What can make the closest to a single frequency tone?

[Hermitian]

What (non-electronic) instrument or sound making device makes the closest to a pure single frequency sine wave? I am under the impression that things like string instruments have all sorts of overtones, or, er... stuff.

I was whistling the other day and it came to my mind that a good clean whistler can make a nice tone. However, I am not an expert at these sorts of things.

So, what is it? Is a simple whistle (human lips) pretty close to a sine wave? Is something else better?

[Jaledin]

What do you mean by electronic? A Hammond organ produces very near a sine wave once all the effects are off.

It uses electricity, but it's very much mostly a mechanical instrument. Like a pipe organ having a bellows, I am positive you could get someone to hand-turn the tonewheels and reproduce the sound by using something similar to a mechanical wind up phonograph.

[Musicat]

A flute would be deficient in overtones; a trumpet would have a surplus. I can't think of any acoustic instrument that produces only the primary pitch without some harmonics. The harmonics are what gives an instrument its "color."

Originally Posted by Jaledin

What do you mean by electronic? A Hammond organ produces very near a sine wave once all the effects are off.

It uses electricity, but it's very much mostly a mechanical instrument. Like a pipe organ having a bellows, I am positive you could get someone to hand-turn the tonewheels and reproduce the sound by using something similar to a mechanical wind up phonograph.

Not quite. The tone wheels create sound by electro-magnetic means, not mechanical. Hand-turning, without electricity, there is no sound at all other than the grinding of ancient bearings.

[engineer_comp_geek]

Whistling produces a fairly pure tone. Woodwind instruments are also commonly cited as being the closest instruments to pure sine waves.

[Alka Seltzer]

Originally Posted by Musicat

I can't think of any acoustic instrument that produces only the primary pitch without some harmonics.

This site lets you download a pure sound wave, and as you say no acoustic instrument sounds anything like that. I'm not sure it's physically possible.

Originally Posted by Musicat

The harmonics are what gives an instrument its "color."

Only partly. The initial chaotic sound when the note is first sounded or struck also gives an instrument much of it's character.

[CurtC]

Woodwinds? I can believe flutes, but the others are rich in overtones. Think of the raspy sound from a clarinet or saxophone - that raspiness is the sound of harmonics. That's not even mentioning the oboe and bassoon

[am77494]

A tuning fork

[friedo]

Tuning fork is actually a pretty good candidate. The initial strike is full of noise, but after you wait a couple seconds the tone becomes very pure. It's still not a perfect sine wave but it's probably closer than you'll get with any musical instrument.

[johnpost]

as mentioned a stabilized tuning fork is best, they are used as a frequency source.

other tuning aids like a chime bar or pitch pipe would make cleaner tones.

[RitterSport]

How about a singing wine glass (crystal glass with your finger rotating around the top) -- that always seemed like a very pure tone to me.

[Hermitian]

Ah, I forgot about the ol' tuning fork. That is kinda their job.

[njtt]

I know I have read that the ocarina is the only regular musical instrument to produce a pure sine-wave tone. According to Wikipedia:

The resonator in the ocarina can create overtones, but because of the common "egg" shape, these overtones are many octaves above the keynote scale.

As most ocarinas produce quite high notes anyway, these overtones may well be beyond the range of human hearing.

See also the last paragraph here.

[Saint Cad]

A Captain Crunch whistle can make a pretty pure 2600Hz tone.

[CalMeacham]

Originally Posted by Hermitian

What (non-electronic) instrument or sound making device makes the closest to a pure single frequency sine wave? I am under the impression that things like string instruments have all sorts of overtones, or, er... stuff.

I was whistling the other day and it came to my mind that a good clean whistler can make a nice tone. However, I am not an expert at these sorts of things.

So, what is it? Is a simple whistle (human lips) pretty close to a sine wave? Is something else better?

I once put a microphone into an oscilloscope and whistled. It made what appeared to be a perfect sine wave. I could vary the frequency quite easily and cleanly.


I don't doubt that there were overtones (multiples of the fundamental frequency) -- there are in everything.


A bar, simply supported on each end, will produce a very pure fundamental tone that is a sine wave, but there are inevitably higher order harmonics. This is what you hear with an instrument like a xylophone, glockenspiel, or marimba. It's a very pure tone, and seems to cut through any other sound.


string instruments also produce fundamental tiomes with higher harmonics -- harps, lyres, guitars, and pianos, and all their relatives.

