polluted by other signals at
other frequencies), you can very accurately determine its frequency in
a much shorter time. That's because you can measure the period of a
relatively small number of cycles. But any other signals, especially
ones not harmonically related to the tone you're looking at, will mess
up the waveform so that the period from zero crossing to zero crossing
is not constant from one cycle to the next. Ultimately, you'll be
limited by inevitable noise that will cause the same problem.

I have a frequency counter that finds low frequencies by the method of
inverting the waveform's period (or the period of multiple cycles),
but I can still get better accuracy in a given time using an FFT-based
spectrum analyzer, and have the added benefit of being able to observe
the shape of the FFT'd input spectrum, which gives confidence that the
signal is (or isn't) clean enough to use for accurate frequency
measurement. With an Agilent 89410 analyzer, I can get a 3200 point
FFT with 1Hz span centered down to 1 millihertz resolution, but at
that span and than number of points, it takes llllooooong time to
make a measurement. On the other hand, with that a priori knowledge
about the signal, I can resolve easily a tenth of the spacing between
FFT points, knowing the details of the windowing function (which
determines the filter shape that each FFT point represents).

Cheers,
Tom

17. ### Jim ThompsonGuest

If these are wire strings, might one simply excite them with a small
signal... say an AGC'd oscillator loop, then measure the frequency
with a counter?

...Jim Thompson

18. ### John LarkinGuest

If you've got a steady-state oscillation, a simple frequency counter
should do just fine. Even a cheap crystal timebase will be stable to a
ppm per month, often a ppm per year.

I wonder what the tempco of a steel string will be. That's probably
the dominant thing that walks the frequency around. 10, 20 PPM/K?

Say, how does the sound of a piano change with temperature? All that
wood and steel must move around a lot.

Email me for the contact. jjlarkin atsign highlandtechnology dthing
cthing.

John

19. ### eromlignodGuest

Please read all of my posts in this thread. I have infinite sustain
time and I don't need to use a frequency counter to determine
frequency. The frequencies are much too low for that. I can measure
the period in the time of one vibration of the string (<40ms) and it
is much more accurate.

Don

20. ### eromlignodGuest

I already know all of this. I'm not tuning a piano, I'm analyzing the
individual harmonics of a string.

Don

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