I’ve been playing around with design suggestions from some whistle design software under development. At present, the only thing it optimizes for is intonation: making it as easy as possible to play a whistle in tune. It would seem that large holes tend to make it easier to get the intonation right. On cylindrical whistles, it particularly favours large holes for T2 and B3, whereas most commercial whistles seem to have B2 as the largest hole.
As an example, for an un-tweaked high-D Feadog that I have here, aiming for Just Intonation, it suggested T2 and B3 as large as possible. When I limited the holes to 7.7 mm, it suggested:
All the holes would be farther down the tube than their current positions, but since it’s a small whistle anyway there wouldn’t be a problem with finger stretch.
Any suggestions for what design considerations besides intonation would favour the traditional designs?
Well, usually B2 is larger to aid in half-holing an Fnat. I’m unsure of why the very lowest hole is so small on many whistles. It’s not like it’s a stretch or anything, and it’d give an E-flat which can be a nice pickup note…
With the alternative hole diameters you suggest in your example you will get something like the following distances between some holes (centre to centre):
for top fingers:
T1-T2: 26.8mm
T2-T3: 17.2mm
for bottom fingers:
B1-B2: 10.2mm
B2-B3: 27.3mm
in other words you get vastly different spacings between the fingers, and especially B1-B2 distance is too short to be fingered. I would aim for roughly equal distances for T1-T2 and T2-T3 as well as B1-B2 and B2-B3, for ergonomic reasons. That is the main reason B1 is kept small and B2 fairly large, because it increases the distance between those two holes. Likewise especially for lower whistle keys B3 is kept smaller, in order to locate the hole further up the tube, to make the B2-B3 stretch possible.
I wrote “roughly equal distances for T1-T2 and T2-T3”, but often I make T2-T3 a little less than T1-T2, again especially for larger whistles, as it is more comfortable.
In my own whistle calculator, which I just made more user friendly (I hope), it suggests for initial hole diameters the following:
http://music.bracker.co/Music/Whistle_Calculator
When you select a key, it automatically selects a suitable tube size and populates the hole diameters with the values calculated with those factors above. One can change them at will afterwards, and often needs to do this, to get a layout which is actually comfortable enough for the finger stretches.
My limited experience in making whistles suggests two or three things :
Any software used is unlikely to be totally accurate for the material I’m working with
Small holes make for many more cross-fingering options but a quieter instrument.
Large holes make half-holing almost mandatory for most notes other than the “basic eight” of the diatonic scale, but a louder whistle.
Ultimately, I suspect most “lower-price” commercial whistles use a very similar hole-size combination simply because that’s what gives the best compromise and overall range with a thin-wall tube.
Thanks for the link, Hans. I forgot about your implementation of Flutomat.
The B1-B2 distance comes out as 12 mm (see below), which is a bit small. What would you say would be the minimum distance between fingers?
Calculators based on Flutomat consider only the first octave, and as far as I know don’t take cross-fingerings into account. According to my calculator, the recommendations of your calculator look very good in the first octave (which is at least some evidence that my calculator isn’t way off track). C-nat comes out naturally about 20 cents sharp, but can be blown in tune. (The dimensions I came up with produce exactly the same result.) In the second octave, however, you’ll have to blow quite a bit harder to keep the notes in tune. Going from middle-D to high-E, for example, will need an extra push on the E, or it will end up over 10 cents flat. At the top of the second octave, going from high D to high C-nat or C# will require a push on the lower note, or it will end up about 25 cents flat.
With the dimensions I came up with, the prediction is that all of the notes in the second octave will be pretty easy to keep in tune, except for the high C#, which will tend to be about 15 cents flat without a compensating push.
I’m using OXXOOO for low C-nat, OXOXXX for high C-nat, OOOOOO for both C#, and OXXOOO for high D. On both designs, OXXXOO is way too sharp for the high C#.
Here’s the full comparison. The original Feadog, by the way, plays consistently sharp on everything.
Hmm, more tantalizing hints about this whistle calculator in development…
Of the cheapie whistles that I’ve tried, the Feadóg D tube is the one whose tonehole layout I’ve been most happy with. On just about all the others, I’ve had to carve/tape significantly to get it to play a scale that doesn’t require big adjustments in breath pressure to blend with other instruments. However, I’d like it at least as well if the B3 were larger and farther down the tube. [Again, looks in mirror…]
Here are some consequences of hole sizing that I’ve compiled from reading up on the internet as well as my own experiments in PVC instrument building and cheapie surgery. They can each apply to the tone hole lattice as a whole, or to the effect of a single hole’s size:
The smaller the tone holes are in relation to the bore diameter, and the thicker the wall at the tone holes, the more responsive the instrument will be to cross-fingerings–the extreme example being recorders and baroque traverso.
The size of a tone hole (and other factors) determine the cutoff frequency of that hole, meaning the highest frequency that isn’t significantly attenuated. (http://www.phys.unsw.edu.au/jw/fluteacoustics.html#cutoff) The larger the hole, the higher the cutoff frequency, and the brighter the note. If all the holes are larger, then the instrument’s cutoff frequency as a whole is higher, and the tone of the instrument is brighter (and thus perceived as louder). This same phenomenon provides an instrument with larger holes an extended high range compared to an instrument with smaller holes–the extreme example being the Boehm flute.