You also get good fundamentals from wind instruments -- flutes, fifes, coke bottles you blow across the top of, organ pipes. (Reed instruments are more complex)

[Leo Bloom]

Orchestras take their onstage pitch by the oboe. Of course it's not a pure sine wave -- it is clearly an oboe, after all -- but its purity of tone and its loudness (and, I suspect, the extraordinary sensitivity of how local conditions effect pitch with reeds) sets the tone. Finally the concertmaster matches it and the rest of the herd tune up.

[EmilyG]

Originally Posted by njtt

I know I have read that the ocarina is the only regular musical instrument to produce a pure sine-wave tone. According to Wikipedia:

As most ocarinas produce quite high notes anyway, these overtones may well be beyond the range of human hearing.

See also the last paragraph here.

Here's some additional information on the acoustic properties of the ocarina (warning: Comic Sans) :
http://www.fl-oca.com/eng/ocarina1.htm

[drewtwo99]

One of my fellow physics teachers had a student who was one of the best vocalists in the state. He had her sing into a microphone a given pitch (she had perfect pitch and could hit any note within her range on request). He used it as a demonstration, and said the sine wave she could create was perfect.

[Leo Bloom]

Singing in a tile shower stall --or better yet, a metal enclosure -- will increase purity enormously.

[Learjeff]

Originally Posted by am77494

A tuning fork

Bingo. We have a winner. :-)

[Leo Bloom]

Why does the tuning fork work so well? (Real question.)

Because it's just closely ping-ponged air?

[Learjeff]

Originally Posted by friedo

Tuning fork is actually a pretty good candidate. The initial strike is full of noise, but after you wait a couple seconds the tone becomes very pure. It's still not a perfect sine wave but it's probably closer than you'll get with any musical instrument.

Actually, if you strike it correctly (e.g., against your knee, with jeans on, or the palm of your hand), there is very little percussive tone.

Don't strike a tuning fork on a hard surface. Not good for the tuning fork, not good for the hard surface, and not as good for tuning.

After striking the tuning fork, press the base of it to the bridge of your guitar, or face of your violin, for a nice amplifier. That also helps you hear the beats to tune against. When tuning a guitar, play the A string 2nd harmonic, and match that to the tuning fork, with no beats. Tune the guitar, then repeat the process.

[Learjeff]

Originally Posted by Leo Bloom

Why does the tuning fork work so well? (Real question.)

Because it's just closely ping-ponged air?

Because it's designed to be resonant at a single frequency (based on the length of the tines). The tines counter-oscillate in a very stable pattern. Almost all of the flexing happens in the curved part of the shape, the straight tines don't flex much at all. Not because they're stronger there, but because of the way the forces naturally add up.

The air has very little to do with it. That's a good thing; the temperature, humidity, and pressure won't affect the note.

The thing the tuning fork lacks is a good means to transmit the vibration into the air, which is why you hold it against some part of an instrument that's designed to turn vibrations in the wood (or whatever) into vibrations in the air. Even a table works remarkably well.

[Francis Vaughan]

Looking at the waveform on an oscilloscope is an almost useless way of determining the level of harmonic content, unless the harmonics are of really high amplitude. You can have significant low order harmonics present and the eye really can't pick the difference between the slightly thinner, fatter or slightly rounded waveform and a pure sine. A Fourier transform on the other hand is the correct mechanism, and an FFT analyser will give you a direct readout of the harmonics.

Bowed instruments are inherently driven by a triangle wave - the bow string catches and releases the vibrating string, and so are filled with harmonics. Woodwinds are driven by a vibrating reed, which similarly is an asymmetric drive. Brass much the same, but mostly worse. So pure resonator devices like a flute wins here. Even a tuning fork will have some harmonic content. A simple analysis of the geometry will show that there are subtle non-linearities in the coupling of the forces. But as far as simple mechanical devices go, it is pretty hard to beat.

[BigT]

Originally Posted by Leo Bloom

Orchestras take their onstage pitch by the oboe. Of course it's not a pure sine wave -- it is clearly an oboe, after all -- but its purity of tone and its loudness (and, I suspect, the extraordinary sensitivity of how local conditions effect pitch with reeds) sets the tone. Finally the concertmaster matches it and the rest of the herd tune up.

I'm pretty sure the part in parentheses is the most important. If it were about getting the exact pitch, you'd just use a tuner.

