Okay...help. I don't get what this is exactly.

This has been bothering me for like 3 days.

Someone showed me this Alban Berg thing and it has a piano part that had some moments where there was like a piano chord written in the music, but I guess you just press the keys down with one hand and hold them down without playing the chord and like, bash another chord with the other hand and then release and you kind of hear the first chord resonating out without having actually played it. That may have sounded nonsensical but I was sort of confused by the whole thing, never heard of it.

What is this called?? Is this used much? The chord that isn't directly played is notated with these diamondy noteheads. help!

It works because of the harmonic series, and has to do with the way a sound waveform is set up. Let's say you press the third C below middle C (the bottom C on the piano) while holding down the C one octave above. The frequency of the upper C is twice that of the lower - this is why the octave is the most consonant interval.

Imagine a sinewave. The lower C has a waveform that crests half as often as the upper C - it's got half the frequency. Thus, if those two sinewaves are superimposed one on top of the other, they're going in the same direction from the same point once for every crest of the lower C, and every other crest of the higher C.

When the higher string is undamped, the lower string's vibration strikes the higher string and sets up a sympathetic vibration because of the similarity in produced waveform, and thus similarity in the characteristics of the string itself (this has to do with composition and thickness, not just length, thank goodness 'cause the lowest notes on a piano would require strings a mile long). If you have two strings of the same frequency and set one to vibrating, the sympathetic vibration would be even stronger. Note that the sympathetic vibration will work better the more accurately tuned your piano is.

Higher partials in the harmonic series are also possible to generate through sympathetic vibration, though not as strongly. The G above the higher C, if undamped, will also vibrate; it is three times the frequency of the lower C, so the waveforms coincide every third crest of the lower note.

The partials in the harmonic series are thus because they are each exact multiples of the fundamental:

One octave = double the frequency

Octave + fifth = triple the frequency

Two octaves = four times the frequency

Two octaves and a third = five times the frequency

Two octaves and a fifth = six times the frequency

This is because of the exponential nature of the chroma of musical tones. An octave involves a doubling, a fifth involves increasing by half, a fourth involves increasing by a third, and so on. Thus, say you start on A=440 and add a fifth, then a fourth, to make an octave:

440+220(a fifth's half-doubling)=660, the E above A=440;

660+220(a fourth's addition of one-third)=880, the A above A=440, an octave-doubling.

Notice that an octave and a fifth, which is a frequency multiplication by three, involves first a doubling, then an addition of half that result. Thus:

A=440+440 to go up an octave results in A=880;

A=880+440 to go up a fifth results in A=1320, which is A=440 x 3.

Fun, huh? Sorry if I got way too technical. I just find it fascinating, and thought you might like to know why harmonics work. As for harmonics on a piano, I've done them before and they're cool, but they're so weak on most pianos that I have no idea why any composer would use them in a serious work. Seems to me more "just because I can" than for actually reinforcing a piece; also, works containing piano harmonics are made less accessible because of the fact that they require expertly tuned pianos to be performed with any degree of success.

Wonderful piece that uses harmonics on the piano:

Deux Etudes de Sonorit

Hm, interesting. I wonder why that is? Anyway, the point is that some pianos do harmonics better than others. For performance of such a piece, some pretty specific tuning would be required.

Thanks, all of you. I'm not too familiar with these kinds of techniques, none of the instruments I've played have the ability to do these types of special effects so it's all new to me! :)

Thanks, all of you. I'm not too familiar with these kinds of techniques, none of the instruments I've played have the ability to do these types of special effects so it's all new to me! :)

all pianos can do it, just the sound comes out better on some than others.

simply play a C major chord on middle C but without actually letting the hammers touch the strings (just press down.really slowly on the notes until you feel them "click" into place), and HOLD the notes while

playing fortissimo, in octaves (for best results) a C major arpeggio from the very lowest range of the piano - just play C - E - G (marcato and staccato). then listen carefully and you should hear that chord you played in the middle of the piano reverberate in sympathetic vibration.

Lies.

I've never played an instrument that couldn't produce harmonies in some form.

What do you play?

:) Okay Chris, now I feel like an idiot, I had a feeling that writing something like that would get me busted for lack of knowledge. Like I said, I don't know much about the concept of harmonics (which apparently describes this odd effect in the piano music I was shown). Maybe it's a broader definition that I don't understand still.

