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Tube of delight!

#1 2008-08-25 06:28:38

Kiku Day
Shakuhachi player, teacher and ethnomusicologist
From: London, UK & Nørre Snede, DK
Registered: 2005-10-07
Posts: 922
Website

Shakuhachi measurements

Dear all.

As a part of my PhD thesis, I have measured and collected measurements for hundreds of shakuhachi. I can see now that I especially need to have more measurements of jinuri/jiari shakuhachi than I have.
So, I was wondering if you would be kind to help me with this, and send me measurements of your own shakuhachi to me, please. smile
These numbers will be used to compare jinashi and jinuri's development in construction over time.

The measurement I need are the following in metric (thus millimeters - if you can't measure in metric please do send in imperial and I can convert later).

• Maker:
• Date of measurements taken:
• Length of the whole flute:
• Distance between bottom hole to hole 1 (from edge of hole - not middle):
• Distance between hole 1 and 2:
• Distance between hole 2 and 3:
• Distance between hole 3 and 4:
• Distance between hole 4 and top of flute:
• Distance between hole 5 and top of the flute:
• Depth of mouthpiece (just the few millimeter little dip of the blowing edge):
• Angle of mouthpiece: (If you use the side of the flute as the one straight line. Since this needs special equipment never mind if you don't have it:
• Width of mouthpiece (from where the little dip begins to the other side):
• Weight of the flute (if not possible never mind):
• Outer circumference (measured 10 cm down from the top):
• Width of hole 1 vertical:
• Width of hole 1 horizontal:
• Width of hole 2 vertical:
• Width of hole 2 horizontal:
• Width of hole 3 vertical:
• Width of hole 3 horizontal:
• Width of hole 4 vertical:
• Width of hole 4 horizontal:
• Width of hole 5 vertical:
• Width of hole 5 horizontal:
• Bottom hole vertical:
• Bottom hole horizontal:
• Top hole vertical:
• Top hole horizontal:


Hope you don't think this is too much to ask.
I hope you can help! I would be very grateful to you smile

You can send the results to: kiku [at] kikuday.com or just hit the reply bottom here... although the results may only be fun for me.
But.... we could also say if you post the measurements here, we can have a competition who sends most measurements of different flutes. The winner will receive... an Olympic gold medal! wink

Last edited by Kiku Day (2008-08-25 07:38:15)


I am a hole in a flute
that the Christ's breath moves through
listen to this music
Hafiz

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#2 2008-08-25 11:27:26

Kiku Day
Shakuhachi player, teacher and ethnomusicologist
From: London, UK & Nørre Snede, DK
Registered: 2005-10-07
Posts: 922
Website

Re: Shakuhachi measurements

Yep, anything as long as it is a jinuri !
Apparently I have been biased when doing the data collecting in Japan and totally forgot about jinuri (or rather my PhD was at a point where I didn't see that jinuri measurements were necessary too). So yes! Any jinuri with or without hanko, names and which-ever length would be much appreciated!

Perhaps you could take your measuring gear with you to Prague and measure people's flutes. They may only think you are almost as crazy as me!
And perhaps it will make me share my favourite Croyden Gear out a little more easily! wink

Last edited by Kiku Day (2008-08-25 11:29:19)


I am a hole in a flute
that the Christ's breath moves through
listen to this music
Hafiz

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#3 2008-08-25 18:26:16

Horst Xenmeister
Shiham
From: Germany
Registered: 2007-05-26
Posts: 69
Website

Re: Shakuhachi measurements

I Horst Xenmeister go to Prague, against good bier und wurst. But to measure things is against Zennatur. Does cast form or PVC necessity measure bore? No. Straight impact. Just blowing. Sound is not measured except by birds. Vary importanting that wurst is not longer than 1,3 in the length. In this case is better more short. Short best way.


i am horst

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#4 2008-08-26 02:39:44

Kiku Day
Shakuhachi player, teacher and ethnomusicologist
From: London, UK & Nørre Snede, DK
Registered: 2005-10-07
Posts: 922
Website

Re: Shakuhachi measurements

Horst, you are going to Prague?I should have gone too...
Measuring may be against zennatur, but I need to do it for my research... sorry. Many makers walk around measuring shakuhachi, so measuring is no new phenomenon to shakuhachi. I am not measuring to create the ultimate shakuhachi. wink
But I would be very interested to know welche Wurst must nicht lang werden? And why not more than 1.3? Is that because it would be uncomfortable to eat?


