Conical bore and tone holes

[jiminos]

if i may be allowed.... having played guitar for about 35 years, i can assure you that Hans' info is correct. additionally, if you lightly touch the vibrating string of a guitar at the 12th fret (equal to one half the length of the string), the tone produced will be one octave higher than that produced by plucking an unfingered string.

it was this info that helped me map out the fingerhole placements on the flutes i make. it seems to work, after making adjustments for human "limitations," all of my final flutes have excellent intonation. like any cylindrical flute/whistle, the upper registers need to be "blown" into tune, but they are very close before being "blown" in. using a wedge similar to doug tipple's tipple-fijardo wedge helps a lot with upper register tuning/intonation.

and i agree, hans... man, this stuff is fun!

be well,

jim

[Gregrussell]

The resulting spread of holes has again nothing to do with the Golden Proportion. I aim to have somewhat equal distances between holes 1, 2 and 3, as between holes 4, 5 and 6. This is of course a big "somewhat", and usually a compromise between equal spacing and acoustically efficient spacing is best.

Great fun, all of this!
~Hans

Hans, I am just a simple Carpenter from out around the bay and can't argue with anyone with more then grade five.....I divide by 1.618, drill my holes...and play a tune.. as in the diagram above drawn by me...(no camera tricks) shows accurate placement. and by the way seem to work just fine...however it sounds you have put alot of study into this and frankly the thought of it all mesmorizes me again if you divide by 1.618 you will find the hole layout...I've done it about 500 times...I feel confident that the next whistle will work out just fine again

great fun

[jiminos]

well, i'm intrigued enough by the 1.618 that i'm going to give it a go on my next flute. so, i thank you for posting the pic, greg.

be well,

jim

[Carey]

Boy, we're having some fun now. Messing with all these variables at once makes my head spin. But getting them all to happy values is the the point, so they all need to be messed with.

Greg, interesting application of Phi here. I'm not quite able to follow your drawing and comments. You start with a good bell note and divide that length by Phi to find what? The spot where an octave D would go? I assume that's your "D" in the drawing that doesn't match a hole. Then you divide that by Phi to find ... (and I'm missing something here.)

Using the notation of L1 for left hand top finger etc. what would your procedure be?

Bell note length / Phi = What?
What / Phi = L1 or is it R1?
R1 / Phi = R2?
R2 / Phi = R3?

I'd like to explore this approach some, but I want to start with your method rather than err and make up something of my own. (But I suppose that's part of the tradition. It's how new tunes are born!)

Cheers,

Carey

[GordonH]

The method I used was percentages which is probably the same thing

Once you have the tube of your low D copper whistle cut to
the proper length to sound a low D note, carefully measure
the distance from the mouthpiece "lip" to the right hand end
(open-end) of the instrument.

The center of the 1st hole (the hole nearest the mouthpiece)
should be located 44.74% of this overall "lip" to open-end
measurement.

The center of the 2nd hole should be located 52.47% of this
overall "lip" to open-end measurement.

The center of the 3rd hole should be located 60.38% of this
overall "lip" to open-end measurement.

The center of the 4th hole should be located 68.82% of this
overall "lip" to open-end measurement.

The center of the 5th hole should be located 74.93% of this
overall "lip" to open-end measurement.

The center of the 6th hole (the hole nearest the open end of
this whistle) should be located 84.10% of the overall "lip"
to open-end measurement.

How to convert these percentages into actual measurements:
- First move the percentage's decimal point two
units to the left (ie: 44.74 becomes .4474)
- Then simply multiply this number by the
"lip" to open-end distance

http://www.ehhs.cmich.edu/~dhavlena/low-d.htm

[hans]

The method I used was percentages which is probably the same thing. ....

This is all very well for scaling to different tube lengths (different tonic notes), but it depends on leaving the hole diameters the same, and leaving the tube diameter the same, and leaving the tube wall thickness the same. Vary any of these, and you need a different set of hole location.

~Hans

[Gregrussell]

Boy, we're having some fun now. Messing with all these variables at once makes my head spin. But getting them all to happy values is the the point, so they all need to be messed with.

Greg, interesting application of Phi here. I'm not quite able to follow your drawing and comments. You start with a good bell note and divide that length by Phi to find what? The spot where an octave D would go? I assume that's your "D" in the drawing that doesn't match a hole. Then you divide that by Phi to find ... (and I'm missing something here.)

Using the notation of L1 for left hand top finger etc. what would your procedure be?

