Getting the hard, dark, tone

[david_h]

I was meaning this sort of thing: http://en.wikipedia.org/wiki/Inharmonicity

For some things that you hit it seems to be a case of not even in the same ball park - its just a clang. But for some instruments slight departures might influence percieved 'in tuneness' with other instruments. And confuse an electronic tuner maybe ? Is a flute one of them ?

[Terry McGee]

Woah, this stuff is coming faster than I can handle! Let me see if I can answer maybe one or two matters and then take a break!

Let's imagine we have a typical early 19th century flute, that has a pretty well tuned middle D (oxx xxx) but a quite flat low D (xxx xxx). You play low D blowing at the edge, you get a flat low D. You play middle D blowing at the edge, you get a well tuned middle D. OK so far?

Now let's turn on the Fast Fourier Transform tool and analyse those notes. The "blown at the edge" low D has some low D, some middle D and other harmonics. They are all flat, but are in perfect tune with each other. Because, as mentioned further up, the jet switching action "resets" the clock every cycle.

Play the middle D. It also has some harmonics. They are all in good tune, and are in tune with each other, for the same reason, the switching action resets the clock at every cycle.

Now go back to low D and direct the jet towards the centre of the flute. Because the jet isn't aimed at the edge but is offset from it, the resultant wave is no longer symmetrical - it no longer approximates a sine wave. Less of the energy goes to the fundamental (low D), and more into the harmonics (middle D and above). The cycle time is determined by the amount of time the aggregate amount of air takes to whoosh down the tube and back. If it has to go the full way you get flat low D timing. If it only has to go halfway, you get in-tune middle D timing. If it has a mix of both components, it will take a mix of those timings. As we redirect more and more of our energy from the fundamental to the harmonics, the tuning will shift more and more from that related to the fundamental to that related to the harmonics, in this case from flat to good.

Even though we might have shifted all our energy from the fundamental to the harmonics, we still hear it as low D pitch. That's because our ear can do FFT. If the fundamental of a complex note is completely removed (eg by a notch filter), the brain computes the missing fundamental by detecting the ratios of the harmonics. We really are quite clever (even those who think this topic is boring!).

You can see that if the low D had been in good tune with the rest of the flute, changing from blowing at the edge to blowing down would not have affected the tuning, because both cycle timings were OK.

Are we happy so far? If not, which bit needs clarifying? If so, what's the next question?

Terry

[hans]

From that wikipedia article:

When a string is bowed or tone in a wind instrument initiated by vibrating reed or lips, a phenomenon called mode-locking counteracts the natural inharmonicity of the string or air column and causes the overtones to lock precisely onto integer multiples of the fundamental pitch, even though these are slightly different than the natural resonance points of the instrument. For this reason, a single tone played by a bowed string instrument, brass instrument, or reed instrument does not exhibit inharmonicity.

You could add the flute to the list of instruments which exhibits mode-locking. That is exactly what a player does by playing a note. The constant windstream excites a constant resonance, with exact multiples of the fundamental in the partial harmonics.

[david_h]

Are we happy so far?

Almost thanks

If not, which bit needs clarifying?

Am I right to understand that when blowing down jet switching (mode locking) is still happening and resetting the clock (so harmonics are in tune with each other) but that the resonance of the in-tune middle d is 'taking control of' the jet switching ?

[benhall.1]

OK, thanks David. I get the "inharmonicity" thing now. Though, if a flute is "mode-locked" I'm unclear why it matters. If I'm way off the point, don't worry about me - I'm quite happy here. You just go on without me and enjoy yourselves.

[david_h]

OK, thanks David. I get the "inharmonicity" thing now. Though, if a flute is "mode-locked" I'm unclear why it matters. .

If mode-locked it doesn't matter but we got in a pickle in another discussion over that and someone (maybe me ) brought up what Terry had said. Which is why I was after confirmation from the man himself. If mode-locked the electronic and software tuner bashers will have to find another explanation for them being 'wrong'. Or a better explanation of 'wrong'

[benhall.1]

OK, thanks David. I get the "inharmonicity" thing now. Though, if a flute is "mode-locked" I'm unclear why it matters. .

If mode-locked it doesn't matter but we got in a pickle in another discussion over that and someone (maybe me ) brought up what Terry had said. Which is why I was after confirmation from the man himself. If mode-locked the electronic and software tuner bashers will have to find another explanation for them being 'wrong'. Or a better explanation of 'wrong'

Ah. Right. I think I've caught up ...

[I.D.10-t]

So if we were to take a look at the three eras how do Quantz, Rockstro, and Boehm styles compare?

Under certain circumstances this rule would, of course, require modification, but in any case a sufficient portion of the lip should be left free to protrude so that it may cover from one to three-quarters of the area of the mouth-hole, as may be required.

To produce a soft, clear tone in the upper notes, the lip must cover about three parts of
the mouth-hole, and be hardened by the pressure of the flute;- but here the upper lip must project, and the soft or interior part only come in contact with the lower lip [more pouting?]. The embouchure [opening] must be proportionately small with the reduced size of the mouth-hole, and the breath (jet) forming a line nearly horizontal.

So is the lower lip acting as a shutter, changing depending on the note?

[hans]

Now go back to low D and direct the jet towards the centre of the flute. Because the jet isn't aimed at the edge but is offset from it, the resultant wave is no longer symmetrical - it no longer approximates a sine wave. Less of the energy goes to the fundamental (low D), and more into the harmonics (middle D and above). The cycle time is determined by the amount of time the aggregate amount of air takes to whoosh down the tube and back. If it has to go the full way you get flat low D timing. If it only has to go halfway, you get in-tune middle D timing. If it has a mix of both components, it will take a mix of those timings. As we redirect more and more of our energy from the fundamental to the harmonics, the tuning will shift more and more from that related to the fundamental to that related to the harmonics, in this case from flat to good.

