# Best way to measure precise harmonics?

• posted

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

• posted

On a sunny day (Thu, 18 Oct 2007 06:22:06 -0700) it happened eromlignod wrote in :

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?

• posted

** 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

• posted

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

John

• posted

Yeah, yeah...go f*ck 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

• posted

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

• posted

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

• posted

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 =^.^=

• posted

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

• posted

John Larkin hath wroth:

Bad news. Piano harmonics are not exact integer multiples. See:

especially the section on "harmonics and tuning". If it were exact integers, it would be easy.

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:

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.

```--
Jeff Liebermann     jeffl@cruzio.com
150 Felker St #D    http://www.LearnByDestroying.com```
• posted

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

• posted

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.

```--
Paul Hovnanian	paul@hovnanian.com
-----------------------------------------------------------------------```
• posted

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```
• posted

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

• posted

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

• posted

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

```--
|  James E.Thompson, P.E.                           |    mens     |
• posted

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

• posted

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 (

• posted

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

Don

• posted

Sorry, I didn't get that the signal came off a piano string.

Even bells have non-trivial harmonic relationships, and nearby modes. I'd guess that a bell is more linear than a piano string.

I don't think a single scaler "frequency" will be too meaningful, although it might do for tuning, once you normalize that number to something that sounds right.

My bell-tuning friend soon discovered that tweaking them wasn't a simple mathematical procedure.

John

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