I am a hole in a flute
that the Christ's breath moves through
listen to this music
Hafiz

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#5 2008-08-26 10:11:08

Kiku Day
Shakuhachi player, teacher and ethnomusicologist
From: London, UK & Nørre Snede, DK
Registered: 2005-10-07
Posts: 922
Website

Re: Shakuhachi measurements

THANK YOU fouw.

Many precious drops of whisky will be waiting for you when we meet next time (hopefully not in that long).
Thank you for all your work measuring the two shakuhachi.
They will go into my giant excel sheet.


I am a hole in a flute
that the Christ's breath moves through
listen to this music
Hafiz

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#6 2008-08-29 05:31:53

Kiku Day
Shakuhachi player, teacher and ethnomusicologist
From: London, UK & Nørre Snede, DK
Registered: 2005-10-07
Posts: 922
Website

Re: Shakuhachi measurements

Just want to say thank you to the people who have sent me emails with measurements.
I could easily use more! wink


I am a hole in a flute
that the Christ's breath moves through
listen to this music
Hafiz

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#7 2008-09-03 08:26:12

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

Re: Shakuhachi measurements

Kiku--

I will try to send some measurements soon. Are you interested in all sizes or only 1.8s?

I'm sorry to have to say this, but the most important measurements would be those of the bore: this is what has changed most over time. I do know, however, that most people do not have the tools to do these measurements.

More later.

Toby

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#8 2008-09-03 08:47:36

Kiku Day
Shakuhachi player, teacher and ethnomusicologist
From: London, UK & Nørre Snede, DK
Registered: 2005-10-07
Posts: 922
Website

Re: Shakuhachi measurements

Toby wrote:

Kiku--

I will try to send some measurements soon. Are you interested in all sizes or only 1.8s?

I'm sorry to have to say this, but the most important measurements would be those of the bore: this is what has changed most over time. I do know, however, that most people do not have the tools to do these measurements.

More later.

Toby

Hi Toby.

That is extremely nice of you. I am looking forward for the measurements and I am interested in all sizes as long as they are jinuri.
I am really grateful to everybody who have sent me measurements! Thank you all!
The forum is at its best when we can help each other.

I will be looking into the bore shapes of the 60 modern jinashi shakuhachi I have x-rayed as that is my main topic - apart from the practical side which is playing new pieces. These x-ray pictures I am comparing with the x-rays of Edo period jinashi that Shimura et al have taken and with some x-rays Tairaku has taken of some excellent shakuhachi from his collection.
I didn't think of that it could be useful to compare some of the measurements of jinashi shakuhachi with measurements from jinuri when I was on fieldwork.... and this is the reason for why I have to ask the shakuhachi community for help.
The measurements of the holes do give me an indication of the bore shape but they surely don't tell me the whole story, of course.


I am a hole in a flute
that the Christ's breath moves through
listen to this music
Hafiz

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#9 2008-09-11 08:51:11

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

Re: Shakuhachi measurements

Kiku,

Just a question before I start measuring: you say you want the distance from the bottom hole (edge) to hole 1. Do you mean the end of the flute to the bottom of hole 1, or the front edge of the bottom hole, go up, bend around the root end and on to the bottom of hole 1?

FWIW, acoustically the important measurement would be from the bottom edge of the flute to the center of hole 1. If you measure from the bottom hole around the edge to hole 1 you are getting the thickness of the bottom of the culm into the equation, which has no bearing on anything but aesthetics, so I'm a bit confused.

Just to be precise, when you specify the distance between the holes, do you mean from the center of one hole to the center of the other, or the top of the lower hole to the bottom of the upper one.

I just want to get this right.

BTW Meijiro has a wonderful tool for measuring the inside of shakuhachi: something like a dial caliper with extremely long spring-loaded arms--about 25 cm. Unfortunately it is quite expensive (about 60,000 yen IIRC), but if you are really serious about doing precise bore measurements it would come in very handy. I use a set of different-diameter rubber discs which are OK, but can't precisely measure at all points (obviously) and can't accurately measure non-circular bores.