Terry, I am sorry, I don't get you!
First: "The cycle time is determined by the amount of time the aggregate amount of air takes to whoosh down the tube and back."
You are talking about a wave front, right? Not actual volume of air going down and up the tube. But all finger holes are closed for bottom D, so the wave goes all the way in all cases, if you blow softly, a "pure" D, or blow a "hard" D, or even overblow and produce a first octave D. So why would a change from soft to hard, from purer, more sinusoidal, to more edgy, reedier, change the frequency of the fundamental? I think that was David's question too.

You seem to suggest that there is a mix of frequencies from the fundamental and its harmonics (multiples) and from the first overblown note and its harmonics, the latter of which may be more in tune (relative to other notes) than a"flat" bottom D.

Or do you think that the flat bottom D has actually partials which are not multiples of the fundamental, but are in tune with the first overblown note, first octave D?

[Rob Sharer]

Bully for him, but this stuff bores me senseless.

So go play your flute.

Will do, of course. I've said me piece.

By the way, I'm oddly touched that you recognize my moods!


Rob

[Terry McGee]

Terry, I am sorry, I don't get you!

Don't apologise, it just means I'm not explaining it well enough. I'm not finding it easy to find the right words!

First: "The cycle time is determined by the amount of time the aggregate amount of air takes to whoosh down the tube and back."
You are talking about a wave front, right? Not actual volume of air going down and up the tube.

Correct. The air doesn't go so far, it's just the wavefront.

But all finger holes are closed for bottom D, so the wave goes all the way in all cases, if you blow softly, a "pure" D, or blow a "hard" D, or even overblow and produce a first octave D.

This stuff is hard because we can't see it. Let's move temporarily into something we can see. Play the D string of a guitar, and the whole thing vibrates, with maximum movement ("displacement") at the midpoint. Pluck it again, but with your finger lightly resting on the string at the midpoint (fret 12), and it will play the second harmonic. Now there is a node (NO DisplacEment) at the midpoint, and maximum displacement at the 1/4 and 3/4 points. Both halves of the string are vibrating separately, in unison with each other, at the octave.

With the flute the same happens. On the tube we can play low D (xxx xxx) or middle D (oxx xxx). Instead of laying our finger on the middle of the string, we open a hole at the middle of the tube, making it impossible for the lower note to sound. So only the higher one does.

We can take the analogy further. If we go back to playing the whole string, and pluck in the middle, we get a very round low D, the guitar equivalent of blowing at the edge. If we pluck near to the bridge, the equivalent of blowing downwards in the flute, we get a harder D which is a mix of pure full-string sound, and lots of harmonics caused by the sections of string vibrating separately.

Coming back to the flute then, we can see that middle D does use up the whole tube, but that there are two vibrating air columns in there, sitting end-to-end. At that point it's interesting to contemplate what a different world those two systems are living in. One of them enjoys the freedom of the head and large end of the bore down to hole L1. The second system is forced to endure the tight end of the bore. Oh those lucky vibrating air columns that get born in Boehm flutes!

So why would a change from soft to hard, from purer, more sinusoidal, to more edgy, reedier, change the frequency of the fundamental? I think that was David's question too.

Good question. It doesn't actually change the fundamental frequency - that's locked in by the physical dimensions. What it does is eliminate it (more or less) from the mix, allowing the two serial middle D resonances to set the timing.

You seem to suggest that there is a mix of frequencies from the fundamental and its harmonics (multiples) and from the first overblown note and its harmonics, the latter of which may be more in tune (relative to other notes) than a"flat" bottom D.

Or do you think that the flat bottom D has actually partials which are not multiples of the fundamental, but are in tune with the first overblown note, first octave D?

Best way to look at is is that the length of tube set out by the fingering (and allowing for end effects like my ugly face hanging over the embouchure hole, and the finite size of the D hole, modified by the C# and end section), has a series of resonances possible to it, notably D4, D5, G5, D6, etc. Their frequencies are pretty much set in concrete, apart from our ability to lip all of them up or down a little. If the flute were perfect, they would also be in perfect tune with each other. But, given the extreme complexity of the tube shape we talked about earlier (the lack of symmetry for both ends of the tube), that's not likely. We makers try to do our best!

So if you play them all separately, you will get all those notes with their variable tunings. If you can conspire to play only some of them, you'll get a tuning based on the mix of harmonics included.

In most flutes, the maker has managed to get middle D pretty good, even if low D is really flat. If our mix is low D prominent, the mix will be flat. If we can tune out low D, we can eliminate our worst problem. And we get a nice reedy tone at the same time.

Hope that's getting clearer!

Terry

[an seanduine]

Perhaps this article might help: http://www2.slac.stanford.edu/vvc/theory/resonance.html

Bob

[Denny]

oh no, not .... Galloping Gurdy again

Good move with the strings Terry.

We're still 4 to 5 pages too early to mention the back of the throat/inside of mouth bit, ain't we?

[an seanduine]

Flutes of course, are resonant cavities, rather like the vacuum between some eyes,not strings.
Galloping Gurty, of course, is much closer to a string.

Oh,no! String Theory again

Bob

[Terry McGee]

We're still 4 to 5 pages too early to mention the back of the throat/inside of mouth bit, ain't we?

Yeah, I think so, especially on a family website like this.

I guess you're talking about the alleged impact on tone of resonances in the mouth and vocal cavities? A very interesting one because it's hard to see much scope for interaction across the jet (the pushing string uphill problem). But it should be possible to test for it by adding a variable volume artificial mouth at the back of the artificial lips in the artificial flute blower. I'll take that one on notice!

Subduction Leads to Orogeny

Never take getting your schist together for granite.

Terry