So in response to your question:

How do you produce an effect under this definition on a kazoo?

no, but seriously -

how does this apply to a clarinet? Just by giving it its unique tone or altering the sound of separate notes by using different techniques or something? I am so confused right now. I'm not sure how my initial question relates to this.

AHHH I am lost. I kinda get the idea about the wavelengths and such, but my clarinet teachers never sat down with me and were like, "okay, let's talk about harmonics." I just...ug.

Actually, I believe the "squeak" a lot of players get before they learn to control tones is an instance of a harmonic on a clarinet. I could be wrong, though. If that's true, playing harmonics on clarinet would involve controlling that "mistake" that beginning players make.

I have no idea about harmonics on oboe. For the brass family, as well as flute, the harmonics are just a part of playing the instrument normally.

Actually, I believe the "squeak" a lot of players get before they learn to control tones is an instance of a harmonic on a clarinet. I could be wrong, though. If that's true, playing harmonics on clarinet would involve controlling that "mistake" that beginning players make.

Indeed it is just an harmonic. Actually, all notes abover the break are simply harmonics of the funadamental (lowest note). All notes up to middle B-flat are fundamentals and anything higher are harmonics. Once you get to the C above the stave, the notes go into a second set of harmonics.

If I remember, I'll record this to demonstrate.

The Clarinet is the odd one out in woodwind, because it has a cylindrical bore (not tapered). The flute, oboe and bassoon have conical bores (the bores get bigger further from the mouthpice). Therefore, the first harmonic of these instruments is an octave, rather than the twelfth of a clarinet. Again, if I remember, I shall record to demonstrate (except the oboe, which I don't play).

Clarinets are excellent for extended techniques, especially multiphonics - which is the technique of getting multiple pitches out at the same time. The bassoon is very good at this, too. I have never tried them on the flute, though. Again, I'll try to remember to record a demonstration of this.

Send me a PM to remind me if I forget!

Hm. Any tone can be considered a fundamental, actually. The fairly low notes we usually consider "fundamentals" are considered such because they are the lowest notes available on the instrument. The fundamental is simply the slower of two waveforms, while its exact multiple is the "harmonic". Thus, even the fundamentals are harmonic to something... because there are certainly frequencies below even the piano keyboard's range, those tones would be fundamental to their higher relatives!

On saxophone and clarinet, there is a register key that changes the dynamics of the instrument as a whole, enabling higher pitches to be played. Double horn and valved trombone have the same mechanism, though the alteration made in the instrument is different in magnitude. Harmonics created on an instrument usually involve changing technique at the mouth rather than pressing a key, so it might be argued that tones produced using register keys are not harmonics.

I think that's splitting hairs, though. It's safest to speak about harmonics when speaking about a special technique, like playing on nodes for string instruments, or sympathetic vibration in a piano.

Man, that got a little confusing! More proof that words are NOT what they attempt to represent.

On a related note, about piano figuration: notice how left-hand arpeggios usually closely follow the proximity pattern of the harmonic series (higher notes closer together)? I think it probable that this is because the first note sets up a fundamental, and our ear responds readily to successive approximate multiples of that first pitch. I'll have to mention this to my science professor. Consonance is really defined by how often two or more waveforms end up in the same place at the same time - this is why an octave is the most consonant interval. By that token, Romantic-period sweeping arpeggios that closely follow the harmonic series could really be said to be the logical fulfillment of the "absolute consonance" standard of the church fathers who created monophonic chant!

...um, "successive approximate multiples"? I think I need sleep.

Oh, and by the way, the flute isn't conical. I think you've got it backwards... from what I recall, flute, oboe, and bassoon are cylindrical, while clarinet and saxophone are more conical.

I guarantee a flute is conical. Measure one! Flutes, bassoons, oboes and saxophones are indeed conical - their bores all taper. The Clarinet is the only orchestral woodwind instrument with a cylindrical bore. (Edit: that is, until you get to the bell - which tapers out in order to amplify the sound.)

An interesting one is that the recorder (flute a bec) is an inverse conical bore - so the end is narrower than the top.

Conical = a bore that gets wider as it gets longer

Cylindrical = a bore that is the same width wherever along the bore.