Toby

Last edited by Toby (2008-09-11 08:56:35)

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#10 2008-09-11 10:08:37

edosan
Edomologist
From: Salt Lake City
Registered: 2005-10-09
Posts: 2185

Re: Shakuhachi measurements

Toby wrote:

If you measure from the bottom hole around the edge to hole 1 you are getting the thickness of the bottom of the culm into the equation, which has no bearing on anything but aesthetics, so I'm a bit confused.

Just to be precise, when you specify the distance between the holes, do you mean from the center of one hole to the center of the other, or the top of the lower hole to the bottom of the upper one.

I just want to get this right.

I was wondering about this as well. Doesn't make complete sense to me, either.


Zen is not easy.
It takes effort to attain nothingness.
And then what do you have?
Bupkes.

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#11 2008-09-11 14:59:43

Kiku Day
Shakuhachi player, teacher and ethnomusicologist
From: London, UK & Nørre Snede, DK
Registered: 2005-10-07
Posts: 922
Website

Re: Shakuhachi measurements

Toby wrote:

Kiku,

Just a question before I start measuring: you say you want the distance from the bottom hole (edge) to hole 1. Do you mean the end of the flute to the bottom of hole 1, or the front edge of the bottom hole, go up, bend around the root end and on to the bottom of hole 1?

FWIW, acoustically the important measurement would be from the bottom edge of the flute to the center of hole 1. If you measure from the bottom hole around the edge to hole 1 you are getting the thickness of the bottom of the culm into the equation, which has no bearing on anything but aesthetics, so I'm a bit confused.

I meant the bottom edge on the front side of the flute to the beginning of hole 1 - e.g., the bottom end of hole 1. I have created a system that will calculate the middle of the hole by using the vertical and horizontal measurements of it - which would be more accurate than a human saying 'this is about the middle' using eyesight. Sorry not to have been able to express that clearly enough. And thank you for making this clarification possible.

Toby wrote:

Just to be precise, when you specify the distance between the holes, do you mean from the center of one hole to the center of the other, or the top of the lower hole to the bottom of the upper one.

The top of the lower to the bottom of the upper - for the same reason as above. smile

Toby wrote:

BTW Meijiro has a wonderful tool for measuring the inside of shakuhachi: something like a dial caliper with extremely long spring-loaded arms--about 25 cm. Unfortunately it is quite expensive (about 60,000 yen IIRC), but if you are really serious about doing precise bore measurements it would come in very handy. I use a set of different-diameter rubber discs which are OK, but can't precisely measure at all points (obviously) and can't accurately measure non-circular bores.

Yeah, they are great. I didn't get one because my project is more about jinashi than jinuri, and jinashi can often be too long for this measuring tool. Some jinashi have too many places too narrow for it to pass too... so I used x-ray instead - which has its downsides too if it was necessary with extremely precise measurements. But for my projects looking at the bore shapes x-ray proved to be great.

Toby, thanks for doing this. And again thank you to all of you who have sent me measurements ! It is much appreciated ! ! !

Kiku


I am a hole in a flute
that the Christ's breath moves through
listen to this music
Hafiz

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#12 2008-09-11 21:38:31

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

Re: Shakuhachi measurements

Kiku,
Two final (I hope) questions:  1) In measuring from hole 4 to the top of the flute: should the upper limit be the highest edge of the utaguchi (before the dip) or the bottom of the dip? I assume the former...

and 2) For an overall length, should the measurement be from the bottom of the root to that same point along the front or the side? This can be significantly different with curved bamboo.

Best,

Toby

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#13 2008-09-11 23:16:04

Yooper
Member
From: Michigan, on the WI border
Registered: 2007-11-26
Posts: 57

Re: Shakuhachi measurements

Are any of those x-rays available for viewing online?


"Simple and artless."

