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#1 2010-10-01 13:56:32

PSmith
Member
From: Vancouver, BC
Registered: 2008-09-08
Posts: 29

Desgining for harmonics

I am studying a piece for jinashi that calls for several notes to be played as harmonics (overtones) in the 3rd octave. I am working on a hocchiku what will bring out these harmonics. I am interested in what aspects of flute design are best for this. What pointers does everyone else have?


Longer, narrow bores give more harmonics. Consider Koncovka overtone flutes that have 50:1 aspects ratio (ratio of bore width to length.)

Navaching: Want more harmonics? Engineer in more backpressure [via aspect ratio] and make the holes bigger.

Navaching: A narrow and/or shallow utaguchi favors the harmonics and upper registers (and lowers the pitch.)

Toby: Actually, rounding the edges of the holes somewhat is ALWAYS desirable acoustically, both inside (undercutting) and outside. Sharp edges anywhere where air flows cause turbulence, robbing acoustic efficiency and actually hard-limiting sound output at higher dynamic levels.

What about bore surface, rough versus lacquered?


And yes, my wife is complaining about the sustained high pitches as I struggle at them. Can I come over to your place to practice?

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#2 2010-10-02 07:59:05

Toby
Shakuhachi Scientist
From: out somewhere circling the sun
Registered: 2008-03-15
Posts: 405

Re: Desgining for harmonics

Coupla things. Yes, a narrow bore favors harmonics, as does a smooth bore. I doubt that the utaguchi really matters, as it is all a matter of jet timing, and that is controlled by the embouchure, jet length (lips to utaguchi edge) and blowing pressure. Backpressure? That's bullshit. A narrow bore favors high harmonics but not because of backpressure, and be aware that a narrow bore favors higher modes at the expense of power in the first mode (otsu). Yes, larger holes can help, but be careful because screwing with the sizes too much can affect notes that depend on cross-fingerings (a hole closed below a hole that is open).

The main thing that affects overtones, though, is the bore aspect, as in the actual geometry of the bore: if that is not correct the harmonics will no longer be in correct integer ratios with the fundamental. This does not create "inharmonic" harmonics, since there is a phenomenon called "mode-locking", in which the dominant frequency forces all the partials into line, but if the actual resonances of the tube are incorrect, it makes the partials weaker (muddy sound, or resistance, or poor response, or all of those). More importantly, when you blow up to the kan and dai-kan, there is no more fundamental to rule the roost, and the notes get out of tune, or very difficult to play, or sometimes will not play at all--especially in the third octave.

On a jinashi, life gets difficult, as we are more or less constrained to the bore that nature gave the bamboo. So it is more or less a matter of luck. I once made a 2.6 jinashi at a John Neptune workshop at Meijiro. I arrived late, and all the pretty bamboo culms were gone. I took one that had a funny curve, so that I had to make it with a convex curve, like an alto clarinet. But acoustically, it was the best piece of all, and plays all the way up to the top of the dai-kan.

I do suggest that you work hard with the garibo to bring the diameter of the bore at the nodes as close as possible to that of the bamboo above and below. You do not want "waves" in the bore--you want the minimum amount of perturbation possible. And most definitely get it as smooth as possible. This means a hell of a lot of sanding, but for the dai-kan this is helpful. But at the end of the day, if the bore geometry is not good, you will not get a good third octave.

Toby

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#3 2010-10-02 11:39:40

Yungflutes
Flutemaker/Performer
From: New York City
Registered: 2005-10-08
Posts: 1061
Website

Re: Desgining for harmonics

PSmith wrote:

I am studying a piece for jinashi that calls for several notes to be played as harmonics (overtones) in the 3rd octave. I am working on a hocchiku what will bring out these harmonics. I am interested in what aspects of flute design are best for this. What pointers does everyone else have?

Navaching: A narrow and/or shallow utaguchi favors the harmonics and upper registers (and lowers the pitch.)

Yes. In my experience, shallower utaguchi facilitates the highest notes. Pitch depends upon player.

What about bore surface, rough versus lacquered?

Yes, Smooth and lacquered bore brings out the higher partials.

If you're looking to tweak a particular harmonic, try moving a tuning bead around the top 1/4 of the flute first.

And yes, my wife is complaining about the sustained high pitches as I struggle at them. Can I come over to your place to practice?