Unfortunately, some of your physics is a little wrong:

Hm. Any tone can be considered a fundamental, actually. The fairly low notes we usually consider "fundamentals" are considered such because they are the lowest notes available on the instrument. The fundamental is simply the slower of two waveforms, while its exact multiple is the "harmonic". Thus, even the fundamentals are harmonic to something... because there are certainly frequencies below even the piano keyboard's range, those tones would be fundamental to their higher relatives!

I'm not entirely sure what you're getting at. The fundamental is the lowest natural note the pipe can play. If the pipe is vented (with an octave or vent key), a note in the harmonic series pops out. The flute of course has no vent key for this purpose and requires breath pressure and embouchure changes in order to go up and down the harmonic series. The flute is, however, the easiest instrument on which to demonstrate the harmonic series. Play a bottom C and then try to go higher without changing the fingering. The next properly sounding note up is C one octave above the fundamental. The next note is G - then C - then C / E / G ... and so on. It is with this knowledge that upper register fingerings (and their slight mis-tunings) can be understood! A 'd' above the stave is normally fingered 'thumb + 2 + 3' (the right hand little finger is irrelevant in this exercise). This is just a way of making a G fingering play a D. Removing the first finger acts like a vent in order to get the second note in the harmonic series of G. (G / G / D / G / etc.)

On saxophone and clarinet, there is a register key [that enables] higher pitches to be played. Double horn and valved trombone have the same mechanism, though the alteration made in the instrument is different in magnitude. Harmonics created on an instrument usually involve changing technique at the mouth rather than pressing a key, so it might be argued that tones produced using register keys are not harmonics.

This is not quite so. The octave keys or vent keys are exactly the same as touching a node on a string to make it vibrate at an harmonic somewhere along the harmonic series. The double horn (there are also some triple horns, for high F - so that they have F / Bb / F') and valved trombone just extend the pipework in order to change the fundamental.

I hope all this is making sense.

There is loads of info on the internet if you want to do some research. Make sure you go to an academic page, though, as there are many web pages out there with mis-information on them.

Edit 2: Sticking a reed on the end of the instrument thereby closing the pipe at one end only confuses things - the clarinet's lowest note is lower than it would be if the end was open because of the cylindrical bore and the closed end.

Actually, I believe the "squeak" a lot of players get before they learn to control tones is an instance of a harmonic on a clarinet. I could be wrong, though. If that's true, playing harmonics on clarinet would involve controlling that "mistake" that beginning players make.

You are correct about squeaks. Technically the "real" range of the clarinet is from E below middle C to Bb in the center of the staff. All the notes above the "break" are technically harmonics, but they sound like "normal" notes and are part of regular clarinet playing. The same is true for most instruments.

A cooler instance of harmonics on the clarinet, however, is to finger a B (middle of the staff), close off the end of the clarinet by setting it the bell on the floor or on your knee (while playing) and "lipping" up and down different notes. These notes sound kinda like controlled squeaks. The notes also belong in the predictable sequence of the harmonic series. Using the same fingering, you can play "charge" "taps" etc... just like a bugle player!

try it.

The more posts I read, the more I am starting to get it. When it was first presented to me, I saw it as simply an "effect" but now I see that the definition of harmonics is extremely broad. Man, every time I ask what I think is a simple question I end up learning a books worth on the topic! I LOVE this place!!! :P

Now you need to create a thread asking about how a pitch is often made up of a collection of overtones. *grin*

For months, I had touse harmonics to get my saxophone to play above a "d", you know the one with the register key.

It was broke, and it got fixed and now it doesn't squeak as much.

Unfortunately, some of your physics is a little wrong:

No, my physics are quite sound (I even have a science prof to back me up); however, as you point out, the "fundamental" on a given instrument is a little different and much more specific. Simply put, one waveform is fundamental to another if the other's frequency is an exact multiple of the first. In the physics of sound, the terms "harmonic" and "fundamental" are relative.

I've never really read anything on the physics of sound. All these concepts about waveforms and such are things I figured out for myself on napkins at lunch, literally. I presented all my reasoning to this science professor, a Dr. Ben Duecker, who confirmed that what I'd figured out was correct. His son is a musician, so he's looked into this stuff a lot.