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#14 2008-09-12 03:11:56

Kiku Day
Shakuhachi player, teacher and ethnomusicologist
From: London, UK & Nørre Snede, DK
Registered: 2005-10-07
Posts: 922
Website

Re: Shakuhachi measurements

Toby wrote:

Two final (I hope) questions:  1) In measuring from hole 4 to the top of the flute: should the upper limit be the highest edge of the utaguchi (before the dip) or the bottom of the dip? I assume the former...

1) You are right; the former

Toby wrote:

and 2) For an overall length, should the measurement be from the bottom of the root to that same point along the front or the side? This can be significantly different with curved bamboo.

I usually do it on the front side, but I will try to follow the curve so that the measured result is as close as possible to the length of the bamboo. And again as 1) I measure up to the highest edge of the utaguchi.

Yooper wrote:

Are any of those x-rays available for viewing online?

I haven't finished the analysis of the x-ray photos yet, so I haven't put anything up in public yet. But you are right, it might be a good idea to put some online. It will have to be when I am finished with the writing... so sometime early next year. It is a good idea, Yooper. Thanks for mentioning it.


I am a hole in a flute
that the Christ's breath moves through
listen to this music
Hafiz

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#15 2008-09-12 10:21:00

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

Re: Shakuhachi measurements

Kiku:

First one--a 2.0 "collective effort" by the three makers listed. Made sometime (I guess) between 1930-1950.

• Maker: Chikuyo Ebinuma, Yasuhiro, Chikusen
• Date of measurements taken: 2008/09/12
• Length of the whole flute:  607 (2.0 shaku)
• Distance between bottom hole to hole 1: 125.20
• Distance between hole 1 and 2: 49.87
• Distance between hole 2 and 3: 49.56
• Distance between hole 3 and 4: 51.27
• Distance between hole 4 and top of flute: 285.5
• Distance between hole 5 and top of the flute: 241.0
• Depth of mouthpiece (just the few millimeter little dip of the blowing edge): 4.5
• Angle of mouthpiece: 30.6 degrees
• Width of mouthpiece (from where the little dip begins to the other side): 17.8
• Weight of the flute: 402 grams
• Outer circumference (measured 10 cm down from the top): 110.49
• Width of hole 1 vertical: 11.42
• Width of hole 1 horizontal: 10.31
• Width of hole 2 vertical: 10.53
• Width of hole 2 horizontal: 10.48
• Width of hole 3 vertical: 9.84
• Width of hole 3 horizontal: 9.32
• Width of hole 4 vertical: 10.69
• Width of hole 4 horizontal: 10.4
• Width of hole 5 vertical: 9.04
• Width of hole 5 horizontal: 9.78
• Bottom hole vertical: 18.06
• Bottom hole horizontal: 18.26
• Top hole vertical: 20.41
• Top hole horizontal: 20.33


Toby

Last edited by Toby (2008-09-12 10:22:00)

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#16 2008-09-12 11:20:15

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

Re: Shakuhachi measurements

One more for today. My favorite 1.8, made around the end of the 19th or beginning of the 20th century. Nice solid piece of bamboo with a uniquely wide and beautifully symmetrical root. Very large bore, but plays well and solidly up to the top of dai kan, and, most surprisingly, with good intonation at A = 440. You can see where the bamboo skin has actually been dissolved by body acids where the finger rests between holes 1 & 2.

http://i471.photobucket.com/albums/rr78/kymarto/root_end.jpg


• Maker: Chikudo (Meiji jidai)
• Date of measurements taken: 2008/09/12
• Length of the whole flute:  545 (1.8 shaku)
• Distance between bottom hole to hole 1: 113.10
• Distance between hole 1 and 2: 42.93
• Distance between hole 2 and 3: 43.03
• Distance between hole 3 and 4: 44.57
• Distance between hole 4 and top of flute: 254
• Distance between hole 5 and top of the flute: 217
• Depth of mouthpiece: 4.2
• Angle of mouthpiece: 27.5 degrees
• Width of mouthpiece (from where the little dip begins to the other side): 16.1
• Weight of the flute: 424 grams
• Outer circumference (measured 10 cm down from the top): 111.55
• Width of hole 1 vertical: 11.62
• Width of hole 1 horizontal: 10.50
• Width of hole 2 vertical: 11.22
• Width of hole 2 horizontal: 10.78
• Width of hole 3 vertical: 11.48
• Width of hole 3 horizontal: 9.76
• Width of hole 4 vertical: 11.44
• Width of hole 4 horizontal: 10.75
• Width of hole 5 vertical: 11.44
• Width of hole 5 horizontal: 10.65
• Bottom hole vertical: 18.18
• Bottom hole horizontal: 18.18
• Top hole vertical: 20.93
• Top hole horizontal: 21.88