Bell note length / Phi = What?
What / Phi = L1 or is it R1?
R1 / Phi = R2?
R2 / Phi = R3?

I'd like to explore this approach some, but I want to start with your method rather than err and make up something of my own. (But I suppose that's part of the tradition. It's how new tunes are born!)

Cheers,

Carey

Hi Carey.... will post an accurate drawing later this evening...bit busy right now, I used a generation as an example I'll show it again with accuraqte lines...and i'll show this wide bore High D in comparison



Greg

[hans]

Here is my own drawing and calculating attempt:



The Burke D hole location are measured from foot end.
The equal diameter hole location are calculated.
The divisions by Phi (1.618) are calculated and drawn to scale.
You can see plenty of mismatches.
Note especially locations for hole 4 and 5:
Since there is only a semi-tone step between F# and G these holes end up very close together if tone holes are equally sized.
Therefore hole 4 is made small, to move higher, and hole 5 larger, to move down. This gives a more practical finger distance on the Burke, even though it is not an equal distance from 4 to 5 and 5 to 6.
Funnily enough the "Divide by Phi" method arrives at exact equal distance for 4 to 5 and 5 to 6. And it arrives at unequal (i.e. golden proportion) distances for 1 to 2 and 2 to 3, whereas the spacing is much more equal due to going up the scale by whole tones (no semi-tone step involved). [And Greg, please accept my apologies in case I misunderstood your method and got it wrong as a consequence!!]

So I conclude the "Divide by Phi" method is poor in finding suitable hole locations. In fact it is pretty impossible to put hole 5 at 62 mm from the end, it would be too large!

Of course one could carry on and divide further by Phi, till one gets values which can be subtracted from other values to give us the desired value. But that would proof nothing. You would just use a different number system.

~Hans

[hans]

PS: this is an interesting study for hole placement:
http://www.navaching.com/shaku/holes.html
I will try and transfer this approach to six hole flute design.

Cheers,
~Hans

[highwood]

I'm going to stay out of the hole placement discussion except to note that it is the position, size, and length of the hole that matters, oh and the other holes, and the bore, and ... So one can put the holes somewhere and then adjust the size to tune - within reason!

Anyway to return to conical v cylindrical: the formula for hole position/size/depth is the same for cylinders and cones (of either direction, that is like a conical flute or an oboe for example). So the spreadsheet of Peter Kosel (varying the bore diameter at the hole position) will work within its limitations of using a first order approximations to equations which approximations themselves.

Now this also means that this will a second iterative process because the spreadsheet calculates the hole position and depending where that is the bore will vary, so you have to recalculate the bore, which will change the position, and then...

I found the spreadsheet to be a reasonable first approximation, and worked around its limitations by changing the note frequencies which got me closer but I still had to experiment. Then I bought a book. Still working on it but the first whistle was much closer to the design parameters, and I'm still working on the equations. I expect in the end that the equations will just be a good start and that several (or many) prototypes will be required. Then again the first whistle I made is not all that bad - I just think, no I know I can make a better one.

Bill

[jemtheflute]

With my school project conduit tube piccolos (cylindrical with Tipple-Fajardo wedge), when I was doing the specific R&D for them I started off with a Flutomat calculation for my tube ID and a set embouchure size and asked it to set for tone-hole sizes that I could drill with standard drill bits and not need to file into tune (if accurately centred!), i.e. 0.5mm gradations. I made one and tested it against my tuner - not bad without the wedge, but of course Flutomat can't programme for that.... It wasn't perfect, though. I then tested the tuning with the wedge and estimated the positional corrections - and established them (within 3 trials) by trial and error. They now turn out pretty consistently. Because my hole sizing was constrained by classroom manufacturing considerations, the hole spacing is little unusual - L2 (B tone-hole) is rather down-tube of its more common location, but the next size down drill would have made it too high for comfort. R1&2 are also a little closer together than often seen, though less so than on Pratten style flutes.

So, I see little point in trying to do this stuff from first principles, though having some understanding of those is worthwhile..... there are various relatively simple ways to get initial specs - when I first tried bamboo flute-making and later conduit tubes in pre-Internet days I just measured a whole bunch of instruments available to me - about 8 various flutes and whistles both cylindrical and conoid, converted those measurements into percentages of sounding length, averaged the results and used those figures to mark out my tubes, then drilled small holes and filed out to pitch (by ear with bamboo in my student days; I bought a Korg tuner when I used conduit tube in the mid 1990s). The results were pretty decent, but there are better starts to be had now, like the Flutomat - but whatever start you work from, no matter how scientific you get about it, you will have compromise choices to make, and then I think you will still have to tweak the design produced by theory with pragmatic empirical observation! Once you've done that you may arrive at a design that you settle on and standardise for production....but don't expect simply to be able to replicate it by scaled expansion or contraction for different pitch instruments (for starters, you're unlikely to have enough gradations of tubing available for that!) - you'll still have to re-do the empirical tweaking for those.