Yes! M-F, 10am-2:30pm. Upper West Side, NYC


"A hot dog is not an animal." - Jet Yung

My Blog/Website on the art of shakuhachi...and parenting.
How to make an Urban Shakuhachi (PVC)

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#4 2010-10-02 18:50:39

Itamar Foguel
Member
From: Israel
Registered: 2009-09-13
Posts: 120
Website

Re: Desgining for harmonics

This is all very interesting...
im still dreaming of the day i will be able to collect and edit the info on this forum and make myself a small makers booklet...
since up until now this forum has been my best  source of professional info (still looking up for the day i would be able to afford a trip abroad to meet a pro in person) better then the limited amount of  books on the subject and other sites...

If somebody is up to compile the stuff on this forum i would be more then glad to help.

and again, all the input here is very much appreciated,
thank you.

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#5 2010-10-04 00:15:42

Alan Adler
Member
From: Los Altos, California
Registered: 2009-02-15
Posts: 78

Re: Desgining for harmonics

You can find photos and data on my experimental flutes with wide blowing edges elsewhere in this forum.  I've tested edge-widths ranging from about 50% of bore to 100%.  The widest edges gave the greatest harmonic timbre.  Reducing edge-width only slightly (from 100% of bore down to about 80%) substantially reduced harmonic content.

I've also noted that thin-walled tubes give greater harmonic content.  I've tried plastic and metal ranging from about 0.7mm to 4mm.  Thinner has more harmonics, but I haven't noticed much change below about 1.5 mm. 

Very sharp edges also enhance harmonics and allow the pipe to speak more readily.  I use a microscope when sharpening my edges.

Shakuhachi, baroque recorders, and baroque flutes all have tapered bore.  Cylindrical bores greatly enhance harmonics.  Oboes have expanding bores.  I'd like to try that some time.  I like the timbre of oboes, which are rich in even harmonics.

Cross-fingering chokes harmonics.

Of course embouchure has a great affect.  Varying the timbre with my embouchure is an aspect of end-blown flute playing that I especially enjoy.

Finally, power has a big effect.  Blowing stronger adds harmonics.

Best,

Alan

Last edited by Alan Adler (2010-10-04 00:29:56)

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#6 2010-10-04 03:37:25

Toby
Shakuhachi Scientist
From: out somewhere circling the sun
Registered: 2008-03-15
Posts: 405

Re: Desgining for harmonics

I'd like to add a few comments to Perry and Alan.

Most probably a shallower utaguchi facilitates harmonics by making it easier for the player to reduce the distance between lip opening and utaguchi edge. In terms of jet timing, distance is a first-order function while speed is a second-order function, IOW to achieve the octave jump, a player has to either blow four times as hard or reduce the jet length by half, and it is obvious which of these is easier. But they are not exactly the same. Reducing the jet length generally shades more of the top opening, which lowers pitch. Simply changing the jet length would result in a rather weak and flat octave. Blowing harder raises pitch, so blowing four times as hard would tend to make the octave loud and somewhat sharp. It also changes the timbre, as described below. Therefore experienced players change both blowing speed and jet length to achieve the desired pitch, dynamic and timbre.

Alan has some interesting observations, but we need to explore them a bit more deeply. First of all, there is no acoustical explanation as to why a thinner-walled tube would produce different harmonic content. My guess is that this has to do with what happens at the blowing edge (if it is indeed true) and is not due to different vibrations at the tube walls. As I mentioned, recent research into the vibration of tube walls has shown no significant vibration even when the tube is 15 micrometers thick (1/7 the thickness of a sheet of paper), and even when the tube is forced into significant vibration by physically deforming the cylindrical tube into an ellipse, those vibrations only affect a few notes and even then only very slightly.

Alan, I assume when you speak about sharp edges you are speaking about the blowing edge. I did not mention this, but it is indeed an important condition for achieving more content in the upper partials.

The question of taper is rather complex. A flute is essentially a tube open at both ends, speaking of acoustic boundary conditions. This is quite different than an oboe or a clarinet, which is acoutically a tube closed at one end. A closed tube produced only odd harmonics if it is cylindrical (clarinet or panpipes), but all harmonics if it is conical (oboe or saxophone). A cylindrical tube open at both ends (flute) produces all harmonics, and a positively flaring tube on a flute is musically useless. A reverse taper on either a closed or open tube will have two (generally rather minor) effects: First, it will stretch the modes a bit, making the lower octave a bit flat compared to the upper. This allows the player to blow harder in the lower notes without the notes going sharp. Second, it offsets the acoustic minima compared to the maxima, and this has the effect of stabilizing the pitch somewhat in the higher notes, but both these effects are quite minor.