[wheresmymind]

Originally Posted by BigT

I'm pretty sure the part in parentheses is the most important. If it were about getting the exact pitch, you'd just use a tuner.

Yeah, I seem to remember learning it was because oboes are very difficult to tune, so rather than having the orchestra sit there for hours while the oboe fiddles about, they all just tune off of him.

[Leo Bloom]

The history of practical standard pitch, so to speak, is long and quite interesting. I'll make a quick list of fun facts if the thread continues to drift that way.

[Pitchmeister]

Originally Posted by BigT

I'm pretty sure the part in parentheses is the most important. If it were about getting the exact pitch, you'd just use a tuner.

The thing is, nowadays most oboists do use a tuner to deliver their perfect 443 (or 442, or 440) Hz A to the orchestra.

[Napier]

Originally Posted by wheresmymind

Yeah, I seem to remember learning it was because oboes are very difficult to tune, so rather than having the orchestra sit there for hours while the oboe fiddles about, they all just tune off of him.

Ditto.

[Learjeff]

Originally Posted by Francis Vaughan

Looking at the waveform on an oscilloscope is an almost useless way of determining the level of harmonic content, unless the harmonics are of really high amplitude. You can have significant low order harmonics present and the eye really can't pick the difference between the slightly thinner, fatter or slightly rounded waveform and a pure sine. A Fourier transform on the other hand is the correct mechanism, and an FFT analyser will give you a direct readout of the harmonics.

Good point.

[jovan]

Originally Posted by Francis Vaughan

Looking at the waveform on an oscilloscope is an almost useless way of determining the level of harmonic content, unless the harmonics are of really high amplitude. You can have significant low order harmonics present and the eye really can't pick the difference between the slightly thinner, fatter or slightly rounded waveform and a pure sine. A Fourier transform on the other hand is the correct mechanism, and an FFT analyser will give you a direct readout of the harmonics.

Bowed instruments are inherently driven by a triangle wave - the bow string catches and releases the vibrating string, and so are filled with harmonics. Woodwinds are driven by a vibrating reed, which similarly is an asymmetric drive. Brass much the same, but mostly worse. So pure resonator devices like a flute wins here. Even a tuning fork will have some harmonic content. A simple analysis of the geometry will show that there are subtle non-linearities in the coupling of the forces. But as far as simple mechanical devices go, it is pretty hard to beat.

Thank you. I'm surprised at the number of slightly-confused answers in this thread. To reiterate: looking at the shape of a waveform is nearly pointless. Something may look a lot like a sine wave, but actually contain noticeable frequency content above the fundamental.

A nitpick, though, bowed-strings are roughly modeled by a sawtooth wave, not a triangle wave.

(I'm also at a loss to understand how a sound being deficient in overtones would rule it out as a sine tone candidate: a sinusoid has no overtones.)

Anyway, I ran FFTs of some of the sounds mentioned in the thread.

Let's start with a transverse flute. The bright horizontal lines represent the harmonics. The fewer, the closer to a "pure" tone. As you can see, the transverse flute isn't anywhere close to a sine tone. The vertical ripples are caused by slight vibrato and tremolo.

We move on to finger on glass. There's a very noticeable (both visually and sonically) second harmonic. There are also inharmonic components that give the sound a distinctive colour. In a purely harmonic sound, the partials (horizontal lines) should be evenly spaced, but you can see that this is not entirely the case.

There there is the ocarina. The second harmonic is very weak, but the third is comparatively strong. The fourth is also weak, and the fifth is a bit stronger. There isn't much past that, which is consistent with the way the ocarina sounds; it's very close to, but not quite exactly a pure tone.

Finally, a tuning fork. We see some harmonics after the fork is struck (on the left of the plot), but they quickly fade out. After that, it's pretty much a single lonely harmonic. In other words, a pure sinusoid.

[Chronos]

It's my understanding that a clarinet is almost completely impure: The fundamental is extremely low-amplitude, with most of the sound coming from the overtones. But because of the way our ears and brain work, a bunch of overtones without the fundamental still sounds like the same note as the fundamental.

[Francis Vaughan]

A nitpick, though, bowed-strings are roughly modeled by a sawtooth wave, not a triangle wave.

Ack!! Quite right. The important bit is that the fast edge of the wave is the release from the bow, and the slow edge the drag by the bow.