Last edited by Toby (2008-09-12 11:28:32)

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#17 2008-09-12 20:51:10

Jeff Cairns
teacher, performer,promoter of shakuhachi
From: Kumamoto, Japan
Registered: 2005-10-10
Posts: 517
Website

Re: Shakuhachi measurements

I have a question or two that have bothered me for some time that Toby makes reference to . But first,  forgive my ignorance here.  When referring to 'Dai Kan' what are you actually referring to?  I assume that 'Dai Kan' is any note within the third octave from the root note.  So when you refer to 'the top of dai kan' are you talking about playing hi in the third octave?  If you are suggesting that you play to dai kan no hi which would correspond to C on an 1 shaku 8 sun could you supply me with the fingerings for dai kan no chi and dai kan no hi?  For that matter, could you supply fingerings for the entire dai kan register?  In the chikuyusha repetoire, dai kan no re is the highest note written as far as I know and is found in the piece Zangetsu.  As a final question, do any third octave notes have different names than in the previous two octaves? 
I appreciate any answers to these questions.
cheers.


shakuhachi flute
I step out into the wind
with holes in my bones

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#18 2008-09-12 21:54:24

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

Re: Shakuhachi measurements

I have never studied shakuhachi and so am a complete ignoramus when it comes to the traditions, let's get that straight here at the beginning. I defer to all who actually know what they are talking about. I, like Jeff, assume that the dai-kan starts at third ro and continues as high as you can go.

I like this fingering chart: http://www.shakuhachi.com/Y-FingeringChart-p1.html

The only note not included in that chart (see also page 2) that I know is ro4, which (on a good flute) can be found by blowing like a maniac with all fingers down except LH index finger.

I am not allowed to practice the dai-kan when my wife is at home...

Toby

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#19 2008-09-13 04:51:34

Bruce Hunter
Member
From: Apple Valley CA
Registered: 2005-10-10
Posts: 258

Re: Shakuhachi measurements

Toby wrote:

The only note not included in that chart (see also page 2) that I know is ro4, which (on a good flute) can be found by blowing like a maniac with all fingers down except LH index finger.

I am not allowed to practice the dai-kan when my wife is at home...

Toby

And that's the reason beginning wind players and beginner bands sound like they do. My decibel meter is at the shop, but I just played a RO4 at what I can reasonably estimate at less than 50db. Perry Yung's flutes, for instance, all arrive at my house with a RO1 of at least 80db, just for reference. Blowing hard is not the answer. Blowing smart is the answer, which, I realize is no answer, but what the hey! 8^)

Let's see if I can describe how  _I_  do this, (your mileage may vary): tongue hard forward and hard up; lower jaw out and up; hard support from the diaphragm; release a very small amount of very fast air. It helps to "hear" the pitch before it is played.

Be aware, also, that a flute will not give you a note until it thinks you are ready. That was a very hard lesson for me to learn in the beginning.

Wow! A built-in goal! Keep at it until your wife  _asks_  you to "Please play some of those pretty tunes way high up there." 8^)

Keep at it, and give us some fingerings for that 4th octave!

later...


Develop infallible technique and then lay yourself at the mercy of inspiration. - Anon.

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#20 2008-09-13 05:50:54

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

Re: Shakuhachi measurements

Actually I am quite adept up there, and can play them quietly and well--legacy of years of playing flute and piccolo--but my wife just hates high notes, which I love.

Acoustically speaking, getting the phase relationship of the jet adjusted so that the high notes will sound requires adjusting both its velocity and length. You can achieve it just by adjusting velocity, but it varies as the square of the frequency, so without adjusting jet length (as in "meri") you will definitely wake up all the neighborhood dogs, and be sharp to boot. Shading the length increases end correction at the top, lowering pitch, and since it has a linear relationship with frequency allows you to blow much less hard.  This is made even more important by the fact that all end-blown flutes play the highest notes up to 25 cents sharp. The only thing worse than loud and shrill is loud and shrill and sharp.