Cross-fingerings reduce harmonics due to the effects of an open-hole lattice. However in the dai-kan it is often necessary to cross finger notes to achieve the correct venting, in order to detune and/or inhibit the lower resonance enough that the higher resonance can become primary, so this observation does not really apply to playing in the dai-kan.

Embouchure is important. The size of the jet stream, governed by the lip opening, has some effect on harmonic structure, as does the angle at which the jet intersects the blowing edge. Blowing power is highly important. It has been found that harmonics increase at the square of their order as blowing speed increaes. IOW, blowing twice as hard means that (theoretically) the fundamental gets twice as loud, the octave harmonic gets 4x as loud, the 12th 9x, the second octave 16x, etc. Practically this is limited by many factors, but harmonic content is highly increased by harder blowing.

Toby

Last edited by Toby (2010-10-04 03:42:16)

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#7 2010-10-04 19:36:44

Karmajampa
Member
From: Aotearoa (NZ)
Registered: 2006-02-12
Posts: 574
Website

Re: Desgining for harmonics

We can change the shape of our embouchure from an 'Oooo' single point blow to an 'Eeee' with a frown wide line blow. This of course takes practice to get good control and also alters the timbre/harmonics.
This increases the quantity of jet contact with the edge.

I like to incorporate both postures depending on what sound I want.
K.


Kia Kaha !

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#8 2010-10-05 00:03:53

Alan Adler
Member
From: Los Altos, California
Registered: 2009-02-15
Posts: 78

Re: Desgining for harmonics

Greetings Toby,

Regarding thin walled tubes.  I do not think the walls vibrate.  I doubt that there would be any timbre effect attributable to wall thickness for flutes which have no finger holes. 

Rather the short effective "acoustic chimney height" of the finger holes in thin walled tubes facilitate harmonics. 

As you and I discovered together, my thin walled tubes do not change pitch when cross-fingered (though the timbre is muted), yet we found thicker walled tubes did change pitch when cross-fingered.

Incidentally, the distance from the gap between my lips to my blowing edge is about 4 mm.  What is that distance (to the center of the arc) for a shakuhachi?

Best regards,

Alan

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#9 2010-10-05 03:48:26

Toby
Shakuhachi Scientist
From: out somewhere circling the sun
Registered: 2008-03-15
Posts: 405

Re: Desgining for harmonics

Hi Alan,

Ah yes, I had forgotten about chimney height. Yes, in fact the height of tone holes does change their characteristics. More depth increases effective impedance, which makes them appear smaller, and that will lower the cutoff frequency and inhibit higher harmonics. 4mm would be about the deep limit for a shakuhachi utaguchi. Generally I believe it ranges between 2-3 mm, but maybe Perry or Karmajampa could confirm this.

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#10 2010-10-05 04:23:40

Karmajampa
Member
From: Aotearoa (NZ)
Registered: 2006-02-12
Posts: 574
Website

Re: Desgining for harmonics

I am with Toby on 2-3 mm depth for the utaguchi curve. I also like to widen the curve diameter by shaping the underside.
I also think a shallow curve gives greater meri response though this is  dependant on the shape of the rest of the chin-rest shaping, and what is not often mentioned is not everyone's face has tfhe same profile and proportions. A bit of customizing may be useful.

K.


Kia Kaha !

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#11 2010-10-06 00:10:35

Alan Adler
Member
From: Los Altos, California
Registered: 2009-02-15
Posts: 78

Re: Desgining for harmonics

But what is the approximate distance from the center of the arc to the gap in your lips while you are playing?

Best,

Alan

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#12 2010-10-06 01:01:39

Karmajampa
Member
From: Aotearoa (NZ)
Registered: 2006-02-12
Posts: 574
Website

Re: Desgining for harmonics

Playing 'keri' I may be close or slightly outside the depth of the curve, i.e. close to the line dissecting the outer points of the curve.
Playing 'meri' my lips are almost touching the edge, possibly only 1mm from the bottom of the curve. If I close the opening in my playing lips they will touch each side of the edge, i.e. upper and lower.
But my flutes vary from 2-5mm in the depth of the curve. This seems to vary with the diameter of the bore at the blowing end which influences how much the lips enter the bore. so with a wider bore the curve depth may be a little deeper.