We are talking about a specific length of pipe or string rather than the random frequency that you're talking about. Of course one waveform is fundamental to another, but you can't argue against the harmonic sequence of a given length.

When you have a string of eight foot and stop it at four foot, you get an octave above the fundamental. When you stop it at six foot, you get the next harmonic - an octave and a fifth. The next is two octaves. These harmonics are not fundamentaly, and that is the principle we've been talking about. We've not been talking about random waveforms but specific notes that are made from a specific fundamental.

I've never really read anything on the physics of sound.

Indeed?

I prefer to rely on research rather than rhetoric of saying 'I confirmed this theory with so-and-so who will mean nothing to you other than sound impressive'.

Another interesting principle to research is as to why French Horns are notorious for their ability to split notes easily. Most brass instruments play notes close to their fundamentals - in the first two/three octaves or so. The range of the french horn is so wide, that at the top (ie, far away from the fundamentals) the notes that come out are so close together that it is very difficult to 'select' which note to play without occasionally going between two or three notes.

I still do not entirely agree with the way you wrote this statement:

Hm. Any tone can be considered a fundamental, actually. The fairly low notes we usually consider "fundamentals" are considered such because they are the lowest notes available on the instrument. The fundamental is simply the slower of two waveforms, while its exact multiple is the "harmonic". Thus, even the fundamentals are harmonic to something... because there are certainly frequencies below even the piano keyboard's range, those tones would be fundamental to their higher relatives!

I think you're possibly trying to introduce 'upper partials' into the argument. If not, I really don't know what you're getting at.

Are you saying that lower notes are possible on a piano without changing the tuning? Or perhaps lower notes with longer or looser strings are possible? The latter is correct, because you'd just be introducing a new fundamental. Note that the piano does not rely on harmonics (ordinarily) for its basic pitches. The string that is typically tuned to A=440Hz has a fundamental of 440Hz. Any upper partials are defining in the tonal quality of the note but arbitrary to this discussion. The note A=220 is one octave lower than A=440, but this is not because the 440Hz is an harmonic of 220Hz for they are different strings! They are their own harmonics.

Each string can sound its own fundamental and a number of harmonics in its own harmonic series. It can't produce a lower sound.

Maybe that's not what you're saying: in which case, you need to clarify some of your statements!

Not quite, Chris. Actually, David, I don't need to clarify anything, you're assuming I'm talking about tones produced by instruments, and I already said I'm not. I'm just talking about the physics of sound.

We've not been talking about random waveforms but specific notes that are made from a specific fundamental.

Yes, I knew that's what you were talking about; I was talking about tones as waveforms, and that's what tones are. While I refer to the relation between tones acoustically, you continually assume I'm referring to the technique of producing them on a specific instrument.

Are you saying that lower notes are possible on a piano without changing the tuning?

Same error. Note that when you read what I said, "there are certainly frequencies below even the piano keyboard's range," I was not talking about frequencies produced by a piano. This should have been obvious from the fact that I said they're outside the instrument's range.

I prefer to rely on research rather than rhetoric of saying 'I confirmed this theory with so-and-so who will mean nothing to you other than sound impressive'.

I didn't say this to make myself sound credible as a scientist or anything, only to illustrate that I like thinking about this stuff. You are taking all of this FAR too seriously, and we don't need to have an argument. We're not even disagreeing on anything, though you seem to see it that way. Simmer down, please, it's uncharacteristic of you to get ruffled like this.

I see. Apologies for assuming you were talking directly about the subject of the thread.

We're not even disagreeing on anything, though you seem to see it that way. Simmer down, please, it's uncharacteristic of you to get ruffled like this.

I wasn't taking anything you were saying as wrong, necessarily - I was questioning how you were describing it. Or being ruffled, as you call it.

Flutes are still conical... *grin*

Flutes are still conical... *grin*

LOL... sticking to your guns, eh? :D Well, I just hope you don't put this as an answer on some test. :)

It's better than saying that a cylindrical bore gets wider... *grin*

I think those pieces are actually by Morel.... (I'm looking at the music right now) They're very cool!

LOL! Where'd you find that picture?

Actually, that's an old system that has a conical bore going the same way as a recorder - ie it gets narrower further away from where the air goes in. It looks like an old Boehm system instrument.