Jet size affects loudness, and the rub is that as you decrease your lip aperture to play more softly it becomes ever more critical to have adequate control to place it properly at the utaguchi edge. Beginners usually do not have that control, and therefore blow big, which is what shatters the crystal...

I agree that it is helpful to "previsualize" the sound, which gets kinesthetic memory going. One of the great woodwind teachers, when asked how to learn to play beautifully, said: "Imagine the sound you want to make, and then make it."

Actually due to acoustic limitations arising from the small holes of the shakuhachi (in relation to its bore size), it is impossible to get much above ro4. Even the concert flute with its large holes can only get a few notes above that.

BTW when you speak decibel ratings: at what distance from the mic and with what mic?

Toby

Last edited by Toby (2008-09-13 09:55:33)

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#21 2008-09-13 09:01:02

Jeff Cairns
teacher, performer,promoter of shakuhachi
From: Kumamoto, Japan
Registered: 2005-10-10
Posts: 517
Website

Re: Shakuhachi measurements

Thanks Toby and Bruce.  There's work to be done.


shakuhachi flute
I step out into the wind
with holes in my bones

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#22 2008-09-13 14:11:05

Bruce Hunter
Member
From: Apple Valley CA
Registered: 2005-10-10
Posts: 258

Re: Shakuhachi measurements

Jeff Cairns wrote:

As a final question, do any third octave notes have different names than in the previous two octaves? 
cheers.

I'm researching this info also. What I have so far:

hole order 54321, O - open, C - closed, H - half

Do-Re-Mi name - Fingering - Ro-Tsu_Re name
Eb - OOCOC - Ni Shi Go No Ha;
Eb - OCOCC - San No Hah kari
E - OCOOC - Yon No Hah (or Shi);
or
E - HCOOO;
Gb - CCCCO - Tsu Dai Kan;
G -CCCOO - Re Dai Kan;
or
G - COCCO;
Ab - COCOO - San Go No Re;
A - COCCC - Chi Dai Kan;
Bb - OCCCO - Hi No meri Dai Kan

In this acoustic regime, fingering can be *very* flute/player dependent For instance, for Chi Dai Kan, I use CCOCO which theoretically should be Bb, but it's so flat it's really close to A.

Research continues...


Develop infallible technique and then lay yourself at the mercy of inspiration. - Anon.

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#23 2008-09-13 14:31:58

Bruce Hunter
Member
From: Apple Valley CA
Registered: 2005-10-10
Posts: 258

Re: Shakuhachi measurements

Toby wrote:

Actually due to acoustic limitations arising from the small holes of the shakuhachi (in relation to its bore size), it is impossible to get much above ro4. Even the concert flute with its large holes can only get a few notes above that.

BTW when you speak decibel ratings: at what distance from the mic and with what mic?

Toby

The fun begins! Using your fingering for RO4, COCCC, (CCOCC also works, but may be a bit sharp), and moving to OOOCC, TSU4 dai meri happens. COCOO might yield Re4 meri. OCCCO gives Tsu4 meri.

I use the built-in mic in the decibel meter, and the distance is about 4 inches since I'm working on long flutes, and need to be close enough to read the numbers. I realize there is probably a standard distance, but I'm using the information for my own purposes only. If you or anyone knows of a "standard" please advise.

later...


Develop infallible technique and then lay yourself at the mercy of inspiration. - Anon.

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#24 2008-09-15 14:24:19

Dun Romin
Member
From: Holland
Registered: 2008-04-19
Posts: 136

Re: Shakuhachi measurements

And in addition to Bruce's list, after Bb I continue on my tozan with:
B - OCOOO
C - CCCOC
Db - COCOC

I know there is also a D"" played like CCCCO, but I don't (yet?) succeed in getting its sound out.


Tomorrow's wind only blows tomorrow. (Koji)

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#25 2008-09-16 09:23:21

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

Re: Shakuhachi measurements

I find OCCCC to give an excellent E4 on at least one of my flutes. Even better than ro4.

Toby

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