Good point.

The angle of the utaguchi wedge is relevant. I use the bamboo, I don't make an insert. While the bamboo edge is quite sharp and strong, there is also a bit of fine  serration from the fibres

K.


Kia Kaha !

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#13 2010-10-06 22:43:58

Toby
Shakuhachi Scientist
From: out somewhere circling the sun
Registered: 2008-03-15
Posts: 405

Re: Desgining for harmonics

Alan,

Getting a note to play depends on the timing of the air jet--the pulse that travels across the jet and makes it divert in and out of the hole must be "in sync" with the standing wave in the tube, in order to reinforce that standing wave. Jet timing depends on two factors, jet length (distance from lip aperture to blowing edge) and air speed. If you blow harder, you can have a longer jet (kari) and if you have a shorter jet you can blow more softly (meri). But the relationship of jet timing to tube length is a fixed quantity, so to speak, and does not vary according to player or flute.

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#14 2010-10-06 23:47:50

Karmajampa
Member
From: Aotearoa (NZ)
Registered: 2006-02-12
Posts: 574
Website

Re: Desgining for harmonics

That is interesting as I have always primarily regarded 'meri' and 'keri' as relating to pitch and the opening and closing of the utaguchi aperture, but as you point out, soft and hard blowing is also an aspect here, leaving volume aside for the moment.

K.


Kia Kaha !

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#15 2010-10-07 03:17:39

Toby
Shakuhachi Scientist
From: out somewhere circling the sun
Registered: 2008-03-15
Posts: 405

Re: Desgining for harmonics

It is a combination of both decreasing/increasing the end correction of the the top opening and raising/lowering the pitch through harder/softer blowing. They are interactive. When you meri you decrease the jet length, so that you have to blow less forcefully in order not to break up to the next higher mode. This automatically also lowers pitch. And of course by decreasing the jet length you end up covering more of the end hole, which decreases pitch further.

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#16 2010-10-07 11:22:52

Yungflutes
Flutemaker/Performer
From: New York City
Registered: 2005-10-08
Posts: 1061
Website

Re: Desgining for harmonics

Toby wrote:

Hi Alan,

Ah yes, I had forgotten about chimney height. Yes, in fact the height of tone holes does change their characteristics. More depth increases effective impedance, which makes them appear smaller, and that will lower the cutoff frequency and inhibit higher harmonics. 4mm would be about the deep limit for a shakuhachi utaguchi. Generally I believe it ranges between 2-3 mm, but maybe Perry or Karmajampa could confirm this.

Hi Toby, Yes, 2-3mm depth is ideal on most flutes for most people today. It is an amiable depth for the "middle way". Many of the oldest flutes that have come through my shop have no depth at all (even new ones made by Okuda sensei). And when I visited the Seikado workshop in Kyoto in early 2003, the lowest dip of the utaguchi depth on some of Kitahara's most modern Tozan flutes were close to 5mm.

Essentially, how a player plays and her style dictates a lot of the design of a shakuhachi.

Hope this helps.

Namaste, Perry


"A hot dog is not an animal." - Jet Yung

My Blog/Website on the art of shakuhachi...and parenting.
How to make an Urban Shakuhachi (PVC)

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#17 2010-10-07 14:10:28

radi0gnome
Member
From: Kingston NY
Registered: 2006-12-29
Posts: 1030
Website

Re: Desgining for harmonics

Toby wrote:

They are interactive. When you meri you decrease the jet length, so that you have to blow less forcefully in order not to break up to the next higher mode.

I understand that some people like to blow the meri notes louder, at least sometimes, and sacrifice a nice clear quiet tone for a more "sandy" but louder one by doing so. What's going on acoustically with that?


"Now birds record new harmonie, And trees do whistle melodies;
Now everything that nature breeds, Doth clad itself in pleasant weeds."
~ Thomas Watson - England's Helicon ca 1580

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#18 2010-10-07 22:57:06

Toby
Shakuhachi Scientist
From: out somewhere circling the sun
Registered: 2008-03-15
Posts: 405

Re: Desgining for harmonics

That's turbulence at the blowing edge.

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