All other things being equal, an instrument with larger holes will have the first and second registers wider of each other than an instrument with smaller holes. This can be compensated for by changes in the bore. That’s one of the reasons that carving out certain holes on a cheapie whistle can improve it–it doesn’t just even out the scale; it also helps to counteract the second octave’s tendency to flatness.
Increased evenness of venting causes an instrument to have a more even tone from note to note and more even intonation across multiple registers. (http://www.mcgee-flutes.com/vent_charts.htm) Again, the extreme example is the Boehm flute. On a simple-system instrument, however, this does not directly translate to having all the holes the same size: the B1 hole, for example, needs to be significantly smaller than the holes around it to give even venting, because it’s the only one with a (usually quite large) hole just one semitone south of it, instead of two semitones. One of the many features that I love about Twjcalc (http://twjcalc.sourceforge.net/2.10/TWJCalc2.10.html) is that it provides a venting chart for your design, calculated as “cutoff ratio = cutoff frequency / base frequency” of every hole.
Any change to the sizing and placement of the holes on an instrument is probably going to affect the way that the instrument responds to alternative fingerings from the middle of the second octave on up. For example, the size of the T3 hole affects whether XXO XXO gives a high G# (like on my Feadóg D), or a high B (like my MK low D), or a train whistle sort of sound (like, IIRC, the Bracker low D). The sizes of T1 and T3 both will, I believe, affect the way that the instrument responds to fingerings for high Cnat.
Back when I had the tour Reviol low D, I noticed that it had unusually large top hand holes. In particular, T2 and T3 both were about as large as B2! The Reviol, out of any whistle I’ve ever played, had the easiest, best-behaved, best in-tune high register (high A and up). Compared to the Reviol, those high notes seem like a struggle on most other whistles. And, coincidentally, the high Cnat fingering that you mentioned in a previous thread (OXO OOO) worked perfectly on the Reviol.
[Rereads post before submitting] Wow, I just said a lot of things right after waking up. Some of it’s likely to be inaccurate or poorly stated. I’m open to correction!
Does your Feadóg tube have the same dimensions as my Feadóg tube? In its current state, I don’t think you’d be happy with mine. It isn’t even in tune with itself in the first octave.
I feel bad about this … Realistically, it’s not likely to be ready for you for quite awhile. Would you prefer I just shut up about it until it is ready?
Does your Feadóg tube have the same dimensions as my Feadóg tube? In its current state, I don’t think you’d be happy with mine. It isn’t even in tune with itself in the first octave.
Comments like that always intrigue me. So I played into a tuner.
First of all, every note on the whistle will fluctuate with the pressure your blow it at. I don’t think you’ll hit any note spot on every time, at best you tune the longer notes as you go along. The scale was fine, I know I tend to blow a just(-ish) intoned scale but I could easily blow the thirds up to ET. My octaves were pretty much spot on, with the exception of the high b which was a bit flat compared to the first octave but well within the range of a just intonation b.
I think that’s pretty decent and also just about as much as you can ask for, taking into account the effect the player has on the intonation (i.e. unless you design a head that does not allow for any fluctuation of pitch with varying pressure or air speed notes are likely to vary a bit. And in the knowledge that wind instruments are not push button fixed pitch instruments).
Well, alright, the XXX XXX is slightly sharper than I like, and the OXX XOX Cnat needs to be blown gently, but it’s definitely my favorite of the cheapie D tubes I’ve tried. I stuck a tiny blob of poster putty just inside the bell, because I like the bell note to be in-tune at just under the breaking point, so that I get the loudest bell note possible.
FWIW, my Feadóg tube is a Feadóg Pro tube, but really, I doubt that yours and mine are any different. Is there a brand of cheapie high D whose scale you think is as good as, or better than, the Feadóg’s?
The low D on my Feadóg starts around 580 Hz, and breaks around 597. Like Stanton, I like to blow the low D just a bit under the breaking point, and I’m guessing that most players will be similar. This puts it around 20 cents sharp (30 cents at most). The B will sound down around 970 or so, but is very hard to hold steady below 1010 or so, which puts it at least 50 cents sharp of a JI B (979 Hz) and 20 cents sharp relative to the D. The XOOOOO fingering doesn’t break until 1047, a nice ET C-natural.
For predictable intonation while playing, I’m assuming that most players will expect the breath requirements to go steadily upward as they go up the two-octave scale. Different players may have different preferences as to how fast the requirements go up, but I think everyone would appreciate a regular increase. That’s what I’m referring to when I say things like, “C-nat comes out naturally about 20 cents sharp, but can be blown in tune.”
This is a ordinary brass Feadóg, nothing special. I picked it for this thread because I figured its pattern of hole sizes would be easily recognizable. I don’t mean to suggest the performance of this particular whistle is characteristic of Feadógs in general, and I regret that it has taken that turn.
As for cheapie whistles, we’ve got a Jerry Freeman Generation Bb here that has intonation about as close to ideal through both octaves as I could realistically hope for. Perhaps I should take a closer look at that whistle …
. I don’t mean to suggest the performance of this particular whistle is characteristic of Feadógs in general, and I regret that it has taken that turn.
Well, the thing is, Feadógs are pretty consistent. So when you say yours ‘isn’t even in tune with itself in the first octave’ it is pretty much what you’re saying. My experience is very different so I can’t help wonder what the story is there.