It's my understanding that a clarinet is almost completely impure:

Another good one are very big organ pipes. Something that surprised me quite a bit. There is some energy at the fundamental, but harmonics totally dominate the sound. Some of the perception of deep bass may come from the missing fundamental effect.

[Francis Vaughan]

Anyway, I ran FFTs of some of the sounds mentioned in the thread.

Lovely

[Musicat]

Originally Posted by jovan

Anyway, I ran FFTs of some of the sounds mentioned in the thread.

Let's start with a transverse flute. The bright horizontal lines represent the harmonics. The fewer, the closer to a "pure" tone. As you can see, the transverse flute isn't anywhere close to a sine tone. The vertical ripples are caused by slight vibrato and tremolo.

We move on to finger on glass. There's a very noticeable (both visually and sonically) second harmonic. There are also inharmonic components that give the sound a distinctive colour. In a purely harmonic sound, the partials (horizontal lines) should be evenly spaced, but you can see that this is not entirely the case.

There there is the ocarina. The second harmonic is very weak, but the third is comparatively strong. The fourth is also weak, and the fifth is a bit stronger. There isn't much past that, which is consistent with the way the ocarina sounds; it's very close to, but not quite exactly a pure tone.

Finally, a tuning fork. We see some harmonics after the fork is struck (on the left of the plot), but they quickly fade out. After that, it's pretty much a single lonely harmonic. In other words, a pure sinusoid.

I am unable to interpret your FFTs. A spectrum or acoustic response curve vs. time would mean more to me. But I question your interpretation of the flute, at least. I recall the settings on a Hammond organ when I used to play it, and a simulated flute was a "6-4", which means a lot of the fundamental and about a 2/3 level of the octave up, but nothing more. That's about as pure as you can get and still sound like an acoustic instrument (a fundamental only would be purer, but sound a more electronic). A brass simulation had many overtones; a clarinet, only the odd ones.

Where did you get the sound samples? Can they be relied upon to be accurate, with no coloring or distortion introduced by the recording?

[Chronos]

I am unable to interpret your FFTs. A spectrum or acoustic response curve vs. time would mean more to me.

I think those are spectra. At least, that's what they look like to me, and that's the usual output of a Fourier transform.

[Musicat]

A spectrum analysis, to me, means something like this, this, or this.

[ZenBeam]

They are spectra along the vertical axis, and time along the horizontal axis, with the magnitude represented by color. Frequency increases from bottom to top, and time increases from left to right.

[jovan]

Originally Posted by Musicat

I am unable to interpret your FFTs. A spectrum or acoustic response curve vs. time would mean more to me. But I question your interpretation of the flute, at least. I recall the settings on a Hammond organ when I used to play it, and a simulated flute was a "6-4", which means a lot of the fundamental and about a 2/3 level of the octave up, but nothing more. That's about as pure as you can get and still sound like an acoustic instrument (a fundamental only would be purer, but sound a more electronic). A brass simulation had many overtones; a clarinet, only the odd ones.

Where did you get the sound samples? Can they be relied upon to be accurate, with no coloring or distortion introduced by the recording?

I'm sorry, I forgot to link to the original sound files I used.

Tuning fork
Finger on glass
Ocarina
Transverse flute

The plots are standard short-time Fourier transforms generated using the nice (and free) package Sonic Visuzaliser, although most audio editing or analysis software will output similar plots. I used a window size of 8192 samples, which obscures some of the temporal detail but provides decent resolution on the frequency axis.

For those who are not familiar with FFTs or short-term Fourier transforms, the idea is this: the Fourier transform is a mathematical formula that allows you to take any arbitrary wave (i.e. sound) and describe it as the sum of an arbitrary number of sinusoids (sine or cosines). In other words, this means that you can create any and all sounds just by adding sine waves. It also means that the sine wave is the "purest" or simplest sound. Harmonic sounds are made up of sine waves that have frequencies that are integer ratios of some base frequency, the fundamental.

The classical Fourier transform is one of the most useful mathematical formulas ever discovered, but there's at least one major problem: it sucks at describing how sounds change over time. The way to get around this is the short-time Fourier transform. You essentially slice the sound in overlapping snippets and perform a Fourier transform on those.

The fast Fourier transform (FFT) refers to algorithms for rapidly computing the Fourier transform of a digitally-sampled wave. The accuracy of the FFT is determined by the size of the data, which is why longer windows yield a more accurate description of the frequency content of the sound.