As for Golden Numbers and all that jazz, that starts to open the can of worms (where d'you put it Denny?) that is Temperament. You can't avoid it of course, but you really don't want to go there too seriously! I've been reading some textbooks about it recently........ I can't cope with the Maths, but I can understand the concepts, and it's a mare! Take my advice, settle for an approximation of Equal Temperament (and Golden Numbers won't help there).

BTW, I'm thinking of making a batch of my piccolos for sale - fixed pitch, D only, plain and simple.....anyone interested? (pm me if so.) It won't be for a few weeks yet, though - other stuff taking priority like accounts and tax return before Jan 31!

[Mitch]

With conical bores, the holes have to be smaller. Small as the cone steepens untill the limit gets reached and you end up with a Clarke. But that's OK too because you can reign-in the super-loud second octave. The holes get made big to move them down the tube - that's handy if you want to fit your stubby humany fingers on them.

In the end it's whatever you like and you will have to walk the road a few thousand miles before you have any idea that you are such a fool - and why it's OK to be a fool.

Whistles can be gotten to heuristically faster than mathematically for one very important reason:
It is related to why people cannot mathematically predict weather for further than 3 days before becoming drastically wrong.

The universe is protected from the perversions of humans by a collection of dragons - there is a special green one that stops all pennywhistles being the same and boring the hide off of everyone.

Just make whistles - the dragon likes that

[Gregrussell]

With conical bores, the holes have to be smaller. Small as the cone steepens untill the limit gets reached and you end up with a Clarke. But that's OK too because you can reign-in the super-loud second octave. The holes get made big to move them down the tube - that's handy if you want to fit your stubby humany fingers on them.

In the end it's whatever you like and you will have to walk the road a few thousand miles before you have any idea that you are such a fool - and why it's OK to be a fool.

Whistles can be gotten to heuristically faster than mathematically for one very important reason:
It is related to why people cannot mathematically predict weather for further than 3 days before becoming drastically wrong.

The universe is protected from the perversions of humans by a collection of dragons - there is a special green one that stops all pennywhistles being the same and boring the hide off of everyone.

Just make whistles - the dragon likes that

I Like that mitch, as for me...I won't post anymore of my ideas here lol, ...I'll just keep to myself!
Hans, the layout you illistrated was wrong...just wing it! you'll be much happier Mitch is right!!

[Mitch]

THe ideas are oK - it's the effort that makes the difference.

[hans]

as for me...I won't post anymore of my ideas here lol, ...I'll just keep to myself!
Hans, the layout you illistrated was wrong...just wing it! you'll be much happier Mitch is right!!

Greg - I would love to learn why my diagram is wrong, it seems just like yours.

I am so sorry! I never intended to offend you. I just tried to understand your method. I was insensitive as I did not realise that you would take any critic on applying the Golden Ratio to whistle design so serious, that it seems to be a religious thing. Sorry! I did not think we would have a fallout over whistle design methods because of science vs religion here. Oh dear!

In the end, re whistle design, whatever works for you works, never mind what unusual method you use. I totally respect you for the efforts and the outcome, especially creating superb new whistles and expanding the low whistle designs! And I thank you what you have shared here about your whistle making process. It has stimulated much interest in me, and others, and helped me to deepen my limited understanding of whistle and flute design.

My own approach is a mix of empirical, practical experimentation, and theoretical analysis using mathematical methods based on acoustic physics. The modelling software I have used is limited and leads to approximations of a good model. Fine tuning and voicing is an art. In that respect I can agree with Mitch that every whistle is different, if ever so slightly. Still, with a good mathematical approach you can come up with new models, not based on copies of other instruments. Refining the model so the new instrument is in tune etc may be necessary using some practical experimentation. And manual fine tuning and voicing is always necessary.

Anyway, I hope we can share more of this here. It is fascinating to see the many approaches whistle designers took, to see so many very different whistle models. There is a lot more variation in the whistle world than in the simple flute world. There is more design from first principles and more experimentation. All of this is most encouraging!

Cheers,
Hans