In the plots I made, the horizontal axis is time. The vertical axis is frequency. The amplitude of each frequency band is shown by the colour, with brighter colours louder.

As for the quality of the recordings, I think they're good enough to answer the OP.

The Hammond "flute" sound mimics the flute stops on pipe organs rather than actual flutes. Of course, these stops are so named because they resemble flute sounds, but in this case the flutes are recorders and such, not transverse flutes.

[Voluble]

Originally Posted by drewtwo99

One of my fellow physics teachers had a student who was one of the best vocalists in the state. He had her sing into a microphone a given pitch (she had perfect pitch and could hit any note within her range on request). He used it as a demonstration, and said the sine wave she could create was perfect.

Unfortunately, he didn't have the slightest idea what he was talking about.

Human voices are very messy things and can't come close to producing a clean sign wave... let alone a perfect one. Obviously, if she could produce a pure sign wave it would sound nothing like a human voice at all. If you were to take any DAW and look at the waveform of her voice you would be shocked at how little it looks like a pure tone. An FFT would likewise reveal a bit of a mess.

But that is what gives the human voice its character.

[Jaledin]

Originally Posted by Pitchmeister

The thing is, nowadays most oboists do use a tuner to deliver their perfect 443 (or 442, or 440) Hz A to the orchestra.

Hey. Why don't they just use a tuning fork? Tuners need, like food and water and a litter box to be happy.

[johnpost]

you can tune a piano

[Jaledin]

In Russia piano tunes you.

OH more seriously I've been listening to Andras Schiff on the French Suites for a couple hours -- whoever teched his piano really knew what he or she was doing. The unisons are off but I'm assuming that's after one suite and got bent out. The action he favors (again, I'm assuming he has the piano set up the way he likes it) is interesting. http://www.youtube.com/watch?v=QeBz6...eature=related

[Musicat]

Originally Posted by Voluble

Human voices are very messy things and can't come close to producing a clean sign wave... let alone a perfect one. Obviously, if she could produce a pure sign wave it would sound nothing like a human voice at all.

That's a sine wave, not a sign wave. A sign wave would be like, "Hey, look over there -- a big-ass billboard!"

[Leo Bloom]

Originally Posted by Jaledin

....whoever teched his piano really knew what he or she was doing. The unisons are off but I'm assuming that's after one suite and got bent out. ....

One of these two statements must be false.

[Jaledin]

No, I'm thinking that's what happened -- are you serious that a good talented tech can prevent some flexion of the pins/tuning over the course of a few hours of marathon Bach playing?

Willing to admit you might be right -- just never heard that techs could compensate in advance for that kind of thing. But I'm not a piano tuner, and not a technician -- in fact all I know about piano is you hit the keys hard wearing a helmet! Shed some light, man!

Oh, that is a good run Schiff did on the French suites. I forgot about him for twenty years -- good stuff. His corrante on that one is not too brilliant the way I think about a corrante but he makes up for it in spades with the voice leading and some intelligent phrasing and probably some historical work on the ornamentation.

[johnpost]

Originally Posted by johnpost

you can tune a piano

but you can't tuna fish

nobody took the bait.


i recalled that catchy title, though not who or what. looked it up. REO Speedwagon album. cover art has a tuning fork in the mouth of a fish.

[Leo Bloom]

Originally Posted by Jaledin

No, I'm thinking that's what happened -- are you serious that a good talented tech can prevent some flexion of the pins/tuning over the course of a few hours of marathon Bach playing?

Willing to admit you might be right -- just never heard that techs could compensate in advance for that kind of thing. But I'm not a piano tuner, and not a technician -- in fact all I know about piano is you hit the keys hard wearing a helmet! Shed some light, man!

Oh, that is a good run Schiff did on the French suites. I forgot about him for twenty years -- good stuff. His corrante on that one is not too brilliant the way I think about a corrante but he makes up for it in spades with the voice leading and some intelligent phrasing and probably some historical work on the ornamentation.

I'll take this off-thread, if you like.

[Dead Cat]

If whistling does indeed produce such a pure tone, is that why whistling a tune in unison with another person is so difficult, whereas singing a tune in unison with another person is comparitively easy? Do the overtones of the singing voice mask imperfections in the exact pitch being produced, such overtones not being present in whistling?

[Leo Bloom]

We're better at larynx control than lip control.

I wonder if French people whistle better than Americans do. I remember after good French vowel classes my lips feeling quite sensitive, almost tired in a way.